Comparative Study of Hybrid Artificial Intelligence Approaches for Predicting Peak Shear Strength Along Soil-Geocomposite Drainage Layer Interfaces

Geocomposite Drainage Layers (GDL) are increasingly applied in extensive geotechnical and geoenvironmental applications [1‐3]. GDLs can replace the need for graded sand and gravel to effectively drain excess water and reduce pore water pressure, improving the stability of engineering projects [4]. Particularly for GDLs utilised in the capping and lining systems of landfills, they can also provide separation and reinforcement functions and perform as a capillary break to prevent the migration of contaminated water and gas produced from the waste [5]. In practical engineering, GDLs are commonly installed underneath cover soil above containment facilities, and the interface shear strength between GDL and cover soil governs the stability of the system [6].

Previously, many series of laboratory tests have been conducted to determine the shear strength along soil-GDL interfaces [7‐11]. However, soil-GDL interface testing is expensive and time-consuming. Also significantly, in real engineering projects, the specific materials to be used on site are usually selected well after the design stage. This allows a better pre-estimate of interface shear strength before the specific materials are determined.

Accurate forecasting models that can evaluate the shear strength of soil-GDL interfaces can substantially overcome many of the existing challenges. Due to the complex mechanism of soil-GDL interaction and the multiple influence variables of the shear strength along soil-GDL interfaces, it is difficult for the simplified empirical models established by adopting traditional statistical methods to adequately present the complicated non-linear relationship between the variables that influence the interface shear strength. This has driven the search for reliable methods with high accuracy to forecast the shear strength of soil-GDL interfaces.

With the advance of computer science, the machine learning-based approach has attracted considerable scientific attention and has been extensively adopted in geotechnical engineering to model complex non-linear relationship between multi-inputs and outputs [12‐16]. Pham et al. [17] applied Particle Swarm Optimisation (PSO) -Adaptive Network based Fuzzy Inference System (PANFIS), Genetic Algorithm (GA)—Adaptive Network based Fuzzy Inference System (GANFIS), Support Vector Regression (SVR), and Artificial Neural Networks (ANN), to predict the shear strength of soft soil. Their results show that the forecasting performance of the machine learning algorithms is satisfactory. Qi et al. [18] put forward five machine learning models including logistic regression (LR), multilayer perceptron neural networks (MLPNN), decision tree (DT), gradient boosting machine (GBM), and SVR, optimised by adopting firefly algorithm (FA), to predict the stability of hanging walls, and the research denotes that the estimating accuracy of the models is appreciated. Ceryan et al. [14] compared the performance of ANN, and SVR with different kernel functions in assessing the tensile strength of rock, and concluded that SVR with the least squares kernel function is more powerful in predicting the tensile strength. Overall, based on the aforementioned analysis, machine learning techniques are efficient for describing the non-linear relationship in multi-variable problems.

Compared to other topics in geotechnical engineering, the application of machine learning approaches in evaluating the peak shear strength along soil-geosynthetics interfaces is rare. Debnath and Dey [19] proposed an ANN model to predict the shear strength of cohesive soil-geosynthetics interfaces based on the input parameters: dry density and moisture content of soil, normal stress, adhesion and frictional angle of the soil-geosynthetics interfaces. It is necessary to optimise the algorithms to increase the forecasting precision of machine learning models and conduct comprehensive investigations and compare the applicability for different machine learning algorithms to assess the peak shear strength of soil-GDL interfaces.

In this paper, a comprehensive investigation and comparison of the applicability for five different machine learning models including, Backpropagation Artificial Neural Network (BPANN) and Support Vector Machine (SVM), with hyperparameters optimised by Particle Swarm Optimisation Algorithm (PSO) and Genetic Algorithm (GA), respectively, and Extreme Learning Machine (ELM) optimised by Exhaustive Method, in estimating the peak shear strength of soil-GDL interfaces was conducted. Also, the relative significance of influence factors to the peak shear strength was analysed. After that, an empirical equation for assessing the peak shear strength was proposed to facilitate the peak shear strength prediction for geotechnical engineering personnel with limited knowledge of machine learning technique.

This paper employs three types of machine learning algorithms, namely, BPANN, SVM and ELM. For optimizing the algorithms, PSO and GA have been adopted. Among the various positive aspects of employing these algorithms, three key advantages can be highlighted.

A brief introduction and basic specifications of the employed machine learning and optimisation algorithms are presented below.

All machine learning algorithms have several crucial hyper-parameters that can influence their predictive performance significantly [35]. Thus, optimising the hyper-parameters of machine learning algorithms before conducting training operation is needful. In this research, GA and PSO were employed to optimise the hyperparameters for the established BPANN and SVM models, using Root-Mean-Square Error (RMSE) (Eq. 1) as the fitness function. Previous researchers have demonstrated that GA and PSO are more capable of enhancing the machine learning models’ forecasting accuracy than other intelligence algorithms [36‐38].where, n is the specimen data number, \(y_{i}\) is measured data, \(f_{i}\) is forecasting value.

The detailed procedure of employing GA and PSO to optimise the machine learning models is in the following contents: (1) stochastically produce individuals/particles composed of diverse hyperparameter values (2) calculate the fitness value of the individuals according to fitness function (RMSE) through calling the counter machine learning model (3) conduct corresponding operations on the individuals/particles (4) compute the individual/particle’s fitness value again (5) rerun Step 3 and Step 4 until reaching the predetermined ending conditions (6) take the individual/particle having the smallest RMSE value as the optimal individual/particle, and take the optimal individual/particle’s hyperparameter values as the initial hyperparameter values of the built machine learning models (7) train the machine learning models, and carry out prediction, the specific optimising procedure being presented in Fig. 2, the detailed parameter specifications of GA and PSO as tabulated in Table 1.

In this case, the individuals/particles’ fitness value in GA and PSO was attained by adopting k-fold cross-validation method (k-CV) in hyperparameter optimisation. k-CV is an extensively adopted method to validate the machine learning models, In k-CV, the original data are divided into k equal groups. The training of machine learning models is based on k − 1 groups, while the validating is conducted on the remaining group. The training and validating process is repeated k times with different groups as the testing dataset. The average value of the k times forecasting precision is finally adopted as the performance index [39]. In the paper, the training dataset of the established database was utilised as the original data to conduct the k-CV operation on the machine learning models to obtain the indicator value of predicted accuracy (RMSE), and k was taken as 10 considering the database size and the recommendation in literatures [40]. The optimum values of hyperparameters for the machine learning models and corresponding optimising ranges were listed in Table 2.

In this research, the BPANN model optimised by PSO has been proved as an efficient tool for predicting the peak shear strength of soil-GDL interfaces. However, the application of the developed PSOBPANN model for geotechnical engineering personnel with limited or no knowledge of machine learning techniques is of little use. To solve the problem, an empirical equation for forecasting the peak shear strength of soil-GDL interfaces was proposed based on the connection weights and biases of the PSOBPANN models, as shown in Eq. (8) [53]. The connection weights and biases of the PSOBPANN model are tabulated in Table 5. where, \(Y_{n}\) is the normalised predictive values, ranging from − 1 to 1; \(b_{0}\) is the biases of output layer joint; \(w_{k}\) is the connection weights between the kth hidden layer joint and the output layer joint; \(b_{hk}\) is the biases of the kth hidden layer joint; h is the hidden layer joint number; \(w_{ik}\) is the connection weights between the ith input layer joint and kth hidden layer joint; \(X_{i}\) is the ith normalised input parameter, ranging from − 1 to 1; \(f_{sig}\) is Hyperbolic Tangent Sigmoid Transfer Function.

After calculation, the empirical equation for assessing the peak shear strength of soil-GDL interfaces was gained, as expressed in Eq. (9).where, \(Y_{\max }\) and \(Y_{\min }\) are the maximum and minimum values of the peak shear strength in the database, respectively, \(Y_{\max } = 20.14\;{\text{kPa}}\) and \(Y_{\min } = 0.5\;{\text{kPa}}\).

Among Eq. (9):

Among Eq. (10):where, \(g_{i}\) is the connection weight between the ith hidden layer joint and the output layer joint for the established PSOBPANN model, as listed in Table 5.

Among Eq. (11):where, \(h_{i}\) is the bias of the jth hidden layer joint for the established PSOBPANN model, as listed in Table 5; \(p_{j}\) is the connection weight between the jth input layer joint and ith hidden layer joint for the established PSOBPANN model, as listed in Table 5; \(N_{j}\) is the ith normalised input parameter.

To facilitate the practitioners and future researchers to utilise the developed empirical equation (Eq. 8) to predict the peak shear strength of soil-GDL interfaces, a case study is conducted in this session to use Eq. (8) to assess the peak shear strength of clayey soil-GDL interfaces based on a numerical example with real values, and then the predictive peak shear strength of interfaces is compared with the peak shear strength that is measured in laboratory tests to validate the predictive accuracy of the developed empirical equation. The basic properties of the adopted soil-GDL interface and the corresponding input parameter value of the machine learning models are presented in Table 6.

The detailed procedure of using the developed empirical equation (Eq. 8) to predict the peak shear strength of soil-GDL interfaces is following: firstly, the corresponding input parameter values of the interface in Table 6 are normalised by Eq. (2). Secondly, the normalised input parameter values are substituted into Eq. (12) to calculate the values of Ai (i = 1, …, 9), with combining the values of h_i (i = 1, …, 9) and p_j (j = 1, …, 9) in Table 5, respectively. Thirdly, the obtained values of A_i (i = 1, …, 9) are substituted into Eq. (11) to calculate the value of C₁, with combining the values of g_i (i = 1, …, 9) in Table 5. Fourthly, the obtained value of C₁ is substituted into Eq. (10) to calculate the value of Y_n. Finally, the obtained value of Y_n is substituted into Eq. (9) to be renormalised to obtain the value of \(\tau\) that is the predictive peak shear strength of the interface. The predictive peak shear strength of the interface using the developed empirical equation and the measured peak shear strength in laboratory tests is drawn in Fig. 14.

Based on Fig. 14, the predicted peak shear strength of the interface is close to the measured peak shear strength by laboratory tests. This indicates that the developed empirical equation (Eq. 8) has high accuracy to predict the peak shear strength of soil-GDL interfaces. It provides convenience for geotechnical engineering personnel with limited knowledge of machine learning technique to forecast the peak shear strength of soil-GDL interfaces.

According to the sensitivity analysis results, normal stress has the largest influence on the peak shear strength of soil-GDL interfaces. This fact conforms to the findings highlighted by the previous studies [54‐56]. Furthermore, drainage core type (continuous drainage core or drainage core with cut-outs) and moisture saturation affect the peak shear strength as the second and third most influencing factors. As shown in Fig. 15, the interlocking effects between the grooves in geogrid core and soil, leading in superior frictional performance, would have resulted in the higher peak shear strength between soil-GDL with drainage core with cut-outs than that of GDL with continuous drainage core. In terms of the moisture saturation, the large impact of moisture saturation on the peak shear strength of soil-GDL interfaces agrees with the findings from Othman [6].

Shearing surface (flat side or dimple side), soil type (clay, sand and gravel), and consolidation condition are demonstrated to have moderate influence on the peak shear strength. The difference of shear strength for the interfaces between geosynthetics and different types of soil has been reported by many scholars due to the diverse basic properties of soil, including particle shape/angularity, mean grain size, hardness, etc. [44, 57, 58]. In terms of the shearing surface, when the dimple side of GDL is adopted as the shearing surface, the interlocking effects between soil and the dimple drainage core can provide larger shear resistance, leading to higher peak shear strength along the interfaces than that of flat side. The magnitude of interlocking effects enhances with the rise of compaction effort during soil placement, normal stress and moisture saturation, the detailed interaction mechanism between soil and GDL as shown in Fig. 16. In this research, a majority of tests were conducted on soil with low to medium moisture saturation (0%–50%) under low normal stress (less than 60 kPa), and the compaction efforts during soil placement was light, as shown in Fig. 5, with a medium interlocking effect between soil and drainage core. Therefore, the relative importance of shearing surface to the shear strength is manifested to be moderate. In the aspect of consolidation condition, previous studies have indicated that consolidation can increase the shear strength of cohesive soil-geosynthetics interfaces evidently [59, 60]. However, in this research, the tests on cohesive soil-GDL interfaces only account for about 40% of the total tests, as shown in Fig. 5, and other tests were performed on sand and gravel-GDL interfaces. The influence of consolidation condition on the shear strength of sand/gravel-GDL interfaces is not very high. Hence, the relative importance of consolidation condition to the shear strength is indicated as being not very significant.

The variations of input parameters including: geotextile specification (bonding geotextile on both sides or only on the dimple side), soil density, and drainage core thickness are not shown to be vital to the peak shear strength. For the geotextile specification, in the compiled tests, the GDL was clamped firmly on the lower shear box of the direct shear apparatus. When the dimple side was adopted as the shearing surface, the bonded geotextile on the flat side has negligible influence on the shear strength, while when the flat side was chosen as the shearing surface, the bonded geotextile can provide larger friction force, resulting in the higher peak shear strength than that of GDL only bonded geotextile on the dimple side. However, in this research, a large proportion of compiled tests (80%) were conducted on the interfaces between soil and the dimple side of GDL, as shown in Fig. 5, thus, the relative importance of geotextile specification to the shear strength is demonstrated to be low. In terms of soil density, according to the existing research, the peak shear strength of the interfaces is mobilised from two components: the skin friction and the interlocking effects between soil and geosynthetics [44]. The effects of soil density on the interlocking effects are relatively large but on the skin friction is non-obvious [61]. In this research, based on Fig. 5, most of tests were carried out under low normal stress, and the interlocking effects between soil and GDL are not the dominant factor for generating shear resistance, as illustrated in Fig. 16. Thus, the variation of soil density is manifested to have less influence on the peak shear strength. In the aspect of drainage core thickness, the influence of its changes on the peak shear strength is the least among the input parameters. This is because, in this case, the variation in the thickness of drainage core does not change the dimension of the cuspate elements on the drainage core, which has marginal influences on the interlocking effects and skin friction between soil and GDL, contributing less to the change of the peak shear strength.

The predictive precision and reliability of the established machine learning models can be improved further when a larger database is available, whilst some larger databases of geosynthetics tests exist the data is often incomplete making the application of machine learning impossible [62‐66]. Secondly, there may some other influence variables for the peak shear strength of soil-GDL interfaces which were ignored during the compilation of database for modelling, such as mean grain size of soil, etc. In the future, it is worthy to adopt more influencing variables to conduct machine learning modelling, which may enhance the predictive ability of the machine learning models. Thirdly, the value ranges of some adopted input parameters, such as normal stress, moisture saturation of soil, etc., are small, thus, an attempt to expand the value ranges of some input parameters can further increase the generalisation ability of the established machine learning models and have a better understanding about the relative importance of the influence variables to the peak shear strength.

In this paper, based on the compiled database, an investigation and comparison of the applicability for five different machine learning models including, BPANN and SVM, with hyperparameters optimised by PSO and GA, respectively, and ELM optimised by Exhaustive Method, in predicting the peak shear strength of soil-GDL interfaces was conducted. Also, the sensitivity analysis was conducted to assess the relative significance of influence variables based on the PSOBPANN model with the optimal estimating performance among the forecasting models, and corresponding mechanism analysis was performed. Moreover, to facilitate the forecasting of the peak shear strength for geotechnical engineering personnel, an empirical equation for assessing the peak shear strength based on the PSOBPANN model was proposed. Based on the results and discussion presented earlier, the following major conclusions can be made: