Modeling of unconfined compressive strength of soil-RAP blend stabilized with Portland cement using multivariate adaptive regression spline

Abstract

The recycled layer in full-depth reclamation (FDR) method is a mixture of coarse aggregates and reclaimed asphalt pavement (RAP) which is stabilized by a stabilizer agent. For design and quality control of the final product in FDR method, the unconfined compressive strength of stabilized material should be known. This paper aims to develop a mathematical model for predicting the unconfined compressive strength (UCS) of soil-RAP blend stabilized with Portland cement based on multivariate adaptive regression spline (MARS). To this end, two different aggregate materials were mixed with different percentages of RAP and then stabilized by different percentages of Portland cement. For training and testing of MARS model, total of 64 experimental UCS data were employed. Predictors or independent variables in the developed model are percentage of RAP, percentage of cement, optimum moisture content, percent passing of #200 sieve, and curing time. The results demonstrate that MARS has a great ability for prediction of the UCS in case of soil-RAP blend stabilized with Portland cement (R² is more than 0.97). Sensitivity analysis of the proposed model showed that the cement, optimum moisture content, and percent passing of #200 sieve are the most influential parameters on the UCS of FDR layer.

Keywords

full-depth reclamation / soil-reclaimed asphalt pavement blend / Portland cement / unconfined compressive strength / multivariate adaptive regression spline

Introduction

There are several pavement recycling methods which are implemented for improving the quality of flexible pavements, among which full-depth reclamation (FDR) is regarded as one of the most effective ones [¹]. In FDR method, the whole thickness of asphalt concrete layer is pulverized with a part of the subsequent layer and accordingly, it is stabilized to design a stabilized base course [²]. The use of FDR leads to an increase in the bearing capacity, structural strength, stability, and lifetime of pavement. In addition, it can develop pavement serviceability [³–¹⁰]. The stabilization of soil and reclaimed asphalt pavement (RAP) mixture with appropriate stabilizer such as Portland cement leads to an increase in strength and stiffness [¹¹].

Based on the results of the previous studies, an increase in RAP content and a decrease in cement content in the mixture results in reducing the content of the optimum moisture and maximum dry density of the stabilized material [⁶,¹²–¹⁴]. Contrarily, some researchers like Puppala and Bang, in their studies, failed to achieve a significant trend for optimum moisture content (OMC) and maximum dry density when an increase occurred in the amount of cement [¹¹,¹⁵]. In addition, increasing the cement content in soil-RAP blend, leads to an increase in unconfined compressive strength (UCS) [⁶,¹²,¹³,¹⁵–¹⁷].

Predicting the strength of the stabilized soil based on mix and curing time parameters plays a significant role in controlling and assuring the quality of the mixed design. Several researches were conducted for designing the appropriate models for predicting the UCS of the stabilized soils using machine learning algorithms [¹⁸–²⁵]. Das et al. [¹⁸] implemented ANN and support vector machine (SVM) in order to estimate the maximum dry density and UCS related to the cement stabilized soil according to soil plasticity (LL, PI), sand content (S), clay content (C), moisture content (MC), gravel content (G), and cement content (CC) as input parameters. In addition, by considering the criteria for different statistical results, they concluded that the SVM is regarded as a better prediction technique, compared to ANN [¹⁸].

In another study, Güllü utilized genetic expression programming (GEP) in order to model the UCS and elasticity modulus of clay stabilized with the bottom ash through employing an experimental database. Based on GEP method, bottom ash dosage, dry unit weight, relative compaction, brittleness index, and energy absorption capacity were considered as the independent variables of the study. Based on the results, a high degree of accuracy was observed when the GEP-based formulas were used for predicting UCS and modulus of elasticity [²⁰].

MolaAbasi and Shooshpasha, implemented polynomial-type neural network for the purpose of predicting the UCS of cement-zeolite stabilized sand. To this end, zeolite and CC, porosity, and curing time were considered as the predictors. Based on the results, generalized polynomial-type neural network had a high level of accuracy for predicting the UCS [²²].

In another study, Mozumder et al. utilized SVR technique in order to assess the UCS of geopolymer stabilized clayey soil. The results indicated that the SVR is regarded as an effective method in order to predict the UCS of geopolymer stabilized clayey soil. In addition, an increase in binder content resulted in increasing the UCS and reducing plasticity parameters [²³].

However, there are some drawbacks for using artificial intelligence models such as ANNs and SVR. For example, the knowledge acquired during the model training is implicitly stored and accordingly it is difficult to reasonably interpret the general results. In addition, ANNs technique requires a large database for training network, cross-validating and testing. In such cases other methods like multivariate adaptive regression spline (MARS) [²⁶] and hybrid nonlinear surrogate models [²⁷–³³] can be employed for modeling.

Today, the use of machine learning algorithms in civil engineering is widely used [³⁴–³⁶], and MARS is one of these algorithms. MARS is considered as one of the new methods for developing appropriate formula based on experimental results. MARS technique has been already implemented in civil engineering in order to model the doweled pavement performance, estimate the asphalt mixture deformation, analyze shaking table tests of reinforced soil wall, determine the undrained shear strength of clay, predict the frequency for simulating asphalt mix fatigue, as well as evaluating elastic modulus of jointed rock mass [³⁷–⁴⁶].

Zhang and Goh, in their study implemented MARS in order to analyze the geotechnical engineering systems. Based on the results, MARS is computationally more efficient and appropriate for selecting the optimal model since it can design flexible models by using linear regression and approximate the model by separating different slopes in distinct intervals of the input variables [⁴⁷].

In addition, Suman et al. developed models for predicting the UCS of cement stabilized soil based on MARS method. In this study, liquid limit, plastic index (PI), percentage of sand (S), percentage of gravel (G), MC, and the CC were considered as the predictors. In order to design UCS model, 51 samples were selected for data analysis. The results indicated that the MARS method can be regarded as an appropriate method for predicting of UCS of cement stabilized soil [⁴⁸].

Generally, UCS is utilized in order to design, quality control, and the quality assurance of the final product in FDR projects. Based on the literature review, no appropriate model has been proposed for predicting UCS of soil-RAP blend stabilized with Portland cement.

In the present study, MARS technique is implemented to develop a formula in order to evaluate the UCS of soil-RAP blend stabilized with Portland cement. This formula can be used for predicting UCS of FDR layers with respect to OMC, percentage passing through No. 200 (75 µm) sieve, RAP content, as well as CC and curing time. In comparison with the UCS which is a time consuming test due to need for curing, all input parameters of proposed model can be estimate using relatively simple and fast laboratory tests. The general flowchart of the present research is demonstrated in Fig. 1.

Experimental program

Material

Soil

In the present study, two different aggregate materials were mixed with different percentages of RAP. The first aggregate material was obtained from the existing aggregate course under the asphalt concrete layer of a street in Sirjan and the second aggregate material was taken from the aggregate base material depot in Sirjan. Figure 2 represents the grain size distribution curve of these two aggregate materials. Regarding gradation, the first aggregate material was approximately similar to the grain size distribution type III of subbase material [⁴⁹]. However, the second aggregate material was almost close to the grain size distribution type III of base material [⁴⁹]. Table 1 indicates both physical and mechanical characteristics related to these two aggregate materials. According to Iranian code of IHAP (2010), the standards used for aggregate base and subbase are given in Table 2. Regarding the standard, the first aggregate material (SP-SC) is similar to the subbase although there are a slight difference in sand equivalent value. In addition, the second aggregate material (GW-GC) is almost identical to base material by considering some slight differences in sand equivalent value and the crashed rate in two faces.

RAP

As shown in Fig. 3, Wirtgen recycler WR 2500 was employed to pulverize the RAP material from a street in Sirjan. Based on the unified soil classification system, the RAP was classified as SP category, includes non-plastic materials. The amount of bitumen (ASTM D-2172) and water absorption (ASTM C127) in RAP material were measured as 4.5% and 2.34%, respectively. Figure 4 illustrates grain size distribution curve of the RAP material.

Portland cement

Type II of Portland cement was used in this study. Physical and chemical properties of Portland cement are given in Table 3.

Laboratory tests

With respect to the thickness of asphalt concrete layer in Sirjan streets and literature review, different mixtures with 0/100, 20/80, 40/60, and 60/40 of RAP to soil ratios were stabilized by adding 3%, 4%, 5%, and 6% of Portland cement for the purpose of creating a dataset for modeling using MARS. In the first stage, both OMC and maximum dry density of each mixture were specified by using modified Proctor test according to ASTM D-180 method C. Based on this method, the mold height and diameter is 116.43 mm and 101.16 mm, respectively. Then, the samples were placed under the room temperature 72 hours before performing the test in order to eradicate the moisture. Finally, particles with the size more than 2.5 cm were eliminated.

The soil was placed into the mold in five layers and each layer was exposed to 56 blows. Then, the UCS test was conducted according to method A of ASTM D1633 by considering the loading rate of 1 mm/min. The molds used for UCS test and compaction test were in accordance with ASTM D-180 method C. The compacted samples were poured inside a plastic bag in order to eliminate the change of moisture and accordingly were cured for 7 or 28 days. In order to enhance the accuracy of the test, the UCS was determined based on the average of two measurements. For this purpose, two samples were cured for 7 days and two samples were cured for 28 days. The final amount of UCS for each specific curing time (7 or 28 days) was assumed as the average of the two UCS measurements. Tables 4 and 5 represent the results of final UCS obtained for SP-SC and GW-GC soil, respectively.

Theory of MARS

MARS is an adaptive regression technique in order to solve regression-type problems [⁵⁰]. MARS is a ‘white box’ technique by which physical laws and underlying physical relationships of the system are explained [⁵¹]. No specific hypothesis is necessary about the underlying functional relationship between the variables related to the input and output. The end points of the segments are called “knots”. A knot represents both the ending of one region of data and the beginning of another. Accordingly, the piecewise curves known as “basis functions”, result in enhancing the flexibility of the model, allowing for bends, thresholds, and other departures from linear functions.

MARS model is written as follows:

(1)f(X)={\beta }_{\mathrm{0}}+{\displaystyle \sum _{n=\mathrm{1}}^N{\beta }_n{B}_n(X)},

where {{\displaystyle \beta }}_{\mathrm{0}}represents the coefficient of the constant basis function B₀(X)=1, B_n(X) indicates the nth basis function, which is related to a single spline function or product of two or more, B_n displays the coefficient of the basis function, and N denotes the number of basis functions in the model. Each basis function, B_n(X), is regarded as one of the three forms: a constant, a hinge function (x_i− t_k) ₊ or (x_i− t_k)_, and a product obtained from two or more hinge functions, which can play the role of a model interaction between two or more variables as follows:

(2){(x-{\mathrm{t}}_{\mathrm{k}})}_{+}=\max (\mathrm{0},x-{\mathrm{t}}_{\mathrm{k}})=\{\begin{array}{l}x-{\mathrm{t}}_{\mathrm{k}},\begin{array}{lll}& \mathrm{i}\mathrm{f}& x\ge {\mathrm{t}}_{\mathrm{k}}\end{array}\\ \mathrm{0},\begin{array}{lll}& & \mathrm{e}\mathrm{l}\mathrm{s}\mathrm{e}\end{array}\end{array},

(3){(x-{\mathrm{t}}_{\mathrm{k}})}_{-}=\max (\mathrm{0},{\mathrm{t}}_{\mathrm{k}}-x)=\{\begin{array}{l}{\mathrm{t}}_{\mathrm{k}}-x,\begin{array}{lll}& \mathrm{i}\mathrm{f}& {\mathrm{t}}_{\mathrm{k}}\ge x\end{array}\\ \mathrm{0},\begin{array}{lll}& & \mathrm{e}\mathrm{l}\mathrm{s}\mathrm{e}\end{array}\end{array},

where t_k represents a constant, named “knot”.

The MARS algorithm includes forward step and backward pruning process in order to fit the related data. . In forward step, the process begins with the intercept{{\displaystyle \beta }}_{\mathrm{0}}, and the basis functions are added in each subsequent step in order to decrease the errors in training step, resulting in creating an over-fitted model. However, generalized cross-validation (GCV) technique is implemented to prevent from over fitting during backward pruning process. The GCV penalizes both basis functions and knots, which results in decreasing the over-fitting or improving generalization of the model. In order to calculate GCV for the data with N samples, the following eqation can be used:

(4)\mathrm{G}\mathrm{C}\mathrm{V}={\displaystyle \frac{(\mathrm{1}/N^{\prime })\sum _{i=\mathrm{1}}^N{\displaystyle {[y_i-f(x_i)]}^{\mathrm{2}}}}{{\left[\mathrm{1}-{\displaystyle \frac{M+{\displaystyle \raisebox{1ex}{$d(M-\mathrm{1})$}\!\left/ \!\raisebox{-1ex}{$\mathrm{2}$}\right.}}{N^{\prime }}}\right]}^{\mathrm{2}}}},

where M represents the number of basis functions, d indicates the penalizing parameter, N^{\prime } is the number of data points, and f(x_i) is considered as the predicted values of the MARS model. The denominator of GCV plays a significant role in increasing variance when an increase takes place in the complexity of the related model. The number of knots is represented by (M− 1)/2 in the denominator. Therefore, GCV is capable of penalizing basis functions and knots.

Evaluation of models performance

The performance of MARS model was estimated by the following measures:

Root Mean Square Error (RMSE)

(5)\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{\mathrm{1}}{M}}{\displaystyle \sum _{i=\mathrm{1}}^M(h_i-}{t}_i{)}^{\mathrm{2}}}.

Coefficient of determination (R²):

(6)R^{\mathrm{2}}={\left[{\displaystyle \frac{{\displaystyle \sum _{i=\mathrm{1}}^M(h_i-{\bar{h}}_{})(t_i-{\bar{t}}_{})}}{\sqrt{{\displaystyle \sum _{i=\mathrm{1}}^M{(h_i-{\bar{h}}_{})}^{\mathrm{2}}}{\displaystyle \sum _{i=\mathrm{1}}^M{(t_i-{\bar{t}}_{})}^{\mathrm{2}}}}}}\right]}^{\mathrm{2}}.

Mean absolute deviation (MAD):

(7)\mathrm{M}\mathrm{A}\mathrm{D}={\displaystyle \frac{{\displaystyle \sum _{i=\mathrm{1}}^M\left|h_i-t_i\right|}}{M}}.

Mean absolute percentage error (MAPE):

(8)\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}={\displaystyle \frac{{\displaystyle \sum _{i=\mathrm{1}}^M\left|h_i-t_i\right|}}{{\displaystyle \sum _{i=\mathrm{1}}^M{h}_i}}}\times \mathrm{100},

where M is the number of observations, h_i is the ith observed value, \bar{h} is the mean h value, t_i is the ith predicted value, t is the mean t value.

Lower values ​​for RMSE, MAD, and MAPE will provide better performance. In fact, for a precise error-free model, one can expect R² equal to one, RMSE, MAD, and MAPE equal to zero.

Prepared dataset

In the present study, data from laboratory studies related to UCS of cement stabilized soil-RAP was used. In this data set, percentage of RAP, percentage of cement, OMC, percent passing of #200 sieve, and curing time were considered as independent and effective variables on UCS. The statistical data of the data set are presented in Table 6. The minimum and maximum values ​​of each of the variables indicate good dispersion and the standard deviation values ​​represent the uniformity of the data. In order to model UCS using the MARS method, 70% of the data were considered as training data and 30% of the data were considered as test data.

Modeling of UCS using MARS

In order to select the optimum number of bias functions of MARS model, a computer code was developed in MATLAB. This code evaluates the RMSE of MARS model in case of training and testing set with respect to different number of bias functions by a loop and selects the optimum number of bias functions which results in minimum value of RMSE. The optimum number of bias functions was determined as 9.

The developed MARS model based on 45 training data is as follows:

(9)y=\mathrm{3195.519953}-\mathrm{13.94474567}\times B{F}_{\mathrm{1}}+\mathrm{12.03780013}\times B{F}_{\mathrm{2}}+\mathrm{417.1049021}\times B{F}_{\mathrm{3}}-\mathrm{306.7007775}\times B{F}_{\mathrm{4}}+\mathrm{24.14206345}\times B{F}_{\mathrm{5}}-\mathrm{9.35865622}\times B{F}_{\mathrm{6}}+\mathrm{247.7770048}\times B{F}_{\mathrm{7}}-\mathrm{60.35251782}\times B{F}_{\mathrm{8}}+\mathrm{2.765849242}\times B{F}_{\mathrm{9}},

The parameters defined in Eq. 9 are as follows:

BF₁ = max(0, RAP-20),

BF₂ = max(0, 20-RAP),

BF₃ = max(0, C-5),

BF₄ = max(0, 5-C),

BF₅ = max(0, CT-7),

BF₆ = BF₁*max(0,P₂₀₀ -8),

BF₇ = max(0,P₂₀₀-8),

BF₈ = BF₆*max(0,OMC-6.02),

BF₉ = BF₆*max(0,6.02-OMC),where RAP= content of RAP (%); C= cement content (%); CT= curing time (day); P₂₀₀= percentage passing through the No. 200 (75 µm) sieve; and OMC= optimum moisture content (%).

Figures 5(a) and 5(b) show the performance of the MARS model in the prediction of the UCS of the training and testing sets. As can be seen, the values ​​of R² is 0.9744 and 0.9727 in case of training and testing sets, respectively. Also, with regard to the error range shown in the figures, it can be seen that the MARS model allows for prediction of UCS with an error of less than 10%. Table 7 indicates the value of the statistical parameters of the MARS model.

In order to compare MARS results with results of artificial neural network (ANN), the MATLAB neural network toolbox was used for implementation of ANN. The testing set (30% of total data) was assumed same as MARS and training set (60% of total data) and cross validating set (10% of total data) were selected randomly from the training set of MARS. Before running the ANN method in MATLAB, the data were normalized between 0 and 1. With the aim of preventing the negative effects of random allocation of initial weights and biases on the performance of the trained ANN, a code was developed in MATLAB. This code actually handles the trial and error process automatically to determine the optimum architecture of ANN. After the evaluation of neurons of hidden layer by program, the best ANN architecture with the minimum RMSE was chosen. The Levenberg-Marquardt algorithm was used to train the neural network.

Optimization of ANN architecture showed that the optimum architecture of ANN is 5-8-1, where 5 is the number of inputs, 8 is the number of neurons in hidden layer and 1 is the number of outputs. Also the hyperbolic tangent sigmoid transfer function (tansig) in hidden layer and linear transfer function (Purelin) in output layer was used.

Results of modeling using ANN showed that the coefficient of determination (R²) between observed and predicted values of UCS for training, cross validating and testing sets is 0.992, 9135, and 0.938, respectively. In general, it is observed that the accuracy of ANN method with respect to training set is higher than MARS method but MARS shows superior performance in case of testing set. This result confirms that the modeling using ANN is very sensitive for over fitting (high accuracy in case of training set and low accuracy in case of testing set). In contrast, MARS method has higher generalization capability because it gives almost same coefficient of determination (R²) values in case of both training and testing sets.

Importance degree of different parameters

Cosine amplitude method (CAM), variance-based methods, Fourier amplitude sensitivity test (FAST), Extended Fourier amplitude sensitivity test (EFAST) are some methods which can be used for sensitivity analysis and to determine the importance degree of different parameters on the UCS [²⁸–³²,⁵²], in this research CAM was employed. In CAM method, all of data pairs are expressed in the common X-space. They can be considered as a data array X defined as Eq. (10) [⁵³].

(10)X=\{x_{\mathrm{1}},x_{\mathrm{2}},x_{\mathrm{3}},\mathrm{...},x_n\},

where x_i is a vector with length of m which is shown as follows:

(11)x_i=\{{x_i}_{\mathrm{1}},x_{i\mathrm{2}},x_{i\mathrm{3}},\mathrm{...},x_{im}\}.

Equation (12) can be used to compute the strength of the relationship between xi and xj:

(12)R_{ij}={\displaystyle \frac{{\displaystyle \sum _{k=\mathrm{1}}^m{x}_{ik}{x}_{jk}}}{\sqrt{{\displaystyle \sum _{k=\mathrm{1}}^m{x^2}_{ik}}{\displaystyle \sum _{k=\mathrm{1}}^m{x^2}_{jk}}}}}.

The higher value of R_ij shows the greater the relationship between a specific input parameter and the model output.

Figure 6 shows the importance of each of the parameters on the UCS of the cement stabilized base contain RAP. This sensitivity analysis was carried out based on a set of 64 experimental data in this study. Regarding Fig. 6, it can be seen that in the range of data evaluated in this paper, the percentage of cement, OMC and also the percent passing #200 sieve have the highest impact and the parameter of the RAP content has the least impact on UCS.

Effect of error in measuring of input variables on the UCS

The effect of the error of measurement of input parameters on the predicted UCS using the MARS model is shown in Fig. 7. For this purpose, the UCS of each specimen was predicted by taking into account the error rate of the input parameters in the range of −10% to 10% and the other parameters being kept constant by the MARS model. Then, according to the measured and predicted values, the MAPE data were calculated according to Equation (8). As evidence, the UCS of FDR layer strongly reacts to the changes in the error rate of the OMC measurement and results shows much higher MAPE than other parameters. For example, a 10% error in measuring the OMC in the laboratory will result in an error of about 25.5432% in predicting UCS, which indicates the importance of the accuracy of measuring this parameter in laboratory studies. In addition, it is observed that the error in measuring the curing time has the least effect on the accuracy of prediction of UCS. For example, measuring the curing time with a 10% error would cause an average error of 3.4084% (MAPE= 3%) in predicting compressive strength.

Parametric study of MARS model

Time constraints and lack of sufficient facilities are usually the main obstacle to laboratory studies. In most cases, the study of the effect of each variable on the test results in a wide range of domains requires the production of large samples and it takes long time. Among the advantages of making predictive models, it is possible to use these models to perform parametric studies and to examine the effect of each input variable on the output of the model.

In this research, based on the MARS model, the effect of changes in the percentage of RAP, percentage of cement, OMC, percent passing #200 sieve, and curing time were studied on the UCS of the base stabilized RAP. For this purpose, each of the variables in the minimum and maximum range presented in Tables 5 and 6 have been changed. In cases where one of the variables was required to be kept constant, the average value calculated for that variable was used (rap, cement, OMC, and the percent passing #200 sieve was 30, 4.5, 6.3, and 9.5, respectively). In addition, the standard curing time was considered 28 days.

Effect of OMC

OMC is required to achieve maximum compaction in the process of mixing in FDR method. Past research has shown that adding water to less or more than OMC reduces UCS [⁵⁴]. On the other hand, according to previous studies, increasing the amount of cement could increase the UCS of the mixture of stabilized soil-RAP [⁶,¹³,¹⁷,⁵⁵]. As shown in Fig. 8, the UCS value decreases by increasing the OMC, in particular from a given value. In other words, it can be seen that with increasing MC at first there is no significant change in UCS, but after increasing the optimum moisture from a given value, the UCS begins to sharply decrease.

Effect of RAP

According to previous studies, increasing the amount of RAP in a stabilized mixture decreases UCS [1⁵,⁵⁵]. This is also shown in the parametric analysis performed on the MARS model (Fig. 9). As shown in Fig. 9, the slope of the UCS with the increase of the RAP for different cement percentages is the same. This research shows that there is no significant change in UCS with increasing RAP amounts from 0% to 20%, while with increasing RAP to the values more than 20%, the UCS decreases dramatically.

Effect of curing time

Overall, previous researches have shown that increasing curing time will increase UCS [⁶,¹²,¹³,¹⁵–¹⁷]. This is also visible in Fig. 10. As shown in Fig. 10, the slope of the UCS is equal to the various RAP proportions.

Effect of percent passing #200 sieve

One of the parameters affecting UCS is the percent passing #200 sieve. As shown in Fig. 11, results of this study show that for 0% and 20% of the RAP, the increase in the percent passing #200 sieve leads to an increase in the UCS at a constant rate. However, for a proportion of 40% and 60% of the RAP, an increase in the percent passing #200 sieve leads to a decrease in the UCS. This confirms that at the higher RAP content, the percent passing #200 sieve has a diverse effect on the UCS. Contrary in case of lower RAP content, the percent passing #200 sieve has a positive effect on the UCS.

Conclusions

The results of this research can be summarized as follows:

1) The addition of cement, improves greatly the soil strength of cement stabilized base layer. For the cement contents studied here, UCS is increased by adding cement or decreasing RAP.

2) This study shows that the error bias of MARS model for predicting UCS is less than 10%, and also the values ​​of R² based on training and testing sets is 0.9744 and 0.9727, respectively.

3) Modeling of UCS using ANN method showed that R² between observed and predicted values of UCS for training, cross validating and testing sets is 0.9920, 9135, and 0.9380, respectively. This result confirms that the MARS method has higher generalization capability because it gives almost same R² values (about 0.97) in case of both training and testing sets.

4) The MARS model, defined by percentage of RAP, percentage of cement, OMC, percent passing #200 sieve and curing time has been shown to be a more appropriate model to evaluate the UCS of soil-RAP blend stabilized with Portland cement.

5) Parametric analysis using CAM shows that the percentage of cement, OMC and percent passing #200 seive are the most influencing factors on the UCS and RAP content is the least.

6) Investigating the effect of the error rate on the input parameters indicates that the FDR layer is highly sensitive to variations in the error rate of OMC.

7) This research shows that there is no significant change in UCS with increasing RAP amounts from 0% to 20%, while with increasing RAP to the values more than 20%, the UCS decreases dramatically.

8) Investigating the effect of each of the input parameters on the UCS shows that increasing the OMC and the RAP, decreases UCS and increasing curing time and cement increases UCS. The effect of the percent passing #200 sieve shows that for a RAP percentage of 0 and 20, the increase in the percentage of percent passing #200 sieve leads to increase UCS and for a RAP percentage of 40 and 60, the increase in the percent passing #200 sieve results in decreasing the UCS.

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