Prediction of Pile Running during Installation Using Deep Learning Method

Abstract

Pile running during the installation of offshore large diameter pipe piles poses a significant challenge to construction safety and pile bearing capacity. This paper proposes a deep learning (DL)-based method for predicting pile running occurrences. Utilizing a dataset of pile installation records collected from various construction sites, the DL model was trained and tested. The predictive capacity of the DL model was compared with conventional analytical methods, demonstrating its superior performance in terms of accuracy and robustness. Additionally, the SHAP (SHapley Additive exPlanations) method was employed for the sensitivity analysis of the model’s input variables, and the resultant importance ranking agreed well with the findings of existing studies, thus enhancing the reliability and interpretability of the model’s predictions.

1. Introduction

The foundation of many offshore structures, including wind turbines and oil and gas platforms [1,2,3], relies on driven open-ended steel pipe piles. With offshore structures growing heavier, they often necessitate large-diameter pipe piles (LDPPs) to withstand the loads from the structure’s weight, wind, and waves. To ensure seamless pile driving without on-site splicing and to streamline the installation process, LDPPs are frequently fabricated as single segments. This approach not only enhances installation efficiency, but also reduces the risk of premature refusal [4,5].

However, due to their considerable length and weight, LDPPs are susceptible to a potential issue during the pile driving process, known as pile running. This phenomenon occurs when the pile unexpectedly penetrates the seabed under its own weight at an uncontrolled speed. Pile running can lead to various consequences, such as damage to the hydraulic control system of the driving hammer or even loss of the hammer into the water. Moreover, it can result in inaccuracies in the target penetration depth and the designed elevation of the pile, which, in turn, may affect the pile’s bearing capacity. Pile running is not uncommon in offshore engineering practice, particularly in carbonate soils [6,7] or layered seabeds with alternating strong and weak layers [8], where the soil resistance to driving can abruptly decrease during pile driving and become significantly smaller than the submerged weight of the pile. Therefore, accurately predicting the occurrence of pile running has significant practical importance in offshore engineering.

Considerable research has been devoted to predicting the occurrence of pile running. For instance, Yan et al. [9] proposed a predictive method based on the limit equilibrium of pile weight and soil resistance, yielding promising results in practical applications. Sun et al. [10,11,12] introduced static-equilibrium-based methods for predicting pile running, where dynamic skin friction of the pile is determined from the degradation of static skin friction. Zhao et al. [5] conducted larger deformation finite element analysis to simulate the pile running phenomenon on layered soil. In these methods, predicting pile running relies on comparing the pile weight with soil resistance. However, accurately calculating the resistance is challenging and influenced by numerous factors, including the complex material properties of soil layers, the diameter and wall thickness of the pile, and pile–soil interactions such as interface degradation, soil remolding during driving, and soil plugging effects [13]. Furthermore, most contemporary methods are essentially empirical and inherently involve various subjective assumptions and simplifications. Therefore, they may only be applicable under some specific conditions and have limited predictive accuracy in practical engineering.

In recent years, the rapid advancement of artificial intelligence technology and computing resources has introduced the deep learning (DL) method [14,15] as a powerful alternative across various traditional domains. The DL model excels in feature extraction and mapping, enabling the direct modelling of complex nonlinear relationships from training data without relying on theoretical assumptions. Consequently, it often yields superior predictive performance compared to conventional methods. Moreover, as additional training data become available, the DL model can be iteratively fine-tuned and improved, enhancing its adaptability and dynamic predictive modeling capability [16].

The DL method has found successful applications in geotechnical engineering, including deriving constitutive modeling of soil [17], predicting pile settlements [18] and bearing capacities [19], assessing landslide failure susceptibility [20], and more [21,22]. Demonstrating remarkable accuracy and robustness, the DL model has proven its effectiveness in various areas. This study extends the application of the DL method to the prediction of pile running. Utilizing a comprehensive dataset collected from different construction sites in China, the DL model was trained and tested. To assess its performance, the results were compared with conventional methods, where pile running occurrence was determined by comparing pile weight with soil resistance. Furthermore, sensitivity analysis of the model’s input variables was conducted to enhance interpretability.

The remainder of the paper is organized as follows: Section 2 provides a brief introduction to the dataset, the development procedure of the DL model, and the formulations of the conventional methods; Section 3 evaluates the predictive performance of the DL model and analyzes the sensitivity of the input variables; Section 4 concludes this paper.

2. Methodology

2.1. Dataset

Experimental data from practical engineering projects involving LDPPs were employed to train and test the DL model. This dataset, encompassing information on 17 piles, was collected from six construction sites associated with offshore wind power projects in China. It includes the geometrical characteristics of each pile and the soil properties of the layered seabed.

The geometrical characteristics consisted of the diameter (D), length (l), and weight (w) of the piles. Figure 1 illustrates the relationships between D, l, and w for these piles. It reveals variations in diameter ranging from 5.5 m to over 9 m, lengths spanning from 65 m to beyond 100 m, and weights ranging from 600 tons to 1800 tons. This diversity underscores the wide range of geometrical specifications observed in the piles considered in this study.

The soil layer properties were determined through laboratory tests and piezocone penetrometer test (CPTu).

Table 1. The soil properties for a construction site.

No.	Soil Type	d (m)	${\mathit{\gamma }}^{\prime }$(kN/m3)	Dr (%)	φ (°)	cu (kPa)
1	Mud	2.4	6.5	/	/	26
2	Silty clay	7.6	7.0	/	/	31.3
3	Silty clay with silty sand	12.0	8.4	/	/	57.3
4	Silty sand with silty clay	16.5	9.5	35	31	/
5	Silty clay with silty sand	20.7	8.5	/	/	78.3
6	Silty sand-1	21.9	9.5	30	30	/
7	Silty sand-2	25.5	10.0	55	35.3	/
8	Silty sand-3	41.3	10.6	65	36.3	/
9	Silty sand-4	60.5	10.5	60	36.3	/

provides an example of the laboratory test results for soil samples obtained at a construction site, detailing the soil type of each layer, depth of the bottom of the layer (d), submerged unit weight (${\gamma }^{\prime }$), relative density (D_r), friction angle (φ), and undrained shear strength (c_u). φ and c_u were determined from direct shear test and unconsolidated–undrained triaxial tests, respectively. It could be observed that the soil profile was mainly composed of mud, silty clay, and silty sand. Through CPTu, the cone tip resistance (q_c), side friction resistance (f_s), and pore water pressure (u) were measured during the penetration process.

Experimental data corresponding to each pile were divided into segments with a fixed depth interval of 0.02 m. The input variables for the DL model comprised the diameter and weight of the piles, along with soil properties obtained from laboratory tests and CPTu. The DL model’s output was an index indicating the occurrence of pile running at a specific depth. A value of unity signified that the pile running was expected, whereas a value of 0 indicated that the pile running was not anticipated.

Before inputting data into DL models, preprocessing is typically necessary. Normalization is a widely adopted technique used to rescale data from different variables to the same scale, which has been shown to reduce computational costs and improve the convergence of DL models [23]. The following equation was used to rescale the data to the range of [0, 1]:

$$\overline{x}=\frac{x-\min (x)}{\max (x)-\min (x)},$$

(1)

where x is the data sequence before normalization, $\overline{x}$ is the data sequence after normalization, and max(x) and min(x) are the maximum and minimum values of the data sequence, respectively.

The dataset is typically divided into three parts: training set, validation set, and test set. The training set is primarily used to optimize the trainable parameters of the model, enabling it to capture the underlying patterns and relationships within the data. The validation set is used to fine-tune the model’s configuration, aiding in preventing overfitting and optimizing the model’s generalization capabilities. Finally, the test set, which is completely separate from the training and validation process, is used to assess the final predictive performance of the trained model. In this study, the data from each pile were alternately used as the test set, while the remaining data were utilized as the training and validation set.

2.2. DL Model Development

In this study, the multilayer perceptron (MLP) was chosen as the architecture for the DL model. The MLP is the most basic type of neural network, comprising a three-block architecture—an input layer, hidden layers, and an output layer—as depicted in Figure 2. There can be one or multiple hidden layers, which determines the depth of the network. Each layer contains a set of neurons serving as the processing units. Each neuron gathers information from all neurons in the preceding layer and propagates its outputs to all the neurons in the succeeding layer, which can be mathematically expressed as follows:

$$x^l=f(W^l{x}^{l-1}+b^l), l=1, \dots , L,$$

(2)

where the superscript l denotes the layer index, and W^l and b^l are the weight matrix and bias vector, respectively. x¹ and x^L represent the input and output layers, respectively. f is the activation function, introducing nonlinear properties into the network to model complex relationships.

Despite its simplicity and efficiency, the MLP remains one of the most commonly used DL models [21,24], widely applied in various domains such as pattern recognition, regression analysis, and predictive modeling [25,26,27,28]. Although its predictive capacity may not match that of more sophisticated DL architectures, the MLP demonstrates remarkable generalization capabilities and high adaptability to dataset with limited sizes [29].

Prior to training, the model’s hyperparameters, which control its configuration and training procedure, must be assigned. In this study, a grid search was performed over the main hyperparameters that are critical to the predictive capacity of the model, such as the number of layers and neurons per layer. Other hyperparameters were set to their most commonly used values. The optimal hyperparameters are summarized in

Table 2. The hyperparameters for the DL model.

Hidden Size	Activation Function	Validation Split	Batch Size	Optimizer	Loss Function	Early Stopping Patience
3 × 64	ReLU	0.1	128	Adam	MSE	20

. The MLP model comprised three hidden layers, each containing 64 neurons. The rectified linear unit (ReLU) [30] was chosen as the activation function for these layers, a widely adopted activation function in DL.

Training a DL model is an optimization process, where the trainable parameters (i.e., weights and biases) are iteratively updated to minimize the discrepancy between predicted and true values. This discrepancy is quantified by a loss function, and the mean squared error (MSE) is selected as the loss function:

$$\mathrm{MSE}=\frac{1}{n}{\displaystyle \sum _{i=1}^n{\left({\widehat{y}}_i-y_i\right)}^2},$$

(3)

where n is the dimension of the output, ${\widehat{y}}_i$ and y_i are the predicted and true values, respectively. The Adam optimizer is chosen to update trainable parameters, implementing an adaptive stochastic optimization method that is robust and well-suited for various DL problems [31].

To mitigate overfitting, a regularization strategy, called early stopping [32], is employed. During training, the model’s performance is evaluated on both the training and validation sets. When the validation error begins to plateau or increase, it indicates that the model has reached its optimal generalization capacity. Any further training is likely to lead to overfitting, prompting the training process to stop. The patience was set to 20 in this study; corresponding loss curves for the model on the training and validation sets are presented in Figure 3. The training loss steadily decreased, while the validation loss initially mirrored the training loss but subsequently plateaus, indicating potential for overfitting. The application of early stopping leads to termination of the training process at about 300 epochs.

2.3. Traditional Methods

To further evaluate the predictive capacity of the DL model, its accuracy was compared with the traditional methods, where the occurrence of pile running is judged by comparing the weight of the pile with soil resistance. The following methods are used to calculate soil resistance: API [33], ICP-05 [34], UWA-05 [35], and UWA-13 [36]. Notably, the ICP-05 and UWA-05 methods are applicable only to sandy soil, while the UWA-13 method is designed for clayey soil. Thus, for layered soils containing both sand and clay, two hybrid methods are adopted: one combining ICP-05 and UWA-13, and the other combining UWA-05 and UWA-13.

In the API method, the unit shaft resistance, τ_f, and unit tip resistance, q_t, for clayey soil are calculated as follows:

$$\left\{\begin{array}{c}{\tau }_f=\alpha c_u\\ q_t=9c_u\end{array}\right.,$$

(4)

where c_u is the undrained shear strength of the soil and α is the shaft friction factor for clay, given by the following equation:

$$\alpha =\left\{\begin{array}{c}0.5{\psi }^{-0.5}, \mathrm{for} \psi \le 1\\ 0.5{\psi }^{-0.25}, \mathrm{for} \psi > 1\end{array}\right.,$$

(5)

where ψ is a strength factor calculated as follows:

$$\psi =\frac{c_u}{{{\sigma }^{\prime }}_{v0}},$$

(6)

where ${{\sigma }^{\prime }}_{v0}$ is the in situ vertical effective stress at the specific depth.

For sandy soil, the τ_f and q_t can be calculated as follows:

$$\left\{\begin{array}{l}{\tau }_f=\beta {{\sigma }^{\prime }}_{v0}\\ q_t=N_q{{\sigma }^{\prime }}_{v0,tip}\end{array}\right.,$$

(7)

where β is the shaft friction factor for sand given by:

$$\beta =\left(1-\sin \phi \right)\tan {\delta }_f,$$

(8)

where φ is the internal friction angle of soil and δ_f is the interface friction angle.

In the ICP-05 method, τ_f and q_t are calculated as follows:

$$\left\{\begin{array}{l}{\tau }_f=a\left[0.023b{q}_c{\left(\frac{{{\sigma }^{\prime }}_{v0}}{p_a}\right)}^{0.1}\max {\left(\frac{h}{R^{*}},8\right)}^{-0.4}\right]\tan {\delta }_f\\ q_t=A_r{q}_{c,avg}\end{array}\right.,$$

(9)

where a and b are loading factors, and are set as 1.0 for pile under compression; q_c is the cone tip resistance measured from CPTu; p_a = 100 kPa is the atmospheric pressure; h is the distance of the point from the pile tip; R^* is the equivalent radius for the open-ended pile, and can be obtained from Equation (10); $A_r=1-{(D_i/D)}^2$ is the area ratio; and q_c,avg is the average value of q_c measured over the 1.5 pile diameter range, both above and below the pile tip.

$$R^{*}=\frac{\sqrt{D^2-D_i^2}}{2},$$

(10)

where D and D_i are the outer and inner diameters of the pipe pile, respectively.

In the UWA-05 method, τ_f and q_t are calculated as follows:

$$\left\{\begin{array}{l}{\tau }_f=a\left[0.03q_c{A}_{r,eff}^{0.3}{\left(\frac{{{\sigma }^{\prime }}_{v0}}{p_a}\right)}^{0.13}\max {\left(\frac{h}{D},2\right)}^{-0.5}\right]\tan {\delta }_f\\ q_t=0.6A_{r,eff}{\overline{q}}_c\end{array}\right.,$$

(11)

where ${\overline{q}}_c$ is the average q_c obtained from the Dutch method [37], and A_r,eff is the effective area ratio, calculated as follows:

$$A_{r,eff}=1-{\left(\frac{D_i}{D}\right)}^2\min \left(1, {\left(\frac{D_i}{1.5}\right)}^{0.2}\right).$$

(12)

In the UWA-13 method, q_t is obtained from Equation (9), while τ_f is calculated as follows:

$${\tau }_f=0.055q_{ct}\max {\left(\frac{h}{R^{*}},1\right)}^{-0.2}.$$

(13)

where q_ct is the corrected cone resistance, calculated as follows:

$$q_{ct}=\left\{\begin{array}{c}1.14q_c, \mathrm{for} \frac{q_c}{{{\sigma }^{\prime }}_{v0}}\le 6\\ q_c, \mathrm{for} \frac{q_c}{{{\sigma }^{\prime }}_{v0}}> 6\end{array}\right..$$

(14)

3. Performance

3.1. Predictive Accuracy

This section focuses on the predictive accuracy of the DL model on the test data. Notably, each pile in the dataset is alternately employed as the test set to assess the predictive capacity of the DL model.

Figure 4 illustrates the distribution of predictive accuracy on the test data using a boxplot. It is evident that the MLP significantly outperforms the other methods and exhibits superior accuracy. The mean accuracy of the MLP is approximately 0.89, contrasted with the considerably lower accuracy of around 0.4 observed from the other methods, demonstrating the exceptional predictive capacity of the MLP. Additionally, the MLP offers a narrower accuracy distribution compared to the other methods, as indicated by the range from the minimum to the maximum of the box, while the other methods exhibit wider distribution. A wider distribution signifies a higher degree of variability, indicating that the method is more sensitive to the conditions of construction sites. Therefore, the MLP not only offers higher accuracy, but also better applicability and robustness.

Figure 5 presents the prediction of pile running occurrence for two pile cases, where the dots denote that pile running occurred at the corresponding depth. The predictions of the MLP align well with the test data at different depths, demonstrating the superior predictive capacity of the DL model. The DL model can accurately reproduce both the initial pile running caused by the pile’s own weight and the surface weak soil layer, as well as pile running incidences during the driving process. In contrast, traditional methods tend to underestimate the likelihood of pile running occurrence and are only applicable at the early stage of the pile installation.

However, it is important to recognize that the DL model’s accuracy and generalizability is highly dependent on the quality and diversity of the training data. The model may not perform as well when applied to construction sites with soil properties or conditions that significantly differ from those in the training dataset. Furthermore, while the DL model demonstrates superior performance in predicting pile running occurrences, it may require substantial computational resources for training and may not be as easily interpretable as traditional methods, which could be a limitation in practical applications where transparency and explainability are crucial.

3.2. Sensitivity Analysis

The sensitivity of each input variable was analyzed using the SHAP (SHapley Additive exPlanations) method [38], which provides a unified measure of variable importance based on game theory principles to interpret the predictions of a machine learning model. Each input variable is assigned a value, known as the SHAP value, to quantify its specific contribution to the model’s prediction.

By analyzing the SHAP values, one can gain a comprehensive understanding of how each input variable influences the model’s output. This is particularly valuable in DL models. Due to the complex architecture of DL models, interpreting the relationship between inputs and outputs is challenging [39], rendering DL models as black boxes. The SHAP method offers a viable approach to dissect the model, facilitating a detailed exploration of the importance of each input variable. This enhances the interpretability of the model and provides insights into the underlying patterns and relationships within the data that the model has learned. Such analysis is crucial for building trust in the model’s predictions and ensuring that the model’s decisions align with the established domain knowledge.

Figure 6 illustrates the mean SHAP value for different input variables. It is evident that the penetration depth (d) and weight (w) of the pile are the two most critical variables in determining the occurrence of pile running. This is logical because the total resistance of the soil is directly influenced by the penetration depth of the pile, and a greater difference between the pile weight and soil resistance would result in a higher risk of pile running. Additionally, the diameter of the pile (D) exhibits a high SHAP value, as the size of the diameter significantly influences the soil plugging effect, which has a considerable impact on the bearing capacity and drivability of the pile [40]. Furthermore, variables measured from the CPTu, such as the cone tip resistance (q_c), side friction resistance (f_s), and the pore water pressure (u), are the least important variables. This can be attributed to the close correlation between the soil parameters and the CPTu data [41,42], leading to information redundancy and lower SHAP values. These results demonstrate that the SHAP method reliably ranks the importance of the input variables, which is in alignment with the findings of existing studies in the field.

4. Conclusions

This paper introduces a DL-based framework for predicting the occurrence of pile running. The model was trained and tested using a comprehensive dataset comprising 17 pile driving cases collected from practical construction sites. The input variables included geometrical information of the pile and soil properties obtained from laboratory tests and CPTu. Comparative analysis was conducted to evaluate the predictive performance of the model against traditional methods, in which three distinct formulations were utilized to calculate soil resistance. Additionally, the SHAP method was employed to analyze the importance of the input variables.

The DL model demonstrated a high level of accuracy in predicting pile driving occurrences, surpassing traditional methods in terms of both predictive accuracy and robustness under varying conditions. Additionally, the SHAP method has proven effective in conducting sensitivity analysis, offering a reliable ranking of variable importance that aligns well with established domain knowledge, thereby enhancing the interpretability of the model.

Despite these successes, it is noteworthy that the model’s performance is significantly influenced by the quality and representativeness of the training data. The current dataset may not fully capture the variability of real-world conditions, which could limit the model’s applicability to untested scenarios. Future work could focus on expanding the dataset to include a broader range of soil types and construction scenarios.

The successful integration of the DL model into the prediction of pile driving not only improves the predictive accuracy, but also suggests its potential for broader applications within the field of geotechnical engineering, such as the prediction of soil settlement and assessment of slope stability.