Prediction and Stability Assessment of Soft Foundation Settlement of the Fishbone-Shaped Dike Near the Estuary of the Yangtze River Using Machine Learning Methods

Abstract

Fishbone-shaped dikes are always built on the soft soil submerged in the water, and the soft foundation settlement plays a key role in the stability of these dikes. In this paper, a novel and simple approach was proposed to predict the soft foundation settlement of fishbone dikes by using the extreme learning machine. The extreme learning machine is a single-hidden-layer feedforward network with high regression and classification prediction accuracy. The data-driven settlement prediction models were built based on a small training sample size with a fast learning speed. The simulation results showed that the proposed methods had good prediction performances by facilitating comparisons of the measured data and the predicted data. Furthermore, the final settlement of the dike was predicted by using the models, and the stability of the soft foundation of the fishbone-shaped dikes was assessed based on the simulation results of the proposed model. The findings in this paper suggested that the extreme learning machine method could be an effective tool for the soft foundation settlement prediction and assessment of the fishbone-shaped dikes.

1. Introduction

The fishbone-shaped dikes are a series of dikes that are placed similar to a fishbone in the channel of the Yangtze River. They are built to protect the beach from erosion and increase the water-depth of the channel. This type of beach is in the middle of the channel, which is susceptible to erosion by the currents. As these dikes are placed like a fishbone on the head of the beach, they can divide the water flow and protect the beach from erosion efficiently. As for the fishbone-shaped dikes built near the estuary of the Yangtze River, they were submerged and constructed with stones thrown from the ships, meaning the water-depth from the top of these dikes to the water surface could be 10 m or more. These dikes are attacked by both the wave and the current flows, and the hydrodynamics characteristics of this area are complex. Meanwhile, the unsteady and unpredicted sediments erosion occurs near these dike toes under the combined action of waves and currents [1]; furthermore, the strength of the dike foundation could be weakened by the wave loading [2]; as a consequence, the running condition of these fishbone-shaped dikes should be assessed in a timely manner in order to repair these dikes before their damage. The stability of the foundation of the fishbone-shaped dikes plays a key role in the running condition of these dikes, while most of these fishbone-shaped dikes were built on the soft soil, which has high compressibility and low resistance [3,4], which indicated that the foundation of the dikes was not stable enough, especially during the construction process. As a consequence, the settlement of the fishbone-shaped dike built on the soft-foundation should be monitored and predicted during its running time, in order to clarify the stability of the foundation and these dikes.

A survey of previous studies shows that a lot of research on the settlement monitoring and prediction of the soft foundation has been carried out. The three-points method, Asaoka’s method, and the hyperbola method are the most widely used methods to predict the settlement based on the measured settlement in the field. For example, the settlement of a sea dike project was observed by Zhang and Zheng [3], and the settlement curve was analyzed by using the empirical logarithmic curve and hyperbola method to assess the stability of the sea dike foundation. In fact, since the settlement results predicted by different methods are not exactly the same, the researcher needs to decide which one to choose. In addition to these measured-data-based methods, some more complex methods were proposed. A Pareto multi-objective optimization-based back analysis method for consolidation settlement was developed to predict a highway trial embankment settlement [5], and the result demonstrated the feasibility of this method. These two methods can be perceived to be similar to the method of data fitting, which has a good performance for previous and known data prediction but has a relatively weak ability to predict future trends. The elastoplastic finite element method (FEM) incorporating the SYS Cam-clay model was proposed to simulate the settlement of a reservoir dike, which is used to predict the settlement based on a 2D simulation model [6]; these models show good performance for predicting a settlement by comparing the measured and predicted data. These methods require many input parameters, and the model establishment procedure is very complex, which indicates the inconvenience of applying these methods for this project.

In recent years, machine learning approaches have been widely used for regression [7,8,9,10] and classification [11,12] in water engineering, such as scour depth prediction [13], riprap stone size prediction [14], and rivers dispersion coefficient prediction [15]; these approaches were also applied to predict the settlement of the soft foundation, and a list of these approaches is shown in

Table 1. The prediction methods referred to in this paper.

Researcher	Method	Method Evaluation
Zhang and Zheng [3]	Empirical logarithmic curve and hyperbola method	Low prediction accuracy for future trends
Yafei Zheng et al. [5]	Pareto multi-objective optimization
Toshifumi Shibata [6]	Elasto-plastic FEM	2D settlement process simulation model, complex model building process
Samui [16]	Support Vector Machine	Many input parameters need to be optimized during the learning process
Scott Kirts et al. [17]	Support Vector Machine
Wang, Gou and Qin [18]	Wavelet smooth relevance vector machine
A. Pourtaghi et al. [19]	Artificial Neural Network

. The support vector machine (SVM) was applied to predict the settlement of shallow foundations on cohesionless soils by Samui [16], and the simulation results showed that the SVM could be a practical tool for predicting the settlement of the foundation [17]. A smooth relevance vector machine with a wavelet kernel (wsRVM) was developed and applied by Wang, et al. [18]. to study how ground surface settlements operateWang, Gou and Qin [18]. In addition to the RVM method, the ANN (Artificial Neural Network) method was also applied to predict the ground surface settlement with a proper prediction accuracy [19]. These machine learning methods also require many input parameters in the establishment procedure, and these input parameters need to be optimized during the learning process. In addition, since the size of the training samples, which is the measured settlement values, is small most of the time, a machine learning algorithm is required which has a good generalization performance based on the small sample of training data.

In the present study, we explorer the ability of the extreme learning machine (ELM) for the fishbone-shaped dike settlement prediction. The ELM is a robust machine learning algorithm based on the single-hidden-layer feedforward network (SLFN) [20], which was very simple in the neural network architecture. Previous studies have shown that the ELM could be used in wide areas, such as classification [21,22,23,24] and regression [25,26,27,28], and shows a good generalization performance at extremely fast learning speeds [29] with small-scaled training samples; therefore, the ELM model was proposed to predict the settlement of the fishbone-shape dike based on limited measured data. Compared with other machine learning methods, the ELM model has more neuron networks and a training process with faster learning speed. Meanwhile, compared with other geotechnical methods, the ELM model could predict the time-varying settlement and consolidation with higher prediction accuracy. This is the first study on the application of ELM in fishbone-shaped dike settlement prediction of the soft foundation, and the findings in this study will make a contribution to the fishbone-shaped dike settlement prediction and the stability assessment of the soft foundation based on limited measured settlement samples.

This paper is organized as follows: the in situ monitoring case and the ELM modes establishment procedure are presented in Section 2. In Section 3, the application of the ELM approach for stability assessment of the soft foundation of the fishbone-shaped dike is discussed. The main findings of this paper are summarized in Section 4.

2. Materials and Methods

2.1. The In Situ Monitoring Case

The Manyusha beach protection project is part of the 12.5-m Deep-Water Channel Training Project on the Yangtze River below Nanjing, which is located in the Yangzhong Reach near the estuary of the Yangtze River. Yangzhong Reach is influenced by both the tidal and the current, and the sediments transport is driven by the ebb current. Strongly scour and erosion occurred on the upstream and downstream part of the Manyusha beach in recent years, and the shoal formed near the channel. The unsteady shoal and the shallow water will decrease the channel construction carrying capacity. As a consequence, the channel training project needed to be accomplished in this reach to prevent the unfavorable riverbed evolution.

The submerged fishbone-shaped dikes were built on the Manyusha beach to prevent the beach from erosion, as shown in Figure 1. The dikes were constructed by the stones thrown from the ships. The cross section of the dikes is presented in Figure 2. As presented in Figure 2, the dikes were built on the rib-shape sandbag mattresses, which were used for covering the surface of the beach. The toe of the dike was covered by a layer of stones. The articulated concrete block mattresses (ACB mattresses) were constructed next to the rib-shape sandbag mattresses, as an extra measure to protect the beach and dikes from erosion.

The medium size of the bedload was 0.2 mm, and the medium size of the suspended load was 0.008 mm. The Manyusha beach was formed by sediment deposition. It is revealed by drilling that the soil layers are the quaternary alluvial strata, as shown in Figure 3. The saturated silt and silty clay layers are the typical weak foundation; therefore, the bearing capacity of the beach was not strong enough for the construction foundation of the dikes. Moreover, one aspect worth mentioning is that the dikes were submerged most of the time, and hence the settlement of the soft foundation was not similar to that on the land. The unpredictability of settlement and displacement of the dikes will occur after the construction of the dikes, which would reduce the regulation effect of the dikes. As a consequence, a security system was designed to monitor the settlement of the submerged dike under the tidal and current attack.

Two monitoring points were selected as P1 and P2, as shown in Figure 2. At each point, the same settlement monitoring system was placed; hence, in this paper, only the P1 monitoring system was discussed. The layout of the monitoring system is presented in Figure 3. The settlement sensors were fixed on a stick with a certain distance, and the stick was planted into the riverbed before the dike construction, and then the sensors were fixed into the riverbed at different depths. In this case, the settlement of the soil layers, which were 13.89 m, 18.9 m,13.35 m, and 25.38 m deep, were measured by the sensors. Moreover, 165 days of settlement of this section was monitored by this system, and the result is shown in Figure 4. Most of the construction work of the dikes was completed during the first month of the monitoring time; hence, a rapid settlement occurred during that time. In order to build a machine learning model to predict the settlement of the section and assess the stability of the soft foundation of the dikes, the monitoring time and its measured settlement result were used in the following part, based on the principle of the machine learning algorithm.

2.2. Fundamentals of the Extreme Learning Machine

In this paper, the extreme learning machine model is proposed to learn and predict the settlement of the soft foundation. The extreme learning machine is a single-hidden-layer feedforward network (SLFN) proposed by Huang, Zhu and Siew [20], and this method is particularly useful in regression and classification [31]. In the following subsection, a brief introduction about the fundamentals of extreme learning machine models is given to clarify the process details of the ELM model establishment. More information about ELM models can be found in Huang, Zhu and Siew [20,29], Huang, Huang, Song and You [31].

The goal of the learning process is to find the relationship between input training data sets and output training labels. Considering a single-layer feedforward neural network (SLFN) with n neurons in the input layer, l neurons in the hidden layer, and m neurons in the output layer, the general structure of SLFN could be shown in Figure 5:

The weight $\mathit{w}$ between the neurons in the input layer and the neurons in the hidden layer could be expressed as

$$\mathit{w}={\left[\begin{array}{ccc}{\omega }_{11}& \dots & {\omega }_{1n}\\ ⋮& ⋮& ⋮\\ {\omega }_{l1}& \dots & {\omega }_{ln}\end{array}\right]}_{l\times n},$$

(1)

where ${\mathit{w}}_{\mathit{j}\mathit{i}}$ is the weight between neuron i in the input layer and neuron j in the hidden layer.

Meanwhile, the weight $\mathit{\beta }$ between the neurons in the hidden layer and the neurons in the output layer could be expressed as

$$\mathit{\beta }={\left[\begin{array}{ccc}{\beta }_{11}& \dots & {\beta }_{1m}\\ ⋮& ⋮& ⋮\\ {\beta }_{l1}& \dots & {\beta }_{lm}\end{array}\right]}_{l\times m},$$

(2)

where ${\mathit{\beta }}_{j\mathit{m}}$ is the weight between neuron j in the hidden layer and neuron m in the output layer.

The bias b in the hidden layer is

$$\mathit{b}=\left[\begin{array}{c}\begin{array}{c}{b}_1\\ b_2\end{array}\\ \begin{array}{c}⋮\\ b_l\end{array}\end{array}\right].$$

(3)

For the given training samples Xand the output matrix Y

$$\mathit{X}={\left[\begin{array}{ccc}{x}_{11}& \dots & x_{1Q}\\ ⋮& ⋮& ⋮\\ x_{n1}& \dots & x_{nQ}\end{array}\right]}_{n\times Q}$$

(4)

$$\mathit{Y}={\left[\begin{array}{ccc}{y}_{11}& \dots & y_{1Q}\\ ⋮& ⋮& ⋮\\ y_{m1}& \dots & y_{mQ}\end{array}\right]}_{m\times Q}.$$

(5)

Assuming that the activation function in the hidden layer was g(x), then the SLFN output T is

$$\mathbf{T}=\left[{\mathit{t}}_{\mathbf{1}},{\mathit{t}}_{\mathbf{2}},\dots {\mathit{t}}_Q\right],{\mathit{t}}_{\mathit{j}}=\left[\begin{array}{c}{t}_{1j}\\ ⋮\\ t_{mj}\end{array}\right]=\left[\begin{array}{c}\sum _{i=1}^l{\beta }_{j1}g\left({\mathit{w}}_{\mathit{i}}{\mathit{x}}_{\mathit{j}}+b_i\right)\\ ⋮\\ \sum _{i=1}^l{\beta }_{im}g\left({\mathit{w}}_{\mathit{i}}{\mathit{x}}_{\mathit{j}}+b_i\right)\end{array}\right] (j=1,2,3, \dots , Q) ,$$

(6)

where ${\omega }_i=\left[{\omega }_{i1},{\omega }_{i2},\dots {\omega }_{im},\right]$, $x_j={\left[x_{1j},x_{2j},\dots ,x_{nj}\right]}^T$.

The above equation can be rewritten in the following form:

$$\mathit{H}\mathit{\beta }={\mathit{T}}^{\prime },$$

(7)

where $T^{\prime }$ is the transposed matrix of T, and His the hidden layer output matrix of the neural network, which is as follows:

$$\mathit{H}\left({\mathit{\omega }}_1,{\mathit{\omega }}_2,\dots {\mathit{\omega }}_l,b_1,b_2,\dots b_l,{\mathit{x}}_1,{\mathit{x}}_2,\dots ,{\mathit{x}}_{\mathit{Q}}\right)={\left[\begin{array}{c}\begin{array}{ccc}g\left(w_1,b_1,{\mathit{x}}_{\mathbf{1}}\right)& \dots & g\left(w_l,b_l,{\mathit{x}}_{\mathbf{1}}\right)\end{array}\\ \begin{array}{ccc}& ⋮& \end{array}\\ \begin{array}{ccc}g\left(w_1,b_1,{\mathit{x}}_{\mathit{Q}}\right)& \dots & g\left(w_l,b_l,{\mathit{x}}_{\mathit{Q}}\right)\end{array}\end{array}\right]}_{Q\times l}.$$

(8)

The minimum norm least-squares solution of $\underset{\mathsf{\beta }}{\min }H\beta -T^{\prime }$ is unique, which is

$$\widehat{\mathit{\beta }}={\mathit{H}}^{+}{\mathit{T}}^{\prime },$$

(9)

where ${\mathit{H}}^{+}$ is the Moore–Penrose generalized inverse of the matrix of H.

The difference between the ELM and other traditional neural network algorithms is that the weight w between the neurons in the input layer and the neurons in the hidden layer and the bias b in the hidden layer are randomly selected in the ELM model training process. The unknown weight β between the hidden layer and the output layer could be determined by Equation (9). This simplified training process makes the ELM model many times faster than that of other traditional feedforward learning algorithms [27]. For training an ELM assessment model, only the neuron numbers and the activation function should be given in the former, and this makes the training process more efficient. More details about the ELM theory could be found in the studies of Huang, Zhu and Siew [29] and Huang, Huang, Song and You [31].

The commonly used activation functions are as follows:

Sigmoid function,

$$g\left({\mathit{w}}_{i}x+b_i\right)=\frac{1}{1+\left(exp\left(-{\mathit{w}}_{i}x+b_i\right)\right)};$$

(10)

sin function,

$$g\left({\mathit{w}}_{i}x+b_i\right)=\sin \left({\mathit{w}}_{i}x+b_i\right);$$

(11)

hardlim function,

$$g\left({\mathit{w}}_{i}x+b_i\right)=\{\begin{array}{c}1 {\mathit{w}}_{i}x+b_i\ge 0\\ 2 {\mathit{w}}_{i}x+b_i<0\end{array};$$

(12)

trigonometric basis function,

$$g\left({\mathit{w}}_{i}x+b_i\right)=\{\begin{array}{c}1-\left|{\mathit{w}}_{i}x+b_i\right| -1\le {\mathit{w}}_{i}x+b_i\le 1\\ 0 else\end{array};$$

(13)

and radial basis function,

$$g\left({\mathit{w}}_{i}x+b_i\right)=exp\left(-\frac{\left|\right|\mathit{x}-{\mathit{w}}_{\mathit{i}}\left|\right|{}^2}{b_i^2}\right).$$

(14)

2.3. Establishment of Models

The previous study showed that, in the establishment process of the extreme learning machine models, the selection of the activation functions and the number of hidden neurons had little influence on the prediction accuracy of these models based on the small size of training samples [8]; therefore, in this paper, only the sigmoid function was selected as the activation function to establish the prediction models. The settlement of the 25.38 m-depth layers in the P1 section was investigated in this paper to clarify the feasibility of this approach. During the entire monitoring period, the monitoring interval time was from 4 days to 24 days. As presented in Figure 4, the soft foundation settlement under the stone ballast varies according to a nonlinear function during the monitoring time, and hence a time-based data-driven model was considered to be established to predict the settlement of the soft foundation. To establish a machine learning model, the training samples should be decided at first. The first two input parameters that should be considered are the stones ballast days (T) and the monitoring interval time ($T_{\Delta }$). The daily settlement ($Z_{\Delta }$) in the last monitoring period could be considered an important reference for settlement prediction in the next period, which indicates the settlement varies trend of the last period. Therefore, the stones ballast days (T), the monitoring interval time ($T_{\Delta }$), and the daily settlement ($Z_{\Delta }$) are selected as the input parameters of the ELM models. For training these models, the first 150 days of monitoring results are taken as the input training samples and the output samples, and the measured results of 158 days and 165 days ballast are considered as the verification data. Three different models are established according to the number of the hidden neurons in the hidden layer, named M5 model, M10 model, and M15 model with 5, 10, and 15 hidden nodes in the hidden layers, which are based on the fundamental of this algorithm. The details of each model are shown in

Table 2. The detail of each model.

Model	Inputs	Number of Hidden Neurons	Output	Structure of the Model
M5	$T,T_{\Delta }$,$Z_{\Delta }$	5	Z	3 × 5 × 1
M10	$T,T_{\Delta }$,$Z_{\Delta }$	10	Z	3 × 10 × 1
M15	$T,T_{\Delta }$,$Z_{\Delta }$	15	Z	3 × 15 × 1

, and the model establishment process is shown in Figure 6.

3. Results and Discussion

3.1. Validation and Analysis of the Proposed Machine Learning Approach

The prediction performances of M5, M10, and M15 models for the soft-foundation settlement within 165 days after the construction process were presented in

Table 3. The prediction performances of different models.

Ballast Days	Measured mm	M5		M10		M15
		Prediction mm	Error %	Prediction mm	Error %	Prediction mm	Error %
33	7.75	7.75	0.06	7.75	0.04	7.75	−0.01
37	8.57	8.49	−1.01	8.57	−0.04	8.57	0.00
43	8.85	8.78	−0.77	8.85	0.01	8.85	−0.01
46	9.02	8.98	−0.46	9.02	0.00	9.02	0.00
49	9.20	9.51	3.47	9.20	0.01	9.19	−0.01
54	10.47	10.34	−1.26	10.45	−0.16	10.47	0.00
58	10.95	11.06	0.97	10.97	0.20	10.95	−0.01
64	11.33	11.51	1.54	11.38	0.41	11.33	−0.01
69	11.85	11.73	−1.00	11.91	0.49	11.85	−0.02
72	12.06	11.93	−1.02	11.98	−0.59	12.06	0.01
76	12.19	12.18	−0.09	12.25	0.46	12.19	−0.03
83	12.71	12.59	−0.93	12.63	−0.62	12.72	0.06
90	12.92	12.94	0.16	12.88	−0.30	12.92	0.00
100	13.30	13.28	−0.17	13.24	−0.42	13.29	−0.06
124	13.75	13.86	0.77	13.75	0.01	13.75	0.00
132	13.82	13.92	0.75	13.93	0.79	13.82	−0.02
143	14.03	14.05	0.15	14.09	0.41	14.04	0.09
150	14.24	14.11	−0.89	14.16	−0.54	14.23	−0.07
158	14.41	14.17	−1.69	14.24	−1.17	14.39	−0.11
165	14.52	14.21	−2.12	14.30	−1.48	14.55	0.23

. As can be inferred from the table, the maximum error of the M5 model for the settlement prediction within 150 days after the construction process is 3.4%, and the average error of this model is 0.48%. As for the M10 model, the maximum error is 0.79%, corresponding to an average error of 0.22%. The performance of the M10 was much better than the M5 model. A significant prediction accuracy development was presented by using the M15 model. As can be inferred from the table, the maximum error of this model within 150 days after the construction process is 0.1%, corresponding to an average error of 0.02%.

Further research about prediction performances of these models is shown in Figure 7, which presents the errors between the predicted values and the measured values at each measured time. Meanwhile, in order to evaluate the assessment performance of these ELM models, the bias (BIAS), correlation coefficient (CC), scatter index (SI), and index of agreement (I_a) are introduced as follows:

$$BIAS={\displaystyle \sum }_{i=1}^N\frac{1}{N}\left(Y_i-X_i\right)$$

(15)

$$SI=\frac{\sqrt{\frac{1}{N}{\sum }_{i=1}^N{\left(Y_i-X_i\right)}^2}}{\overline{X_i}}$$

(16)

$$CC=\frac{{\sum }_{i=1}^N\left(X_i-\overline{X}\right)\left(Y_i-\overline{Y}\right)}{\sqrt{{\sum }_{i=1}^N{\left(X_i-\overline{X}\right)}^2}{\sum }_{i=1}^N{\left(Y_i-\overline{Y}\right)}^2}$$

(17)

$$I_a=1-\frac{{\sum }_{i=1}^N{\left(Y_i-X_i\right)}^2}{{\sum }_{i=1}^N{\left(\left|\left(Y_i-\overline{X}\right)\right|+\left|\left(X_i-\overline{X}\right)\right|\right)}^2},$$

(18)

where X_i are the measured values, and their average is $\overline{X;}$ Y_i are the predicted values, and their average is $\overline{Y};$ and N is the number of observations.

It can be derived from Figure 7 that the error line of the M15 model matched perfectly with the zero-error line, meanwhile, the error line of the M5 model had the largest fluctuation, compared to the zero-error line. Furthermore, the M5 model has the largest Bias and SI value and has the lowest CC and Ia values, as shown in Figure 8, which indicates that the prediction accuracy of the M5 model was the lowest. The results also suggest that the number of hidden neurons could determine the prediction accuracy of ELM models.

These models also predicted the settlement of the soft foundation after 158 days loading and 165 days loading as validation for these models. As presented in Table 3 and Figure 7 and Figure 8, the M15 model had the highest prediction accuracy, corresponding to an average error of 0.17%. The prediction accuracies of M10 and M5 models were not as high as that of the M15 model. The prediction error of M5 and M10 models was from 1.17% to 2.12%. Additionally, the index values of CC, SI, Bias, and Ia show that the M15 model has the best prediction performance, and it could be used for predicting the settlement in the future time with reliable results.

3.2. Stability Assessment of the Fishbone-Shaped Dike’s Soft Foundation

In order to assess the stability of the submerged fishbone-shaped dike, further research was conducted by predicting the settlement of the soft-foundation in the next 800 days using the validated M15 model. Based on the difference of measurement interval time, two prediction models of the M15–D5 (interval time 5 days) and M15–D10 (interval time 10 days) models were established. The prediction performances of these two models could clarify the influence of measurement interval time on the simulation accuracy. The soft foundation of the dikes could be regarded as stable when the daily settlement was below 0.01 mm/d. The predicted settlement value by using the M15–D5 and M15–D10 models is presented in Figure 9, and the daily settlement is presented in Figure 10. A significant finding in Figure 9 was that the predicted results by the M15–D5 and M15–D10 models were almost the same, which indicated that the interval time has little influence on the model prediction value. The daily settlement decreased exponentially with the increase of ballast days. The daily settlement decreased to 0.01 mm/d in 335 days after the construction process, which indicated that the soft foundation of the fishbone-shaped dike tended to be stable. The settlement of this moment was 17.08 mm, and this could be considered the final settlement predicted by this machine learning approach. In 745 days after the construction process, the daily settlement decreased to 0.001 mm/d, and the total settlement was 18.72 mm at this measured time. A settlement of 1.64 mm occurred after the initial stabilization of this soft soil layer.

The final settlement was not easily predicted by the theoretical methods, and it was calculated by a simplified method, using the measured data most of the time to assess the stability of the soft foundation. The frequently used method to predict the final settlement of the soft foundation settlement based on the measured data were the three-point method, Asaoka’s method, and the hyperbolic method, and the consolidation of the soft soil could be computed by using the measured settlement value and the final settlement value. The final settlement values computed by different methods are listed in

Table 4. Final settlements using different methods. [30].

Method	Final Settlement (mm)
three-point method	15.08
Asaoka’s method	15.30
hyperbolic method	20.09
M15	17.08

. The final settlement value computed by the three-point method was approximately equal to the value computed by Asaoka’s method. The final settlement value computed by the hyperbolic method was much bigger than those computed by the three-point method and Asaoka’s method, which was 20.09 mm. The final settlement predicted by the M15 model was 17.08 mm, which was in the middle range of these predicted settlement values. A previous study showed that the final settlement predicted by the three-point method and Asaoka’s method was underestimated [32] since the secondary consolidation settlement was not considered in these methods. As a consequence, the consolidation of the soft soil layer may also have been underestimated. The M15 model built based on an extreme learning machine algorithm that can predict daily settlement could be used to predict the consolidation changes with time.

Based on the settlement prediction result of the M15 model, the consolidation of this layer is presented in Figure 11. It can be derived from the figure that after the construction process, the consolidation of this layer was 71%, corresponding to a consolidation of 60% computed by Asaoka’s method, which indicated that the main settlement occurred during the construction process. At the end of the monitoring period, the consolidation of this layer was 85%, the soil compression deformation had been basically completed. The soil compression process slowed down after the construction process, which could be supported by analyzing the daily settlement shown in Figure 11, and the soft foundation of the fishbone-shaped dike gradually turned to be stable.

4. Conclusions

In this paper, a novel approach was proposed to predict the settlement of the soft foundation of the fishbone-shaped dikes based on a small size of training samples using the extreme learning machine, and the following conclusions have been drawn:

(1) Three models (M5, M10, and M15) were built by using the measured settlement data. The simulation results showed that the M15 model had the highest prediction accuracy with a good fit of the measured data. The simulation results showed that the prediction settlements of the M15–D5 and M15–D10 models were basically the same, and the monitoring interval time ($T_{\Delta }$) had little influence on the prediction accuracy of the ELM models;

(2) The final settlements predicted by different methods were not the same, and the time-varying consolidation of the deep soil layer predicted was predicted by the M15 model. The main settlement occurred during the construction process, and then the soil compression process slowed down, which indicates the soft foundation of the fishbone-shaped dike gradually turned to be stable;

(3) The ELM model has a simple training process and high prediction accuracy, which could be a useful tool for the stability assessment of the related project, providing the settlement and consolidation prediction as reference.