**1. Introduction**

Zambia is a key transit country in the north–south corridor as it sits between and borders eight countries in the region, viz. Tanzania, the Democratic Republic of Congo, Botswana, Namibia, Zimbabwe, Mozambique, Angola and Malawi. With a virtually non-functional rail system, various mining products and equipment are transported in and out of the mines in the Copperbelt Province to South Africa, Tanzania and other countries in the region mostly by road.

Zambia has a total gazetted road network of 67,671 km, 40,454 km of which comprises the Core Road Network (CRN). The CRN is defined as the bare minimum network that Zambia requires to be maintained continuously and on a sustainable basis to realize its social and economic potential. The CRN infrastructure in Zambia consists of a sparsely interconnected network of Trunk (T), Main (M), District (D), Primary Feeder (PF) and Urban (U) roads. Table 1 shows the breakdown of the CRN in Zambia [1].

The traffic growth rate on major highways, in particular the truck traffic, has been increasing day by day in Zambia due to its geostrategic location and international trade corridor, subsequently leading to the premature failure of roads [2]. A recent study on the condition of the roads showed that as of 2014, less than 25% of the CRN was paved, and close to half of the paved road network was in a fair to poor condition [1].


**Table 1.** Zambia's Core Road Network (CRN) (2014).

One of the most prominent defects, particularly on major highways, is rutting failure [2]. This type of failure is prominent in sections where traffic is forced to stop or move at a slow pace, thereby increasing the loading on the road pavement. Thus, the failure is load-related and it eventually escalates to include other defects such as cracking, potholing, etc.

Rutting is defined as a longitudinal surface depression occurring in the wheel paths of roadways due to repeated traffic loading. It accumulates incrementally with small permanent deformations from each load application over the pavement's service life. It is often followed in later stages by an upheaval along the sides of the rut. The decreased thickness in the rutted portions may accelerate fatigue cracking and eventual loss of the surfacing [3]. Rut depth (RD) is one of the most commonly used index variables for quantifying pavement surface rutting. This index has been traditionally measured manually, using a gauge with either a straightedge or a wire. The method is considered "a reliable and low budget option" [4].

Rutting failure not only reduces the lifespan of the road but is also a serious safety issue for road users. When the vehicle moves along the rutted portion of the pavement, steering becomes difficult and it reduces driving comfort. If rainwater pools in the rutted wheel path, it can result in hydroplaning and spray that reduces visibility. To this extent, rutting has become such a serious problem of modern-day roads that countries such as the United States have taken it as one of the design criteria for asphalt pavements [5].

Most Zambian roads are constructed of flexible pavements. Flexible pavements are roads constructed of several layers of natural or treated granular material covered with one or more waterproof bituminous surface layers (e.g., asphalt). They are so named because the total pavement structure deflects or flexes under loading. The objective with the design of a flexible pavement is to avoid the excessive flexing of any layer, the failure of which will result in the over-stressing of the layer, which ultimately will cause the pavement to fail [6].

The layer(s) in which rutting occurs is influenced by the loading magnitude and the relative strengths of the pavement layers. Stresses within the layer of a pavement structure are determined by applied load, individual and combined layer thickness and layer material properties [7].

The Mechanistic-Empirical Design Guide (MEPDG) has defined three distinct stages for the permanent deformation behavior of asphalt pavements under a given set of material, load and environmental conditions. This is shown in Figure 1 [5]. The primary stage has a high initial level of rutting, with a decreasing rate of plastic deformation, predominantly associated with volumetric change. The secondary stage has a small rate of rutting, exhibiting a constant rate of change of rutting that is also associated with volumetric changes; however, shear deformations increase at an increasing rate. The tertiary stage has a high level of rutting predominantly associated with plastic (shear) deformations under no volume change conditions.

**Figure 1.** Typical repeated load permanent deformation behavior of pavement materials.

Generally, there are two causes of rutting in asphalt pavements—the accumulation of permanent deformation in the asphalt-surfacing layer and the permanent deformation of subgrade or underlying layers. In the past, subgrade deformation was considered the primary cause of rutting and many pavement design methods applied limiting criteria on vertical strain at the subgrade level. However, recent research has indicated that most of the rutting occurs in the upper part of the asphalt surfacing layer. Nonetheless, these two causes of rutting can act in combination, i.e., the rutting could be the sum of permanent deformation in all the layers [2,8,9].

The determination of which layer in the pavement structure is responsible for rutting failure is the first step toward arriving at a remedial measure.

The destructive methods of trenching and coring have traditionally been used for rutting failure investigations. Field trenching is conducted to expose the layers of the pavement so that they can be studied. The thickness of the layers, i.e., asphalt, the base and the subbase, are measured and plotted to show the deflections in the layers. Alternatively, core samples can be obtained at a constant spacing on a lane to determine the layer thicknesses of the pavement layers and the results can be plotted (similar to trenching) to determine the contribution of each layer to rutting due to changes in thickness and deflections of the pavement layers. The Dynamic Cone Penetrometer (DCP) Test has also been used to determine the strength of the pavement layers by calculating the California Bearing Ratio (CBR) of the pavement layers. The knowledge of the strengths of the existing pavement layers at a rutted section of the road can be used to deduce whether the ruts have been caused by weak structural layers, the subgrade or whether it is restricted to the surface. These methods are, however, time consuming and costly and may lead to weaknesses in the pavement structure if not repaired properly.

TPAM is one of the non-destructive techniques developed to determine the source of rutting in a pavement structure. The method was suggested by White et al. [7], who conducted extensive computer analyses using Finite Element Methods (FEM) to simulate rutting failures in Hot-Mix-Asphalt (HMA) surface mixtures, base courses and subgrades. Transverse surface profile characteristics indicative of failure within specific structural layers were then determined in the form of simple distortion parameters, and specific criteria were developed for these distortion parameters. The criteria were applied to an analysis of full-scale accelerated pavement test (APT) data, confirming that the relative contributions of the layers to rutting in an HMA pavement could be determined from an analysis of its transverse surface profile. This followed works such as [10], wherein the authors hypothesized that the area under the transverse surface profile could be used to predict the source of rutting from within the pavement structure. The authors of [11] also suggested that quantifying transverse profile

measurements presented a potential method of determining the cause of rutting in the absence of traffic, structural and environmental data.

Another study [12] found that TPAM is one of the most accurate and precise methods of establishing the cause of rutting failure. The study used trenching, coring and Falling Weight Deflectometer (FWD) tests to validate the method. The authors of [13] also used the TPAM to determine the source of rutting failure on a 300 m section of the N5 National Highway in Pakistan. The study determined that most rutting was mainly due to the shear failure of the HMA layer. It was also observed that an increase in rut depth resulted in an increase in negative area and a reduction in positive area of the profile. The results were validated using the trenching method.

The TPAM was also used to determine the source of rutting on the Belbis-Zagazig Road in Egypt. A study determined that 60% of the rutting resulted from the HMA, 30% from the base layer and 10% from the subgrade. The authors concluded that the TPAM proved to be a good diagnostic tool for determining the source of most of the rutting failure [14].

The goal of this publication is to highlight the results of a study undertaken to establish the layer(s) responsible for rutting failure using the TPAM on some selected sections of road in the Copperbelt Province of Zambia.

The traditional methods of coring and trenching are the most commonly used methods of determining the source of rutting failure. However, these two methods are destructive, in that the subsurface layers must be exposed by excavating a trench or coring and then restored after rut investigations. This may lead to weaknesses at the joints, resulting in the shortening of the lifespan of the pavement if not repaired properly. Furthermore, these destructive methods are time-consuming, costly and inconveniencing to road users.

TPAM has been suggested as a simple yet effective way of determining the rutting failure source within the pavement structure through theoretical and analytical analyses of surface profiles, with little to none of the challenges associated with trenching and/or coring.

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

A typical transverse profile is shown in Figure 2. The method of analysis with the TPAM is explained below.

The first and last points of the profile line are joined to establish a reference line (indicated by the dotted line). The portion of the area above the line is considered as positive area (Ap) and the portion below the reference line is considered as negative area (An). The maximum rut depth (D) is computed by firstly drawing a line joining the high points of the profile known as the wire line; the maximum rut depth is then equal to the line with the maximum length drawn between the profile line and the wire line in a direction perpendicular to the wire line.

**Figure 2.** Plot of transverse profile from the edge of a shoulder to the center line of a lane. Ap = area above dotted line; An = area below dotted line; D = maximum rut depth.

The positive and negative areas are calculated by plotting the profile to scale in AutoCAD or other software.

The distortion parameters, i.e., the total area, termed 'distortion' and the ratio of the positive or negative area to the total area, termed 'ratio of distortion' are computed by the following equations [7].

$$\mathbf{A} = \mathbf{A}\_{\mathrm{P}} + \mathbf{A}\_{\mathrm{n}} \tag{1}$$

$$\mathbf{R} = \mathbf{A}\_{\mathrm{p}} / \mathbf{A}\_{\mathrm{n}} \tag{2}$$

where

A = total area (mm2); R = ratio of area; Ap = positive area (mm2); An = negative area (mm2).

In predicting the layer responsible for rutting distress, it is also necessary to compute some critical coefficients by the following equations:

$$\mathbf{C}\_{1} = (-858.21)\,\mathrm{D} + 667.58\tag{3}$$

$$\mathbf{C}\_2 = (-1509)\,\mathrm{D} - 287.78\tag{4}$$

$$\mathbf{C}\_3 = (-2120)\,\mathrm{D} - 407.95\tag{5}$$

where

C1 = theoretical average total area for HMA failure (mm2);

C2 = theoretical average total area for base/subbase failure (mm2);

C3 = theoretical average total area for subgrade failure (mm2);

D = maximum rut depth (mm).

These equations are called equations of trend lines for HMA, base and subgrade failure modes in failure criteria.

Based on the characteristics of a given surface profile and the criteria described above, the mode of failure can be inferred [7] as follows:

1. Failure has occurred in the HMA layer if both the following conditions are satisfied:

$$R > 0.05\tag{6}$$

$$A > (\mathbb{C}\_1 + \mathbb{C}\_2)/2\tag{7}$$

2. Failure has occurred in the base/subbase layer if both the following conditions are satisfied:

$$R < 0.05 \tag{8}$$

$$A > (\mathbb{C}\_2 + \mathbb{C}\_3)/2\tag{9}$$

3. Subgrade failure has occurred if no failure can be determined from the previous comparisons.

The method of analysis is summarized in the flow chart shown in Figure 3.

**Figure 3.** Illustration of the procedure for failed layer prediction [15].

A visual condition survey was undertaken to identify and select road pavements exhibiting rutting failure that were thus suitable for investigation. Three roads were selected, namely Kitwe-Ndola Road, Kitwe-Chingola Road and Chibuluma Road, all within the Copperbelt Province of Zambia.

#### *2.1. Kitwe-Ndola Road*

On the Kitwe-Ndola Road, the TPAM and trenching were conducted on a selected rutted section. The results of the profile analysis were compared to the trenching method for purposes of validation.

The pavement transverse profile was analyzed by measuring rut depths on a heavily rutted section of the road. This was done using the straight edge and gauge method. Four measurements were taken every 15 m on the rutted section. Profile measurements were taken at intervals of 200 mm from the shoulder edge to the center line of a lane. Four trenches were excavated at each point where a profile analysis was conducted. The excavation was done from the edge of the shoulder to the center line of a lane. The thickness of the asphalt and underlying layers were measured at intervals of 200 mm equal to the spacing used for rut depth measurements.

Figures 4–7 show the straight edge and gauge measurements and trench measurements on the Kitwe-Ndola Road.

**Figure 4.** Trench measurements of Pit 1 (Kitwe-Ndola).

**Figure 5.** Trench measurements of Pit 2 (Kitwe-Ndola).

**Figure 6.** Profile measurements on Kitwe-Ndola Road.

**Figure 7.** Trench measurements of Pit 3 (Kitwe-Ndola).
