Analysis of correlation and sensitivity influences on the variation of mechanical parameters of proximate structures in the delta region

The Delta region, characterized by its low-lying and flat terrain, hosts numerous extensive and profound foundation pits, slopes, and embankment constructions, frequently clustered in close vicinity to each other [1-5]. However, these constructions, plagued by extended construction timelines and the intricate, ever-evolving environmental conditions, are subjected to a confluence of factors such as rainfall, groundwater fluctuations, stress variations, and others. This combination poses significant challenges to managing construction safety risks. Consequently, meticulous scientific monitoring and control of parameters including rainfall, displacement, groundwater level, anchor stress, and anchor cable stress are imperative during the construction phase. Current research endeavors, though abundant in their examination of the correlational dynamics with the mechanical parameters between the stability of foundation pits, slopes, and embankments amidst multifaceted factors, lack depth in quantitatively pinpointing the intrinsic sensitivities that underlie these intricate interdependencies. Therefore, there is a need for an innovative analytical approach capable of elucidating the underlying sensitivities of structural systems under the influence of multiple factors. Such an approach would facilitate a comprehensive assessment of the overall safety landscape, vital for safeguarding and mitigating risks associated with the construction of extensive foundation pits, slopes, and embankment projects.

In this scholarly endeavor, we delve into the multifaceted mechanical parameters that have the potential to precipitate instability concerns in foundation pits, slopes, and embankments. To address this intricate issue, three methodologies are typically employed: Theoretical analysis, experimental research, and numerical simulation. In terms of theoretical analysis, experts have utilized a diverse array of analytical methodologies, including fuzzy hierarchical analysis, fault tree analysis, the limit equilibrium method, and the stratum loss method. These tools serve to scrutinize the intricate interplay between alterations in the stress parameters within foundation pits, slopes, and embankments, and their subsequent impact on stability and potential damage scenarios. These methods are inherently uncomplicated, intuitive, and computationally straightforward, offering a robust theoretical framework for examining the multi-faceted effects of various factors on such structures. Nevertheless, a prerequisite for these analyses is the a priori establishment of the inherent soil relationships, a task that can be quite challenging. Moreover, acquiring accurate model parameters poses another hurdle. Notably, these calculations tend to incorporate a conservative safety margin, often resulting in outcomes that significantly diverge from reality, ultimately leading to the unnecessary expenditure of resources [6-10]. In terms of experimental research, scholars have diligently delved into the stability and damage process of foundation pits, slopes, and embankments. This has been achieved through a comprehensive suite of experiments, including, centrifuge tests, indoor pressure tests, model tests, CPTU tests, and on-site monitoring tests. Following these rigorous tests, they systematically analyze the cumulative effects of various mechanical parameters on the soil pressure profiles within each structure. These methodologies are rooted in vast experimental datasets and employ practical boundary conditions, coupled with straightforward calculation parameters that offer broad applicability. While these methods efficiently isolate numerous pivotal mechanical parameters from the test outcomes, quantifying the specific impact of each factor remains a challenge. Additionally, they fail to encapsulate the intricate interplay between macrostructural features and soil heterogeneity, which significantly influences geotechnical behavior, thereby introducing a degree of imprecision [11-16]. In the realm of numerical simulation, researchers employ commercial software packages, including ABAQUS, PLAXIS, PFC, and FLAC, to investigate the stability and displacement dynamics of foundation pits, slopes, and embankments, both unsupported and with engineered support systems, under diverse operational conditions. This approach facilitates the proposal of stability control strategies tailored to deep foundation pits, slopes, and embankments subjected to multi mechanical parameters. These techniques offer significant advantages in capturing the continuous degradation, instability, and substantial deformation patterns exhibited by ground-based structures. However, it is important to note that numerical modeling often necessitates the consideration of the entire system encompassing the foundation pit, surrounding structures, and the soil matrix. Consequently, the intricate mechanical parameters interplay of deformations between these components, particularly the coupled effects, may not be fully represented. This limitation hinders the precise quantification of the individual influence of each mechanical parameter on the structural integrity of the system, as highlighted in previous studies [17-27]. In summary, the majority of theoretical, experimental, and numerical simulation methods rely on correlation analysis to study the variations within closely related structural mechanical parameters. However, there exists a notable gap in the thorough examination of the inherent sensitivities that influence the correlations between structural changes in the mechanical parameters and the quantification of their contributing factors. Consequently, it is imperative to devise an intelligent analysis methodology capable of efficiently managing the overall stability of geotechnical structures in deltaic regions. To achieve this, the analysis of models and indicators pertaining to sensitive mechanical parameters holds paramount importance, as it is fundamental to ensuring the scientific and effective stability of the system. The advantages and disadvantages of the various methods and their applications are shown in Table 1.

Table 1.

Advantages, disadvantages, and applications of different methods [34]

Serial Number	Method	Advantage	Disadvantage	Application
1	Linear regression prediction	Good at acquiring linear relationships in the dataset; easy to operate; fast training and prediction speed.	The measurement data are discrete, and the prediction accuracy is affected by complex geological conditions.	It is suitable for low latitudes and there is no covariance between each dimension.
2	Grayscale Model	Simple and practical; few model parameters.	Little fault tolerance; not suitable for long-term forecasting.	It is suitable for short-term prediction.
3	Support vector machine	Simple algorithm; good robustness (in the case of small samples).	Limited by the sample size; when the sample size is too large, the accuracy will be affected.	It is mainly used for data classification but can also be used for regression prediction.
4	Time series	It allows for full consideration of the impact of seasonal and cyclical variations on specific points in time.	Single linearity, stable monitoring time, equidistant data feature.	It is applied to predicts related to its own previous period.
5	Neural network technology	Better nonlinear mapping capability; better self-learning and self-adaptive capability; certain faulttolerance capability.	With low learning efficiency, slow convergence speed, and easy to fall into a local minimum state.	Theoretically, it can be mapped to any function.

For feedforward neural networks, robustness is reflected in their ability to maintain good prediction performance even when the input data contains noise, outliers, or distributional biases [28, 29]. Feedforward neural networks show high robustness in dealing with abnormal data by virtue of their powerful feature extraction ability, nonlinear fitting ability and adaptive learning ability. In the application of classical and hybrid tools, feedforward neural networks can be combined with other algorithms or tools to jointly improve the overall performance and stability of the system. In addition, feedforward neural networks show high robustness in dealing with anomalous data and have been validated in many studies[30-33].

To address the aforementioned challenges, this research introduces an innovative intelligent analysis approach that establishes the fluctuations in multifaceted influencing factors and the intricate interplay among various structural components mechanical parameters. The proposed model meticulously represents target measurement points, incorporating multiple influencing mechanical parameters and elucidating the intricate relationships between diverse structural elements. This framework enables the identification of pivotal influencing factors that significantly impact the mechanical parameters of the geotechnical structural system. Furthermore, a rigorous quantitative analysis is conducted on these identified sensitive factors, providing a deeper understanding of their influence.

2

Material and methods

The Delta region is characterized by extensive waterways and lakes, prompting the construction of numerous buildings directly on the water. This results in a dense clustering of foundation pits, embankments, and slopes, with each structure intimately interacting with its surroundings [35-37]. Excavation of foundation pits disrupts the original soil equilibrium, inevitably exerting influence on adjacent structures, potentially causing additional deformation, structural tilting, cracking, and other forms of damage. Thus, ensuring the structural safety of these neighboring foundation pits is a pivotal concern that must be thoroughly addressed in design analyses. To gain a deeper understanding of the effects of foundation pit excavation on proximate structures, this study employs a multi-structure, multi-influence correlation model to simulate the mechanical parameters interplay between foundation pits, slopes, and embankments. This approach leverages time-series data from carefully selected monitoring points within each structure. The primary objective is to maximize the reliability and continuity of monitoring points during periods of rainfall, ensuring robust data for mechanical parameters analysis. The study considers multiple input mechanical parameters, such as rainfall, groundwater levels, and stress variations, while assessing structural displacement as the key output mechanical parameters. By examining the stress and deformation patterns of adjacent structures during excavation, the study further evaluates the sensitivity of each structure under the specified support scheme. This comprehensive analysis sheds light on the complex interactions and potential vulnerabilities, facilitating the development of more effective design and mitigation strategies. The methodology’s detailed steps and workflow are illustrated in Figure 1.

2.1

Principles of Intelligent Analysis of Multi-Influence Factor and Multi-Structures Mechanical Parameters Correlation

In the construction of deep foundation pits, slopes, and embankments, a multitude of mechanical parameters can potentially hinder the progress and safety of the process. To mitigate the occurrence of accidents and incidents during this critical phase, a meticulous examination of these impeding factors is paramount. Implementing an appropriate and scientifically rigorous monitoring and evaluation framework is essential to ensuring the safety of construction operations [38, 39].

In the examination of the construction process of a complex structure system influenced by multiple variables, the customary focus tends to lie solely on analyzing the correlations between mechanical parameters variations in patterns, as cited in previous studies [40, 41]. However, the critical aspect of delving into the intrinsic sensitivity impacts and accurately quantifying these sensitivities has been conspicuously overlooked. This conventional approach falls short in its ability to comprehensively evaluate the overall stability of deep foundation pits and their adjacent structures, ultimately hindering a precise assessment of the construction safety of the entire geotechnical structure system.

To rectify the aforementioned challenges, the present study investigates the mechanical patterns of diverse structures under the combined influence of rainfall, groundwater levels, and stress conditions. It delves into the underlying mechanisms that govern these changes. Utilizing feed-forward neural network analysis, we develop a multi-structure correlation model that comprehensively incorporates the effects of multiple influencing mechanical parameters.

The basic steps of model construction are as follows:

The initial step in model construction entails the selection of test mechanical parameters. Specifically, the displacement of the embankment serves as the primary test mechanical parameters. Subsequently, a range of factors that influence this displacement are identified and employed as test factors. These encompass rainfall, the axial force applied by the foundation anchor cable, the groundwater level beneath the foundation, as well as various displacement metrics pertaining to the foundation piles and slope anchors, including their horizontal and vertical displacements. Additionally, the groundwater level and displacements of the side slopes are also considered.

Subsequently, Gray correlation analysis is conducted on the selected test mechanical parameters. In this analysis, either the horizontal displacement (S) or the vertical displacement (J) of the embankment serves as the reference mechanical parameters series. The feature sequences comprise various mechanical parameters that potentially influence these displacements, including rainfall (RF), the axial force of the pit anchor cable (M), the groundwater level within the pit (SW), the horizontal and vertical displacements of the pit pile top (WY and CJ, respectively), the axial force of slope anchors (JM), the groundwater level and both horizontal and vertical displacements of the slopes (PSW, PWY, and PWX, respectively). Following this, the determination coefficients and gray correlation coefficients of these sequences were meticulously analyzed.

In an ideal scenario, the embankment, being an integral structural element, would solely require assessment for its stability under the influence of rainfall. Nevertheless, the significance of factors like groundwater levels and the stress conditions within adjacent deep foundation pits and slopes cannot be overlooked. Consequently, we adopt a methodology where the time-series data from embankment gauges serve as the primary target values, while variations in rainfall, slope, and foundation pit gauge time-series act as the explanatory variables. This approach facilitates the development of a comprehensive multi-influence factor, multi-structure mechanical parameters change correlation model aimed at predictive analysis.

Specifically, to gain insights into the inherent sensitivities that modulate the inter-structural mechanical parameters change correlations, we fitted the time-series data from rainfall, slope, and foundation pit gauges to the corresponding embankment gauge time-series. This approach allowed us to formulate predictions, as depicted in Figure 2, which highlights the intricate relationships between these mechanical parameters.

In Figure 2, RF_i denotes the rainfall on day i (1 ≤ i ≤ n), n is the total number of days in the time-series, M is the axial force of the foundation pit anchor cable on day i, SW_i is the foundation pit groundwater level on day i, WY_i is the horizontal displacement of the foundation pit pile top on day i, CJi is the vertical displacement of the foundation pit pile top on day i, JM_i is the axial force of the slope anchor on day i, PSW_i is the slope groundwater level on day i, PWYi is the vertical displacement of the slope on day i, PWX_i is the horizontal displacement of the slope on day i, S_i is the horizontal displacement of the embankment on day i, and J_i is the vertical displacement of the embankment on day i.

The proposed model enables us to comprehensively monitor the real-time dynamics of various structural responses as they evolve under the influence of multiple mechanical parameters. By doing so, it safeguards the integrity and stability of adjacent structures during foundation pit excavation. This, in turn, offers a valuable reference framework for future investigations into the transformation patterns of similar multi-geotechnical structures, particularly when subjected to changes in their surrounding environment.

2.2

Multi-influence factor multi-structure mechanical parameters change correlation model

2.2.1

Determination of sample space for multi-influence factor multi-structure mechanical parameters change correlation model

The variations observed in geotechnical structural displacements exhibit a robust correlation with various influencing mechanical parameters, as documented in prior studies [34, 42-44]. Through meticulous fieldwork and exhaustive analysis, we have identified a comprehensive set of eleven key mechanical parameters, categorized into stress, strain, and environmental categories, that serve as primary influencers. In this research endeavor, the foundation for our multi-influence factor, multi- structural mechanical parameters change correlation model is firmly established upon the base information derived from eleven distinct types of monitoring data, as illustrated in Figure 2.

2.2.2

Construction of feedforward neural network

The feed-forward neural network design tailored for the multi-influence factor, multi-structure mechanical parameters change correlation model is elucidated through the flowchart presented in Figure 3. Utilizing rainfall data alongside the field-measured metrics of foundation pits, slopes, and embankments, an (n × 1) sample space matrix is constructed, as exemplified in Figure 2, and fed into the neural network for training purposes. The refinement of neural network parameters ensues through iterative processing of each training sample space until a predetermined convergence error threshold is attained. Subsequently, the model’s accuracy is gauged by assessing the relative error between observed and predicted outputs, drawing upon the validation protocols outlined in previous studies [34, 42, 43]. Equipped with this validated model, we embark on conducting both the multi-influence factor, multi-structure mechanical parameters change correlation analysis and the interaction analysis. Ultimately, these endeavors yield insights into the intrinsic sensitivity impacts underlying the proximity structure mechanical parameters change correlations.

The current study adopts a three-layered feed-forward neural network architecture to facilitate the learning and predictive analysis of the sample data. This model is specifically tailored to address a one-dimensional, non-linear time-series process, as elaborated in Section 2.1. Consequently, the output layer of the network is designed to comprise a single node, adhering to the principles of intelligent analysis pertaining to the multi-influence factor multi-structure mechanical parameters change correlation.

2.3

Methods for analyzing sensitive influences correlation with mechanical parameters changes in geotechnical structures

To effectively address the intricate issue of multifactorial statistical analysis concerning structural mechanical parameters changes in proximal structures within the delta region and perform a rigorous sensitivity analysis, a computational approach that offers both swiftness and robust adaptability is imperative. Consequently, integrating gray system theory with a neural network methodology emerges as a fitting solution for the intricate data mining tasks inherent in multifactor statistical and sensitivity analyses [45, 46]. In this study, we employ this hybrid approach to pinpoint and quantify the sensitivity of various factors influencing geotechnical structural mechanical parameters changes. The methodical steps undertaken are outlined below:

To evaluate the efficacy of the proposed multi-influence factor multi-structure mechanical parameters change correlation model, we initially assessed its predictive performance using the coefficient of determination (R²), which ranges from 0 to 1. An R² value closer to 1 indicates superior model performance. Additionally, we employed additional metrics, namely Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), to further validate the accuracy of the neural network.

Subsequently, drawing upon gray correlation analysis theory, we quantitatively assessed the impact of multiple influencing mechanical parameters on the structures, utilizing gray correlation coefficients as the basis for our evaluation [47, 48]. This step allowed us to quantitatively characterize the interdependencies among the various factors.

1

α_{i} = \frac{\min_{i} {| x_{0} (1) - x_{1} (1) |, | x_{0} (2) - x_{1} (2) |, \dots, | x_{0} (k) - x_{1} (k) |} + ρ \max_{i} {| x_{0} (1) - x_{1} (1) |, | x_{0} (2) - x_{1} (2) |, \dots, | x_{0} (k) - x_{1} (k) |}}{\begin{matrix} | x_{0} (k) - x_{1} (k) | + ρ \max_{i} {| x_{0} (1) - x_{1} (1) |, | x_{0} (2) - x_{1} (2) | \dots, | x_{0} (k) - x_{1} (k) |} \end{matrix}}

\[{{\alpha }_{i}}=\frac{{{\min }_{i}}\{|{{x}_{0}}(1)-{{x}_{1}}(1)|,|{{x}_{0}}(2)-{{x}_{1}}(2)|,\ldots ,|{{x}_{0}}(k)-{{x}_{1}}(k)|\}+\rho {{\max }_{i}}\{|{{x}_{0}}(1)-{{x}_{1}}(1)|,|{{x}_{0}}(2)-{{x}_{1}}(2)|,\ldots ,|{{x}_{0}}(k)-{{x}_{1}}(k)|\}}{\begin{matrix} |{{x}_{0}}(k)-{{x}_{1}}(k)|+\rho {{\max }_{i}}\{|{{x}_{0}}(1)-{{x}_{1}}(1)|,|{{x}_{0}}(2)-{{x}_{1}}(2)|\ldots ,|{{x}_{0}}(k)-{{x}_{1}}(k)|\} \\ \end{matrix}}\]]

where α_i denotes the gray correlation coefficient, p is the resolution factor (which is set as 0.5 in this paper), x₀(k) is the column vector for each influence factor, and x₁(k) is the column vector of the structures.

In the next phase, we integrated the correlation coefficients by applying a weighting scheme to derive the final Gray Correlation Degree (GCD). This approach enabled us to obtain a comprehensive understanding of the overall correlation patterns.

Finally, we leveraged the correlation analysis outcomes to interpret the neural network’s output as a weighted summation of all possible paths through the network, with the weights corresponding to the phase factors. This methodology is conceptually akin to path integrals in quantum mechanics, and we formulated the multi-structure multi-factor influence relations using equations (2) through (5).

2

α_{h} = \sum_{i = 1}^{N} v_{i h} x_{i} + r_{h},

\[{{\alpha }_{h}}=\underset{i=1}{\overset{N}{\mathop \sum }}\,{{v}_{ih}}{{x}_{i}}+{{r}_{h}},\]

3

b_{h} = f (α_{h})

\[{{b}_{h}}=f({{\alpha }_{h}})\]

4

y_{j} = \sum_{h = 1}^{q} w_{h j} b_{h} + θ_{j},

\[{{y}_{j}}=\underset{h=1}{\overset{q}{\mathop \sum }}\,{{w}_{hj}}{{b}_{h}}+{{\theta }_{j}},\]

5

f (x) = \frac{1}{1 + e^{- x}}

\[f(x)=\frac{1}{1+{{e}^{-x}}}\]

where N is the number of influencing factors, vih is an N-dimensional weight vector, x_i,(i = 1, 2,......,N) is the column vector value corresponding to the time-series, h is the number of nodes in the implicit layer, r_h, is the threshold parameter of the neural network from the input layer to the hidden layer, q is the number of nodes in the output layer, w_hi is the weight parameter of the neural network from the hidden layer to the output layer, θ_j is the threshold function from the hidden layer to the output layer of the neural network, and y_j (j = 1) are the predicted output values of the structure monitoring points corresponding to the time-series.

In the fifth step of our analysis, we derived the training parameters of the neural network to quantify the impact contributions of various influencing mechanical parameters on the structure. Specifically, we assessed the contributions of rainfall, groundwater level, stress changes, and other condition variations. This allowed us to rank their relative significance as impacting factors. Consequently, we achieved a quantitative analysis of the impact sensitivities between the structure system and its contributing mechanical parameters, offering insights into their interplay.

3

Results and Discussion

3.1

Case Study

The present study focuses on slopes and embankments adjacent to typical foundation pits in South China. Utilizing a feed-forward neural network approach, a comprehensive correlation model is devised to analyze and quantify the interplay between multiple factors and structural mechanical parameters alterations. This model undergoes rigorous testing and validation to ensure its accuracy. As depicted in Figure 4, the project site boasts a lengthy excavation depth, reaching into slightly weathered granite. With a support perimeter approximating 620 m and an excavation depth spanning 4.25 to 11.35 m, the foundation pit encompasses a surface area of roughly 18,457 m². Reinforced by grouted piles and anchor cables, the foundation pit is situated amidst unique geographical features: a river embankment to the west, characterized by a river bottom at 22 m and a width of 14 m, and a substantial slope to the east, peaking at approximately 19 m and stabilized with spray anchors.

During the construction phase, an extensive monitoring program was implemented, encompassing 11 key parameters: rainfall (RF), anchor axial force within the foundation pit (M), groundwater levels within the pit (SW), horizontal and vertical displacements at the top of foundation pit piles (WY and CJ, respectively), anchor axial force and groundwater levels, as well as horizontal and vertical displacements, for both side slopes (JM, PSW, PWY, PWX) and the embankment (S, J). The spatial distribution of these monitoring points is illustrated in Figure 5, while Table 2 provides a concise summary of the primary monitored variables.

Table 2.

Main monitoring items.

Serial Number	Object	Monitoring items	Unit	Obtain access
1	Climate	RF	mm	Weather forecast
2	Foundation pit	M	kN	SSC-101 Frequency reading instrument
		SW	mm	SVW-1 Electric water level gauge
		WY	mm	TS30 Total station
		CJ	mm	DNA03 Electronic level
3	Slope	JM	kN	SSC-101 Frequency reading instrument
		PSW	mm	SVW-1 Electric water level gauge
		PWY	mm	TS30 Total station
		PWX	mm	DNA03 Electronic level
4	Embankment	S	mm	DNA03 Electronic level
		J	mm	TS30 Total station

All mechanical parameters data, except for rainfall, were collected manually to ensure accuracy and consistency. Damaged monitoring points were excluded, and the raw data underwent preprocessing to refine its quality. For non-synchronous monitoring data of the structural elements, we applied the linear trend method to adjacent points, filling in gaps to create continuous time-series data. Consequently, we constructed comprehensive time-series profiles for the eleven monitoring mechanical parameters indicators listed. Figure 6 illustrates the monthly variations in rainfall, alongside monthly averages of other monitored parameters, for brevity and clarity in visualization.

The time-series analysis of the monitored points in the structural system reveals a climatic pattern of mild winters with minimal rainfall and hot, rainy summers. The temperature peaked above 30°C, while monthly rainfall exceeded 188 mm, indicating that rainfall cannot be overlooked as a factor influencing the foundation pit, slope, and embankment. In response to rainfall, the groundwater level within the structural system underwent significant fluctuations, primarily tracking seasonal rainfall patterns. Regarding stress conditions, both the foundation pit anchor cables and slope anchors initially exhibited high axial stress levels. However, upon the cessation of construction activities, these stresses gradually decreased and stabilized. Likewise, the displacements observed in the structural system exhibited a general trend of gradual stabilization.

3.2

Results of the intelligent analysis of the correlation of multi-influence factors and multi-structure mechanical parameters changes

The dataset was partitioned into training and test sets, with 80% of the test indicators and factors allocated to the former for model training, and the remaining 20% serving as the test set for evaluation. In Section 2.2, a feed-forward neural network model was devised to establish correlations between multiple influencing factors and resultant structural mechanical parameters changes. This model underwent training, and subsequently, a comparative analysis was conducted between the anticipated and the predicted outputs, as illustrated in Figure 7.

Figure 7 presents the results of the curve comparison, revealing a congruency between the trajectory of the training result curve and the measured curve. This congruence underscores the efficacy of the chosen test indicators, factors, and the multi-influence factor to multi-structure mechanical parameters change correlation models employed in this study. As anticipated, the models yielded favorable outcomes, with high correlation coefficients (R² ranging from 0.91 to 0.97), low root mean square errors (RMSE ranging from 0.078 to 0.194), and minimal mean absolute errors (MAE ranging from 0.003 to 0.019). The findings demonstrate that the model is capable of elucidating the intricate relationships between physical and mechanical parameters and their subsequent impacts on various monitoring points across multiple structural configurations under the influence of diverse factors. Furthermore, the model exhibits remarkable precision in both prediction and fitting, underscoring its potential for practical applications.

Furthermore, to quantitatively assess the degree of correlation among various influence mechanical parameters, Gray correlation theory was employed, utilizing Equation (1). Subsequent to weighted analysis, the definitive Gray Correlation Degree (GCD) for each influence factor indicator was derived, with the computed outcomes presented in Figure 8.

The quantitative analysis presented in Figure 8 reveals a robust correlation, with Gray Correlation Degrees (GCD) ranging from 0.848 to 0.976, between the studied structures and key influencing mechanical parameters such as groundwater level, rainfall, anchor cable axial force, and anchor rod axial force. This indicates the reliability of the proposed multi-influence factor, multi-structural mechanical parameters change correlation model. Conversely, for slopes, the spatial positioning led to weaker correlations between their vertical displacement changes and the impact of structures mechanical parameters, as evidenced by lower GCD ranging from 0.586 to 0.648.

To establish the connections between input and output variables, we leveraged the parameters of the multi-influence factor, multi-structure mechanical parameters change correlation model during the training phase. These correlations, pertaining to structural mechanical parameters monitoring points under multiple influencing factors, were quantitatively described using Equations (2) through (5).

In this model, N = 9, vih is a 9-dimensional weight vector, h = 3, and q = 1.

As an example, the predictive analysis of the multi-influence factor multi-structure mechanical parameters change correlation model in Figure 7(a) yielded the following values for vih, r_h, w_hj, and Θ_j: $\begin{matrix} v_{i h} (9 \times 3) = & [\begin{matrix} - 0.003 & 0.396 & - 0.044 & 0.152 & - 0.050 & 0.287 & 0.022 & - 0.202 & - 0.131 \\ 0.071 & 0.118 & 0.151 & - 0.270 & - 0.468 & 0.405 & - 0.410 & - 0.469 & - 0.367 \\ - 0.072 & - 0.452 & 0.212 & 0.419 & - 0.458 & - 0.127 & - 0.298 & - 0.024 & - 0.277 \end{matrix}], \\ r_{h} = {[\begin{array}{l} 0.471 & 0.153 & - 0.404 \end{array}]}^{T} \\ w_{h j} = [\begin{array}{l} 1.501 & 0.186 & 0.273 \end{array}], \\ θ_{j} = {[- 0.320]}^{T} . \end{matrix}$ \[\begin{matrix} {{v}_{ih}}(9\times 3)= & [\begin{matrix} -0.003 & 0.396 & -0.044 & 0.152 & -0.050 & 0.287 & 0.022 & -0.202 & -0.131 \\ 0.071 & 0.118 & 0.151 & -0.270 & -0.468 & 0.405 & -0.410 & -0.469 & -0.367 \\ -0.072 & -0.452 & 0.212 & 0.419 & -0.458 & -0.127 & -0.298 & -0.024 & -0.277 \\ \end{matrix}], \\ {} & {{r}_{h}}={{[\begin{array}{*{35}{l}} 0.471 & 0.153 & -0.404 \\ \end{array}]}^{T}} \\ {} & {{w}_{hj}}=[\begin{array}{*{35}{l}} 1.501 & 0.186 & 0.273 \\ \end{array}], \\ {} & {{\theta }_{j}}={{[-0.320]}^{T}}. \\ \end{matrix}\]

To identify the monitoring indicators that exert the most significant influence on structural system mechanical parameters variations, we conducted a sensitivity analysis leveraging the trained feedforward neural network model. This analysis ranked the influencing factors according to their respective contributions, which were derived from the neural network’s connection weights. These weights, as discussed in prior studies (refs. [49, 50]), reflect the relative importance of the input variables in shaping the model’s output. The results of this analysis are presented in Figure 9.

Furthermore, we conducted a sensitivity analysis to evaluate the impact of various influencing mechanical parameters on the behavior of geotechnical structures, focusing on their significance. As depicted in Figure 9(a), the sensitivity ranking of the factors affecting the horizontal displacement of the structure was derived. Notably, stress conditions (M, JM) exhibited a substantially higher sensitivity to horizontal displacements compared to climatic factors (e.g., RF) and water table variations (PWS, SW). Conversely, other conditions, such as displacement synergies, displayed an intermediate sensitivity level, falling between stress-induced and climatic/water table-related effects. This disparity stems from the fundamental principle that structural deformation arises from alterations in the initial stress state, particularly due to the unloading effect at critical surfaces. Consequently, mechanical parameters are inherently more sensitive and play a pivotal role. Meanwhile, metrics indirectly linked to mechanics, like displacements, may exhibit hysteresis effects.

Regarding the horizontal displacement, the correlation between rainfall and groundwater level changes was less pronounced. This can be attributed to the horizontal hydrophobic drainage system in the structure, which leads to a stronger correlation between groundwater level variations and vertical displacements through alterations in effective stress within the strata. When analyzing the sensitivity to vertical displacement, as illustrated in Figure 9(b), stress state changes again emerged as the most significant factor. Unlike horizontal displacements, vertical movements were more responsive to groundwater level fluctuations than displacement synergies, while rainfall effects were least significant.

Therefore, for horizontal displacements, stress conditions and displacement synergies, with groundwater level changes, can be considered as sensitive influences on the proximal structural system, in descending order of sensitivity. Conversely, for vertical displacements, stress, groundwater, and displacement should be synergistically regarded as sensitive factors, also in descending order. Other factors, notably rainfall, can be categorized as sub-sensitive influences.

Given the exclusive consideration of these pivotal influencing mechanical parameters, and under the assumption that extraneous conditions, such as temperature fluctuations, wind velocity, and anthropogenic impacts, can be disregarded, we conducted a rigorous quantitative assessment of the sensitivity to the effects emanating from various structures. This analysis is succinctly illustrated in Figure 10.

In summary, practical engineering endeavors ought to prioritize the meticulous monitoring of high- stress indicators (M, JM) within structural systems, alongside the intricate interplay of inter-structural mechanical parameters. By conducting real-time analyses of these indicators’ time-series data, we can promptly address potential issues through engineering interventions or maintenance procedures, thereby safeguarding the overall safety and stability of geotechnical structures. Nevertheless, it is imperative not to overlook the substantial influence of groundwater level fluctuations and rainfall patterns, both of which can significantly impact the vertical displacement of structures. Where feasible, additional monitoring points should be established to track indicators directly tied to the structural mechanical parameters. Furthermore, groundwater conditions, rainfall, and other pertinent factors should be continually monitored and holistically assessed throughout the construction phase. These considerations hold paramount significance for the design, construction, operational efficiency, and long-term maintenance safety of building systems.

4

Conclusion

This study introduces an intelligent analytical approach grounded in a feed-forward neural network, aimed at elucidating the intricate relationships among diverse mechanical parameters influencing variations across multiple structural components. By constructing a correlation model tailored to these structural changes, the methodology pinpoints crucial influences that are intimately linked to alterations in the geotechnical structure system mechanical parameters. Furthermore, it conducts a rigorous quantitative sensitivity analysis, thereby unraveling the enigmatic correlation between adjacent structures and the overarching stability control of the system.

Applying this multi-factor, multi-structure mechanical parameters correlation model, formulated using the feed-forward neural network algorithm, to a prototypical geotechnical structure system in Southern China yielded promising results. Notably, the model demonstrated a strong fit for engineering applications, as evidenced by its high-performance metrics (R2 ranging from 0.91 to 0.96, RMSE ranging from 0.078 to 0.194, MAE ranging from 0.003 to 0.019, and GCD from 0.848 to 0.976). The quantification of influential mechanical parameters underscores novel insights into the safe design and monitoring strategies for structural systems, while also facilitating the exploration of latent factors within engineering contexts.

The established correlation model, which integrates the effects of multiple structures and mechanical parameters, serves as a valuable reference for enhancing the safety of design, construction, operation, and maintenance processes associated with typical structure systems in deltaic regions. Additionally, it offers a pertinent framework for quantitative evaluations of the impacts and sensitivities of adjacent geotechnical structures mechanical parameters in disparate geographical regions.

CRediT authorship contribution statement

Data curation, Qinghe Zeng, Jiu Guan; Formal analysis, Qinghe Zeng, Jin Liao; Funding acquisition, Zhen Liu; Investigation, Qinghe Zeng, Jin Liao; Methodology, Jin Liao and Feng Gao; Project administration, Qinghe Zeng, Jiu Guan; Writing – original draft, Qinghe Zeng, Jin Liao; Writing – review & editing, Qinghe Zeng, Jin Liao, Jiu Guan, Feng Gao, and Zhen Liu.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

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.

Lingua:: Inglese

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Analysis of correlation and sensitivity influences on the variation of mechanical parameters of proximate structures in the delta region

Qinghe Zeng

Jin Liao

Jiu Guan

Feng Gao

Zhen Liu

Pubblicato online: 27 feb 2025

Ricevuto: 15 ott 2024

Accettato: 15 gen 2025

DOI: https://doi.org/10.2478/amns-2025-0142

Parole chiaveCorrelation, Sensitive impact factors, Mechanical parameter variations, Proximate Structures, Delta region

© 2025 Qinghe Zeng et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Parole chiave
Correlation, Sensitive impact factors, Mechanical parameter variations, Proximate Structures, Delta region