Study on GA–ANN-Based Prediction of Paving Time of Cement-Stabilized Layer above Ultra-High-Filled Subgrade

Abstract

In mountainous areas, high-filled subgrade often experiences significant post-construction settlement. Prematurely paving the cement-stabilized gravel layer on an unstable subgrade can easily lead to subsequent cracking. To accurately predict the settlement of high-filled subgrade and determine the appropriate timing for paving the cement-stabilized layer, this study proposes a subgrade settlement prediction method combining an Artificial Neural Network (ANN) with a Genetic Algorithm (GA). Using monitoring data from a high-filled subgrade on a highway in Hunan Province, China, a GA–ANN model was established to predict settlement curves. The predicted data from the GA–ANN model were compared with measured data and ANN predictions to validate the advantages of using GA–ANN for subgrade settlement prediction. The results indicate that the GA–ANN model significantly outperforms the ANN model due to GA’s ability to provide more reasonable weight biases for ANN through global search optimization. Predictions of settlement data beyond 50 days using both ANN and GA–ANN showed that the GA–ANN prediction curve closely matched the measured curve, with a basic deviation within ±3 mm. In contrast, ANN’s prediction error gradually increased to over 5 mm as the observation time increased, with predicted values lower than measured values, leading to an overly optimistic estimation of early settlement convergence. Based on the predicted data and settlement standards, the estimated timing for laying the stabilized layer was determined. During the laying process, no cracking was observed in the stabilized layer. The project has been in operation for six months, with the road surface in good condition. This study provides a valuable reference for the laying of stabilized layers on similar high-filled and ultra-high-filled subgrades.

1. Introduction

Mountain highway construction usually encounters significant challenges due to rugged terrain, steep gradients, and complex geological conditions. The necessity to manage large volumes of tunnel spoil and excavation material often leads to the implementation of high or even ultra-high subgrade to ensure highway alignment meets standards [1]. During the construction period, controlling settlement in high subgrade sections is particularly challenging. After filling completion, these subgrades often require several months (typically spanning the rainy season) to stabilize, resulting in considerable uncertainty. Prematurely paving the upper cement-stabilized layer without ensuring stable subgrade settlement can easily result in subsequent cracking. Therefore, high-filled subgrades are generally among the last to be paved, thus constraining the overall project timeline. Accurate simulation and prediction of high subgrade settlement, along with a reasonable estimation of the timing for paving the cement-stabilized layer, are crucial for ensuring both the quality and progress of the project [2].

The conventional methods for predicting subgrade settlement primarily utilize single curve fitting techniques, including the exponential and hyperbolic approximation [3], Asaoka method [4], and Poisson method [5], among others. However, when settlement data are complex, the accuracy of prediction results heavily relies on manual data selection. The combined model approach [6,7] improves prediction accuracy by combining individual curves with certain weights, but it is relatively cumbersome to operate. This is especially true for the allocation of weights, which still requires further research. Inversion techniques, such as layered iteration [8] and settlement inversion based on Biot consolidation theory [9], excessively rely on the quality of data; thus, their application is constrained by data-related problems. Subgrade settlement is a nonlinear problem influenced by multiple factors and characterized by complexity and variability. The use of artificial neural networks (ANNs), a type of implicit mathematical processing method, does not require the establishment of a mathematical model and has advantages in solving various nonlinear problems [10,11,12,13]. ANN has already found some applications in the field of subgrade settlement prediction. For example, He [10] used neural networks to predict settlement for the high-fill subgrade composed of carbonaceous rock on the Hechi to Baise expressway. Miao [11] developed an ANN program to predict the deformation of the subgrade for the Qinghai–Tibet Railway.

However, ANN is optimized using the gradient descent method, which, due to the multi-objective and nonlinear characteristics of the model, can only find local optimal solutions in some cases and cannot find the global optimal solution. The literature [14] has pointed out disadvantages with using ANN for predicting complex geotechnical deformations, such as the slow convergence speed and unstable system training. Therefore, improving ANN has become a research hotspot [15,16]. Evolutionary algorithms such as genetic algorithm (GA) and particle swarm optimization (PSO) have been applied to find the optimal values of the weights for the ANN. Evolutionary algorithms can assist artificial neural networks (ANNs) in achieving global minima, thereby enhancing the network’s predictive performance. In this context, Mousavi et al. [17] introduced a hybrid neural network combined with simulated annealing to forecast daily solar radiation. Alsarraf et al. [18] utilized the PSO-ANN technique to predict the exergetic performance of a building-integrated photovoltaic/thermal system. Mosallanezhad and Moayedi [19] explored the effectiveness of an integrated imperialist competitive algorithm ANN for estimating the pull-out resistance of screw piles. Muhammad [20] used a novel hybrid artificial intelligence (AI)-based model, which was developed by the combination of artificial neural network (ANN) and Harris hawks’ optimization (HHO), to predict the settlement of the GRS abutments. Although evolutionary algorithms have proven efficient in solving engineering problems, few studies on the application of evolutionary algorithms and hybrid methods for the prediction of paving time for highways have been reported in the literature.

This paper leverages the global search advantages of the genetic algorithm (GA), combining ANN with GA to address the issue of the water-stable layer paving time for the high-fill subgrade of a highway in a mountainous area of Hunan Province. Using subgrade settlement monitoring data, the GA–ANN model was trained and established to predict subsequent subgrade settlement data. The measured data, ANN prediction data, and GA–ANN prediction data were compared, validating the advantages of using GA–ANN for high-fill subgrade settlement prediction. Finally, based on the predicted data and the settlement rate threshold, the paving time of the cement-stable layer was estimated, providing a basis for early construction organization and serving as a reference for similar future projects.

2. GA–ANN Theory

Artificial Neural Networks (ANNs) are frequently utilized for establishing nonlinear mapping relationships. In this study, the default ANN employed is the commonly used Backpropagation Artificial Neural Network (BPANN), characterized by its forward information propagation and backward error feedback mechanisms. The network architecture consists of an input layer, a hidden layer, and an output layer. BPANN is based on the gradient descent to search for adaptation. Equations (1) and (2) illustrate the adjustment methods for weights w_ij and biases b_ij.

$$w_{ij}=w_{ij}-{\eta }_1{\displaystyle \frac{\partial E(w,b)}{\partial w_{ij}}}=w_{ij}-{\eta }_1{\delta }_{ij}{x}_i$$

(1)

$$b_j=b_j-{\eta }_2{\displaystyle \frac{\partial E(w,b)}{\partial b_j}}=b_j-{\eta }_2{\delta }_{ij}$$

(2)

where: E—error function; η₁, η₂—learning rate; x_i—node output values.

For complex nonlinear functions, it is challenging to effectively address optimization problems solely through neural network training. One of the advantages of Genetic Algorithms (GAs) is their ability to perform global searches, thereby mitigating the risk of being trapped in local minima. Consequently, the GA–ANN hybrid model leverages GA as a robust search algorithm to identify the optimal weights and biases for the Artificial Neural Network (ANN), thereby improving the ANN’s predictive performance. The fundamental framework of the GA–ANN model is illustrated in Figure 1.

The genetic algorithm searches for the best adapted individual after a series of genetic operations such as selection and crossover. For the selection operation, the selection probability p_i of individual i is as follows:

$$p_i={\displaystyle \frac{(k/F_i)}{{\displaystyle \sum _{j=1}^N(k/F_j)}}}$$

(3)

where: F_i—fitness value of individual i; k—coefficient; N—number of individuals in the population.

If a crossover is performed for two chromosomes a_k and a_l at position j, the operation is as follows:

$$\left\{\begin{array}{l}{a}_{kj}=a_{kj}(1-b)+a_{lj}b\\ a_{lj}=a_{lj}(1-b)+a_{kj}b\end{array}\right.$$

(4)

where: b—random number between [0, 1].

If the jth gene a_ij of the ith individual is mutated, the operation is as follows:

$$a_{ij}=\left\{\begin{array}{l}{a}_{ij}+(a_{ij}-a_{\max })\ast f(m),r>0.5\\ a_{ij}+(a_{\min }-a_{ij})\ast f(m),r\le 0.5\end{array}\right.$$

(5)

where: a_max—upper limit of gene a_ij; a_min—lower limit of gene a_ij; f(g) = r₂ (1 − g/G_max)²; r₂—random number; m—current number of iterations; G_max—maximum number of evolutions; r—random number between [0, 1].

Typically, the accuracy of the trained model needs to be evaluated based on a number of metrics, including the correlation coefficient R², the root mean square error RMSE, and the mean absolute percentage error MAPE, which are calculated using the following formulas:

$$R^2={\displaystyle \frac{{\left({{\displaystyle \sum }}_{i=1}^n\left(y_{im}-{\overline{y}}_{im}\right)\left(y_{ip}-{\overline{y}}_{ip}\right)\right)}^2}{{{\displaystyle \sum }}_{i=1}^n{\left(y_{im}-{\overline{y}}_{im}\right)}^2{{\displaystyle \sum }}_{i=1}^n{\left(y_{ip}-{\overline{y}}_{ip}\right)}^2}}$$

(6)

$$RMSE=\sqrt{{\displaystyle \frac{{{\displaystyle \sum }}_{i=1}^n{\left(y_{ip}-y_{im}\right)}^2}{n}}}$$

(7)

$$MAPE={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=1}^n(\frac{\left|y_{ip}-y_{im}\right|}{y_{im}}})\times 100\%$$

(8)

where: y_im and y_ip—measured and predicted values for the ith output; ${\overline{y}}_{im}$ and ${\overline{y}}_{ip}$—measured and predicted averages; n—number of samples.

3. Project Overview

A proposed highway bridge in Hunan Province is located in the Wuling Mountain area of western Hunan. The region has an average annual rainfall of nearly 1500 mm and features mountainous gully topography with significant elevation variations. The ground elevation near the bridge site ranges from 288 m to 399 m. The highway alignment is separated into two directions, with one bridgehead connecting to a deep excavation section and the other adjacent to a tunnel entrance. Due to considerations for local road usage, spoil disposal, and environmental protection, the bridge has been redesigned as a subgrade (Figure 2).

The maximum height of the fill slope is 86.3 m, with slope ratios from bottom to top of 1:2.0, 1:2.0, 1:2.0, 1:2.0, 1:1.75, 1:1.5, 1:1.75, and 1:1.5, categorizing it as a typical high or even ultra-high subgrade. To reduce post-construction settlement of the high subgrade and limit lateral deformation of the subgrade, multiple layers of geocells were installed. Additionally, heavy tamping was performed every four meters of fill height, combining point tamping with full-area tamping.

After the completion of the subgrade filling, monitoring of the horizontal deformation and settlement of the subgrade was conducted. The monitoring plan is illustrated in Figure 3. Five settlement monitoring sections, with a total of 10 settlement monitoring points F1~F10, are arranged on the upper surface of the subgrade with a longitudinal distance of about 30 m. According to the “Design Specification for Highway Subgrades” (JTG D30—2015) [21] of China, a subgrade with filling height exceeding 20 m is considered a high-filled subgrade, while anything below this height is considered an ordinary subgrade. Therefore, sections F1–F10 and F2–F9 belong to the high-filled subgrade section, and the rest of the sections are in the ordinary subgrade range. Benchmark piles are installed on a solid foundation outside the deformation zone. They should be calibrated every three months, and concrete markers should be embedded. Settlement monitoring is conducted by using the Chinese KCYSB-044 level instrument. The monitoring class and accuracy requirements are in accordance with the “Code for Engineering Survey” (GB50026-2020) [22] of China (see

Table 1. Monitoring measurement accuracy requirements.

Deformation Measurement Class	Vertical Deformation Monitoring		Horizontal Deformation Monitoring
	Mean Square Error in Elevation of Deformation Points/mm	Mean Square Error in Elevation of Adjacent Settlement deformation points/mm	Mean Square Error of Deformation Point Position/mm
fourth class	±2.0	±1.0	±12.0

).

Other monitoring points as shown in Figure 3 were used for slope horizontal deformation monitoring, which were represented by 150 mm × 150 mm × 1500 mm C25 concrete prefabricated piles, with embedding prisms at the pile top. A typical slope horizontal monitoring point is shown in Figure 4.

4. Data Pre-Processing and Sensitivity Analysis

4.1. Data Pre-Processing

To ensure the predictive performance of the model, it is necessary to have a sufficient amount of data for training. However, due to on-site construction constraints, observations are conducted approximately every three to four days, resulting in excessively sparse data points. Therefore, cubic spline interpolation was employed to process the original observation data, resulting in a total of 100 data sets with a time interval of 0.5 days for training. The data preprocessing is illustrated in Figure 5.

The floating-point numerical interval of the input and output values can significantly affect the prediction results of the model, so the original data set must be normalized as follows:

$$y_i={\displaystyle \frac{x_i-x_{\min }}{x_{\max }-x_{\min }}}$$

(9)

where: x_i—any value in the sample data; x_max—the maximum value in the sample data; x_min—the minimum value in the sample data; y_i—the value after the normalization process, ranging from [0, 1].

4.2. Algorithm Parameter

The measured settlement data (see part of it in Appendix A) were divided into 70% training set and 30% test set. From the data curve used for training, the monitoring time t (days), the historical settlement data s_t−15 (mm) 15 days ago, and the historical settlement rate v_t−15 (mm/month) 15 days ago are extracted as input data, so the input layer contains three neurons, the hidden layer neurons are set to six, and the output layer neurons are set to two, which are the current settlement value s_t and the current settlement rate v_t. For the genetic algorithm, the parameters are set as follows: the initial population number is 100, the number of evolutionary generations is 200, the crossover probability is 0.5, and the mutation probability is 0.03.

4.3. Sensitivity Analysis

The One-at-a-Time (OAT) method is a common approach in sensitivity analysis used to assess the sensitivity of model outputs to changes in input variables. The core idea of this method is to change only one input variable at a time while keeping the other input variables constant, thereby observing the changes in the output variable. Additionally, there is another class of sensitivity analysis methods, named Global Sensitivity Analysis (GSA), which is a comprehensive approach to determining how the variability in model input parameters affects the output across the entire parameter space. Unlike local sensitivity analysis, which examines changes near a nominal point, GSA assesses the impact of input parameters over their entire range. Common GSA methods include Sobol and FAST (Fourier Amplitude Sensitivity Test). The advantages of GSA include providing a full picture of input–output relationships as well as reflecting complex interactions and nonlinear effects. But GSA requires a large number of model evaluations, which can be expensive and time-consuming. For this paper, considering the preliminary sensitivity analysis and the model with fewer parameters, OAT was chosen.

The steps of the OAT method in this paper are as follows:

(1) Setting the Baseline

Select the mean of the input variables as the baseline and calculate the output value at the baseline:

$$Y_0=f(X_0)$$

(10)

where X₀ is the baseline of the input, f is the model, and Y₀ is the output at the baseline.

(2) Univariate Perturbation

Change each input variable one by one while keeping the other variables constant. The perturbation method used in this paper is to increase or decrease the variable by one standard deviation. For each variable X_i (i = 1, 2, …, k), the output after perturbation is:

$$Y_i^{+}=f(X_0+\mathsf{\Delta }{X}_i)$$

(11)

$$Y_i^{-}=f(X_0-\mathsf{\Delta }{X}_i)$$

(12)

where ΔX_i is the standard deviation.

(3) Calculation of Sensitivity Indices

Sensitivity is typically measured using the standard deviation or the root mean square error (RMSE) of the output changes. In this paper, the standard deviation is used. The sensitivity S_i of each input variable X_i can be calculated using the following formula:

$$S_i={\displaystyle \frac{\left|Y_i^{+}-Y_0\right|+\left|Y_i^{-}-Y_0\right|}{2}}$$

(13)

(4) Ranking Variables by Sensitivity

Based on the calculated sensitivities, the variables are ranked in order of their sensitivity.

The calculated sensitivities indicate that, for the current settlement, the sensitivity of the historical settlement rate 15 days prior v_t−15 is 12.6434, the sensitivity of the number of days t is 11.8258, and the sensitivity of the historical settlement 15 days prior s_t−15 is 11.419. The ranking of sensitivities is as follows: v_t−15 > t > s_t−15, while the rank for the current settlement rate is as follows: t > v_t−15 > s_t−15.

5. Predictive Analysis

5.1. Model Training

Considering that the neural network has a certain degree of randomness, the average value is taken as the output value after repeating the training 10 times. To verify the advantages of the GA–ANN model, the ANN was also used for training, and the prediction accuracy of both models was evaluated as shown in

Table 2. Comparison of prediction accuracy.

Measurement Points	Model	Training Set Accuracy Index		Testing Set Accuracy Index
		RMSE/mm	MAPE/%	RMSE/mm	MAPE/%
F1	ANN	0.721	8.1	1.017	7.7
	GA–ANN	0.332	3.9	0.385	3.0
F2	ANN	0.753	10.7	1.397	8.3
	GA–ANN	0.317	6.5	0.611	6.0
F9	ANN	0.682	9.4	1.422	9.7
	GA–ANN	0.207	5.1	0.532	4.0
F10	ANN	0.815	13.2	1.615	12.0
	GA–ANN	0.415	9.3	0.844	10.5

.

Using point F1 as an example, the accuracy metrics from the training set indicate that the root mean square error (RMSE) is 0.721 mm and the mean absolute percentage error (MAPE) is 8.1% when employing the ANN model. Conversely, with the GA–ANN model, the RMSE is reduced to 0.332 mm and the MAPE to 3.9%. For the testing set, the ANN model yields an RMSE of 1.017 mm and a MAPE of 7.7%, whereas the GA–ANN model achieves an RMSE of 0.385 mm and a MAPE of 3.0%. Compared to the ANN model, the GA–ANN model exhibits lower RMSE and MAPE values, indicating a significant reduction in prediction error.

In summary, when the prediction model is ANN, the average RMSE for the training set across the four measurement points is 0.743 mm, and the average MAPE is 10.4%. For the testing set, the average RMSE is 1.363 mm, and the average MAPE is 9.4%. In contrast, when using the GA–ANN model, the average RMSE for the training set is 0.318 mm, and the average MAPE is 6.2%. For the testing set, the average RMSE is 0.593 mm, and the average MAPE is 5.9%. According to the literature [15], a MAPE of less than 10% indicates high prediction accuracy, while a MAPE between 10% and 20% denotes good accuracy. Therefore, the prediction performance for points F1, F2, and F9 is highly satisfactory, while the performance for F10 is relatively good. The integration of the genetic algorithm with ANN combines the nonlinear mapping capability of ANN with the global optimization search capability of GA, thereby enhancing the predictive power of the developed network model.

5.2. Predictive Effect of Each Measurement Point

Using the GA–ANN model and the ANN model, subsequent predictions were made for the settlement data at four measurement points: F1, F2, F9, and F10. The predicted curves are shown in Figure 6. It can be observed that the GA–ANN prediction curve exhibits a better smooth shape, with 90-day settlement amounts of 57.2 mm, 40.2 mm, 24.1 mm, and 32.6 mm, respectively. Since F9 and F10 are close to the cut slope side, their settlement values are lower. It is worth noting that during the long-term observation period of this subgrade, rainfall occurred locally around 45 to 60 days, causing the settlement rate to first slow down and then increase. Under this condition, the ANN prediction results were not ideal, with the settlement prediction even showing a short-term rise, indicating a rebound phenomenon (as shown in Figure 6a). In contrast, the GA–ANN prediction curve’s trend during this period was close to the measured curve, indicating that GA–ANN could better predict sudden changes in settlement rates than ANN.

Compared to the ANN prediction curve, the GA–ANN prediction curve is closer to the measured curve, with a basic deviation within ±3 mm. However, as the observation time increases, the prediction error of ANN gradually increases to more than ±5 mm, and the predicted values are lower than the measured values, leading to an optimistic estimation of early settlement convergence.

6. Discussion on Paving Time for Cement-Stabilized Gravel Layer

6.1. Discussion on Slope Horizontal Deformation

Above the subgrade are the cement-stabilized gravel layer and the asphalt layer. The cement-stabilized layer has high rigidity and poor adaptability to uneven deformation, making it prone to cracking. The timing for paving the cement-stabilized gravel layer needs to be determined by both the slope horizontal deformation trends and settlement trends. Since the deformation D_H and deformation rate R_H changes from the first to the fourth grade slope are relatively small and have been in a stable state, the deformation of the fifth to the eighth grade slope is discussed in this paper. Nine monitoring points’ slope deformation and deformation rate curves are shown in Figure 7, Figure 8, Figure 9 and Figure 10, which respectively reflect the states of the eighth to fifth grade slopes from bottom to top. As illustrated in Figure 7 and Figure 8, the initial horizontal deformations of the eighth and seventh grade slopes were relatively large, exceeding 8 mm. This is attributed to the inadequate compaction process during the initial stage of on-site construction. However, about three months after monitoring began, the horizontal deformations stabilized with only minor fluctuations.

As shown in Figure 9 and Figure 10, after optimizing the compaction process, the horizontal deformations at various monitoring points on the sixth and fifth grade slopes were relatively small, staying within 2.5 mm during the first seven months of monitoring. However, a sudden change occurred at measuring points 6-1 and 5-1 in early May 2023, which, upon verification, was caused by disturbances from drilling operations on the sixth and fifth grade slopes.

Additionally, as shown in the figures, the maximum deformation rate absolute value (eliminating outlier) of the fifth grade slope is 2.0 mm/d, while the sixth grade slope’s maximum deformation rate is 1.8 mm/d. For the seventh and eighth grade slopes, although the maximum deformation rates reached 6 mm/d and 7 mm/d, respectively, the deformation rates were within 2 mm/d for the majority of the time. According to China’s “Technical code of construction slope engineering” (GB 50330-2013) [23], the slope can be considered as stable when the horizontal deformation does not exceed 2 mm/d for three consecutive days, which indicates that the slopes at all grades are in a stable state.

6.2. Discussion on Settlement

According to the predicted values, the settlement s_p,t and settlement rate v_p,t of each major monitoring point on top of the subgrade at 60, 70, 80, and 90 days are shown in Figure 11, including the monitoring points of ordinary subgrade sections. From an overall perspective, the settlement value on the side near the subgrade slope is significantly larger than that farther away from the slope, and the settlement value gradually decreases from the high-filled subgrade section to the ordinary subgrade section.

At present, there is no specific settlement requirement for when the cement-stabilized layer can be paved in China. The “Design Specification for Highway Subgrades” (JDG D30-2015) [21] indicates that the paving of soft soil subgrade should be carried out when the settlement monitored for two consecutive months does not exceed 5 mm, which means that the settlement has become convergent and stable. In practical engineering, many technical personnel also use this standard as the basis for judging the stability of subgrade settlement. This article adopts the aforementioned standard and combines it with settlement prediction data (Figure 12). The predicted times for each section to reach the condition suitable for laying the cement-stabilized layer are approximately 63 days for section F4–F7, 72 days for section F3–F8, 103 days for section F2–F9, and 132 days for section F1–F10. Ultimately, considering the actual engineering situation, the plan for laying the cement-stabilized layer is divided into two stages: sections F4–F7 and F3–F8 will commence laying on the 70th day, and sections F2–F9 and F1–F10 will commence laying on the 120th day.

According to the plan above, the construction unit has made the necessary preparations. Before officially entering the site, one week of intensive monitoring was conducted, and the measured values were close to the predicted values, fully meeting the standard of settlement less than 5 mm for two consecutive months. During the paving process, no cracking occurred in the cement-stabilized layer. The project has been open to traffic for six months, and the road surface is in good operating condition (Figure 13).

7. Conclusions

This article combines artificial neural networks and genetic algorithms in machine learning to reasonably predict the settlement of ultra-high subgrades and predict the paving time of cement-stabilized layer. The following conclusions are drawn:

(1)

By introducing the genetic algorithm (GA), the nonlinear mapping capability of the ANN algorithm and the global optimization search capability of the GA algorithm are combined. Compared to ANN, the GA–ANN model has smaller RMSE and MAPE values, with MAPE being less than 10%, indicating relatively ideal prediction accuracy.

(2)

Using the GA–ANN model for subsequent predictions of settlement data at the four measurement points F1, F2, F9, and F10, the prediction curves exhibit a smoother shape and are closer to the measured curves. The GA–ANN model better predicts sudden changes in settlement rates, with a basic deviation within ±3 mm. In contrast, the ANN model has larger prediction errors, with predicted values lower than the measured values, leading to an optimistic estimation of early settlement convergence.

(3)

According to the slope horizontal deformation monitoring data, the slope is in a stable state, despite some adverse effects caused by the filling process or slope construction disturbances.

(4)

Using the predicted settlement curve by GA–ANN and paving requirements, the paving time of the cement-stabilized layer was estimated. According to the estimated time, the contractor carried out construction organization planning in advance, and there was no cracking phenomenon of the cement-stabilized gravel layer during paving. The project has been opened to traffic for half a year, and the pavement is in good operating condition.