A Scenario-Based Simulation Model for Earthwork Cost Management Using Unmanned Aerial Vehicle Technology

Abstract

Risks are involved in every aspect of earthwork projects. This paper specifically discusses the cost risk associated with the volume calculation of such projects. In the design phase, it is not possible to accurately predict the quantity per soil type underground of the site. As a result, there are uncertainties in the excavation cost that may cause cost overrun. There is a need for an innovative method to forecast, control, monitor, and manage excavation cost from design phase to completion. There is, however, an innovative method for calculating volume accurately using a digital surface model method. The digital surface model can be acquired using GPS and unmanned aerial vehicles (UAV). This paper proposes a simulation model which is able to analyze, control, and monitor the cost based on excavation volume so stakeholders are able to gain the actual volume quickly and accurately. Monte Carlo simulation is applied to the excavation volume per soil type, resulting in a range of possible outcomes for excavation cost. The developed model was verified by applying it to an actual case project. Throughout the project, the cost was successfully monitored and maintained below the maximum expected cost. However, the final actual cost in the last simulation almost reached the maximum expected cost, indicating the need for cost monitoring. By periodically comparing the simulation result to the actual excavated volume obtained from the UAV, the proposed model can assist stakeholders in controlling the cost overrun risk and developing strategies during the earthwork life cycle.

1. Introduction

Earthworks are fundamental in the early stage of building projects. They are often performed on location under complex conditions. For example, apartment buildings in big cities are commonly constructed in congested areas and on unstable terrain. In these conditions, contractors are likely to build a retaining wall to assure the safety of excavation on site. Subsequently, many contractors find it risky to execute earthwork [1]. It is therefore very important for developers, designers, and contractors to study risk management of deep basement excavation.

Every aspect of earthwork projects is prone to risk. The five major risks associated with earthworks are time, safety, quality, efficiency, and cost risks [2]. This paper specifically discusses the cost risks associated with earthwork volume calculations. It is typical to find several layers of soil in the earthwork, such as soil and weathered soil, weathered rock, and soft and hard rock [3]. Each soil type has its own excavation cost rates, which affect the total cost of earthworks. For example, it costs more to excavate soft and hard rock than soil because the rocks must be blasted before excavation. Therefore, earthwork volume per soil type must be calculated as accurately as possible in order to plan for construction assets, manage project schedule, and avoid unnecessary cost.

Accordingly, it is important to use a surveying method that can calculate the volume accurately. Advanced technologies in terrain surveying include global positioning system (GPS) and unmanned aerial vehicles (UAV) [4]. The digital surface model (DSM) obtained after processing of GPS or UAV data is deemed accurate when it complies with surveyor standards [5]. A study by Park [6] combined GPS technology and boring tests to generate terrain models per soil strata, which allow calculation of the expected volume per soil type in the planning phase. However, to accurately predict the quantity of soil type is not possible because the subsurface per soil type is generated by interpolating soil data of all boring test results.

Therefore, periodic volume calculation based on UAV photogrammetry is conducted throughout the excavation period to accurately calculate the actual earthwork per soil type. Generally, UAVs are flown every few days to obtain the latest images of terrain. Then, the images are processed using a photogrammetry technique into the current DSM. Subsequently, the current DSM and subsurface per soil type can be overlayed using the DSM method to obtain the earthwork volume [7]. Coupled with the processing and visualization methods developed, contractors can calculate the actual excavated volume per soil type quickly and accurately [8].

Unfortunately, DSM obtained from UAV photogrammetry is only used for progress monitoring reports, whereas the DSM-based earthwork volume calculation has the potential to be associated with the excavation cost rate to produce the excavation cost data. To date, there have been no studies using volume calculation data per soil type to forecast, monitor, control, and manage excavation costs throughout the earthwork life cycle. Therefore, this study proposes a simulation model to manage cost associated with earthwork volume calculation from design phase to completion. Excavation cost scenarios that are possible from the planning stage to the construction stage to completion will be developed. By conducting a simulation of cost calculation in a systematic and accurate manner, we obtain the possible outcome of maximum, average, and minimum cost. Referring to that, we can plan construction assets properly and develop corrective strategies to avoid cost overrun.

The paper is organized as follows: in Section 2, a methodology is presented. Section 3 presents the preliminary study regarding earthwork calculation technique and risk management based on Monte Carlo simulation. Section 4 presents an earthwork management scenario based on UAV from planning to completion. Section 5, Section 6 and Section 7 present the development of causal loop diagram, generation model, and simulation model of earthwork cost management. Section 8 presents the application of the model to a case study. Finally, Section 9 presents concluding remarks along with limitations and future work prospects.

2. Methodology

Figure 1 shows the methodology of this study. First, a preliminary study was conducted which consisted of GPS and UAV usage to obtain the DSM, the modeling concept of risk management, and how earthwork volume calculation can be used in the simulation model to manage excavation cost. Previous studies related to simulation techniques in project management and earthwork management are also explored. Second, an earthwork management scenario which elaborates the earthwork process from design, planning, excavation, to completion phase was developed. The factors influencing cost, such as earthwork volume and cost unit rate per soil strata, are studied. Third, a generation model showing the mathematical equation between cost influence factors and excavation cost was developed. Then, the causal loop diagram was created based on the factors influencing cost. Fourth, a simulation model for earthwork cost management was developed based on the generated causal loop diagram. Then, a Monte Carlo simulation (MCS) was applied to the expected earthwork volume as one of the factors influencing cost, resulting in a range of possible outcomes for the excavation cost. MCS was applied to the expected earthwork volume representing the uncertainties as the contractors cannot ascertain the earthwork volume per soil strata until the excavation process is carried out. Fifth, the simulation is validated through a case project. If the simulation model is proven to be effective, the simulation can be applied in practice. If not, the simulation model is revised by exercising the earthwork scenario again. Using this simulation model, the contractors can periodically check whether the cost is managed within the range of cost or not. In this way, contractors can analyze, monitor, and control excavation cost systematically.

3. Preliminary Study

3.1. Earthwork Volume Calculation Techniques

Recent advances in technology have allowed contractors to conduct surveys using GPS or UAV technology. In GPS surveys, two stations, a base station and a rover station, are used. While a base station has a fixed position, a rover station is moved by a surveyor from one position to another during the measurement period. The positions of the rover station are collected and processed into the DSM. Because GPS surveys are conducted on foot, they are time-consuming. Moreover, surveyors cannot reach inaccessible areas, resulting in decreased density of recorded positions for the rover station [9].

In contrast to GPS surveys, which require surveys on the ground, UAV surveys are carried out by flying the UAV around the construction site with a predetermined path [10]. A camera mounted on the UAV is used for collecting images of construction sites. The images are arranged using geotagged data as each image has measurement coordinates. Then, the arranged images are georeferenced by using several predetermined ground control points. Based on the georeferenced images, a point cloud is created using the structure-from-motion algorithm. Finally, the point cloud data, which are in a vector data format, are processed using photogrammetry to produce the DSM data, which are arranged in a grid of certain size [7]. The grid cell is called ground sampling distance (GSD) and its size is set by the user.

Surveyors can choose to use GPS or UAV according to their needs. In the planning stage, GPS technology is preferable to UAV because GPS is capable of both terrain and site boundary surveying. However, UAV is more advantageous during the excavation period because it can survey large areas in a short period of time [11]. Furthermore, UAV can move freely in the air, while GPS survey is disrupted by the construction activities on the ground.

In essence, both GPS and UAV can generate a DSM of construction with accuracy that complies with surveyor requirements. DSM is a raster data model, which means that it is very important to carry out the earthwork volume calculation process using the DSM method. As GPS and UAV can only survey the terrain of the site, subsurface per soil strata is needed to be able to calculate the volume per soil type. Therefore, a boring test is conducted in the earthwork planning stage to obtain the columnar section per boring test location [12]. By interpolating the soil data in the columnar section of all boring locations, a model of surface layers per soil type is obtained [13]. Examples of interpolation methods are kriging interpolation [14] and artificial layer [15].

Using the DSM method, the volume of excavation for each soil type can be determined by combining the DSM obtained from GPS or UAV, the subsurface per soil type, and the planned terrain model. The DSM features raster data in a grid form and has a three-dimensional coordinate value. By applying the height to the area of each cell, a square column is created, allowing the volume to be calculated [16]. For each cell $k$ of the grid, its volume ($V_k$) is calculated as shown in Formula (1).

$$V_k=L_k\times W_k\times H_k$$

(1)

where $L_k$ is the length of the cell, $W_k$ is the width of the cell, and $H_k$ is the height of the cell. The length ($L_k$) and width ($W_k$) are equal to the project’s GSD, while the height ($H_k$) is the terrain altitude of each cell at the center of the cell minus the base altitude of each cell at the center of the cell. By adding up the volumes of all cells, we obtain the total volume as shown in Formula (2).

$$Total volume between two DSMs={\displaystyle \sum }_{k=1}^n{V}_k$$

(2)

In this study, data of volume per soil type in the planning stage and during excavation period are compared in a simulation model to manage excavation cost.

3.2. Risk Management Process

In construction, risk management is defined as an organized and comprehensive process of identifying, analyzing, managing, and monitoring risks in order to minimize the negative impact they may have on a construction project [17]. An effective risk management process will help identify major risks and provide strategies for handling them. The risk management process should be established in the earliest stage and integrated throughout the construction project. Therefore, contractors can develop countermeasure strategies and manage the risks during construction.

As a first step in the risk management process, risk identification involves identifying, assessing, and categorizing the initial importance of the risks related to construction projects. In earthworks, estimating and monitoring excavation quantity is crucial [18]. There are inherent risks related to excavation quantity. In the pre-tender stage of earthwork projects, if the volume is not carefully estimated, contractors cannot propose accurate bids and so lose the chance to win a contract. In the planning stage, contractors can make mistakes in calculating the earthwork cost without accurate earthwork volume. Moreover, improper calculation of actual excavation quantity may cause problems in determining the approved progress payment between the contractor and earthwork subcontractor [6].

Risk analysis, as the second step, quantifies the effects of major risks that have been identified [19]. One of the established risk analysis techniques is performed by using an MCS model. The model generates different sets of random values for uncertain parameters and therefore aggregates the combined effects [20]. Some papers have utilized MCS for earthwork management. Easa [21] developed a simulation model for accurately estimating earthwork volumes of curved roadways with complex ground profiles and cross sections. The results show that the simulation model improves the estimates of earthwork volumes compared to traditional and mathematical models. A study by Karabulut [22] compared the critical path method with MCS. The results of MCS show more realistic values since the critical path method did not consider the possible risks that may occur during the construction phases.

Until now, there have been no studies using MCS for forecasting and monitoring excavation costs based on volume calculation data per soil type. Accordingly, this study establishes a simulation model for earthwork cost management using earthwork volume obtained from UAV technology.

3.3. Simulation Model Concept

This section explains the concept of generation and simulation, which is part of the risk management model used by Rachmawati and Kim [23], as shown in Figure 2. This model has been used for various studies including an economic feasibility study of apartment development projects [23,24] and estimation of in situ production of precast members [25].

As an initial step, a generation model was developed to mathematically express the relationship between influence factors and project objectives. Next, a simulation model was established based on the generation model [25]. In the simulation model, the Monte Carlo method was applied by generating different sets of random values for influence factors, resulting in a distribution of possible outcome values. Using MCS, all possible input variables were considered and the likelihood of occurrence of each scenario was calculated. A further development of the simulation model is the optimization model and risk management model. The optimization model is used to find the most suitable value of influence factors among simulated values for the project objectives. A strategy is established in the risk management model by setting the risk range limit: lower and upper control limits for influence factors to manage the project objectives [24]. The simulation model is particularly suitable for this study as the earthwork volume per soil type cannot be calculated accurately before excavation, resulting in many possible outcomes for excavation cost.

4. Earthwork Management Scenario

This section presents details of the development of an earthwork management scenario based on GPS and UAV technology. The scenario was developed in accordance with the earthwork life cycle, as shown in Figure 3. Subsequently, the simulation model can be run in each stage of the earthwork life cycle (t₀–t₄).

The t₀ is the design phase, where the contractor conducts a GPS survey to set the site boundary and to generate the existing terrain surface. In addition, the contractor determines the boring test position that spreads over the project area. Then, the contractor conducts the boring test to obtain the columnar sections. After processing both data, the contractor obtains the surface per soil type. These surfaces are used to design a temporary retaining wall and to calculate the expected volume per soil type. Then, the contractor runs a forecasting simulation to predict the excavation budget. By doing this, the contractor can know the average, minimum, and maximum of the expected excavation cost. It is important to conduct this simulation as the expected volume per soil type may be inaccurate.

After finishing the design phase, the contractor continues with the site opening phase (t₁). The contractor opens bidding to select an earthwork subcontractor. The subcontractor candidates may conduct their own survey to obtain their expected excavated volume. The earthwork volume plays a crucial role in generating the bill of quantities and the schedule for earthwork. A more accurate volume can make the candidates more competitive and help them win the tender. The subcontractor may use a simulation model to assist them in setting the cost contingency after establishing the maximum possible cost.

The chosen subcontractor starts the earthworks in the t₂ phase. In this phase, the subcontractor excavates soil and weathered rock. Throughout the excavation period, the site’s terrain changes continuously. Therefore, the subcontractor employs a UAV with a mounted camera to record the changes in terrain periodically. Using UAV photogrammetry, the images are processed into a DSM. By using the principle of surface comparison from different points in time, the actual excavated volume is obtained. By this time, the general contractor and subcontractor have planned for the actual earthwork volume. Using both data together with excavation unit rate in the simulation model, they can fairly check the actual excavation cost and compare it with the excavation budget. As a result, they can jointly control and monitor the excavation cost periodically.

In t₃, the excavation has reached the soft and hard rock, resulting in the initiation of blasting work. Blasting work includes tasks such as test blasting, determining the amount of explosives according to the blasting vibration speed, and using instruments to assess the blasting vibration. In this phase, the excavation of soil and weathered soil and earth-retaining work still continues. Similar to the t₂ phase, the simulation model is periodically used to compare excavation budget and cost. As a result, the general contractor and subcontractor can manage the cost to make it lower or equal to the budget. The planned quantity as stated in the bill of quantities may differ from the actual quantity according to the UAV. In this case, the cost may increase or decrease from the predicted budget.

Lastly, in t₄, which is at the completion of earthwork, the actual earthwork volume is used as the basis for progress payment. UAV technology that can transparently and quickly generate accurate volume makes this scheme possible. Furthermore, the process of utilizing the simulation model is documented. The documentation acts as lessons learned for the next earthwork project.

5. Causal Loop Diagram

In this section, the interrelationship among factors influencing cost management in a construction project was developed as a causal loop diagram. The causal loop diagram depicts how factors are connected and illustrates the causal relationship between the factors [23]. The factors are represented with text labels and the causal relationships between factors are illustrated with arrows. The arrows are labeled with “s” or “o” to identify the causal effects, where “s” means positive relationship while “o” means negative relationship. Based on the diagram as shown in Figure 4, the planned work determines the budget value positively. The budget value becomes the basis for determining the investment value of a construction project. As the project starts, the actual work influences the investment value negatively. Furthermore, the remaining cost, which is obtained from the remaining work, decreases the budget and the investment value, resulting in cost overrun. When this occurs, cost contingency is secured, resulting in an increased budget. In addition, the budget decreases the value of cost overrun, while the remaining cost increases its value. This causal loop diagram of cost management can be implemented in any construction project throughout its life cycle. This study utilized the causal loop diagram specifically for cost monitoring of earthwork by comparing the planned with the actual excavation volume obtained from UAV.

6. Generation Model Development

The generation model explains the mathematical relationship between excavation budget and excavation cost. The budget is calculated using the planned quantity and excavation unit rate, while the cost is calculated using actual quantity and excavation unit rate, as shown in Figure 5.

The planned quantity ($p_i$) is the quantity for each soil type $i$ obtained from the survey results using a GPS survey and boring test. We obtained the terrain surface from GPS survey and subsurface per soil strata from interpolation of columnar section data of boring tests. By using the principle of obtaining volume based on two surfaces, called the DSM method as explained in Section 3.1, we overlaid two DSMs to calculate the volume. For example, assuming the soil type above the planned terrain is only soft and hard rock, we calculated the expected volume of soft and hard rock by overlaying the subsurface of soft and hard rock as the upper terrain and the planned terrain layer as the base terrain. The formula to calculate the planned quantity ($p_i$) is shown in Formula (3), which is adapted from Formulas (1) and (2).

$$p_i={\displaystyle \sum }_{k=1}^n{V}_k={\displaystyle \sum }_{k=1}^n{L}_k\times W_k\times H_k$$

(3)

The excavation unit cost rate ($u_i$) is the cost per m³ for each soil type $i$. The unit cost rate for each soil type is different because the difficulty level is different. The excavation budget ($f_b$), as shown in Formula (4), is the total planned cost. The excavation budget is calculated by multiplying the expected volume per soil type by the unit cost rate per soil type.

$$f_b={\displaystyle \sum }_{i=1}^l{p}_i\times u_i$$

(4)

Actual excavation quantity ($q_i$) is the quantity for each soil type $i$ obtained from the survey results using UAV. Through photogrammetry-based data processing, we can obtain the current terrain surface quickly and accurately. The volume per soil type can be obtained by overlaying the required terrains. For example, assuming we still only work with soil and weathered soil type, we overlaid the current DSM with the DSM from the previous time point to obtain the volume of soil and weathered soil that has been excavated. The formula to calculate $q_i$ is similar to Formula (3). As we monitored the excavation periodically, we also obtained the DSM per time point periodically. Therefore, we can calculate the total actual excavation per soil type ($q_i$) measured periodically by UAV $j$ times, as shown in Formula (5).

$$q_i={\displaystyle \sum }_{j=1}^n{q}_{i,j}=q_{i,1}+q_{i,2}+\dots +q_{i,n}$$

(5)

Excavation cost ($f_c$), as shown in Formula (6), is the total actual cost. Excavation cost is calculated by multiplying the actual volume per soil type by the unit cost rate per soil type.

$$f_c={\displaystyle \sum }_{i=1}^l{q}_i\times u_i$$

(6)

In the generation model, the excavation budget value is compared to the excavation cost with the objective budget value greater than or equal to the cost value, as shown in Formula (7).

$$\begin{gathered} Budget\ge Cost \\ {f}_b\left(p_i,u_i\right)\ge f_c\left(q_i,u_i\right) \end{gathered}$$

(7)

7. Simulation Model Development

Based on the generation model and causal loop diagram, the simulation model was developed as shown in Figure 6. In the simulation model, MCS was performed from t₀ to t₄ for the planned quantity by soil type, such as soil, weathered rock, and soft and hard rock. As the earthwork had not started yet, from t₀ to t₂, the value of actual quantity was still zero; thus, we could only observe the minimum and maximum value of budget or expected cost. Then, from t₂ to t₄, the actual earthwork quantity was input to the simulation model, and in this time range, simulations should be performed periodically to manage the risk of cost overrun exceeding the budget for the remaining earthwork quantity for each soil type.

Specifically, the initially predicted earthwork quantity for each soil type from t₀ to t₂ in Figure 6 was measured using GPS and boring test results. Then, while excavation was carried out from t₂ to t₄, the actual quantity was accurately measured by the UAV. As a result, the error of the planned quantity was also confirmed per conducted simulation. The error not only increases or decreases the actual earthwork cost but also may cause cost overrun risk for the residual earthwork. Therefore, in order to manage this risk from the start time (t₂) to the completion time (t₄), which takes at least several months, periodic simulations should be conducted to predict the residual earthwork quantity using the accumulated error data for each soil type.

Based on the previously mentioned causal loop diagram and simulation model concept, the simulation models were created using the Powersim Studio 10 Expert program, as shown in Figure 7. Simulation model is developed as a stock and flow diagram. It illustrates the mathematical expression of the system by distinguishing stocks and flows. A stock can accumulate or be reduced while a flow causes the stock to increase or decrease [23]. Expected cost was calculated by adding total monthly cost per soil type. The monthly cost per soil type was calculated by multiplying planned excavation ratio per month by expected total cost per soil type. Lastly, expected total cost per soil type was obtained by multiplying the expected volume and the unit cost rate per soil type. In this simulation, MCS is applied only to the expected volume, and the simulation was performed periodically for the remaining expected volume per soil type. We could then update the excavation ratio for the remaining month in accordance with the project’s target and conditions.

The actual cost was also calculated using the same principle for calculating the expected cost. The only difference is, instead of using excavation ratio per month, we used the actual excavation volume obtained from the UAV. Besides that, it is important to note that, during excavation, we were able to excavate soil type, which differs from what we expect after we studied the DSM. This shows that the subsurface we generated in the planning stage using the boring test result is not accurate, as it was an interpolation result. Therefore, as the excavation progresses, we can update the DSM and more accurately predict the remaining excavation volume.

When we ran the simulation, we set the condition that the total generated random values of expected volume per soil type are the expected volume gained from GPS and the boring test result, with an accepted difference of only ±1%. However, there is a limitation of the simulation in Powersim Studio. Therefore, every time we conducted a simulation, we exported the simulation result to Excel and filtered it in accordance with the condition.

8. Case Application and Discussion

This section verifies the simulation model through case application by running the simulation model at each phase (t₀–t₄) as needed. The project was located in Seoul, Republic of Korea. There were ten buildings in total and each building consisted of five floors below ground and eighteen floors above ground as shown in Figure 8. The excavation included the five floors below ground. A high-density residential area surrounds the construction site, and there is hilly terrain on one side of the site.

As expected, there were three types of soil found during excavation: (1) soil and weathered soil, (2) weathered rock, and (3) soft and hard rock. The earthwork period was nine months from April 2021 to December 2021. The planned excavated volume was 213,017 m³ for soil and weathered soil, 49,079 m³ for weathered rock, and 75,643 m³ for soft and hard rock, with a total of 337,739 m³. Subsequently, the disposal schedule and the expected excavated volume per month were set as shown in

Table 1. Excavation schedule and expected excavated volume plan.

Schedule	Month 1	Month 2	Month 3	Month 4	Month 5	Month 6	Month 7	Month 8	Month 9
Monthly plan	18,900	42,240	42,240	42,240	42,240	42,240	42,240	42,240	23,159
Accumulation	18,900	61,140	103,380	145,620	187,860	230,100	272,340	314,580	337,739
Accumulation progress rate	5.5%	18.1%	30.6%	43.1%	55.6%	68.1%	80.6%	93.1%	100%

. The contractor did not divide the volume per soil type. In this study, the simulation was first conducted before the actual excavation. Then, periodic simulation was conducted during the excavation period to monitor the excavation cost.

8.1. Simulation before Excavation (t₀–t₂ Stage)

In the planning stage, a forecasting simulation was conducted using the expected earthwork volume and cost rate per soil type to obtain the excavation budget because the actual excavation had not been conducted yet. The volume of each soil type was assumed to be normally distributed. A 10% standard deviation of each initial value of soil type was used assuming no extreme variations in soil volume. For each iteration, the MCS randomly selected a value for each soil type, in accordance with specified normal distribution and standard deviation. The initial values of volume and cost rates per soil type were entered as shown in

Table 2. Initial values of independent variables.

Item	Initial Value	Unit
Soil and weathered soil	213,017	m3
Weathered rock	49,079	m3
Soft and hard rock	75,643	m3
Unit price of soil and weathered soil	1.067	USD/m3
Unit price of weathered rock	2.311	USD/m3
Unit price of soft and hard rock	11.244	USD/m3

.

Simulations were performed 10,000 times to forecast the expected excavation cost, as shown in Figure 9 and summarized in

Table 3. Results of forecasting simulation before excavation.

Description	Unit	Minimum	Average	Maximum
Volume of soil and weathered soil	m3	183,717	213,017	245,028
Volume of weathered rock	m3	34,064	49,079	63,583
Volume of soft and hard rock	m3	48,827	75,643	102,637
Total cost	USD	922,304	1,189,570	1,464,419

. Samples of 10,000 simulations were considered sufficient to obtain stable results following Crowder and Moyer [26]. Smaller samples would generate inaccurate results and unbalanced histogram plots, while larger samples would take an unnecessarily long time to simulate. As a result, the average, maximum, and minimum excavation costs were USD 1,189,570, USD 1,464,419, and USD 922,304, respectively. This simulation can be conducted by the contractor before opening tender (t₀–t₁ stage), by subcontractor candidates to set the bidding price (t₁–t₂ stage), or by the chosen subcontractor to monitor the excavation cost (t₂ stage).

8.2. Periodic Simulation during Excavation (t₂–t₄ Stage)

It was planned that, in the first to third month, the excavation was only carried out for soil and weathered soil types. Based on processing on data acquired from UAV technology, the volume of soil and weathered soil that had been excavated until the third month was 119,460 m³. Therefore, there was still 218,279 m³ that needed to be excavated out of a total volume of 337,739 m³.

At the end of the third month, the subcontractor conducted a simulation to monitor the estimated costs that might occur until the end of the excavation period. The initial value of volume was set with 49.079 m³ for weathered rock and 75,643 m³ for soft and hard rock. Simulations were performed to forecast the expected excavation cost, as shown in Figure 10. As a result, the average, maximum, and minimum excavation costs were USD 1,222,749, USD 1,444,984, and USD 1,068,548, respectively. The maximum cost was below the maximum expected cost.

At the end of the sixth month, based on the actual volume based on UAV, the excavation volume was 192,278 m³ for soil and weathered soil, 23,863 m³ for weathered rock, and 42,865 m³ for soft and hard rock. The total land that had been excavated was 259,006 m³ out of 337,739 m³. In this period, there was a change in the position of the retaining wall, which caused an increase in the volume of soil that needed to be excavated by 25,227 m³. Therefore, the total land that still needed to be excavated was 103,960 m³. Based on this condition, another simulation was carried out to estimate the expected cost. Simulations were performed again to forecast the expected excavation cost. As a result, the average, maximum, and minimum excavation costs were USD 1,318,397, USD 1,324,424, USD 1,314,916, respectively. The maximum cost was below the maximum expected cost. This study conducted simulations two times during excavation; however, the subcontractor can run simulation tests several times with different intervals as needed.

8.3. Cost Calculation after Excavation Completion (t₄ Stage)

After the excavation was finished, the subcontractor calculated the actual volume, which was acquired by processing data from UAV. It was recorded that the actual volume was 231,732 m³ for soil and weathered soil, 45,756 m³ for weathered rock, and 85,478 m³ for soft and hard rock. It should be noted that the volume of soil and weathered soil exceeded the maximum estimated value, as shown in

Table 4. Comparison of planned and actual excavated volume per soil type.

Description	Unit	Planned	Actual
Volume of soil and weathered soil	m3	213,017	231,732
Volume of weathered rock	m3	49,079	45,756
Volume of soft and hard rock	m3	75,643	85,478

. This proves that the excavation volume planning cannot be accurate. Therefore, the actual cost was USD 1,314,115, which was higher than the average expected cost (USD 1,189,570) and lower than the maximum expected cost (USD 1,464,419) in the planning stage.

From the multiple simulations above, the data from the previous simulation results are used as the basic data for the next simulation. This illustrates the principle of causal loop diagram where the cost influence factors are interconnected and changed over time according to the defined mathematical definitions [23]. As a result, every time a simulation is conducted, we obtain the possible outcome of maximum, average, and minimum of cost. We can compare it to the result of the forecasting simulation in the planning stage. In this study, the final actual cost was slightly below the maximum expected cost. These results show the importance of running the simulation where the subcontractor can periodically check whether the cost is managed within the cost range or not. In accordance with Turskis et al. [27] who stated cost risks can be managed through risk monitoring techniques by confirming the magnitude of the risk, the simulation model of this study can assist the subcontractor to take countermeasure actions when there is a possibility of the cost being higher than expected. However, this study is limited by only defining the minimum, average, and maximum value of expected and actual cost. The simulation model can be developed further by setting the cost upper limit or cost contingency, in accordance with Hoseini et al. [28] who said cost contingency must be assigned, calculated, and controlled in construction projects. Cost contingency allows earthwork subcontractors to compensate for the uncertainty of excavation volume [29]. The subcontractor can define the cost upper limit or cost contingency in accordance with their confidence level after considering the risks and the uncertainties.

8.4. Visualization of DSM for Excavation Assistance

In addition to using UAV data for obtaining actual excavated volume, stakeholders can use UAV data to visualize the DSM comparison for assistance during excavation. Following the similar approach by Rachmawati and Kim [6], we chose a segment of interest as the excavation target. Figure 11 shows the cross section of DSM on 31 May 2021 and 30 June 2021 along with the design level and three soil strata. This visualization helps stakeholders in observing the progress of excavation and assessing the soil type and the position of soil type that will be excavated next. In this way, stakeholders can discuss and develop strategies regarding technical excavation implementation.

9. Conclusions

This study developed a simulation model that can forecast, control, and monitor the excavation cost using factors that influence excavation, that is, excavation volume and cost rates per soil type. The simulation model was verified through case application throughout the earthwork life cycle, which was the planning, excavation, and completion stage, with results as shown below.

The first simulation was conducted in the planning stage. Probabilistic distribution was applied to expected excavated volume. After running the simulation 10,000 times, the minimum, average, and maximum expected costs were USD 922,304, USD 1,189,570, and USD 1,464,419, respectively. The earthwork subcontractor used the cost range as a basis to control and monitor the cost during excavation. Subsequently, several simulations were run as needed during the excavation period. The second simulation was performed by the end of the third month, when the excavation of the second and third soil layers would be conducted. As a result, the minimum, average, and maximum expected costs of the second simulation were USD 1,068,548, USD 1,222,749, and USD 1,444,984, respectively.

The third simulation was performed by the end of the sixth month due to design changes, resulting in increased excavated volume. At this stage, the actual volume obtained from the UAV differed from the expected volume, indicating that the expected volume in the planning stage was underestimated. After running the simulation, the minimum, average, and maximum expected costs of the third simulation were USD 1,306,076, USD 1,310,074,749, and USD 1,313,564, respectively. The maximum cost of both the second and third simulations was still lower than the maximum expected cost in the planning stage. Therefore, no countermeasure actions were performed. Finally, in the completion stage, the actual volume was recorded and the actual cost was USD 1,314,115, which was slightly below the maximum expected cost. These results show the importance of running the simulation where the contractor can periodically check whether the cost is managed within the cost range. Due to the use of a UAV, stakeholders can acquire the actual volume for the simulation. In the next study, an optimization and risk management model will be developed and added to the existing model of this study to set the cost upper limit or cost contingency in accordance with the subcontractor’s confidence level after considering the risks and uncertainties.