Analysis of ground surface settlement in anisotropic clays using extreme gradient boosting and random forest regression models

Runhong Zhang, Yongqin Li, Anthony T.C. Goh, Wengang Zhang,e, Zhixiong Chen

a Institute for Smart City of Chongqing University in Liyang, Chongqing University, Liyang, 213300, China

b Colloge of Aerospace Engineering, Chongqing University, Chongqing, 400045, China

c School of Civil Engineering, Chongqing University, Chongqing, 400045, China

d School of Civil and Environmental Engineering, Nanyang Technological University, 639798, Singapore

e Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing, 400045, China

Keywords:Anisotropic clay Numerical analysis Ground surface settlement Ensemble learning

ABSTRACT Excessive ground surface settlement induced by pit excavation (i.e. braced excavation) can potentially result in damage to the nearby buildings and facilities. In this paper, extensive finite element analyses have been carried out to evaluate the effects of various structural, soil and geometric properties on the maximum ground surface settlement induced by braced excavation in anisotropic clays. The anisotropic soil properties considered include the plane strain shear strength ratio (i.e. the ratio of the passive undrained shear strength to the active one) and the unloading shear modulus ratio. Other parameters considered include the support system stiffness, the excavation width to excavation depth ratio,and the wall penetration depth to excavation depth ratio.Subsequently,the maximum ground surface settlement of a total of 1479 hypothetical cases were analyzed by various machine learning algorithms including the ensemble learning methods (extreme gradient boosting (XGBoost) and random forest regression (RFR)algorithms). The prediction models developed by the XGBoost and RFR are compared with that of two conventional regression methods, and the predictive accuracy of these models are assessed. This study aims to highlight the technical feasibility and applicability of advanced ensemble learning methods in geotechnical engineering practice.

1. Introduction

A major concern in the design and construction of underground basement structures in a built-up environment is the potential damage to nearby buildings from excessive ground settlement due to stress-relief from pit excavation (i.e. braced excavation) activities.In most braced excavation studies in clay deposits,the clay is assumed to be isotropic.For anisotropic clays,this can be critical as the principal stress rotation changes resulting from the soil excavation may result in the clays exhibiting excessive unloading,compared to the isotropic cases. A detailed study by Hansen and Clough (1981) found that the clay anisotropy can result in a reduction in the basal heave factor of safety and an increase in the wall and ground movements.The evaluation of basal heave stability of anisotropic clays was also considered by Hsieh et al.(2008)and Kong et al. (2012). Brosse (2012) studied the stiffness and shear strength anisotropy of Oxford clay,Kimmeridge clay and Gault clay by carrying out hollow cylinder apparatus (HCA) tests, and the effects of the orientation of the major principal stress (α) on the stiffness and strength properties were thoroughly investigated.Andresen (2002) studied the capacity of anisotropic and strainsoftening clay and proposed a simplified constitutive soil model.Analysis by Teng et al. (2014) for an excavation in Taipei silty clay indicated that the wall and ground movements were 10%-43%larger when soil anisotropy was considered.

In this study,the effects of clay anisotropy on the ground surface settlements for braced excavations were systematically considered using the finite element software PLAXIS2D (Brinkgreve et al.,2017). The NGI-ADP constitutive model (Andresen and Jostad,2002; Grimstad et al., 2012) used in this study is based on the ADP (active-direct shear-passive) concept of Bjerrum (1973). This constitutive soil model has been used by various researchers such as D’Ignazio et al. (2017) and Zhang et al. (2021a, b, c) to evaluate the effects of clay anisotropy on the performance of geotechnical structures.

In recent years, artificial intelligence (AI) algorithms have been used in underground geotechnical applications as prediction models, as they have been shown to be efficient and reliable tools for solving complex geotechnical engineering problems.Leu and Lo(2004)adopted an artificial neural network(ANN)model to predict the excavation-induced ground surface settlement. In the case of the prediction of ground settlement from shield tunneling, promising results were obtained by Suwansawat and Einstein (2006)using the ANN model, by Chen et al. (2019) using a number of ANN algorithms, and by Goh et al. (2018) using multivariate adaptive regression splines (MARS). However, the ensemble learning algorithms such as extreme gradient boosting (XGBoost)and random forest regression (RFR) have not been widely used in geotechnical engineering, even though their good predictive capabilities have been demonstrated by various researchers. For example, Zhou et al. (2017) used the RFR approach for the prediction of ground settlements induced by the construction of a shielddriven tunnel. Zhang et al. (2020a) adopted XGBoost and three other models to predict the surface settlement induced by earth pressure balance shield tunneling.Xie and Peng(2019)utilized the random forest (RF) model for estimating the tunnel excavation damaged zones(EDZs),and the results indicated that the RF model has a good prediction capability.

2. Finite element analyses

2.1. Model description

The ground surface settlement behind a retaining wall is induced by stress-relief from excavation of soil in front of the wall.This settlement is generally affected by various factors such as the excavation geometry, the supporting system (i.e. wall bending stiffness, wall penetration depth, strut spacing and strut stiffness)and the ground conditions (i.e. soil properties). To ascertain the effect of these factors on the ground surface settlement,a series of parametric studies was conducted using finite element modeling to examine the possible effects of the various soil and geometric properties.

The plane strain finite element software PLAXIS2D (Brinkgreve et al., 2017) was adopted in this study. Linear elastic beam and bar elements were used to model the wall and the struts, respectively, while the soils were modeled using 15-noded triangular elements.Fig.1 shows the schematic cross-section of the excavation,and half of the excavation is considered due to symmetry. The left and right boundaries of the finite element model are assumed to be fixed horizontally but free to move vertically, while the bottom boundary is assumed to be fixed both horizontally and vertically.The boundary at the extreme right is located far enough away from the wall(five times the excavation width B)so as to avoid possible influence of the boundary conditions on the excavation response.

Fig.1. Soil and wall profile and typical finite element mesh.

As illustrated in Fig.1, underlying the thick deposit of soft clay deposit layer is a layer of stiff clay.The excavation width B is 20 m,the final excavation depth Heis 10 m, and the wall penetration depth D is either 5 m,10 m or 15 m.

The wall and strut properties and ranges considered for the finite element analyses are shown in Table 2.The struts are installed with a vertical spacing of 2 m and horizontal spacing of 4 m, with the first strut at a depth of 1 m below the original ground surface.The strut stiffness EA is assumed as 6.1×105kN/m,and the elastic modulus Econcof the diaphragm wall is 2.8 × 107kPa.

Table 1 Summary of soil properties.

Table 2 Summary of wall and strut properties.

2.2. Results and analyses

2.2.1. Influence of soil properties

2.2.2. Influence of wall system stiffness lnS

Fig.2. Influence of on δv-max(B/He = 2, D/He =1.5,γ = 16 kN/m3,lnS = 10.13, Gur/= 900).

Fig. 3. Influence of Gur/ on δv-max (B/He = 2, D/He = 1.5, γ = 16 kN/m3, lnS = 4.76, = 50 kPa).

Fig. 4. Influence of γ on δv-max (B/He = 2, D/He = 1.5, lnS = 4.76, = 50 kPa,Gur/ = 900).

Fig. 5. Influence of lnS on δv-max (B/He = 2, D/He = 1, γ = 18 kN/m3, = 60 kPa,Gur/= 900).

Fig.6. Influence of D/He on δv-max(B/He=2,γ=16 kN/m3,lnS=10.13,=50 kPa,Gur/=900).

2.2.3. Influence of excavation geometries (B/Heand D/He)

Fig. 6 shows that the normalized penetration depth D/Hehas a marginal influence on the δv-max. In the previous study by Zhang et al. (2021a), it was found that the penetration depth D has minimal influence on the lateral wall deflections. Consequently, the effect on the δv-maxis also marginal. The normalized excavation width B/Hehas a significant influence on the δv-max, as shown in Fig. 7, with δv-maxdecreasing with the decrease of B/He.

3. Estimation models for δv-max

This section presents a brief introduction of three surrogate models, as well as the prediction results using the XGBoost, RFR,DTR, and PR methods. The feasibility of the XGBoost and RFR models is discussed and the accuracy of the four methods is also compared.

3.1. DTR

DTR(Quinlan,1993)is a nonlinear supervised machine learning model with strong interpretability that is able to summarize decision rules from data sets. The DTR is easy to understand and explain, and able to process large data and categories at the same time in a relatively short time. It is easy to deduce the corresponding logical expression based on a given observation model.It is also suitable for processing samples with missing attribute values.However, for those data with inconsistent amounts of data in each category, the gained results are biased towards those features with more data,which may lead to overfitting and ignore the correlation between the features in the data set.

Fig.7. Influence of B/He on δv-max(D/He=1,γ=16 kN/m3,lnS=8.06, =50 kPa,Gur/=900).

3.2. XGBoost

XGBoost proposed by Chen and Guestrin (2016) is a fully enhanced version of the gradient boosting method. The objective function retains the quadratic term of Taylor’s expansion. The complexity of the tree in the XGBoost algorithm consists of two parts;one is the total number of leaf nodes,and the other is the L2 regularization term of the leaf node score.The L2 smoothing term is added to the score of each leaf node to prevent overfitting.The basic element is classification and regression tree(CART)(Breiman et al.,1984). In the training process, the initial CARTs are generated, the exact greedy algorithm is used to obtain the best split point to find an optimal structure of the tree and then new CARTs are developed based on the former CARTs.XGBoost adds a regularization term to the cost function to control the complexity of the model. The regularization term contains the number of leaf nodes of the tree and the square sum of the L2 modulus of the score output on each leaf node. From the perspective of bias-variance tradeoff, the regularization term reduces the model variance, resulting in a simpler learned model and prevents overfitting.Hence,XGBoost is superior to the traditional gradient boost decision tree (GBDT) method.More details are referred to Chen and Guestrin(2016),Wang et al.(2020), and Zhang et al. (2020a, b, c).

3.3. RFR

RFR refers to an algorithm that integrates multiple trees through the idea of ensemble learning (Breiman, 2001; Cutler et al., 2011).Its basic unit is a decision tree, and it basically is an ensemble learning method, which is a branch of machine learning. RFR consists of multiple CARTs which are trained by randomly selected data and randomly combined feature types.For the training of each CART,some data will be used repeatedly in the training of different CARTs(Zhang et al.,2019).It runs efficiently on large databases,and can handle thousands of input variables without variable deletion.It is particularly useful in estimation, inference, and mapping, so that there is no need to debug many parameters compared with the support vector machine (SVM)method.

3.4. Assessment of XGBoost and RFR models

Fig.9 shows the comparison of the training and testing results of the δv-maxpredictions by DTR, PR, XGBoost and RFR, respectively.The coefficient of determination R2of the four methods are also shown in the plots. The XGBoost and RFR models were found to outperform the DTR and PR models.As shown in the plots,the data are non-uniformly distributed, with the predictions for δv-maxbelow 200 mm showing less scatter compared with the settlement predictions that exceed 200 mm. The PR model gives fairly reasonable predictions for δv-maxless than 200 mm but significantly underestimates the settlement for δv-maxexceeding 200 mm. The XGBoost and RFR models perform better in processing the sparse data (i.e. for δv-maxexceeding 200 mm) compared to the conventional PR and DTR methods.From Fig.9,it is obvious that the data points produced by the RFR and XGBoost models fit well with the reference line, indicating the capability of these two algorithms to predict the maximum vertical displacement, especially for the larger values.

Fig. 8. Spearman’s rank correlation coefficient for parameters.

Compared with the conventional PR model, both the XGBoost and RFR models give better predictions, with the XGBoost performing marginally better than the RFR model, and the RFR performs slightly better than the DTR model. The difference is insignificant in this study as the data are based on hypothetical finite element analyses, which shows less noise. For actual field applications with instrumented results, the use of ensemble learning is expected to outperform the conventional PR method.As a reliable tree-based tool, XGBoost and RFR methods can reach a balance between the predictive accuracy and robustness.

The performance indicators of the various models are shown in Table 3. The performance indicators are the mean square error(MSE), the root mean square error (RMSE), the maximum average error (MAE), and the coefficient of determination (R2). Based on Table 3,from the performance indicators of the training and testing data,it can be concluded that the best predictive model is XGBoost,followed by the RF algorithm.

3.5. Feature importance analysis

Fig. 9. Comparison of predicted and calculated results: (a) Training and (b) Testing.

4. Discussion

In this study, the data used for machine learning are obtained from numerical calculation, assuming idealized wall, geometrical and ground conditions. This study only discussed some particular cases with the geometries as shown in Fig.1 and parameters in the ranges as shown in Tables 1 and 2 Only clays with constant undrained shear strength were considered. For clays with undrained shear strength increasing linearly with depth, the study by Goh et al. (2019) has indicated that the use of the average undrained shear strength can lead to satisfactory estimations of the ground settlement. Furthermore, due to the limitation of the soilconstitutive model NGI-ADP that has been adopted in this finite element study, only the undrained ground surface settlement is considered.The ground surface settlement caused by groundwater drawdown has not been considered in this study.

Table 3 Performance indicators of models.

Fig.10. Feature importance.

5. Concluding remarks

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 52078086 and 51778092), and Program of Distinguished Young Scholars, Natural Science Foundation of Chongqing, China (Grant No. cstc2020jcyj-jq0087). The financial support is gratefully acknowledged.