*Article* **Heuristic and Numerical Geometrical Methods for Estimating the Elevation and Slope at Points Using Level Curves. Application for Embankments**

**Adrian Marius Deaconu 1, \* and Ovidiu Deaconu 2**


**Abstract:** Both the calculation of ground slopes at points on the map and the elevation estimation for these points bear significant importance and also have applications in various domains, such as civil engineering, road and railway design. The paper presents two methods that use level curves: one that is fast and approximate and another which is slower, but more precise. The running speed of the two proposed methods and their results are compared by performing 100 million experiments. The paper also presents how these methods can be applied to optimize embankments. An accurate method to calculate the horizontal plane of the excavation/filling when building a new house is also presented.

**Keywords:** level curves; ground slopes; embankments; road and rail design; optimization

#### O. Heuristic and Numerical Geometrical Methods for Estimating the Elevation and Slope at Points Using Level Curves. Application for Embankments. *Appl. Sci.* **2021**, *11*, 6176. https://doi.org/10.3390/

**Citation:** Deaconu, A.M.; Deaconu,

Academic Editor: Igal M. Shohet

Received: 22 May 2021 Accepted: 29 June 2021 Published: 2 July 2021

app11136176

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#### **1. Introduction**

The possibility of calculating the slope and elevation using level curves has practical applicability in several fields of activity, such as civil engineering [1], architecture [2,3], railway [4], road and bridge engineering [5–8], topography [9], etc. Although the results found can be used in various areas, this article is limited to solving two problems related to civil engineering and to railways, roads, and bridges, both ultimately related to the embankments optimization. The problem is well known, but it was not closely examined by design engineers, who preferred an intuitive, approximate solution. The current article presents a rigorous and mathematically accurate solution to find the optimum between excavations and fillings, resulting in a reduction of the embankments related costs. The article presents in detail the solutions of two concrete problems in two different fields of activity.

The first problem investigated is in the field of civil engineering and consists of determining the optimal elevation corresponding to the finished floor of the ground level, when the building has to be positioned on a slope [1–3]. The second problem investigated is in the design of a new railway or road when there are several fixed points on the topographic map through which the new road [10–13] or the new railway [4,11] will pass.

The designer has to know the slope and elevation in each of these points as accurately as possible. Using the methods proposed in this paper, the two parameters (slope and elevation) can be determined fast and with a high level of accuracy using the level curves of the map, without the need for direct measurement on the spot. Furthermore, when designing roads or railways, the risk of failure, the frictional resistance, the safety factor against sliding or failure, the translational fill failure, or the cut volume and the road fill per meter require knowing the slopes (side slope, cut slope, or fill slope).

The paper is organized as follows: an algorithm to calculate the ground slope at a given point, using level curves, is deduced in Section 2. This problem is reduced to

estimating the shortest segment that connects two lines through a point. Two methods are proposed, a fast and approximate one and a more exact one, respectively. The two methods are compared, and it is shown that the errors of the first method are low. In Section 3, the optimum excavation/filling plane is calculated when a new house is built. Two methods are proposed and discussed in Section 4, where they are compared. To finalize the paper, conclusions will be drawn based on the arguments presented.

#### **2. Materials and Methods**

A method of calculating the soil slope through a given point is being introduced. The input data are: the level curves, in Figure 1, the two level curves located at elevation 610 and, respectively, 620, and the 2D coordinates of a point Q on the topographic map. The direction of the Ox axis is considered from west to east, the direction of the Oy axis is south-north. The output is the slope calculated at point Q. The slope can be determined using two other points collinear with Q for which the elevation is known. The points on the map for which the elevation is known are located on level curves. Therefore, it is enough to find two points collinear with Q located on two different level curves. Of course, for accuracy reasons, it is preferable that Q is located between these 2 points and the distance between the chosen 2 points is minimum. Consequently, the problem can be accurately solved if we determine the closest two level curves to Q (Q is located in between these curves) and two points P<sup>1</sup> and P2, each located on one of the level curves, and the distance between P<sup>1</sup> and P<sup>2</sup> is minimum (see Figure 1).

**Figure 1.** Finding the slope at a point using level curves.

α Since a level curve is approximated with consecutive coplanar segments of straight lines, our problem can be reduced to finding the shortest length segment |P1P2| that connects two coplanar line segments located on two consecutive level curves. When the two 2D points P1(x1,y1) and P2(x2,y2) are determined, they are transformed into 3D points by adding the elevations z<sup>1</sup> and, respectively, z<sup>2</sup> of the level curves on which each of the points are located. Using the 3D coordinates of these 2 points, the slope m = tan(α) at point Q (see Figure 2) can be calculated as follows:

$$\begin{cases} \mathbf{m} = \frac{|\mathbf{z}\_2 - \mathbf{z}\_1|}{\sqrt{(\mathbf{x}\_2 - \mathbf{x}\_1)^2 + (\mathbf{y}\_2 - \mathbf{y}\_1)^2}}\\ \mathbf{a} = \operatorname\*{atan2}\left( |\mathbf{z}\_2 - \mathbf{z}\_1|, \sqrt{\left(\mathbf{x}\_2 - \mathbf{x}\_1\right)^2 + \left(\mathbf{y}\_2 - \mathbf{y}\_1\right)^2} \right) \end{cases} \tag{1}$$

**Figure 2.** Determining the slope at Q using P<sup>1</sup> and P<sup>2</sup> .

The first problem (denoted IPS) intended to be solved is to identify the pair of segments (located on two level curves) to which the finding of the shortest length segment should be applied. Of course, for each of the two level curves, the candidates are the closest segments to point Q. Let us denote by S<sup>i</sup> the set of candidates (segments) for curve i (i = 1, 2). For each pair of segments s<sup>1</sup> ∈ S<sup>1</sup> and s<sup>2</sup> ∈ S2, respectively, the corresponding shortest length segment [P1P2] between s<sup>1</sup> and s<sup>2</sup> is calculated. If s<sup>1</sup> contains P<sup>1</sup> and s<sup>2</sup> contains P2, then the pair (s1, s2) is added to the set (denoted C) of solution candidates for IPS (Figure 3).

**Figure 3.** Finding the closest line segments to Q.

≥ ≥ The set S<sup>i</sup> (i = 1, 2) can be built as follows: first, we find the point T belonging to the level curve i that is closest to Q. We consider then k ≥ 1 points (L1, L2, . . . , Lk) to the left of T on the level curve and k points (R1, R2, . . . , Rk) located to right (see Figure 4). Finally, the set S<sup>i</sup> consists of 2k segments of straight lines given by the consecutive points on the level curve i: Lk, Lk-1, . . . , L1, T, R1, R2, . . . , Rk, i.e.,:

$$\mathbf{S}\_{\mathbf{l}} = \{ [\mathbf{L}\_{\mathbf{h}+\mathbf{1}}\mathbf{L}\_{\mathbf{h}}] | \mathbf{h} = 1, 2, \dots, \mathbf{k} - \mathbf{1} \} \cup \{ [\mathbf{L}\_{\mathbf{l}}\mathbf{T}], [\mathbf{T}\mathbf{R}\_{\mathbf{l}}] \} \cup \{ [\mathbf{R}\_{\mathbf{h}}\mathbf{R}\_{\mathbf{h}+\mathbf{1}}] | \mathbf{h} = 1, 2, \dots, \mathbf{k} - \mathbf{1} \} \tag{2}$$

Now, let us see how k (giving the number of points in the vicinity of T) is considered. Usually (in real tests), k is enough to be 1. In few cases k is found to be greater. So, the calculations are started with k = 1 and, if necessary, it is increased.

The Algorithm 1 for solving IPS (denoted AIPS) is:

**Algorithm 1** Solving IPS (denoted AIPS)

#### **AIPS:** *ϕ*

**Input**: the points of the closest two level curves to Q **Output**: the shortest line segment [P1P<sup>2</sup> ] that connects the given two level curves finished = false; **While** not finished **do** C = *φ* (empty set); Build the sets of line segments S<sup>1</sup> and S<sup>2</sup> (see Equation (2)); **For** each segment s<sup>1</sup> from S<sup>1</sup> **do For** each segment s<sup>2</sup> from S<sup>2</sup> **do** Calculate the shortest length segment P1P<sup>2</sup> that connects s<sup>1</sup> and s<sup>2</sup> and passes through Q; **If** P<sup>1</sup> ∈ s<sup>1</sup> **and** P<sup>2</sup> ∈ s<sup>2</sup> **then** Add [P1P<sup>2</sup> ] to C; **End if**; **End for**; **End for**; **If** C not is empty **then** finished = true; **else** k = k+1; **End if**; **End while**;

> The shortest line segment that connects both level curves is the shortest segment [P1P2] from C.

> After applying AIPS, the problem is reduced to calculating the shortest segment that passes through a given point Q and connects two coplanar lines d<sup>1</sup> and d<sup>2</sup> (Figure 4). We shall denote this problem as SSTPC2L (shortest segment through a point that connects 2 lines). In Figure 4 the points A<sup>11</sup> and A<sup>12</sup> determine the line d1, and the points A<sup>21</sup> and A<sup>22</sup> determine the line d2.

**Figure 4.** Connecting the point Q to the lines d<sup>1</sup> and d<sup>2</sup> .

We present two methods of solving SSTPC2L: an approximate method and an exact mathematical method. These two methods (presented in Sections 2.1 and 2.2) were partially described in [7].

#### *2.1. Heuristic (Approximate) Method for SSTPC2L*

From the topographic map, the point Q is known and two segments A11A<sup>12</sup> and A21A<sup>22</sup> are determined belonging to the level curves from Figure 1 (A11A<sup>12</sup> on curve 610 and A21A<sup>22</sup> on curve 620). These two segments are found according to Figure 3. The method consists of drawing the perpendiculars from the given point Q on the two given lines d<sup>1</sup> and, respectively, d<sup>2</sup> (Figure 5). We construct a line passing through Q which is parallel to the line determined by the feet of the two perpendiculars. The obtained line is denoted by d3, and its intersection with the lines d<sup>1</sup> and d<sup>2</sup> is the searched segment [P1P2] (approximate solution of SSTPC2L).

**Figure 5.** Approximate method of finding points P<sup>1</sup> and P<sup>2</sup> .

Now, let's present how the points P<sup>1</sup> and P<sup>2</sup> are calculated. The equation of the line d<sup>i</sup> (i = 1, 2) starting from the points Ai1 and Ai2 is:

$$\mathbf{y} = \mathbf{m}\_{\mathbf{i}} \mathbf{x} + \mathbf{n}\_{\mathbf{i}\prime} \text{ w} \\ \text{where } \mathbf{m}\_{\mathbf{i}}^{\mathbf{Y}} = \frac{\mathbf{y}\_{i2} - \mathbf{y}\_{i1}}{\mathbf{x}\_{i2} - \mathbf{x}\_{i1}} \\ \text{and } \mathbf{n}\_{\mathbf{i}} = \mathbf{y}\_{i1} - \mathbf{m}\_{\mathbf{i}} \mathbf{x}\_{i1} \tag{3}$$

The perpendicular from Q on d<sup>i</sup> (i = 1, 2) is:

$$\mathbf{y} = \frac{1}{\mathbf{y}\_{\mathbf{m}\_{\mathrm{i}}}} \mathbf{x} + \mathbf{n}'\_{\mathrm{i}\nu} \text{ where } \mathbf{n}'\_{\mathrm{i}} = \mathbf{y}\_{\mathbf{Q}} + \frac{1}{\mathbf{m}\_{\mathrm{i}}} \mathbf{x}\_{\mathbf{Q}} \tag{4}$$

Q୧(x<sup>୧</sup> ୕ , y୧ ୕ ) The foot Q<sup>i</sup> x Q i , y Q i (i = 1, 2) of the perpendicular on d<sup>i</sup> is obtained by solving the system of Equations (3) and (4).

The slope of the line Q1Q<sup>2</sup> is:

ing

$$\mathbf{m}\_{12} = \frac{\mathbf{y}\_2^{\mathbf{Q}} - \mathbf{y}\_1^{\mathbf{Q}}}{\mathbf{x}\_2^{\mathbf{Q}} - \mathbf{x}\_1^{\mathbf{Q}}} \quad \text{y} \tag{5}$$

mଵଶ QଵQ<sup>ଶ</sup> Q(x୕, y୕) Since m<sup>12</sup> is the slope of Q1Q<sup>2</sup> , then the parallel through the point Q xQ, y<sup>Q</sup> is:

$$\mathbf{y} = \begin{array}{c} \mathbf{y} \\ \mathbf{y}\_{\mathbf{Q}} + \mathbf{m}\_{12}(\mathbf{x} - \mathbf{x}\_{\mathbf{Q}}) \end{array} \tag{6}$$

Finally, the points P<sup>i</sup> (i = 1, 2) are obtained by solving the system of Equations (3) and (6). The following Algorithm 2 (denoted A1SSTPC2L) is obtained to solve the problem SSTPC2L:

#### **Algorithm 2** Solving the problem SSTPC2L

**A1SSTPC2L: Input**: Q and the points of the closest two level curves to Q **Output**: The slope at point Q Apply AIPS to find A11, A12, A21, A22; Calculate the point P<sup>i</sup> by solving system of Equations (3) and (6) (i = 1, 2). Calculate the slope at point Q using Equation (1).

#### *2.2. The Exact (Mathematical) Method for SSTPC2L*

For this method, in order to simplify calculus, we apply some initial transformations (rotations and translations) to the points A11, A12, A21, A22, and Q so that the bisector of the angle between the lines d<sup>1</sup> and d<sup>2</sup> becomes parallel to Oy axis and the point Q is in the origin O, i.e., Q = O (0,0). To do so, we first calculate the intersection I of d<sup>1</sup> and d2:

$$\mathbf{d}\_1 \cap \mathbf{d}\_2 = \{\mathbf{I}\} \tag{7}$$

by solving the system of linear equations:

$$\begin{cases} \mathbf{d}\_1: \frac{\mathbf{x} - \mathbf{x\_{11}}}{\mathbf{x\_{12}} - \mathbf{x\_{11}}} = \frac{\mathbf{y} - \mathbf{y\_{11}}}{\mathbf{y\_{12}} - \mathbf{y\_{11}}}\\\mathbf{d}\_2: \frac{\mathbf{x} - \mathbf{x\_{21}}}{\mathbf{x\_{22}} - \mathbf{x\_{21}}} = \frac{\mathbf{y} - \mathbf{y\_{21}}}{\mathbf{y\_{22}} - \mathbf{y\_{21}}} \end{cases}$$

The following transformations to A11, A12, A21, A<sup>22</sup> and Q are applied:


$$\begin{cases} \mathbf{r} = \sqrt{\left(\mathbf{x}\_{12} - \mathbf{x}\_{11}\right)^2 + \left(\mathbf{y}\_{12} - \mathbf{y}\_{11}\right)^2} \\ \cos(\mathbf{u}) = \left(\mathbf{x}\_{12} - \mathbf{x}\_{11}\right)/\mathbf{r} \\ \sin(\mathbf{u}) = \left(\mathbf{y}\_{12} - \mathbf{y}\_{11}\right)/\mathbf{r} \end{cases} \tag{8}$$

After this rotation, the line d<sup>1</sup> is over Ox axis of the map's system of coordinates.

3. Rotation with sin(v) and cos(v), where:

$$\begin{cases} \mathbf{w} = \operatorname{atan2}(\mathbf{y\_{22} - \mathbf{y\_{21}} \times \mathbf{z\_{22}} - \mathbf{x\_{21}}})\\ \cos(\mathbf{v}) = \cos(\pi/2 - \mathbf{w}/2) \\ \sin(\mathbf{v}) = \sin(\pi/2 - \mathbf{w}/2) \end{cases} \tag{9}$$

After this rotation, the bisector of the angle given by lines d<sup>1</sup> and d<sup>2</sup> is over Oy.

4. Translation with (−xQ, −yQ) (Q is moved into origin O)

The following 2 systems of equations have to be solved in order to find the points Pi (xi ,yi ) (i = 1,2) where the lines d<sup>i</sup> (i = 1,2) intersect the line d:

$$\begin{cases} \text{ y } = \mathbf{a\_i x} + \mathbf{b\_i} \\ \text{ y } = \mathbf{a x} \end{cases} \tag{10}$$

Since Ai1, Ai2 define the line d<sup>i</sup> (i = 1,2) in (10) we have:

$$\mathbf{a\_{i}} = \frac{(\mathbf{y\_{i2}} - \mathbf{y\_{i1}})}{(\mathbf{x\_{i2}} - \mathbf{x\_{i1}})} \tag{11}$$

$$\mathbf{b}\_{\mathbf{i}} = \mathbf{y}\_{\mathbf{i}1} - \mathbf{a}\_{\mathbf{i}1}\mathbf{x}\_{\mathbf{i}1} \tag{12}$$

Solving the 2 systems of equations, the points P<sup>i</sup> (xi ,yi ) (i = 1,2) are found, where:

$$\mathbf{x}\_{\mathbf{i}} = \frac{\mathbf{b}\_{\mathbf{i}}}{\mathbf{a} - \mathbf{a}\_{\mathbf{i}}} \tag{13}$$

$$\mathbf{y}\_{\mathbf{i}} = \frac{\mathbf{a}\mathbf{b}\_{\mathbf{i}}}{\mathbf{a} - \mathbf{a}\_{\mathbf{i}}} \tag{14}$$

The distance between P<sup>1</sup> and P<sup>2</sup> must be minimized, i.e.,:

min a f(a) (15)

where:

$$\mathbf{f(a)} = \left(\mathbf{y\_2} - \mathbf{y\_1}\right)^2 + \left(\mathbf{x\_2} - \mathbf{x\_1}\right)^2\tag{16}$$

By replacing (13) and (14) in (16) the following formula for f(a) is obtained:

$$\mathbf{f(a)} = \left(\frac{\mathbf{a\_2b\_2}}{\mathbf{a} - \mathbf{a\_2}} - \frac{\mathbf{a\_1b\_1}}{\mathbf{a} - \mathbf{a\_1}} + \mathbf{b\_2} - \mathbf{b\_1}\right)^2 + \left(\frac{\mathbf{b\_2}}{\mathbf{a} - \mathbf{a\_2}} - \frac{\mathbf{b\_1}}{\mathbf{a} - \mathbf{a\_1}}\right)^2 \tag{17}$$

We make the following notations:

$$\mathbf{a}\_{\rm L} = \min \left\{ \frac{-1}{\mathbf{a}\_{1}}, \frac{-1}{\mathbf{a}\_{2}} \right\} \tag{18}$$

$$\mathbf{a}\_{\mathbb{R}} = \max \left\{ \frac{-1}{\mathbf{a}\_1}, \frac{-1}{\mathbf{a}\_2} \right\} \tag{19}$$

It is easy to see that the function *f* is decreasing for a ≤ aL, and is increasing for a ≥ aR*,* since *f* is continuous, a<sup>L</sup> and a<sup>R</sup> are the slopes of the perpendiculars QQ<sup>1</sup> and QQ<sup>2</sup> from Q on the lines d<sup>1</sup> and, respectively, d2, and "a" is the slope of the line d3. Consequently, there is a minimum of the function f denoted amin in the interval [aL, aR]. So, the value amin is one of the solutions of the equation:

> f ′

$$\mathbf{(a)} = \mathbf{0} \tag{20}$$

on the interval [aL, aR], where:

$$\mathbf{f}'(\mathbf{a}) = 2\left(\frac{\mathbf{a}\_2\mathbf{b}\_2}{\mathbf{a} - \mathbf{a}\_2} - \frac{\mathbf{a}\_1\mathbf{b}\_1}{\mathbf{a} - \mathbf{a}\_1} + \mathbf{b}\_2 - \mathbf{b}\_1\right) \left[\frac{-\mathbf{a}\_2\mathbf{b}\_2}{\left(\mathbf{a} - \mathbf{a}\_2\right)^2} + \frac{\mathbf{a}\_1\mathbf{b}\_1}{\left(\mathbf{a} - \mathbf{a}\_1\right)^2}\right] + 2\left(\frac{\mathbf{b}\_2}{\mathbf{a} - \mathbf{a}\_2} - \frac{\mathbf{b}\_1}{\mathbf{a} - \mathbf{a}\_1}\right) \left[\frac{-\mathbf{b}\_2}{\left(\mathbf{a} - \mathbf{a}\_2\right)^2} + \frac{\mathbf{b}\_1}{\left(\mathbf{a} - \mathbf{a}\_1\right)^2}\right] \tag{21}$$

**Remark 1.** *Since the bisector of the angle between d<sup>1</sup> and d<sup>2</sup> is parallel to Oy axis, it is not difficult to see that*:

$$\mathbf{a}\_{\rm L} = -\mathbf{a}\_{\rm R} \tag{22}$$

In order to obtain the solution amin of the Equation (20), a numerical method [14] can be used such as bisection method [15], or tangent method. Since f ′ (aL) < 0 and f ′ (aR) > 0 => f ′ (aL)·f ′ (aR) < 0, the bisection method is suitable to be applied on the interval:

$$\mathbf{a} \in \left[ \mathbf{a}\_{\mathbf{L}'} \mathbf{a}\_{\mathbf{R}} \right] \tag{23}$$

After amin is calculated, the points P<sup>i</sup> (i = 1, 2) are obtained using (13) and (14) and the distance between these two points is:

$$
\sqrt{\mathbf{f(a\_{min})}} \tag{24}
$$

In order to go back to the initial system of coordinates, the inverse initial transformations must be applied in reverse order to the points P<sup>1</sup> and P2, i.e.,:


4. Translation with (x<sup>I</sup> , y<sup>I</sup> ). The following Algorithm 3 (denoted A2SSTPC2L) is obtained to solve SSTPC2L:


We implemented the above algorithm in Visual C++ and in the bisection method we set the error err = 0.0001 for finding the value amin. In Figure 6, a graphical output of our program is presented.

**Figure 6.** Output of the Visual C++ program.

#### **3. Results**

Besides estimation of the ground slope for a given point, other two possible problems can be solved since we have now obtained a method to calculate the points P1, and P<sup>2</sup> on the closest two level curves to a given point Q so that P1, Q, and P<sup>2</sup> are collinear and the distance between P<sup>1</sup> and P<sup>2</sup> is minimum.

#### *3.1. Elevation Estimation at a Point*

The challenge is to estimate as well as possible the elevation z of a point Q. Assuming that z<sup>1</sup> < z<sup>2</sup> (see Figure 3) and since QQ' is parallel to P2P ′ <sup>2</sup>, in the triangle P1P2P ′ <sup>2</sup> we have:

(x୕ − xଵ)

(x<sup>ଶ</sup> − xଵ)

൫x୕ − xଵ൯

(x<sup>ଶ</sup> − x<sup>ଵ</sup> )

ଶ

$$\frac{\mathbf{z}\_{\mathbf{Q}} - \mathbf{z}\_{1}}{\mathbf{z}\_{2} - \mathbf{z}\_{1}} = \frac{\text{dist}(\mathbf{P}\_{1}, \mathbf{Q}')}{\text{dist}(\mathbf{P}\_{1}, \mathbf{P}'\_{2})} \tag{25}$$

(z<sup>ଶ</sup> − z<sup>ଵ</sup>

ଶ

) ଶ )


ଶ

ଶ

+ ൫y୕ − yଵ൯

<sup>ଶ</sup> + (y<sup>ଶ</sup> − y<sup>ଵ</sup>

From (25) we obtain the elevation of Q:

z୕ = min {z<sup>ଵ</sup>

$$\begin{array}{ccc} \mathbf{y} & \mathbf{y} \\ \mathbf{y} & \mathbf{y} \end{array}$$

, z<sup>ଶ</sup> } + ඨ

z୕ = z<sup>ଵ</sup> + ඨ

$$\mathbf{z}\_{\mathbf{Q}} = \mathbf{z}\_1 + \sqrt{\frac{\left(\mathbf{x}\_{\mathbf{Q}} - \mathbf{x}\_1\right)^2 + \left(\mathbf{y}\_{\mathbf{Q}} - \mathbf{y}\_1\right)^2}{\left(\mathbf{x}\_2 - \mathbf{x}\_1\right)^2 + \left(\mathbf{y}\_2 - \mathbf{y}\_1\right)^2}} (\mathbf{z}\_2 - \mathbf{z}\_1)^2$$

It is immediate that, without the assumption of z<sup>1</sup> < z2, the following formula can be used to estimate the elevation of Q:

$$\mathbf{z}\_{\rm Q} = \min\{\mathbf{z}\_1, \mathbf{z}\_2\} + \sqrt{\frac{(\mathbf{x}\_{\rm Q} - \mathbf{x}\_1)^2 + \left(\mathbf{y}\_{\rm Q} - \mathbf{y}\_1\right)^2}{\left(\mathbf{x}\_2 - \mathbf{x}\_1\right)^2 + \left(\mathbf{y}\_2 - \mathbf{y}\_1\right)^2}} |\mathbf{z}\_2 - \mathbf{z}\_1|\tag{26}$$

#### *3.2. The Slope between Two Points*

The problem of estimating the slope between two points is significant, seeing that when designing roads, the slope between any two points on a road cannot exceed a given maximum slope, e.g., for highways this value has to be less than 6% or 7%. Therefore, the chosen points from the future road can be tested for this eligibility. To do that, we consider the elevations of the points Q<sup>1</sup> and Q<sup>2</sup> calculated using formula (26) and we can estimate the slope m(Q1,Q2) of the road passing through Q1(x1,y1,z1) and Q2(x2,y2,z2) using the following formula (see Figure 7):

$$\tan(\mathbf{Q}\_1 \mathbf{Q}\_2) = \tan(\beta) = \frac{|\mathbf{z}\_2 - \mathbf{z}\_1|}{\text{dist}(\mathbf{Q}\_1 \mathbf{Q}\_2')} = \frac{|\mathbf{z}\_2 - \mathbf{z}\_1|}{\sqrt{(\mathbf{x}\_2 - \mathbf{x}\_1)^2 + (\mathbf{y}\_2 - \mathbf{y}\_1)^2}} \tag{27}$$

**Figure 7.** The slope of the road passing through Q<sup>1</sup> and Q<sup>2</sup> .

#### *3.3. Optimum Excavation/Filling*

m(Qଵ, Q<sup>ଶ</sup> ) = tan൫β൯ = |z<sup>ଶ</sup> − zଵ<sup>|</sup> dist(Qଵ, Q<sup>ଶ</sup> ᇱ ) = |z<sup>ଶ</sup> − zଵ| ඥ(x<sup>ଶ</sup> − xଵ) <sup>ଶ</sup> + (y<sup>ଶ</sup> − yଵ) ଶ When a house is built on sloping land and/or with elevations and depressions, the elevation of a horizontal plane must be calculated so that the excavations over the plane would fill the space below the plane resulting in a horizontal platform on which a house can be built. In such a manner, the optimal solution between excavations and fillings is calculated, resulting in a reduction in the costs of embankments. We shall follow up with a presentation of a method to accurately calculate the elevation of this plane. The well-known "flood fill" algorithm [16] from computer graphics is adapted to deal with this problem. Since the algorithm runs in a discrete space, the coordinates will be transformed into their discrete counterparts.

We start with the level curves from the vicinity of the house (Figure 8). Then a discretization is applied (Figure 9), meaning that the plane is divided into equidistant 2D points, e.g., in Figure 9, the distance of 40 cm between points was considered. The points of the contour of the house are transformed into their discrete counterparts (for each such a point, the closest discrete point is determined). Using Bresenham's algorithm [17], the discrete points of the contour are found (green points in Figure 9). Using a flood fill algorithm [16] in the discrete plane of the house, the discrete points inside the contour are determined (red points from Figure 9). The elevation of each red or green point is calculated using the level curves. Using these elevations, the optimal elevation of the excavation/filling plane is computed. So, the following algorithm denoted AOEF is obtained.

**Figure 8.** Level curves (pink lines) in the vicinity of the house (blue lines): (**a**) 2D view; (**b**) 3D view.

**Figure 9.** Discretization of the plane of the house. Black points are outside the house, green points give the contour of the house, red points are inside.



Using the elevations z<sup>i</sup> , calculate the elevation of the optimal excavation/filling plane (see AHEFP).

π Applying the elevations z<sup>i</sup> of the discrete points Q<sup>i</sup> inside the contour of the house, the elevation of the optimal excavation/filling plane can be determined as follows. The elevations are sorted ascendingly. A horizontal plane π(h) (h is the height/elevation of the plane) is placed consecutively starting with the first (the lowest) elevation, continuing with the second, and ending with the last one (the highest). The following algorithm is obtained:

Algorithm 5 Height of Excavation/Filling Plane (AHEFP):


```
Input: vector of elevations z = (zi
                                       )i = 1, 2, . . . , m;
Sort ascending the vector z;
S = 0;
for i = 2 to n do
       S = S + zi − z1
                        ;
 end for;
S1 = 0;
S2 = S;
for i = 2 to n − 1 do
       S1 = S1 + (i − 1) · (zi − zi-1);
       S2 = S2 − (n − i + 1) · (zi − zi-1);
       if S2 ≤ S1
                   then
              opt = i;
              break;
       end if;
end for;
```
At each iteration of the last "for" loop from AFHEFP, the height of the plane is considered equal to z<sup>i</sup> , S<sup>1</sup> is the sum of the distances between the elevation of z<sup>i</sup> the plane and the elevations below the plane, and S<sup>2</sup> is the sum of the distances between the elevations over the plane and the elevation z<sup>i</sup> of the plane, i.e.,:

$$\mathbf{S}\_1 = \sum\_{\mathbf{k}=1}^{\mathrm{i}-1} \left( \mathbf{z}\_{\mathrm{i}} - \mathbf{z}\_{\mathrm{k}} \right) \tag{28}$$

$$\mathbf{S\_2} = \sum\_{\mathbf{k}=\mathbf{i}+1}^{\mathbf{n}} (\mathbf{z\_k} - \mathbf{z\_i}) \tag{29}$$

when starting a new iteration, S<sup>1</sup> is the sum of i-1 components of z and was calculated in the previous iteration. The new sum S<sup>1</sup> can be obtained from the previous by adding (i − 1) · (z<sup>i</sup> − zi-1).

At the beginning of each iteration, S<sup>2</sup> is the sum of n-i+1 components of z and was calculated in the previous iteration. Thus, using the value of the previous S2, the new sum can be obtained from the previous by subtracting (n − i + 1) · (z<sup>i</sup> − zi-1).

Since S<sup>1</sup> is increasing from 0 to S and S<sup>2</sup> is decreasing from S to 0, the optimum is reached when S<sup>2</sup> becomes less or equal to S1. More exactly, the optimum height of the plane is inside the interval [zopt-1, zopt]. If the values zopt-1 and zopt are close enough, i.e., zopt − zopt-1 < ε, where ε > 0 is the fixed maximum distance to the optimum, e.g., ε = 5 cm, then any of the values zopt-1 and zopt are good approximations of the optimum. If zopt − zopt-1 ≥ ε, then a divide and conquer strategy is applied to get closer to optimum. To do that, two initial planes π(zopt-1) and π(zopt) are considered. A new plane is placed in the middle. If the distance between S<sup>2</sup> calculated for π((zopt-1+zopt)/2) and S<sup>1</sup> for π(zopt-1) is less than the distance between S<sup>2</sup> for π(zopt) and S<sup>1</sup> for π((zopt-1+zopt)/2), then the optimum is further calculated in the interval [zopt-1, (zopt-1+zopt)/2]. Otherwise, the optimum is calculated in the interval [(zopt-1+zopt)/2, zopt] and so on.

Algorithm 6 divide and conquer for optimum excavation/filling plane (ADCOEFP):

**Algorithm 6** Divide and conquer for optimum excavation/filling plane (ADCOEFP)

```
a = zopt-1;
b = zopt;
Sa,1 = S1 − (opt − 1) · (zopt − zopt-1);
Sa,2 = S2 + (n – opt + 1) · (zopt − zopt-1);
Sb,1 = S1
         ;
Sb,2 = S2
         ;
while b − a ≥ ε do
       c = (a+b)/2;
       Sc,1 = Sa,1 + (opt − 1) · (c − a);
       Sc,2 = Sa,2 − (n − opt + 1) · (c − a);
       if |Sc,2 − Sa,1| < |Sb,2 − Sc,1| then
            a = c;
            Sa,1 = Sc,1;
       else
            b = c;
            Sb,2 = Sc,2;
       end if;
end while;
S1 = Sa,1;
S2 = Sa,2;
```
At the end of the while loop, any of the values, a or b are good approximations of the optimum. We considered a as the optimal solution. The approximate excavation volume is V<sup>e</sup> = S<sup>2</sup> · d2, and the filling volume is V<sup>f</sup> = S<sup>1</sup> · d2. Consequently, the difference between the two volumes is:

$$|\mathbf{V\_e - V\_f}| = |\mathbf{S\_2 - S\_1}| \mathbf{d}^2 \le \varepsilon \mathbf{S\_{house}} \approx \varepsilon \mathbf{m} \mathbf{d}^2 \tag{30}$$

So, the two volumes are very similar.

#### *3.4. Numerical Example*

Figure 10 shows a real topographic map for a plot of land on which a house is to be built. The topographic map of the land was drawn up by a topometric engineer, with specific high-precision equipment, called in specialized terms "station." For small areas of land, the station is successively placed and GPS 3D coordinates are measured relative to a fixed position (in our situation it is a terminal in the Black Sea area located at a distance of approximately 717 km). The first chosen points of the topographic survey are those that describe the contour of the plot of land. In our case, the terrain contour is described by the 15 points (numbered in black). These points are inventoried and noted in a table (coordinate inventory) located on the topographic map. The following points will describe the contour of the level elevations, the positioning of the access road, the position of the neighboring houses (they are marked on the map in red together with the elevation), etc. In the case of lands with a high slope, such as the one exemplified, the measured points must be thickened for a greater accuracy of tracing the level curves (in total we have over 100 such points).

The designer receives in electronic format a topographic map similar to the one in Figure 10. On this topographic support, the designer will place the designed building on the scale, having to respect a series of rigors imposed by law, among which: the minimum distance from the property limit and/or from the road axis as in Figure 11. Once the construction is located, the new contour will appear on the topographic map described by a few new points (minimum 4, in the example, for the description of the contour, 6 points are used). A situation plan is drawn up in which, according to the legislation, the 2D coordinates of the corners of the construction must be specified (see Table 1) together with the elevation of the horizontal excavation/filling plane. In Figure 11, this elevation is

denoted by CTA and is estimated at 707 m by the designer. A good determination of this elevation is not easy, especially if the terrain has a high slope.

**Figure 10.** Topographic map.

**Table 1.** The x and y coordinates of the Q points.


A detail of Figure 11 is presented in Figure 12 illustrating the points A 2 <sup>11</sup>, A 2 <sup>12</sup>, A 2 <sup>21</sup>, and A 2 <sup>22</sup> found using the algorithm AIPS.

Table 2 presents the coordinates of the points A k <sup>11</sup>, A k <sup>12</sup>, A k <sup>21</sup>, and A<sup>k</sup> <sup>22</sup> calculated for each point Q<sup>k</sup> (k = 1, 2, . . . , 6) by applying AIPS. Using A2SSTPC2L and (26), the elevation for each point Q<sup>k</sup> (k = 1, 2, . . . , 6) is calculated.

Usually, for the dimensions of the project to be in accordance with the real construction, before commencing all the construction works, a plot is made on the field of the future building. For this purpose, the ground tracing is performed. The corners of the house are very precisely marked (the Q points). In our example, the provided measured elevations of the 6 points are presented in Table 3.

**Figure 12.** Detail of Figure 11 for Q<sup>2</sup> .

Aଵଵ ଵ Aଵଶ ଵ Aଶଵ ଵ Aଶଶ ଵ

Aଵଵ ଶ Aଵଶ ଶ Aଶଵ ଶ Aଶଶ ଶ

Aଵଵ ଷ Aଵଶ ଷ Aଶଵ ଷ Aଶଶ ଷ

Aଵଵ ସ Aଵଶ ସ Aଶଵ ସ Aଶଶ ସ

Aଵଵ ହ Aଵଶ ହ Aଶଵ ହ

Aଵଵ ୩ , Aଵଶ ୩ , Aଶଵ ୩

, and Aଶଶ ୩


**Table 2.** 3D coordinates of the Q points.

**Table 3.** The estimated and the measured z-coordinates of the Q points.


As seen in Table 3, the estimated elevation and the measured one for each Q point are very close. The difference between them is less than 2 cm.

Using the coordinates of the points Q<sup>k</sup> (k = 1, 2, . . . , 6) from Table 1, Bresenham, and, then flood fill algorithms were applied resulting in 803 points located inside the perimeter of the house. The elevations of these points were calculated using A2SSTPC2L and (26). The algorithm AHEFP was applied for these 803 elevations and the height of the horizontal excavation/filling plane was accurately estimated as 706.2571 m, instead of the value 707 m proposed by the designer. Out of the 803 points, 412 were located below the horizontal plane, and 391 had the elevation over this plane.

#### **4. Discussion**

In order to compare the two proposed methods (from Sections 2.1 and 2.2) for determining the points P<sup>1</sup> and P<sup>2</sup> 100 million experiments were performed. For each experiment, two random lines d<sup>1</sup> and d<sup>2</sup> were selected and the point Q was also randomly chosen. The tests were performed using an ASUS ROG GL752VW-T4015D laptop with Intel® Core™ i7-6700HQ 2.60 GHz processor, and 8 GB of RAM.

First, we analyzed the speed of the proposed methods. The total running time of the first method was 5.82 s. The total running time of the second method was 40.14 s. So, the first method is almost 7 times faster than the second one (see Figure 13). The first method is considerably faster because it requires elementary calculations, while the second one runs an iterative algorithm to solve the Equation (18).

**Figure 13.** Running time comparison of the two methods (100 million experiments).

We also calculated the accuracy of the first method against the second method since the error for the second method can be set as low as desired. An average error of 0.61% was obtained, the lowest error being 0 and the highest 1.17% (Table 4). So, we concluded that the accuracy of the approximate first method is good enough.

**Table 4.** Errors of the first method obtained from 100 million experiments.


The steps of positioning the house will be next discussed, and the utility of the methods proposed in this paper will be shown. The designer receives a topographic map in electronic format. On this topographic support, the designer will place the designed building on the scale, having to comply with a series of rigors imposed by law, among which: the minimum distance from the property limit and/or from the road axis, etc. Once the construction is located, the outline of the house described by several new points will appear on the topographic map (minimum 4). At these new points, it is necessary to specify: the coordinates on the three dimensions according to which the elevation is specified, and the distances of the construction location from the property limits. The determination of the coordinates in the plan does not raise any concerns, but there are difficulties in obtaining the real vertical elevation especially if the terrain has a high slope. The article proposes a method for determining the exact elevation of the land at the corners of the building, and in fact for the entire contour. Depending on the contour dimensions, the designer establishes a position of the horizontal plane, a plane that corresponds to the finished floor of the ground level. The decision to establish this quota should be contingent on the volumes of embankments that will be made. The optimum is obtained when the excavation volume is approximately equal to the filling volume. The article solves this problem in Section 3.3.

For the design of a road, a primary route of the road is made on a topographic map and road recognition is performed. A final design of the road follows both along its entire length and on its cross-sections. Figure 14 shows with a red line the optimal trajectory of a road depending on the elevation of the natural land. Because the considered road is a highway, the rules impose stricter restrictions on the slopes. If the allure of the natural terrain in certain areas is followed, the maximum allowed inclination of the road will inevitably be exceeded. As it can be seen in Figure 14, in these areas, measures must be taken to straighten the slope, such as fillings, excavations or the provision of bridges and viaducts, tunnels respectively. Through detailed awareness of the elevations and the inclination of the land in the points near the road, an optimal vertical tracing of the road can be established so that we have minimum excavations and fillings for an imposed road slope, or we can optimize the lengths of the bridges, respectively tunnels [12].

**Figure 14.** The optimal trajectory of a road depending on the elevation of the natural land.

When designing a new road or railway, a number of initial design factors must be taken into account, such as: road category, design speed, width of a traffic lane, number of lanes, traffic frequency, equipment size, etc. Depending on the route imposed on the road, there are also other specific aspects that must be taken into account:


11. If an unstable area such as a headwall must be crossed, consider end hauling excavated material rather than using sidecast methods. Avoid deep fills and compact all fills to accepted engineering standards. Design for close culvert and cross drain spacing to effectively remove water from ditches and provide for adequate energy dissipators below culvert outlets. Horizontal drains or interceptor drains may be necessary to drain excess groundwater [13].

As seen in Figure 15, the angle of inclination of the terrain is an important parameter to know in order to avoid erosion and then landslides [18,19].

From the point of view of the cross-sections, the position of the road in relation to the terrain slope must take into account the above constraints. By the same token, knowing the slope of the land is essential for establishing the position both horizontally and especially vertically of the road, and for achieving a low cost related to the embankment works. This position is established according to the Full Bench Road Prism, which contains the elements in Figure 16.

**Figure 16.** Elements of road prism geometry.

For very steep road areas such as the one in Figure 17, knowing the slope is imperative because substantial savings in embankment volumes can be made, resulting in decreasing the quantities of gabions or excavations [13].

**Figure 17.** Reduction in excavation made possible on a steep slope by the use of cribbing.

The problem related to determining the slope of natural land at a point on the topographic map is necessary both in the longitudinal section and in the cross-section of roads or railways and have the same solution described in Sections 3.1 and 3.2.

The proposed methods can also be applied in environment protection, and hydrotechnical engineering [18,19]. The evaluation of the slope is also necessary for river levees. Slope stability analyses are conducted with rising water levels until certain failure is reached. Discharge occurs at a water height of around 7 cm above the crown, which means the slope would actually fail before reaching the hydraulic heads used for slope stability calculation during the overflow [20].

#### **5. Conclusions**

To conclude, the correct estimation of elevation at points has a practical application to calculate the optimum excavation/filling plane when a new house is built. The article presented a method to estimate accurately the elevation of this plane which reduces the costs of embankments.

When designing a new road or railway, designers need to know the ground slope at some points of the future road or rail as exactly as possible, as well as the elevation of each considered point, and, also, the slope of each consecutive two points. Instead of sending workers on the field to perform measurements, these values can be calculated with very good accuracy using the methods described in Section 2.1, and Section 2.2. Two algorithms

to solve SSTPC2L are presented, a fast and approximate one and an exact but slower one. The error of the first method is low (see Table 1). It has the advantage of being very fast and accurate enough. Thus, if there are many points for which SSTPC2L is applied, the first method can be preferred. However, if we look for a more accurate solution, the second method is more suitable.

**Author Contributions:** Conceptualization, A.M.D. and O.D.; methodology, A.M.D. and O.D.; software, A.M.D.; validation, O.D.; formal analysis, A.M.D.; investigation, O.D.; resources, A.M.D. and O.D. data curation, A.M.D. and O.D.; writing—original draft preparation, A.M.D. and O.D.; writing—review and editing, A.M.D. and O.D.; supervision, A.M.D.; funding acquisition, A.M.D. and O.D. Both authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by University Transilvania of Bras, ov.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Transforming Building Criteria to Evidence Index**

**Géza Fischl \* and Peter Johansson**

Department of Construction Engineering and Lighting Science, School of Engineering, Jönköping University, 553 18 Jönköping, Sweden; peter.johansson@ju.se

**\*** Correspondence: geza.fischl@ju.se

**Abstract:** There is increasing pressure from developers toward architects and engineers to deliver scientifically sound proposals for often complex and cost-intensive construction products. An increase in digitalization within the construction industry and the availability of intelligently built assets and overall sustainability make it possible to customize a construction product. This servitization of construction products is assumed to perform much preferably in satisfying stakeholders' physical, psychological, and social needs. The degree to which these products are performing can be evaluated through an evidence index. This article aims to introduce a conceptual model of an evidence index and test it in the programming stage of a case study. The investigation follows the evidence-based design approach and renders evidence through key performance indicators in the programming stage of the building process. For testing the concept, a case study investigation was performed by simulating a novice research assistant, and the amount of evidence was collected and appraised for evidence index. The case study showed that key performance indicators of a servitized project could be evaluated on a four-point scale. The quality of the evidence index generation depended on the level of expertise the evaluator has in research and the skilful use of scientific databases.

**Keywords:** construction product; servitization; evidence-based design; level of evidence; cognitive buildings

#### **1. Introduction**

A typically assisted workflow by Building Information Modeling (BIM) process is the building performance evaluation [1], for instance, for energy consumption [2] and lighting [3], and air quality through simulations [4]. The optimal building performance can be achieved with technical considerations and a close fit between the building and its users' needs, providing comfort, health, and safety [5]. In terms of a computer-aided approach, development toward an easy-to-use data input is emerging for human behaviour regarding the programming and design phase. For improving design, a variety of quantitative approaches surfaced, like the probabilistic method [6], which reflects variation in the energy consumption models and the agent-based model (see, e.g., in [2,7,8]) that is investigating complex systems composed of interacting agents. In connection to building performance evaluation, a knowledge-oriented value generation process [1,7] in which stakeholders find satisfactory proofs, concerning key performance indicators (KPIs), treated like evidence for reasoning their needs and activities had surfaced. Key performance indicators are instrumental for optimizing the goals of the organization. The organizational goals are usually higher; meanwhile, the KPIs operationalise these goals and make them measurable, understandable, and actionable [8,9]. Therefore, KPIs in the programming and design phase of the building performance evaluation are often connected to the developer's detailed list of building criteria or physical attributes that are expected to be incorporated in the project. This detailed list of building criteria usually emerges through a long-term collaboration between the industry partners to ensure technical and functional service quality. One of this list is the Swedish Program for Technical Standard [8,10], used in the case study below, a database for optimizing healthcare facilities' construction and design. The design criteria

**Citation:** Fischl, G.; Johansson, P. Transforming Building Criteria to Evidence Index. *Appl. Sci.* **2021**, *11*, 5894. https://doi.org/10.3390/ app11135894

Academic Editor: Lavinia Chiara Tagliabue

Received: 16 May 2021 Accepted: 17 June 2021 Published: 24 June 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

are set up with stakeholders, including the construction industry, to deliver a technical service solution to the users. This kind of servitization [11,12] is a key for delivering appropriate performance to stakeholders. In a traditional method, a building developer would provide a facility list that satisfies the needs in a technical/engineering approach, meanwhile, a servitized concept offers KPIs matching the stakeholders' personal needs. Today's technological possibilities allow building upon a new set of servitized construction products that are more efficient and less resource-intensive, connected through smart products and systems, and provide self-learning abilities that deliver an evidence-based optimization. For instance, lighting in an office is set to 200 lux as the general illuminance, but for well-being supportive lighting should include a glare-free setting that helps the individual. Furthermore, considering the daily intake of lighting energy for appropriate circadian rhythm functioning, the KPI should be supporting a human circadian rhythm. The critical issue here is how to assign the appropriate KPI for measuring the intended outcome. That is why researchers had turned their attention to evidence-based design (EBD) as a design method from the field of evidence-based medicine [13]. EBD for the built environment can be defined as the process of design decisions on credible research and lessons learned from previous design experiences as evidence to achieve the best possible outcomes [14,15]. EBD is the antecedent of the building performance evaluation [16,17] and recent research has shown how EBD can be connected to digital tools, like lighting simulations [18]. This research has identified the importance of selecting KPIs (or metrics) for identifying evidence [19] during the evidence-based optimization (EBO). EBO and the current development of cognitive abilities of the building system could lead to better servitization of construction products (Figure 1).

**Figure 1.** Servitisation of construction product in the context of **Figure 1.** Servitisation of construction product in the context of BIM in Industry 4.0, Circular economy, and Intelligent Building Information Modeling (BIM) assets (Adapted from CPA, [20]; p 17).

Promoters of EBO may be representatives of developers, architecture designers, clients, users, researchers, and facility managers for improving an individual's physical, psychological, and social qualities together with environmental sustainability. From this perspective, the attainment of stakeholders' values would ensure the successful implementation of resources to the predefined goal. A possible measure of reaching the predefined goal is to assess an evidence index for all physical attributes or components listed in the building criteria; henceforth, early in the programming stage, the expected evidence index can indicate how well the predefined goals in the building criteria are in line with a scientific level of evidence.

Consequently, this article aims to introduce and, through a case study, test an evidence index capable of describing the level of evidence at the programming stage of a building process. It is assumed that a novice investigator can generate an evidence index, but the results need to be further scrutinized.

#### **2. Methodology**

In this section, the first conceptual method of an evidence index is described, and an enhancement of the EBD process with a cognitive building concept is suggested. Consequently, a case study focusing on an administrative office is tested with the suggested evidence index framework.

#### *2.1. Establishing Evidence Index*

The concept of an evidence index (EI) in a room or a building is complementing a post-occupancy evaluation method (POE) (see, e.g., in [21]). POEs have been around for several decades [16], and the depth of investigations is generally made on three distinct levels [22] (indicative, investigative, and diagnostic). A post-occupancy evaluation system arose for feedbacking stakeholders in building projects regarding how well the building performs after its inauguration in terms of user's satisfaction, energy performance, indoor environmental quality, and sustainability. An EI's conceptual development is originated in the EBD process [23]. The intention with a single value on a room/building project is to inform the stakeholders about the verified level of evidence that the building criteria is setting. As building criteria may arise from a previous POE and most likely a new project organization would introduce these additional values for the programming stage, this act of organizational learning [24] was the forerunner of a cognitive building. Cognition in terms of information processing requires working memory (POE) and long-term memory (building criteria, KPIs) in order to appraise information (evidence) for appropriate response selection [25] (project outcome). Consequently, the state-of-the-art understanding of the cognitive building solution is a sustainable building system that automatically integrates, analyses, and learns from the IoT-generated data [26]. The EI would be benefitting the cognitive building concept through the interconnectedness of scientific databases and machine learning of evidences in scientific publications to find and appraise a project-specific evidence index. For this to become a reality, more knowledge about EBD and EI is needed, and the work described here is a contribution to that.

#### 2.1.1. Evidence-Based Design Process for Cognitive Buildings

POE is an integral part of the EBD process [3,18], which distinguishes between eight phases that refer to a continuous workflow stepwise progression. The modified EBD process fitted to a servitized construction product for cognitive building solution may include the following:


The above-suggested EBD process for cognitive building solution is still ahead of the present reality. However, for the realization of the EI in a non-cognitive building solution, the first three stages of the original EBD process are considered in this article. Starting with the definition of goals and objectives that describes the planned building project's intentions and direction. A team of decision-makers articulate project goals in terms of their desired outcomes. In the case of a well-known building typology to be delivered, the project goals and objectives are revisited from previous successful projects using POE. These building criteria may be industry standards and recommendations. In case of an innovative solution, building criteria are being set intuitively according to the team's experience. When this preliminary programming of domain-specific values is set, the next stage is finding sources for relevant evidence.

#### 2.1.2. Finding Evidence

Relevant evidence is gathered mainly from scientific literature to identify gaps in knowledge and determine what relevant research has already been performed and which needs to be researched. Peavey and Vander Wyst [27] differentiate between evidence that incorrectly refers to a proof of a design decision. This misconception is caused by the difference between the commonly used definition of evidence as proof and the scientific interpretation of evidence. The latter divide evidence into several levels. Another shortcoming of using evidence as a proof is reported by Cama [28] when the practitioner indistictively using the evidence for any kind of built environment. To overcome such a misinterpretation of evidence, a critical interpretation is needed.

The methodological framework for ranking evidence is combined from a series of research design methods that gradually decrease the need for scientific rigour, validity, and reliability. Therefore, the evaluation of the level of evidence prerequisites a qualified person to interpret the specific evidence in accordance with an EBD guideline. This guideline was moulded from Pati [29], Stetler [30], and Stichler [31] recommendations for healthcare design settings (Table 1).


**Table 1.** Levels of evidence as it is originated from healthcare design.

Note. Adapted from Pati [29], Stetler [30], and Stichler [32]. These levels should be used in conjunction with a critical appraisal of quality at each level.

In a building project, ranking of evidence in the early project phase is imperative because it has a significant outcome for the programming stage that will impact the stakeholders' physical, and psychological and social wellbeing. At the critical interpretation of relevant evidence, awareness about potentially misinterpreted evidence can still be resolved in time before the project is suffering from serious financial expenses. However, the level of evidence may require qualified personnel in research methodology who can rank the scientific evidence and still give credits for opinions and individual observations. A categorization of such a comprehensive source of information should be guided by a value-generation process that gives meaning to complicated interpretations of the scientifically produced evidence. Marquardt and Motzek [33] suggested a helpful algorithm for architects and designers to critically appraise the quality of evidence in EBD. By adopting a four-level scale instead of a six-level, as Marquardt and Motzek [34] suggested, the investigation of the quality of evidence may take less time to perform with less trained personnel. To appraise the level of evidence into a four-point scale, Evans (2003, p. 82) published a hierarchy to an indication of the validity and trustworthiness of different types of research. This process assists in the selection of the evidence to guide evidence-based clinical practice. However, a building delivery process is not seen directly as a comparable field of study to clinical practice, yet its systematic research-based approach to identification of evidence makes it possible to apply the principles of research to designers and engineering practitioners. Henceforth, the proposed four-point rating scale is the first attempt to measure the level of evidence in servitized construction delivery using EBD. The highest rating is *excellent*, when the evidence provides the strongest scientific base for the practice. This evidence level is at the least risk of error, therefore it is optimal for the development of practical design guidelines and recommendations. The next highest level is *good*. This rating provides a sound basis for practical cases and is at low risk of error. However, as it may have been generated by single studies, it also highlights areas where replication of research is needed. A less prefered rating is *fair*, which includes varying degrees of risk for error, and it does not provide a strong evidence for the practice. These studies usually represent exploration of interventions. The rationale behind this level is to accept a greater risk of error in the evidence, yet allow further identification of potentially beneficial KPIs that require additional investigation and evaluation. The least preferred and most common level of evidence can be ranked as *poor*, when there is a weak basis for practical use and is at serious risk of error or bias. The four-point scale rating has an advantage on the usability side as an evaluator is forced to avoid central tendencies and needs to be making a decision based on the criteria at hand [35]. The drawback of this four-point scale is tangible when the accuracy of the level of evidence is in question. In the EBD process, the scientific evaluations should be synchronized to laypersons or design

experts too. A four-point category suggested on quality of evidence is summarized and retains the major scientific category differences and the contents (Table 2).

**Table 2.** Modified levels of evidence for quantitative research and EBD project.


Note: Adapted from Pati [29], Stetler [30], and Stichler [32]. These levels should be used in conjunction with critical appraisal of quality at each level.

#### 2.1.3. Critical Review of LOE

Two flow chart diagrams visualize the decision-making procedure evaluating the level of evidence (LOE) with a quantitative or qualitative study by Marquardt and Motzek [33]. These algorithms for rating the evidence distinguishes among six-levels LOE according to Stichler [32]. The step-by-step procedure follows "yes" and "no" options for the main methodological junctions. The answers on these methodological alternatives will eventually lead the rater to various level of evidence. A four-level LOE category is presented in relation to the major study types in Figure 2. When a qualitative or case study is investigated in an interpretative way, the rater evaluates if the study has a literature review, a framework, a clear method reported, and the diversity of views are represented, then the LOE might be reaching a *fair* rating. When these aspects are not addressed in the study, it is assigned as *poor*. For instance, a case study describing the renovation of a building is classified as *poor*, but if the study features several buildings with the same typology, including stakeholder interviews, and has a matching methodology, it is assigned to *fair*. The quantitative study employs statistical analyses and measures outcomes, therefore they belong to the observational study category. These can be a panel, cohort, case-control, and cross-sectional studies. A sample is followed over a period in a panel study, and the effects of exposures are examined. All observational studies are assigned to *fair,* considering a set of samples compared to each other in a methodologically appropriate way. In an experimental study, when the participants are randomly allocated to at least two randomized selected groups and compared under two or more conditions, the study can be called a randomized controlled trial (RCT). In this type of study, one group receives treatment, while the other group does not. The measurements taken in both cases are before and after the treatment.

When the groups are not randomized but grouped due to specific characteristics, the study is considered as quasi-experimental. In some quasi-experimental studies using within-subject tests, the measurements are taken before and after the intervention. If an experimental or quasi-experimental study is well-conducted, it is classified as *good*, otherwise as *fair*. These types of studies are well-conducted if (1) there are two separate groups of participants; (2) there is a low gradual reduction rate, under 20%; (3) the outcomes are analyzed according to initial treatment assignment; and (4) there are reliable outcomes with low dispersion. Additionally, an experimental RCT study is well conducted and can be assigned as *good* if there is a low ascertainment bias at sampling and the study maintain a high quality of blinding of participants and the researcher.

**Figure 2.** Study types in relation to the four-point scale of the level of evidence (LOE) **Figure 2.** Study types in relation to the four-point scale of the level of evidence (LOE). Modified after Marquardt and Motzek [33].

The right side of the diagram (Figure 2), deals with nonsystematic, systematic, and mixed methodology papers. The nonsystematic refers to studies from manufacturers or consultants, including experts' opinions and guidelines of professional organizations and standards. The scientific robustness of the papers is lacking and the critical approach to the investigations is missing. Furthermore, these studies might have financial interest bias. These nonsystematic papers are all rated as *poor*. In contrast to this, the systematic reviews and meta-analyses identify, evaluate, and summarize objective and accurate approaches rated as *excellent* evidence. Meanwhile, in the systematic review and the integrative review with lower quality of study design, the studies summarize merely empirical or theoretical views, therefore they reach a *fair* level.

#### **3. Case Study Application**

The Real Estate (Regionfastigheter) organisation of Jönköping's County Council in Sweden has developed an IT-based management system for controlling and supporting its building process, called Program of Technical Standard (PTS). PTS is a knowledge database containing best practice and specific knowledge about how the building of premises for healthcare should be carried out. PTS is a widely accepted building criteria recommendation in 20 of the 21 County Councils in Sweden [36]. Among other things, PTS contains standard room requirements for various interior amenities and functions.

The case study involved an administrative office (approximately 10 m<sup>2</sup> ; but at least 4.2 m × 2.1 m, Figure 3) from PTS. The detailed list of building criteria for the single person occupancy administrative office was obtained through Regionfastigheter Jönköping, Sweden. The building criteria in the PTS are not explained or categorized in any specific way, making it rather difficult for formulating a prioritization about it. Therefore, the investigation of the list of building criteria was first categorized and later searched to find the value and possible evidence related to the particular criteria.

**Figure 3.** BIM model of administrative office typology visualized after the (After Program of Technical Standard) PTS building criteria. This visualization is done by ArchiCAD 22 Educational edition, Jönköping university.

The case study aimed to investigate the evidence index for this single office occupancy in the programming phase of the design process.

#### *3.1. Procedure and Analysis*

The case study procedure followed Table 3 steps to generate the EI. The manual steps are summarized which are set to make an EI for a servitized construction product. After identifying stakeholder as administrative personnel, the EBD process started. The building typology was set for a healthcare facility, and the building criteria were extracted from the PTS. The evidence and the domain of the evidence were described in each finding. The project relevance was chosen to be on a four-point scale: poor (1), fair (2), good (3), and excellent (4). The applicability of this four-point scale was earlier described. The priority of evidence to be used in the EI calculation was set between low (1), medium (2), or high (3). The assessment process did not aim to collect as many evidence as possible within one building criterion, instead as a general approach it aimed to provide at least one evidence for each criterion. The decision behind this category scale is the ease of use for the rater to set up a quick cognitive process. The LOE was appraised using the diagram of Figure 2 and the reference for the related evidence was indicated. The LOE was set between poor (1), fair (2), good (3), and excellent (4) depending on the scientific approach.

**Table 3.** Procedure to generate the Evidence index for a servitized construction product.


The appraisal of the EI resembled a novice research assistant searching strategy, implying that the person first uses Google or Google scholar engine and, if it is not successful, then uses a university library access for scientific literature.

#### *3.2. Results and Discussion*

The results are presented in Table 4. Altogether, 42 building criteria were taken into consideration when identifying 30 evidence. Among the evidence, best practice indicated a not identified evidence, therefore it was assumed that the building criteria is based on a practical need existing in the construction and use phases. The values for these items were not calculated and counted into the EI. Consequently, the final value on EI was 1.49, which is slightly better than a *poor* level but not reaching *fair*. Due to the high number of *best practice* designations, the novice research assistant had difficulties identifying the scientific evidence describing why specific building criteria exist. As a consequence of this finding, the level of expertise in evaluating healthcare buildings needs to be higher. Regarding the usability of the four-point scale LOE appraisal, it put a high demand on the evaluator to clearly identify the strength of evidence. However, when using internet forums or opinions for the search, the diagram could not be considered for appraising the evidence level. These building criteria were treated as best practices.


**Table 4.** Transformation of building criteria into evidence index.

#### **Table 4.** *Cont.*



**Table 4.** *Cont.*

#### **4. Discussion**

Gedda [62] published an inspirational article on evidence index that is related to evidence-based medicine, in which the author refers to the evidence index as the "factual components on which the main decision-making is based" (p. 1) during a treatment. As evidence-based medicine gave rise to evidence-based design, the promoters of EBD rely on objective scientific data combined with stakeholders' perspective and expertise in the building project. Considering a complex construction project where building criteria are detailed and consensus-based among the partners, an evidence index could be validating the objectivity of the criteria set to fulfil the stakeholders' needs. However, the often servitized and multifaceted criteria in the era of digitalization can be the source of confusion with regards to prioritization between the building criteria to fulfil the project goals. Therefore, this study aimed to test an evidence index during the programming stage of a building process in order to understand the level of objective scientific data involved in the decision making. The study assumed that even a novice investigator could generate an evidence index.

The methodological development for the EI is fundamentally striving for a quantifiable measurement for the stakeholders' interests. The building performance evaluation (BPE)

had always been a building process-oriented approach, and on a larger scale, it incorporates the quantitative research characteristics and the EBD process model. The EBD process model is a combination of quantitative research and a building project process model. Therefore, the use of EBD as the primary process model for EI generation seemed viable (Table 5).

**Table 5.** The main steps for quantitative research (after Polit and Beck [63] and Stichler [31]), evidencebased design (EBD) [23], and building performance evaluation (BPE) [17] are shown.


Note: POE = Post-occupancy evaluation.

The development of EI in this paper mainly focuses on the programming stage, which is an early stage of the building process, but this is the strategically important stage, where servitized construction products review scientific evidence on how well they can support the predefined goals. Theoretically, the EI could be extended throughout the entire EBD or BPE process and inform the stakeholders about the whole building process. The cognitive building solution for delivering EI for a building project is a challenging task. Today, the initial stages within the EBD process had been made by manual effort and resulted in a case study quality. However, the results showed that it was possible to generate an EI value between 1 and 4 on the rating scale and indicate the room EI, the process was time-consuming and often assigning best practice for reasoning for the building criteria. The frequent occurrence of best practices indicates that the level of evicence of the KPI used in a construction project is not measurable. This is troublesome in the present development where KPI based management of construction projects are promoted, mainly due to the new opportunities given by digitalization [1,9].

One of the main characteristics of this EI is the measurement scale on which it measures the scientific evidence. Literature used six to eight-level differentiation between the evidence while the current EI is reduced to four level in order to facilitate a quicker appraisal of the LOE and in the same time better correspond to the 8-point scale of LOE. Furthermore, the four-point scale measurement technic is supporting the evaluator for learning the basic differences when an LOE is appraised. In terms of a design project aiming to deliver a public building, the four-point scale seems appropriate for grasping the array of choices. What might be debatable is that the first level of evidence includes opinions of recognized experts and the use of case studies. In a business where all the experts are proud of their years of experiences, it may generate tension between the stakeholders, depending on who is more trusted in the process. The development of both EI and LOE, described above, has its theoretical background in research theory in general

and having the fact that research theory is internationally applicable indicates that the framework could also be internationally applicable. However, more research on different types of buildings and their contexts is needed to evaluate the general applicability of the proposed framework. Discussion of results from a case study exercise is somewhat a straightforward activity now. As any case study, results bear a low-quality level of evidence. In this investigation, it is also shown that the level of evidence cannot exceed *fair*. However, the experience for the single investigator had been meaningful, as going through a number of building criteria without finding appropriate scientific relevance triggered the curiosity for criteria that cannot be easily found. Regarding the generalizability of the given case study, the findings should be carefully examined. The case study outcome would suggest that a more comprehensive investigation should take place with different background of the investigators and preferably in a randomized manner. As for the PTS, the building criteria is a country-specific knowledge that requires a culturally appropriate building tradition. Employing the same PTS criteria outside of Sweden would not mean failure, but adaptations of the criteria must be considered. With regards to using the building criteria in another building typology, such as, a culture center [64] it can indicate that the builing critera are similar for other building types.

In the future research, an expert pool evaluation of the building criteria may shed light on the various best practice designated findings in the search for evidence. Furthermore, as a concern for the industry regarding cost efficiency, if fresh graduates on first- and second cycle could contribute to the evaluation of evidence, it would generate a more economically feasible way to extend the EI related research.

#### **5. Conclusions**

This study presents the first steps of an EI for a built environment. The study conceptualizes on the basis of the EBD stages a cognitive building solution that is capable of automatizing a series of repetitive and research related tasks regarding evidence appraisal and evaluation. The procedure to establish an EI for the built environment was tested through a case study, in which a novice research assistant approach to evidence appraisal was assessed. The 4-point rating scale, together with a diagram of which studies may fulfil the level of evidence requirements, was used to assess the building criteria. The concept of a cognitive building solution is preferable due to the strenuous job a person needs to perform when evaluating building criteria. The limitation of this study entailed a single evaluator for the transition process of the building criteria into LOE and later to EI. The EI is an initial step for establishing the cognitive building solution for EBD, in which the technological solution is rendered to serve a servitized construction product.

**Author Contributions:** Conceptualization, G.F. and P.J.; methodology, G.F.; formal analysis, G.F.; investigation, G.F.; resources, P.J.; data curation, G.F.; writing—original draft preparation, G.F.; writing—review and editing, G.F. and P.J.; visualization, G.F.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors would like to thank Kaj Granath for his insight and comments on this paper's first version. Furthermore, the authors are grateful for Regionfastigheter Jönköping for sharing their PTS documentation for research purpose.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **BIM-Based Research Framework for Sustainable Building Projects: A Strategy for Mitigating BIM Implementation Barriers**

**Bilal Manzoor 1 , Idris Othman 1 , Syed Shujaa Safdar Gardezi 2 , Ha¸sim Altan 3, \* and Salem Buhashima Abdalla 4**


**Abstract:** Although Building Information Modeling (BIM) can enhance efficiency of sustainable building projects, its adoption is still plagued with barriers. In order to incorporate BIM more efficiently, it is important to consider and mitigate these barriers. The aim of this study is to explore and develop strategies to alleviate barriers in developing countries, such as Malaysia, to broaden implementation of BIM with the aid of quantitative and qualitative approaches. To achieve this aim, a comprehensive literature review was carried out to identify the barriers, and a questionnaire survey was conducted with construction projects' stakeholders. The ranking analysis results revealed the top five critical barriers to be "unavailability of standards and guidelines", "lack of BIM training", "lack of expertise", "high cost", and "lack of research and BIM implementation". Comparative study findings showed that "lack of research and BIM implementation" is the least important barrier in other countries like China, United Kingdom, Nigeria, and Pakistan. Furthermore, qualitative analysis revealed the strategies to mitigate the BIM implementation barriers to enhance sustainable goals. The final outcome of this study is the establishment of a framework incorporated with BIM implementation barriers and strategies namely, the "BIM-based research framework", which can assist project managers and policymakers towards effective sustainable construction.

**Keywords:** building information modeling; sustainable building; construction projects; BIM implementation; stakeholders; barriers

#### **1. Introduction**

With the rapid growth of the construction industry, an increasing number of sustainable building projects are underway all over the world and have far-reaching consequences for national and regional economic development [1]. All other industries rely to some extent on the construction industry because of their high productivity flow through the economy [2]. Similarly, Malaysia's construction industry, like other developing countries, varies from cost, time constraints, and efficiency, resulting in delays [3]. Moreover, due to budget and schedule overrun, most sustainable building projects struggle to achieve their goals. It is therefore important to use advanced digital technologies such as BIM in order to achieve the desired results effectively [4]. Using BIM in sustainable building projects has various advantages, such as reducing errors, rework, and waste [5–7]. In addition, the use of BIM in sustainable building projects facilitates multidisciplinary cooperation between different project teams, achieves the project objective, and increases the productivity of construction activities [8–10]. BIM can be used in any phase of sustainable

**Citation:** Manzoor, B.; Othman, I.; Gardezi, S.S.S.; Altan, H.; Abdalla, S.B. BIM-Based Research Framework for Sustainable Building Projects: A Strategy for Mitigating BIM Implementation Barriers. *Appl. Sci.* **2021**, *11*, 5397. https://doi.org/ 10.3390/app11125397

Academic Editors: Lavinia Chiara Tagliabue and Ibrahim Yitmen

Received: 19 May 2021 Accepted: 8 June 2021 Published: 10 June 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

building projects, such as visualization, cash detection, code checking, communication, collaboration, monitoring, time and cost management [11,12]. BIM also has the potential as a significant technical advancement in traditional CAD, offering more information and interoperability capabilities [13]. BIM has the power to transform the construction industry and is therefore considered to be the future of the construction industry [14].

Since buildings are of high economic value and have a major effect on the environment and quality of life, the construction industry can be considered one of the key elements for society's long-term growth [15]. Buildings are deemed sustainable if their environmental, economic, and social effects on the community have been properly addressed and have contributed to society's long-term growth [16]. In the past, it was anticipated that sustainable buildings would initially cost around 15% more than conventional ones [17].

In addition, it has been found that few studies have been conducted on barriers to the implementation of BIM in sustainable building projects. Memon et al. [4] used a survey of sample size questionnaires (*n* = 95) to report the barriers and found that BIM adoption in Malaysian construction was very low. However, the current analysis expands the scale of the study by increasing the number of survey respondents (*n* = 185). In addition, Zahrizan et al. [18] used the quantitative analysis approach through questionnaire surveys to identify barriers and to report that the lack of BIM awareness is a crucial barrier to the implementation of BIM. Subsequently, Hamid et al. [19] performed a report on barriers but limited to establishing only nine barriers. Wong et al. [20] conducted a recent study that emphasized the importance of transitioning from outdated approaches to sophisticated methodologies such as BIM in order to merge design and construction workflows with the goal of enhancing productivity. Therefore, strategies are needed to make the project successful and help construction stakeholders to perform effectively in order to achieve the sustainable goals.

Hence, this research aims to provide strategies for alleviating barriers with the approach of qualitative analysis and a BIM-based research framework for sustainable building projects. To fulfill the aim of the study, there were four research objectives as follows: (a) to identify barriers from the literature, (b) to rank the barriers with the aid of quantitative approach, (c) to provide strategies in order to mitigate the barriers with the aid of qualitative approach, and (d) to establish a BIM-based research framework integrating barriers and strategies for sustainable building projects. The intent of the research was to explore and uncover new knowledge gaps and practical needs of a BIM-based research framework for sustainable building projects. It would also serve as a theoretical foundation for adopting BIM in sustainable building projects.

The remainder of the paper is arranged in the following way: Section 2 addresses the theoretical background and research gaps. Section 3 explains the related works. Section 4 sets out the research methodology. Subsequently, Section 5 elaborates on the results and discussion. Section 6 explains the comparison of outcomes with other countries. Section 7 introduces the BIM-based research framework and is followed by Section 8, the conclusion, limitations, and future directions.

#### **2. Theoretical Background and Research Gaps**

BIM is defined as "a model of building information that provides full and necessary information to support all life-cycle processes and that can be directly interpreted by computer applications. It includes information on the building itself and its components, and involves information on the properties of the building, such as its structure, shape, material and life-cycle processes" [21]. The term "BIM" has several contradictory and misleading interpretations. Definitions may differ for different people in distinct organizations, depending on their point of views, work types, and functions. From a design perspective, for example, BIM is described as the digital representation of a project's physical and functional qualities, which relates to the methodology and technologies required to generate a model [22]. In the construction industry, BIM is defined as the creation and application of a computer software model to simulate the construction and operation of a facility [23].

The genesis, creation, and expansion of BIM ultimately represented the growth profile of computerization. In the late 1950s, Itek Corporation, a U.S. defense contractor, developed a computer graphics technology suitable for engineering design. This helped design visual representation technologies that had been integrated into commercial engineering design and design products. Subsequently, the idea was transformed into an Electronic Drafting Machine (EDM) [24]. By the mid-1960s, EDMs had been marketed for use by other organizations. During the 1970s and early 1980s, Applicon (founded in 1969 as Analytics, Inc. in Burlington, Massachusetts by a group of MIT Lincoln Laboratory programmers) provided 2D products for electrical design tasks. This included the concept of the printed circuit board and a 3D product named BRAVO! Computer Art and Design [24]. In the early 1980s, the BRAVO! The product has been considerably advanced. Since the early 1980s, Autodesk had been a significant competitor of Applicon and other CAD suppliers. Autodesk continues to be a pioneer in this area [25]. Distinctive characteristics such as structural analysis, monitoring and analysis of energy buildings, construction management, and performance tracking and even worker safety have recently been provided on AEC computer platforms [26]. The word BIM attracted TM/®/©, who began to promote it with their products [27]. In order to increase infrastructure development, reduce costs, and provide general management assistance during any step of construction, the BIM idea was introduced to the construction industry [28].

In the construction industry, barriers to BIM implementation are a challenge for stakeholders to improve sustainable goals. Almost the bulk of research in literature is related to the identification of barriers. For instance, BIM implementation barriers have been highlighted in Hong Kong but are not capable of providing strategies [29]. Similarly, a study was conducted in China and Australia to define, classify, and prioritize these barriers but not to establish strategies [30]. Researchers have recently performed barrierrelated research for promoting sustainable construction. For example, the barriers to strengthening team coordination in BIM-based construction networks and the construction of a conceptual model. This conceptual model offers an intermediate theory, that is, a theoretical basis for guiding further attempts at knowledge formation on the subject [8]. In addition, the advantages and barriers to the implementation of BIM have been applied with a quantitative approach but are not capable of having a strategy to overcome [31]. Therefore, to fill the aforementioned research gap, this study focuses on providing strategies in reducing the barriers for sustainable building projects with the aid of a BIM-based research framework.

#### **3. Related Work**

In this section, related works in the domain of barriers in the global and Malaysian context are discussed.

#### *3.1. BIM Implementation Barriers in Global Context*

Globally, fast growth demands and the overwhelming majority of construction companies have allocated BIM to improve the sustainability goals [32]. In sustainable building projects around the globe, the use of BIM has been advocated by government and professional bodies to provide more collaboration and cooperation between stakeholders in the construction sector and to ensure the quality of the projects [33]. Moreover, countries like the United Kingdom, the United States, Australia have adopted BIM in-depth research and other field areas like project management, facility management, and safety management [34,35]. In Australia and New Zealand, the implementation of BIM is only at level 2, with the main focus being on 2D and 3D collaboration [36]. The researchers revealed that "lack of faith in the integrity of BIM" and "lack of client demand" among other barriers were one of the factors behind the lack of BIM implementation in Australia [37]. Many researchers in Germany, the United Kingdom, Canada, the United States, Denmark, France, China, Brazil, South Korea, and the Middle East [38–46] have also found numerous BIM implementation barriers. It includes lack of BIM experience, investment costs, lack

of awareness, lack of specified standards, market and cultural changes, interoperability problems, lack of specific guidelines for BIM implementation, and habitual resistance to change [31,44,47]. However, it has been found that the construction industry in the United States has engaged BIM in its ventures relative to other industries across the globe [48]. The government's BIM initiative became compulsory in projects in the public sector, beginning in 2016 in the UK [43]. It is therefore noticed that implementation of the BIM in different countries is growing for effective and productive construction [49]. However, there is a need to explore BIM in sustainable building projects for the sake of an eco-friendly environment and prompt sustainable goals.

#### *3.2. BIM Implementation Barriers in Malaysian Context*

In Malaysia, BIM implementation is still in the developing stage. However, the construction industry in Malaysia has taken major steps to encourage and boost construction efficiency at the national level with the introduction of BIM [50,51]. In addition, BIM is mandatory for public projects with a budget of RM 100 million or more from 2018 [52]. According to Datuk Seri Dr Roslan Md Taha (PWD Director-General), a total of 18 construction projects have been initiated by BIM in various construction phases up to 2017 such as SMK Meru Raya Ipoh Perak, Health Clinic Maran Pahang, MACC Selangor Shah Alam, UTHM Batu Pahat Johor and Parit Buntar Hospital [53]. With the continuous implementation of BIM against sustainable building projects in Malaysia, the implementation of BIM still faces numerous barriers and BIM implementation in sustainable building projects has many concerns and challenges. Hence, there is a need to better understand barriers in order to make the construction smoother and more effective for boosting sustainability goals. Various researchers have also highlighted the barriers to BIM implementation. The most critical barrier which was identified by many researchers is high cost [54–57]. Likewise, in Hong Kong and China, high cost is also considered as the BIM implementation barrier [47,58]. Moreover, it was also described as the topmost critical barrier in the Middle East [59]. As a result, high costs are included as one of the barriers since they are commonly available in the literature. In the last year, another study was conducted to explore the level of adoption of BIM in Malaysia. This study found that only 13% of government and private participants use BIM in their organization, which is negative evidence that Malaysia remains a long way from the role it should play in implementing BIM [60]. Therefore, it is recommended to implement BIM by eliminating barriers and providing the strategies for sustainable building projects.

#### **4. Research Methodology**

In this section, a brief explanation of the research methodology has been discussed. The research methodology section comprises data collection and data analysis. In addition, the research design flowchart, as shown in Figure 1, comprises four phases to fulfill the aim and objectives of this study. In the first step, the research aim and objectives were formulated by evaluating the relevant literature and identifying research gaps in previous research performed by researchers. The second phase of the study consists of collecting data from the literature review by defining the implementation barriers of the BIM and developing a questionnaire survey to be distributed among stakeholders (contractors, clients, and consultants). In the third step, the triangulation approach was introduced to achieve the study goal and the study objectives. The method of triangulation consists of two forms of analysis, i.e., quantitative analysis and qualitative analysis. According to Altricher et al. [61], triangulation "gives the more detailed and fair image of the circumstances". In quantitative analysis, the SPSS software package was used to assess the feedback of the respondents. The SPSS software was used to analyze the values of Cronbach's alpha coefficient, Kendall's coefficient of concordance (Kendall's W), Chi-square analysis, and mean score analysis, while NVivo software was used in qualitative analysis to analyze the data collected from interviews. In the final and fourth phase of the study, the recommendation and conclusion were drawn from the analysis results.

**Figure 1.** Research design flowchart.

#### *4.1. Data Collection*

After establishing the aim and objectives of the study in the introduction section, phase 2 of the study was conducted, which consisted of literature review, questionnaire survey, and interview session.

#### 4.1.1. Literature Search Parameters

The purpose of the literature review was to identify barriers with various databases, such as Scopus, Web of Science, Google Scholar, and other relevant publications such as Elsevier, American Society of Civil Engineers (ASCE), Emerald and Taylor and Francis. Keywords such as "building information modeling", "construction industry", "construction projects", and "barriers" were used. Subsequently, the listed publications were screened, primarily by concentrating on the title, abstract, and conclusions, as well as the figures and

tables. Table 1 elaborates the BIM implementation barriers that were used in this research study based on the existing literature.

**Table 1.** Building information modeling (BIM) implementation barriers.


After rigorous review of current literature relating to BIM implementation barriers, various factors were identified. Table 1 elaborates a list of 20 factors that are well documented and hence more applicable. Prior to identification of BIM implementation barriers, it is kept in mind that the selection of well-known factors is more reliable and also easy for the respondents to understand the theme and feedback easily.

Previous studies were used to identify the aforementioned BIM implementation barriers. Following a thorough evaluation of these studies, this study identified 20 potential barriers to BIM implementation, which are presented in Table 1. For example, cost, lack of expertise, and lack of promotion are commonly acknowledged in the literature as crucial barriers to BIM implementation.

#### 4.1.2. Questionnaire Survey

In this section, questionnaire design and responses were examined. The questionnaire survey method was used to collect the data through a quantitative approach. Therefore, the questionnaire was designed after careful consideration of existing literature in the domain of BIM implementation barriers. Prior to the final questionnaire survey, a semi-structured interview was arranged to ensure the potential and appropriateness of the questionnaire in the context of BIM implementation barriers. In the pilot study, the feedback from five participants was used to further improve the questions prior to the actual questionnaire survey. The pilot survey consisted of two professors, two assistant professors, and one postgraduate researcher. The questionnaire was finalized based on feedback from the pilot study. The final questionnaire consists of three parts: (a) research aim and objectives, (b) general information of respondents, (c) rank of the barriers using a Likert scale (1—Strongly Disagree, 2—Disagree, 3—Moderately Agree, 4—Agree, 5—Strongly Agree). A total of 300 questionnaires were sent via email, and 185 feedbacks were received, yielding a response rate of 61%. In addition, the sample size greater than 30 is reliable for further statistical analysis based on central limit theorem [108,109]. Figure 2 elaborates the breakdown of 185 returned questionnaires consisting of positions, working experience, education, and company type.

**Figure 2.** Breakdown of 185 returned questionnaires by Positions, Working Experience, Education, and Company Type (**a**–**d**).

Figure 2 depicts the positions of respondents, which include consultants, contractors, and clients. Consultants accounted for 45% of the total, contractors accounted for 39%, and clients accounted for 16%. Furthermore, 28% had more than ten years of work experience. Similarly, 36% of respondents were Bachelor's degree holders, 30% of respondents were Master's degree holders, 25% of respondents were professional engineers, and 9% of respondents were PhD holders. Furthermore, 16% of respondents worked for a semigovernment organization, 50% of respondents worked for a private organization and 34% of respondents worked for a public organization.

#### 4.1.3. Interview Session

In this section, interview questions design and responses were examined. The method of interviewing was used to gather data using a qualitative approach.

Due to the covid-19 pandemic, the online interviews were conducted using ZOOM software. Prior to conducting an online interview with ZOOM software, a semi-structured interview was created to ensure that all information related to barriers in construction projects could be obtained. In addition, previous studies have shown that the sample size greater than fifteen is effective and accurate for qualitative analysis [110]. The sample size of twenty for this qualitative analysis was therefore deemed to be appropriate. Twenty BIM experts with experience working in academia, industry, and construction projects were selected as participants in this qualitative analysis. Before the interview started, participants received a short introduction to the study and were informed of the anonymity and confidentiality of the information collected. Before the interviews started, demographic information such as gender, educational qualifications, and job experience was collected

from interviewees. Interviewees were interviewed on the basis of the intended interview questions and after each answer, additional follow-up questions were asked as needed. The criteria for selection of participants depends upon: (a) possess working experience more than five years, (b) having excellent educational qualifications, (c) possess strong knowledge of BIM in construction projects. The demographic detail of participants is shown in Table 2.


**Table 2.** Participant demographics (*n* = 20).

It was seen that 100% of the participants were male, while none were female. Similarly, 15% of the participants were Bachelor's degree holders, while 25%, 30%, and 30% of the participants were Master's degree holders, PhD holders, and professional engineers, respectively. In addition, 35% of the participants had career experience of more than 10 years. The demographic analysis indicates that they had broad working experience, qualifications, and skills. Thus, they were considered as suitable interviewees for this research study.

#### *4.2. Data Analysis*

The third stage of study was data analysis. For this purpose, two types of data analysis were elaborated: (a) qualitative analysis via questionnaire survey and (b) qualitative analysis via interview.

#### 4.2.1. Quantitative Analysis

Cronbach's alpha coefficient is used to calculate the internal consistency of the different variables in order to determine the strength of the five-point scales. The value for Cronbach's alpha coefficient in this study is 0.876, which is greater than the threshold of 0.7, which suggests that the data are reliable for further statistical analysis [111]. Furthermore, the mean value technique is used to determine the relative importance of individual barriers. The mean values of individual barriers are computed, ranked, and compared between the three groups (contractors, consultants, clients). Mean value analysis is a technique used to effectively identify key factors among various factors [112]. In addition, Kendall's coefficient of concordance (Kendall's W) is also calculated to measure the agreement of responses in particular groups [113]. The range of the value of Kendall's coefficient of concordance (W) is from 0 to 1. The higher value of W indicates the high level of consensus among the respondents within the group [114,115]. In addition, chi-square analysis should be carried out, if the number of items is greater than seven [116]. In addition, the Spearman's rank correlation coefficient was introduced to calculate the strength of a relationship between two groups [117]. The range of the Spearman's rank correlation coefficient (*rs*) is from −1 to +1. The higher the positive/negative value of *r<sup>s</sup>* , the stronger positive/negative linear correlation [90].

#### 4.2.2. Qualitative Analysis

For analysis of the qualitative study, NVivo 11 was used as one of the available software packages [118]. Using software packages such as NVivo improves the degree of deeper understanding and makes qualitative data analysis quicker and more flexible [119]. In qualitative analysis, coding is considered to be an integrated part of the analysis. The theme of the interview is further summarized through coding for a better analysis of the idea put forward by the participants. The ideas of the interviewees were further listed in 200 codes for qualitative analysis. For instance, the "government must establish a BIM cell unit and allocate a defined budget for BIM implementation." This theme and concept were broken down into "government policies". The details of the coding theme are shown in Table 3.


#### **Table 3.** Coding theme and appropriate definition.

It was shown that interviewees emphasized the enhancement of BIM integrated with academic curricula to overcome the lack of BIM research and implementation. Likewise, a positive attitude and learning environment together with the creation of BIM guidelines are essential for grooming BIM implementation. Furthermore, interviewees suggested that the professional bodies should conduct BIM workshops, courses, and seminars to convey the benefits of using BIM in construction projects. Stakeholders should take part in workshops, seminars, and courses to grow the concept of incorporating BIM in their construction projects. Moreover, interviewees facilitated the development of know-how of BIM implementation, the dissemination of BIM information, and the development of awareness and understanding. Interviewees indicated that the government should assign the budget to BIM and set up a separate BIM-based allocation cell to track the proper use of the allocation budget. However, cooperation with other universities and countries is necessary in order to address the lack of study in the implementation of BIM and in organizations.

#### **5. Results and Discussion**

The follow-up section explores in detail the results of SPSS statistical package, which consists of mean value analysis, Kendall's coefficient of concordance (Kendall's W), chisquare test, and Spearman's rank correlation coefficient, and are summarized in the form of ranking.

#### *5.1. Ranking of BIM Implementation Barriers*

The ranking of BIM implementation barriers is categorized into four parts with the data analysis results using mean value: (a) overall ranking of BIM implementation barriers, (b) ranking according to contractors' perspectives, (c) ranking according to consultants' perspectives, and (d) ranking according to clients' perspectives. Table 4 illustrates the detailed picture of mean value analysis.


**Table 4.** Ranking of BIM implementation barriers.

Table 4 indicates that "unavailability of standards and guidelines" had the highest mean value of M = 4.89, while "competing initiatives" had the lowest mean value of M = 1.92. Likewise, the top five barriers were "unavailability of standards and guidelines", with M = 4.89, "lack of BIM training", with M = 4.78, "lack of expertise" with M = 4.52, "high cost", with M = 4.45, and "lack of research and BIM implementation", with M = 4.03.

#### *5.2. Kendall's Coefficient of Concordance (Kendall's W)*

The value of Kendall's coefficient of concordance (Kendall's W) of overall respondents, contractors' perspectives, consultants' perspectives, and clients' perspectives were 0.183, 0.175, 0.169, and 0.145, respectively. The null hypothesis was rejected because all significance levels were 0.000, which was less than the threshold level of 5%. As a consequence, a substantial level was found among the respondents.

#### *5.3. Chi-Square Test*

The chi-square test was conducted as there were 20 factors in the analysis. The chisquare test should be performed if there are more than seven factors in the study, i.e., the chi-square test values for contactors' perspectives, consultants' perspectives, and clients' perspectives were 68,432, 92,569, and 123,324, respectively. According to the analytical findings, the groups of respondents had significant levels dependent on each other in each group.

#### *5.4. Spearman's Rank Correlation Coefficient*

Spearman's rank correlation coefficient (*rs*) is calculated by the following equation:

$$r\_s = 1 - \left[6\sum\_{n=1}^{5} \frac{\left(\mathbf{d}^2\right)}{n(n^2 - 1)}\right]$$

where *r<sup>s</sup>* = Spearman's rank correlation coefficient; d = the difference between ranks assigned to items; *n* = the number of respondents.

Using Spearman's rank correlation coefficient, the relationship between the perspective of clients, consultants, and contractors with the implementation barriers was shown. Spearman's rank correlation coefficients between all parties were established. The coefficient value between the consultant and contractor was 0.932. The correlation between the client and consultant was 0.892, whereas that between the client and contractor was 0.821. In addition, there was also a significant relationship among the three parties, namely 0.000, 0.000, and 0.005, respectively, which was smaller than the permissible amount of significance (5%). In other words, it can be said that there was a strong correlation between consultant and contractor, client and consultant, and client and contractor.

#### *5.5. Results of Factor Analysis*

Factor analysis was carried out to further explore the barriers of BIM implementation in this study. The KMO value of this study was 0.512, which is acceptable as it satisfies the threshold of 0.50. Values below 0.50 should lead the researcher "to either collect more data or rethink which variables to include" [120]. These results are illustrated in Table 5. The detailed picture of factor analysis of barriers to BIM implementation in sustainable building projects was composed of five groups. These groups were Group 1—Government-related barriers, Group 2—Market-related barriers, Group 3—Personal-related barriers, Group 4—Construction environment-related barriers, and Group 5—Cost–risk barriers.

**Table 5.** Results of factor analysis (FA) on barriers to BIM implementation in sustainable building projects.


#### **6. Results Comparison with Other Countries**

The findings of the current study were contrasted with other countries like China, the United Kingdom, Nigeria, and Pakistan. In addition, Table 6 elaborates the comparison of BIM implementation barriers with other countries.

By contrasting Malaysia's current study with China, "unavailability of standards and guidelines" was ranked first, while in Nigeria, "unavailability of standards and guidelines" was ranked fourth. However, "unavailability of standards and guidelines" could not gain the attention of researchers in the United Kingdom and in Pakistan and thus was marked as not identified. The "lack of BIM training" was not ranked in the top five in the United Kingdom, Nigeria, or Pakistan. However, "lack of BIM training" was labeled as not identified in China. Furthermore, "lack of expertise" was ranked third in the current study in Malaysia as well as in the United Kingdom. The "lack of expertise" in Nigeria was perceived to be the most crucial barrier. Moreover, "high cost" was ranked fourth in the current study in both Malaysia and China, while in Nigeria, "high cost" was ranked third. In addition, "lack of research and BIM implementation" was the least consideration barrier in the United Kingdom, Nigeria, and Pakistan.

These findings provide evidence that more attention needs to be paid to BIM research and implementation in Pakistan and that "lack of research and implementation of BIM" is a crucial barrier that is largely unidentified by researchers. It is also understandable

that variations in ranks are due to different cultures and environmental factors in different countries. From this analysis, the conclusion can be drawn that barriers are similar among different countries but rank distinctively.



#### **7. BIM-Based Research Framework**

In this section, strategies to mitigate the BIM implementation barriers, namely "unavailability of standards and guidelines", "lack of BIM training", "lack of expertise", "high cost", and "lack of research and BIM implementation" were developed with the aid of the BIM-based research framework. This framework consists of two layers, namely the outer layer and the inner layer. The inner layer consists of barriers, while the outer layer, called the "mitigation layer", consists of strategies to overcome barriers.

The strategy to address the "unavailability of standards and guidelines" focused on the proper development of the BIM guidance plan and a positive attitude towards the learning environment. In developing countries, there is a lack of sound guidelines for sustainable building projects, which leads to cost overruns, delays, and waste. There is a need to establish a BIM guidance plan that can encourage and enhance the efficiency of sustainable construction, such as that in developing countries. It is important for owners to draw up a BIM execution plan during the pre-operation process. In addition, the strategy to reduce the "lack of BIM training" barrier is to strengthen BIM courses (linking with academia), seminars, and workshops. It is the liability of the professional bodies to control and track the essential eyes of construction stakeholders and organizations. Training should begin by educating workers on the relevance and usefulness of technology. Employee information on BIM technological innovation can be measured by a written analysis, such as an exit survey. These conclusions are based on responses such as "I think that recruiting skilled workers can be the best option", "I think that professional bodies should track construction organizations", and "I think that BIM courses, seminars and workshops should be made compulsory for stakeholders". In addition, the approach to reduce the "lack of expertise" barrier is to attract BIM experts and generate possible ideas for the appreciation of the use of BIM technology. Hiring BIM experts from developed countries will help to mitigate the barrier. In order to ensure that adequate technical support and expertise is available from the technology partner, construction companies can obtain all relevant information from the manufacturer before promising to incorporate and use the BIM technology. These conclusions are based on responses such as "I think the appropriate approach is to recruit BIM experts from developing countries", "I think the know-how to use BIM needs to be disseminated". Furthermore, a strategy to reduce the barrier of "high cost" is to assign a specific budget for a BIM implementation cell. The government should set up a BIM cell to increase the trust and enthusiasm of building stakeholders. It is the utmost duty of the BIM cell unit to adequately track and monitor the allocation budget and prepare the report by the end of each month. In order to enable construction stakeholders to use BIM technology, vendors should consider modifying their business models to reduce the initial costs of using these technologies. A subscriptionbased model or monthly payment plan over a fixed period may be a preferred model, as construction stakeholders may adjust periodic payments to match their usual billing cycle—shifting most upstream costs. However, daily payments should be reasonable. This is supported by responses such as "I think the government should allocate a budget for the implementation of BIM", "I think the government should adjust its policies", and "I think

there should be a BIM cell unit". Furthermore, BIM-related topics have been included in the curriculum of civil and architectural engineering. Collaboration between universities and the promotion of a research culture will improve the implementation of the BIM. It is the government's duty to expand opportunities for students and faculty members through the development of scholarship programs, as indicated by responses such as "I think by cooperation", "I think fostering understanding of BIM technology", and "I think student exchange programs between universities in developing countries". In addition, a detailed picture of the BIM-based research framework is elaborated in Figure 3.

**Figure 3.** BIM-based research framework incorporating barriers and strategies for sustainable building projects.

#### **8. Conclusions, Limitation, and Future Directions**

BIM has the ability to enhance and ease construction, but there are various barriers that hinder the effectiveness of sustainable building projects. These barriers need to be tackled in order to boost successful and efficient construction. In addition, a comprehensive literature review was undertaken to illustrate the barriers in order to achieve the objectives of this study. Twenty barriers were established with a thorough analysis and proceeded to the questionnaire survey. In this study, the triangulation method consisting of quantitative analysis and qualitative analysis was adopted. In quantitative analysis, the top most barriers were "unavailability of standards and guidelines", with M = 4.89, "lack of BIM training", with M = 4.78, "lack of expertise", with M = 4.52, "high cost", with M = 4.45, and "lack of research and BIM implementation", with M = 4.03, whereas, "competing initiatives" had the lowest mean value of M = 1.92. In qualitative analysis, strategies to mitigate barriers were explored with the help of interviews of BIM experts in academia and in sustainable building projects. It was revealed that BIM workshops, courses, and seminars could enhance and promote the culture of BIM implementation. In addition, collaboration and budget allocation could increase the incentive and trust level of research to address the lack of research and implementation of BIM.

The theoretical contribution of this study is not only to fill the research gap but also to provide a valuable reference for helping stakeholders to mitigate the barriers. As far as the authors' knowledge, the novelty of this study is that there is no comprehensive study conducted in Malaysia to explore strategies in mitigating BIM implementation barriers for sustainable building projects. For practical implications, this study suggests that the BIMbased research framework be executed with ongoing real projects to enable stakeholders to

complete sustainable construction effectively. This study also recommends that researchers create slightly different frameworks on the basis of the same collection of quantitative and qualitative data. While the aim and objectives of this research were accomplished, this study still has some limitations that are worth noting. First, this study was conducted in Malaysia, and therefore the findings in this study might not be applicable in other countries because of cultural differences. Second, in the qualitative study, the sample size could be expanded in order to gain further insight into the reduction of BIM implementation barriers. Finally, these limitations offer a route for potential researchers to verify this research study through case studies of successful construction projects.

**Author Contributions:** B.M.: Conceptualization, investigation, data curation, writing—original draft. I.O.; supervision, writing—review and editing. S.S.S.G., H.A. and S.B.A.; resources, review and editing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data sharing not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

