A soil arching effect degradation rate prediction method based on formation characteristic curve

Abstract

The application discloses a soil arching effect degradation rate prediction method based on a stratum characteristic curve, and aims at solving the problem that the soil arching effect degradation caused by double-line tunnel excavation is difficult to quantitatively characterize. S1, discrete and parameter vectorization are carried out on the monitoring data of the double active door test; S2, an analytical expression of the stratum characteristic curve above the left and right active doors is constructed, and initial boundary conditions and limit stable boundary conditions are determined; S3, a physical guide neural network is constructed, the network parameter iterative optimization is guided through a comprehensive loss function, and optimal fitting parameters and an optimal analytical expression of the stratum characteristic curve are output; S4, the soil arching effect degradation rate η is calculated and constructed, and the quantitative prediction of the degradation degree is completed. The dual guarantee of data fitting accuracy and physical interpretability is realized, and the non-dimensional index of the output degradation rate fills the blank of the unified quantitative index of the soil arching effect degradation under secondary unloading, and can serve the stratum disturbance risk assessment and safety control of the double-line tunnel underpass project.

Description

Technical Field

[0001] This invention relates to the field of interdisciplinary technology of underground engineering and computer algorithms, and in particular to a method for predicting the degradation rate of soil arching effect based on stratigraphic characteristic curves. Background Technology

[0002] With the continuous advancement of urban rail transit construction and underground space development, the construction of double-track tunnels passing under each other in succession is becoming increasingly common. The initial excavation and unloading of the tunnel triggers a redistribution of ground stress, forming a soil arching effect in the unloading disturbance zone, thus achieving stress transfer and balance in the soil. The subsequent excavation of the tunnel causes the foundation to undergo a second vertical unloading, leading to the degradation of the already formed stable soil arching effect, and consequently causing secondary ground deformation and excessive surface settlement, among other engineering risks. The degree of soil arching effect degradation is an important reference for the safety control of double-track tunnel excavation projects, and how to quantitatively characterize it is a key technical issue in this field. Regarding soil arching effect assessment methods, Chinese patent CN118094957B discloses a ground toughness assessment method based on the soil arching effect. By constructing a ground response curve and calculating the soil arching rate corresponding to standardized displacement, a ground toughness assessment model is established to evaluate the extent to which the soil arching effect is utilized under a single excavation condition. However, this method targets the formation process of the soil arching effect caused by a single excavation, assessing the soil toughness under a single unloading condition. It does not address the secondary unloading condition caused by the sequential excavation of dual-track tunnels, nor does it establish a quantitative index to characterize the degree of soil arching effect degradation between two excavations. Therefore, it cannot meet the needs of assessing soil arching effect degradation in the scenario of sequential excavation of dual-track tunnels. Regarding surface settlement prediction methods, Chinese patent CN116579150A discloses a full-stage surface settlement prediction and control method. This method comprehensively considers factors such as soil arching loss and combines the elastic foundation beam theory and Peck's formula to predict surface settlement during the pipe jacking process. This method considers the soil arching effect as one of the parameters affecting surface settlement, but its treatment of the soil arching effect is relatively simplified, only using it as a correction factor in the settlement prediction model. It does not provide a continuous quantitative characterization of the full-cycle evolution of the soil arching effect with excavation displacement, and therefore cannot reflect the dynamic changes of the soil arching effect at different excavation stages. Regarding methods for analyzing the stress evolution of soil arches, Chinese patent CN117786787A discloses a method for studying the soil arch effect in deeply buried double-hole parallel rectangular pipe jacking tunnels. Based on the concept of structural arches, a soil arch stress evolution model is established, and the stress distribution law of the soil arch is derived using limit equilibrium theory. This method focuses on the theoretical analysis of the stress distribution characteristics of soil arches under static conditions, taking the limit equilibrium state as the research object. It fails to continuously describe the dynamic evolution process of the soil arch effect with excavation displacement, and it also fails to establish a quantitative index that can quantitatively characterize the degree of degradation of the soil arch effect under sequential excavation of dual-track tunnels.In summary, existing analyses of stratigraphic characteristic curves primarily focus on qualitative analysis of feature points such as the minimum soil arching ratio, reflecting only specific states of the soil arching effect's evolution and failing to provide a continuous quantitative characterization of the soil arching effect throughout its entire lifecycle. Existing stratigraphic characteristic curve fitting methods often employ purely empirical formulas or numerical fitting methods without physical constraints. Purely empirical formulas suffer from ambiguous physical meanings and poor generalization ability, while pure data fitting without physical boundary constraints is prone to overfitting and extrapolation distortion. Furthermore, current technologies have not yet constructed a quantitative index for the soil arching effect degradation rate with clear physical meaning, failing to transform the differences in stratigraphic response corresponding to two consecutive excavations of a dual-track tunnel into quantifiable actual parameters. This hinders the provision of accurate quantitative support for stratigraphic disturbance control and existing structural safety protection design during dual-track tunnel construction. Therefore, a new technical solution is needed to quantitatively predict the degree of soil arching effect degradation under the condition of consecutive excavations of dual-track tunnels. Summary of the Invention

[0003] The purpose of this invention is to provide a method for predicting the degradation rate of soil arching effect based on stratigraphic characteristic curves, so as to solve the following technical problems existing in the prior art: (1) Existing technologies have not yet formed a clear and unified quantitative characterization method for the soil arching effect degradation caused by the successive excavation of dual-track tunnels, and cannot accurately quantify the degree of soil arching effect degradation; (2) The indoor double-moving door test analysis focuses on the qualitative analysis of characteristic points such as the minimum soil arching rate, which can only reflect the specific state of the soil arching effect evolution and cannot continuously and quantitatively characterize the soil arching effect throughout the entire cycle. (3) Existing methods for fitting stratigraphic characteristic curves mostly use pure empirical formulas or numerical fitting without physical constraints. Pure empirical formulas have vague physical meanings and poor generalization ability. Unconstrained pure data fitting lacks the constraints of physical boundary conditions of soil arching effect, and is prone to problems such as overfitting and extrapolation distortion. (4) Existing technologies have not yet constructed a quantitative index for the degradation rate of the soil arch effect with clear physical meaning, and cannot convert the difference in the stratum characteristic curves corresponding to the two excavations into quantifiable actual parameters, making it difficult to provide accurate quantitative support for the control of stratum disturbance and the design of safety protection of existing structures during the construction of double-track tunnels.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: This invention provides a method for predicting the degradation rate of soil arching effect based on stratigraphic characteristic curves, applied to a scenario of sequential excavation of a dual-track tunnel in a dual-door test simulation, comprising the following steps: S1, the monitoring data of the double-door test staged excavation are discretized and vectorized to construct the parameter vector X1=[δ] corresponding to the left movable door of the tunnel excavation. 1i P 1i ] The parameter vector X2=[δ] corresponding to the right-side movable door of the subsequent tunnel excavation 2j P 2j ] Calculate the soil arch ratio corresponding to the left and right movable doors respectively. and and normalized displacement and ;where δ 1i P represents the measured downward displacement of the left movable gate in the i-th monitoring step. 1i δ represents the measured vertical earth pressure above the i-th monitoring step of the left-side movable gate. 2j P represents the measured downward displacement of the right-side active gate in the j-th monitoring step. 2j P0 represents the measured vertical earth pressure above the right-side movable door at the j-th monitoring step, P0 represents the initial vertical earth pressure of the movable door, and B represents the width of the movable door. S2, construct analytical expressions for the stratigraphic characteristic curves above the left and right active gates respectively. and It also clarifies the initial boundary condition ρ(ξ=0)=1 and the ultimate stability boundary condition ρ(ξ=ξ) that the stratigraphic characteristic curve must satisfy during the evolution of the soil arching effect. max ) = ρ ult ;where ρ ult1 and ρ ult2 These are the limiting soil arching ratios of the left and right stratigraphic characteristic curves, respectively, representing the steady-state value of the soil arching ratio when the soil arching effect is completely stable. and K1 and K2 are the linear attenuation coefficients of the characteristic curves of the left and right strata, respectively, representing the intensity of the linear attenuation of the soil arching rate with displacement; K1 and K2 are the nonlinear evolution rate coefficients of the characteristic curves of the left and right strata, respectively, representing the rate at which the soil arching effect adjusts rapidly with displacement. S3. Construct a physical-guided neural network, inputting the parameter vectors X1 and X2, and combining the analytical expressions ρ1(ξ1) and ρ2(ξ2) of the formation characteristic curve and the physical boundary conditions as physical prior constraints. The network parameters are iteratively optimized through a comprehensive loss function, outputting the optimal fitting parameters a of the formation characteristic curve. 1opt k 1opt a 2opt k 2opt Analytical expression of optimal formation characteristic curve r 1opt ( x 1) and r 2opt ( x 2); S4, based on the analytical expression of the optimal formation characteristic curve r1opt ( x 1) and r 2opt ( x 2) Calculate the baseline integral eigenvalue S0 without soil arching effect, the integral eigenvalue S1 of the characteristic curve of the strata with the left active gate, and the integral eigenvalue S2 of the characteristic curve of the strata with the right active gate, respectively, to construct the soil arching effect degradation rate. This allows for the quantitative prediction of the degree of degradation of the soil arching effect.

[0005] Compared with the prior art, the present invention has the following beneficial effects: (1) An analytical model of the stratum characteristic curve under dual working conditions was established to realize the physical characterization of the evolution and degradation law of the soil arching effect. This invention constructs analytical expressions of the stratum characteristic curve with clear physical meaning for the excavation of the tunnel before and after the excavation, clarifies the physical connotation of the ultimate soil arching rate, the linear attenuation coefficient, and the nonlinear evolution rate coefficient, and defines the physical constraints of the initial boundary and the ultimate stability boundary. It fully analyzes the whole-cycle mechanical mechanism of the formation of the soil arch in the excavation before and the degradation of the soil arch in the excavation after the excavation, avoiding the defects of the traditional pure empirical formula with vague physical meaning and poor generalization ability.

[0006] (2) A physically guided neural network with multiple physical constraints was constructed to ensure the fitting accuracy and physical reliability of the prediction results. The five-layer fully connected physically guided neural network designed in this invention combines a comprehensive loss function consisting of data fitting loss, physical boundary constraint loss, and parameter regularization loss to guide the iterative optimization of network parameters. It not only accurately captures the complex nonlinear relationship of the stratum characteristic curve, but also forces the network training process to always conform to the real mechanical laws of the soil arching effect. This overcomes the problems of overfitting, extrapolation distortion, and deviation from the physical essence of pure data-driven models, and achieves a dual guarantee of data fitting accuracy and physical interpretability.

[0007] (3) The output results directly serve the design and safety control of tunnel engineering and have strong practical application value. The dimensionless index of soil arching effect degradation rate finally output by this invention can directly and quantitatively characterize the degree of degradation of soil arching effect under the successive excavation of double-track tunnels. It fills the gap in the existing technology where there is no unified quantitative index for soil arching effect degradation under secondary unloading. It can be applied to the risk assessment of stratum disturbance, optimization of excavation method, design of support parameters and formulation of protection schemes for existing buildings in the successive underpass projects of double-track tunnels, and provides accurate and direct quantitative basis for the safety control of urban tunnel underpass construction. Attached Figure Description

[0008] Figure 1The diagram illustrates the scenario and system of the embodiment, showing the overall structure of the dual-door test device, which includes five parts: a rigid model box 5, a test soil 8, a high-precision stepper motor 4 with dual independent control, a multi-channel static data acquisition instrument 7, and a PC terminal 6 for data processing and algorithm calculation. The diagram marks key components such as the left movable door 2, the right movable door 3, the high-precision vibrating wire earth pressure gauge 1, the stepper motor 4, and the static data acquisition instrument 7.

[0009] Figure 2 The flowchart shown in this example illustrates the overall process of predicting the soil arching effect degradation rate. It fully demonstrates the four core steps and their logical relationships, from inputting monitoring data from the dual-gate test, analyzing and modeling the stratigraphic characteristic curves, fitting the physical-guided neural network, to calculating the soil arching effect degradation rate.

[0010] Figure 3 The diagram illustrates the architecture of the physically guided neural network in this embodiment, showing the detailed configuration of the five-layer fully connected network architecture, including the input layer, the physical feature encoding layer (64 neurons), the nonlinear mapping fitting layer (128 neurons), the feature compression and smoothing layer (64 neurons), and the output layer, as well as the data flow and feature transfer relationships between each layer.

[0011] Figure 4 This diagram illustrates the integral characteristic values ​​of the soil arching effect throughout the entire life cycle in this embodiment. With normalized displacement ξ as the abscissa and soil arching ratio ρ(ξ) as the ordinate, it visually presents the physical and geometric meanings of the baseline integral characteristic value S0 (area of ​​blue region) without soil arching effect, the integral characteristic value S1 (area of ​​yellow region) of the stratum characteristic curve of the left movable gate, and the integral characteristic value S2 (area of ​​green region) of the stratum characteristic curve of the right movable gate. The diagram includes the baseline without soil arching effect and the optimal stratum characteristic curve ρ of the left movable gate. 1opt (ξ1) and the optimal stratigraphic characteristic curve ρ of the right-side active gate 2opt (ξ2) Three core curves.

[0012] Figure 5 This is a schematic diagram of the formation characteristic curve fitting results in the embodiment. With normalized displacement ξ as the abscissa and soil arching ρ(ξ) as the ordinate, it demonstrates the curve fitting effect of the method of the present invention. The circular scatter points in the figure represent the monitoring data of the double-moving-door test under the initial tunnel excavation condition, and the square scatter points represent the monitoring data of the double-moving-door test under the subsequent tunnel excavation condition. The red curve and the gray curve represent the two optimal formation characteristic curve fitting lines ρ output after optimization by the physical-guided neural network, respectively. 1opt (ξ1) and ρ 2opt (ξ2) intuitively verifies the high-precision fitting capability of the method of the present invention for the formation characteristic curve.

[0013] Markings: 1-Vibrating wire earth pressure gauge, 2-Left movable door, 3-Right movable door, 4-Stepper motor, 5-Rigid model box, 6-PC terminal, 7-Static data acquisition instrument, 8-Test soil. Detailed Implementation

[0014] The specific embodiments of the present invention will be described in detail with reference to the accompanying drawings. It should be noted that the technical terms in the following embodiments are defined as follows: Soil arching ratio characterizes the degree of soil arching effect; the smaller the soil arching ratio, the more significant the soil arching effect. Normalized displacement characterizes the degree of displacement development during the evolution of the soil arching effect, eliminating the influence of the geometric dimensions of the movable gate. The stratigraphic characteristic curve characterizes the curve of the entire evolution process of the soil arching effect, with normalized displacement as the abscissa and soil arching ratio as the ordinate. The physical-guided neural network is a neural network combined with physical boundary condition constraints to ensure that the prediction results conform to the true mechanical laws of the soil arching effect. The soil arching effect degradation rate is a dimensionless index used to quantitatively characterize the degree of degradation of the soil arching effect under sequential excavation of dual-track tunnels. The meanings of the markings in the accompanying drawings are as follows: Figure 1 The following is a schematic diagram of an example scenario and system, illustrating the five components of a dual-door testing system; Figure 2 The flowchart of the soil arching effect degradation rate prediction method in the embodiment shows the sequential relationship of the four core steps S1 to S4. Figure 3 This is a schematic diagram of the architecture of the physical guided neural network in the embodiment, showing a five-layer structure: input layer, physical feature encoding layer, nonlinear mapping fitting layer, feature compression and smoothing layer, and output layer. Figure 4 The diagram below illustrates the integral characteristic value of the soil arching effect throughout the entire cycle in the embodiment, showing the geometric meaning of the baseline integral characteristic value S0 without soil arching effect, the integral characteristic value S1 of the left active gate stratum characteristic curve, and the integral characteristic value S2 of the right active gate stratum characteristic curve. Figure 5 This is a schematic diagram of the formation characteristic curve fitting results in the example, showing the comparison between the optimal formation characteristic curve fitting line and the scatter points of the experimental monitoring data.

[0015] This embodiment provides a method for predicting the degradation rate of the soil arching effect based on stratigraphic characteristic curves. Addressing the core issue of the difficulty in quantitatively characterizing the soil arching effect degradation caused by sequential excavation of dual-track tunnels, it uses an indoor double-moving-door model test as the application scenario. Figure 1As shown, the dual-door test system consists of five parts: a rigid model box 5, test soil 8, a high-precision stepper motor 4 with dual independent control, a multi-channel static data acquisition instrument 7, and a PC terminal 6 for data processing and algorithm calculation. The rigid model box 5 is assembled from high-rigidity tempered glass and an aluminum alloy frame, and is filled with the target stratum soil for the test. Two vertically lifting movable doors of identical size, symmetrically arranged, are reserved at the bottom of the rigid model box 5, with a width of B for each door. The downward displacement of the left movable door 2 is used to simulate the initial tunnel excavation, and the downward displacement of the right movable door 3 is used to simulate the subsequent tunnel excavation. High-precision vibrating wire earth pressure gauges 1 are respectively installed on the top of the left movable door 2 and the right movable door 3 to measure the vertical earth pressure above the corresponding movable door in real time, obtaining the initial vertical earth pressure P0 in the initial static state of the movable door, and the measured vertical earth pressure P above the left movable door 2 at the i-th monitoring step during the entire test. 1i The measured vertical earth pressure P above the j-th monitoring step corresponding to the right-side movable door 3. 2j The bottoms of the left movable door 2 and the right movable door 3 are rigidly connected to independent high-precision stepper motors 4. Each stepper motor 4 has a built-in millimeter-level displacement feedback module, which can precisely control the graded descent rate and downward displacement of a single movable door, simulating the formation and degradation process of the soil arching effect during the unloading of the double-track tunnel excavation. Simultaneously, it outputs in real time the measured downward displacement δ of the i-th monitoring step of the left movable door 2. 1i The measured downward displacement δ of the right-side movable door 3 in the j-th monitoring step 2j The earth pressure gauges installed on both sides of the movable doors and the displacement feedback module built into the stepper motor 4 both have standardized signal output interfaces, which can output earth pressure and displacement monitoring data in real time throughout the test. Both types of monitoring data are uniformly connected to the multi-channel static data acquisition instrument 7. After the static data acquisition instrument 7 performs analog-to-digital conversion, filtering and noise reduction, and time synchronization processing on the acquired raw analog signals, it transmits them in real time to the data processing and algorithm calculation terminal via wired communication. This provides complete raw data support for subsequent monitoring data discretization and parameter vectorization, construction of analytical models of stratigraphic characteristic curves, physical-guided neural network training, and calculation of soil arching effect degradation rate. The data processing and algorithm calculation uses a PC as the terminal, which has a built-in full-process algorithm module for predicting the soil arching effect degradation rate of this invention. The full-process calculation of subsequent implementation steps S1 to S4 can be run on the PC 6, and finally output the optimal analytical expression of the stratigraphic characteristic curve. r 1opt ( x 1) and r 2opt ( x 2), and the predicted results of the soil arch effect degradation rate η.

[0016] like Figure 2As shown, the soil arching effect degradation rate prediction method based on stratigraphic characteristic curves provided in this embodiment includes four core steps, S1 to S4. Step S1 involves inputting the staged excavation monitoring data obtained from the double-door test, discretizing the monitoring data sequence, and vectorizing the parameters to obtain parameter vectors X1 and X2 corresponding to the left door of the tunnel excavation before the excavation and the right door of the tunnel excavation after the excavation. These vectors are used to calculate the soil arching rate ρ corresponding to the left door 2 and the right door 3. 1i and ρ 2j With normalized displacement ξ 1i and ξ 2j Step S2 involves establishing analytical expressions ρ1(ξ1) and ρ2(ξ2) for the stratum characteristic curves above the left active gate 2 and right active gate 3 based on the soil arching ratio and normalized displacement monitoring sequence obtained in S1, and clarifying the initial boundary conditions and ultimate stability boundary conditions that the stratum characteristic curves must satisfy during the evolution of the soil arching effect. Step S3 involves constructing a physically guided neural network consisting of an input layer, a physical feature encoding layer, a nonlinear mapping fitting layer, a feature compression and smoothing layer, and an output layer, using a comprehensive loss function L... oss Guided network parameter iterative optimization, outputting the optimal fitting parameter 'a' for the formation characteristic curve. 1opt k 1opt a 2opt k 2opt Analytical expression of optimal formation characteristic curve r 1opt ( x 1) and r 2opt ( x 2). Step S4 is based on the analytical expression of the optimal formation characteristic curve. r 1opt ( x 1) and r 2opt ( x 2) Calculate the baseline integral characteristic value S0 without soil arching effect, the integral characteristic value S1 of the characteristic curve of the left active gate stratum, and the integral characteristic value S2 of the characteristic curve of the right active gate stratum. Establish and calculate the soil arching effect degradation rate η to complete the quantitative prediction of the degree of soil arching effect degradation.

[0017] The specific implementation process of step S1 is as follows: A graded monitoring sequence is generated for the entire unloading process of the left movable door 2 and the right movable door 3 obtained from the double movable door test. Using an equal displacement interval division strategy, the continuously graded downward monitoring sequence is discretized into m independent monitoring steps for the left movable door and n independent monitoring steps for the right movable door. The displacement node δ of the i-th monitoring step of the left movable door... 1i Satisfy δ 1i=iΔδ1, where Δδ1 is the discrete displacement interval of the left movable door, determined according to the graded downward movement step size of the double movable door test, i is a natural number between 1 and m, and m is the total number of monitoring steps for the left movable door 2. The displacement node δ of the j-th monitoring step of the right movable door 3. 2j Satisfy δ 2j =jΔδ2, where Δδ2 is the discrete displacement interval of the right movable door 3, determined according to the graded downward movement step size of the double movable door test, j is a natural number between 1 and n, and n is the total number of monitoring steps for the right movable door 3. The monitoring parameters corresponding to the monitoring sequences of the left movable door 2 and the right movable door 3 are vectorized to construct parameter vector X1 for the left movable door 2 and parameter vector X2 for the right movable door 3, respectively. The expression for parameter vector X1 of the left movable door 2 is X1=[δ 1i P 1i ] In the formula δ 1i P represents the measured downward displacement of the left movable door 2 in the i-th monitoring step. 1i Let X2 be the measured vertical earth pressure above the left movable gate 2 corresponding to the i-th monitoring step. The expression for the parameter vector X2 of the right movable gate 3 is X2=[δ... 2j P 2j ] In the formula δ 2j P represents the measured downward displacement of the right-side movable door 3 at the j-th monitoring step. 2j The measured vertical earth pressure above the j-th monitoring step corresponding to the right-side movable door 3 is denoted as .

[0018] The parameter vectors X1 and X2 obtained above are used to calculate the soil arch ratio ρ corresponding to the left movable door 2 and the right movable door 3, respectively. 1i and ρ 2j With normalized displacement ξ 1i and ξ 2j The soil arching ratio ρ corresponding to the i-th monitoring step of the left-side active door 2. 1i Calculated as In the formula P 1i Pi represents the measured vertical earth pressure above the left movable door 2 at the i-th monitoring step, and P0 represents the initial vertical earth pressure of the movable door. The initial vertical earth pressures on the left movable door 2 and the right movable door 3 are equal. The soil arching ratio ρ corresponds to the j-th monitoring step of the right movable door 3. 2j Calculated as In the formula P 2j Pj represents the measured vertical earth pressure above the right-side movable door 3 at the j-th monitoring step, and P0 represents the initial vertical earth pressure of the movable door. The soil arching ratio characterizes the extent of the soil arching effect; a smaller soil arching ratio indicates a more significant soil arching effect at the corresponding monitoring step. The normalized displacement ξ corresponds to the ith monitoring step of the left-side movable door 2. 1i Calculated as In the formula δ 1i Let ξ be the measured displacement corresponding to the i-th monitoring step of the left movable door 2, and B be the width of the movable door. The widths of the left movable door 2 and the right movable door 3 are equal. Let ξ be the normalized displacement corresponding to the j-th monitoring step of the right movable door 3. 2j Calculated as In the formula δ 2j Let be the measured displacement corresponding to the j-th monitoring step of the right-side movable gate 3, and B be the width of the movable gate. The normalized displacement is used to characterize the degree of displacement development during the soil arching effect evolution process, eliminate the influence of the geometric dimensions of the movable gate, and realize dimensionless comparison under different working conditions.

[0019] The specific implementation process of step S2 is as follows: Based on the soil arching ratio and normalized displacement monitoring sequence obtained in S1, the analytical expression ρ1(ξ1) of the stratum characteristic curve corresponding to the left active gate 2 and the analytical expression ρ2(ξ2) of the stratum characteristic curve corresponding to the right active gate 3 are constructed respectively. The analytical expression ρ1(ξ1) of the stratum characteristic curve corresponding to the left active gate 2 is as follows: In the formula, ρ1(ξ1) is the soil camber ratio of the left movable door 2 at the normalized displacement ξ1, which is determined based on the double movable door test. ult1 The limiting soil arching ratio is represented by the characteristic curve of the strata on the left, which characterizes the steady-state value of the soil arching ratio when the soil arching effect is completely stable. is the linear attenuation coefficient of the left-side stratum characteristic curve, characterizing the intensity of the linear attenuation of the soil arching ratio with displacement; k1 is the nonlinear evolution rate coefficient of the left-side stratum characteristic curve, characterizing the rate at which the soil arching effect rapidly adjusts with displacement. The analytical expression for the stratum characteristic curve corresponding to active gate 3 on the right side. In the formula, ρ2(ξ2) is the soil camber ratio of the right movable gate 3 at the normalized displacement ξ2, which is determined based on the double movable gate test. ult2 The limiting soil arching ratio is represented by the right-hand stratigraphic characteristic curve, which characterizes the steady-state value of the soil arching ratio when the soil arching effect is completely stable. is the linear attenuation coefficient of the right-side stratum characteristic curve, characterizing the intensity of the linear attenuation of the soil arching rate with displacement, and k2 is the nonlinear evolution rate coefficient of the right-side stratum characteristic curve, characterizing the rate at which the soil arching effect rapidly adjusts with displacement.

[0020] The initial and ultimate stability boundary conditions uniformly satisfied by the characteristic curves of the strata on both sides are clearly defined to constrain subsequent neural network training and parameter optimization, ensuring that the curve evolution conforms to the true mechanical laws of the soil arching effect. The initial boundary conditions are: when the normalized displacement ξ1 of the left movable gate 2 is 0, the movable gate has not undergone downward unloading, the soil arching effect has not yet formed, and the soil arching ratio ρ1 (ξ1=0) = 1; when the normalized displacement ξ2 of the right movable gate 3 is 0, the movable gate has not undergone downward unloading, the soil arching effect has not yet formed, and the soil arching ratio ρ2 (ξ2=0) = 1. The ultimate stability boundary condition is: when the normalized displacement ξ1 of the left movable gate 2 reaches its maximum value ξ...1max When the soil arching effect reaches a fully steady state, the soil arching ratio is equal to the corresponding limiting soil arching ratio ρ. ult1 , satisfying ρ1 (ξ1=ξ 1max ) = ρ ult1 When the normalized displacement ξ2 of the right-side movable door 3 reaches its maximum value ξ 2max At this time, the soil arching effect also enters a completely stable state, satisfying ρ2(ξ2=ξ 2max ) = ρ ult2 For the double-line sliding door test, the maximum value of the normalized displacement ξ1 of the left sliding door 2 is ξ. 1max The maximum value of the normalized displacement ξ2 of the right-side movable door 3. 2max The equality is due to the need for a unified displacement control standard in the dual-line sliding door test to simulate the staged excavation of a parallel tunnel, and the achievement of single-variable control by ensuring consistent displacement boundaries on both sides. Therefore, ξ 1max =ξ 2max .

[0021] The specific implementation process of step S3 is as follows: Figure 3 As shown, the physical-guided neural network is a 5-layer fully connected network architecture, consisting of an input layer, a physical feature encoding layer, a nonlinear mapping fitting layer, a feature compression and smoothing layer, and an output layer connected sequentially. It uses the parameter vectors X1 and X2, processed by discretization and vectorization in S1, as the basic input, and the analytical expression of the stratigraphic feature curve and physical boundary conditions established in S2 as physical prior constraints to complete the entire process of feature learning and parameter fitting. The number of neurons in the input layer is consistent with the dimension of the parameter vectors X1 and X2, used to fully receive and input the normalized displacement and soil camber monitoring data obtained from the left active gate 2 and right active gate 3 in S1, providing the original data foundation for subsequent feature extraction and parameter learning in the network. The physical feature encoding layer has 64 neurons, adopts a fully connected structure, and uses the Gaussian error linear unit (GELU) as the activation function to extract the basic combined features of the input variables, transforming the monitored displacement-soil camber raw data into fitable physical features, completing the basic feature encoding of the input data. The nonlinear mapping fitting layer, with 128 neurons and a fully connected structure, uses the Gaussian Error Linear Unit (GELU) activation function. This core layer captures the nonlinear relationships of the formation feature curves, achieving high-precision mapping and feature extraction of the parameters a1, k1, a2, and k2. The feature compression and smoothing layer, with 64 neurons and a fully connected structure, also uses GELU activation. This compresses high-dimensional features, reduces network complexity, prevents overfitting, and smooths the output features, ensuring the stability of the parameter prediction results. The output layer uses a linear activation function to output the optimal fitting parameters a1, k1, a2, and k2 of the formation feature curve. 1opt k 1opt a2opt k 2opt Substituting the optimal fitting parameters into the analytical expression of the formation characteristic curve of S2, the analytical expressions of the optimal formation characteristic curves on the left active gate 2 and the right active gate 3 are generated. r 1opt ( x 1) and r 2opt ( x 2). Analytical expression of the optimal formation characteristic curve on the left active gate 2 r 1opt ( x 1) For Analytical expression for the optimal formation characteristic curve on the right-side active gate 3. r 2opt ( x 2) for .

[0022] Physically guided neural networks with a comprehensive loss function L oss This serves as the network optimization criterion, guiding the iterative updates of the weight matrices and bias vectors at each layer of the network. The loss value is used to determine network convergence and verify the validity of the results. The comprehensive loss function L... oss Loss function L based on data fitting data Physical boundary constraint loss function L phys and the parameter regularization loss function L reg Weighted composition, comprehensive loss function L oss The expression is In the formula, w1, w2, and w3 are the weighting coefficients of the three types of loss functions, which can be adjusted and determined according to the accuracy of the dual-moving-gate test data and the engineering fitting requirements. Data Fitting Loss Function This is used to measure the deviation between the model-predicted soil arching ratio and the experimentally measured soil arching ratio. It is a core component for ensuring the model's fitting accuracy. The mean squared error loss is used, and the calculation formula is as follows: In the formula, m represents the total number of monitored steps for the left movable door 2, and n represents the total number of monitored steps for the right movable door 3. r 1opt ( x 1) represents the calculated soil arching ratio at normalized displacement ξ1, expressed as the analytical expression of the optimal stratigraphic characteristic curve on the left movable gate 2. ρ1(ξ1) represents the measured soil arching ratio at normalized displacement ξ1 on the left movable gate 2. r 2opt ( x 2) is the calculated soil arching ratio at normalized displacement ξ2, which is the analytical expression of the optimal stratum characteristic curve on the right movable gate 3. ρ2(ξ2) is the measured soil arching ratio at normalized displacement ξ2 of the right movable gate 3.

[0023] Physical boundary constraint loss function L physThis is used to constrain the model output to meet the physical boundary conditions defined in S2, forcing the network training to conform to the true mechanical laws of the soil arching effect, and avoiding distortion of prediction results. The calculation formula is as follows: In the formula, ρ 1opt (ξ1=0) and ρ 2opt (ξ2=0) represent the predicted soil arching ratios of the optimal stratigraphic characteristic curves when the normalized displacements ξ1 and ξ2 are 0, respectively. 1max and ξ 2max The maximum normalized displacements ρ of the left movable door 2 and the right movable door 3 are respectively. 1opt (ξ1=ξ) 1max ) and ρ 2opt (ξ2=ξ) 2max ρ represents the predicted soil arching ratio at the maximum displacement of the optimal stratigraphic characteristic curves of the left movable gate 2 and the right movable gate 3, respectively. ult1 and ρ ult2 These represent the limiting soil arching ratios of the strata characteristic curves on the left and right sides, respectively.

[0024] Parametric regularization loss function L reg To constrain the range of values ​​for the parameters to be fitted, prevent overfitting, and improve the model's generalization ability, L2 regularization loss is used, calculated using the following formula: In the formula, ‖·‖² represents the L2 norm operation.

[0025] The preset loss threshold τ is determined by combining the accuracy of the dual-gate test monitoring data with the engineering fitting requirements. This ensures that invalid network training results are effectively filtered out without overly stringent requirements that could cause the network training to fail to converge. When the comprehensive loss function Loss ≤ τ, the optimal stratigraphic characteristic curve analytical expression output by the network is considered to simultaneously satisfy the monitoring data fitting requirements and the physical evolution law requirements of the soil arching effect, and the process can proceed to the subsequent S4 process. Conversely, if Loss > τ, the process returns to S3, updates the weights and bias parameters of each layer of the network, and retrains until the comprehensive loss function L is reached. oss The threshold requirement is met. The physical-guided neural network, optimized by the comprehensive loss function, can realize the analytical expression for the optimal formation characteristic curve from the monitoring parameter vectors X1 and X2. r 1opt ( x 1) and r 2opt ( x 2) The accurate and reliable mapping ensures that the output results have both physical interpretability and fitting accuracy.

[0026] The specific implementation process of step S4 is as follows: Figure 4 As shown, the optimal fitting parameter a of the formation characteristic curve output by S3 is... 1opt k 1opt a 2optk 2opt Analytical expression of optimal formation characteristic curve r 1opt ( x 1) and r 2opt ( x Based on 2), the integral eigenvalues ​​S0 (without soil arching effect), S1 (left-side active gate stratum characteristic curve integral eigenvalue), and S2 (right-side active gate stratum characteristic curve integral eigenvalue) are calculated respectively. The full-cycle bearing capacity integral eigenvalue S of the soil arching effect is the normalized displacement interval [0, ξ]. max The definite integral of the characteristic curve of the strata is used to characterize the total normalized vertical load borne above the movable gate during the entire tunnel excavation cycle. The larger the S value, the weaker the soil arching effect under the corresponding working condition. max The maximum normalized displacement of the movable gate test is given, with the same value for the maximum normalized displacement of the left movable gate 2 and the right movable gate 3. The baseline integral eigenvalue S0, representing the case where the soil does not exhibit any arching effect and the soil arching ratio is always equal to 1, is calculated using the following formula: The integral eigenvalue S1 of the stratum characteristic curve of the left-hand movable gate corresponds to the full-cycle bearing characteristics of the soil arching effect under the condition of prior tunnel excavation. The optimal fitting parameters are based on the output of S3. a 1opt , k 1opt Analytical expression of the optimal formation characteristic curve above the left active gate 2 r 1opt ( x 1) Calculation, the calculation formula is: In the formula r ult1 The limiting soil arching ratio is the characteristic curve of the strata above the left-side movable gate 2. a 1opt , k 1opt The optimal fitting parameters are the left-side stratum characteristic curve output by S3. The integral characteristic value S2 of the right-side active gate stratum characteristic curve corresponds to the full-cycle bearing characteristics of the soil arching effect under the subsequent tunnel excavation condition, based on the optimal fitting parameters output by S3. a 2opt , k 2opt Analytical expression of the optimal formation characteristic curve above the right-side active gate 3 r 2opt ( x 2) Calculation, the calculation formula is: In the formula, ρ ult2 a represents the limiting soil arching ratio of the stratum characteristic curve above the right-side active gate 3. 2opt k 2opt These are the optimal fitting parameters for the right-side stratigraphic characteristic curve output by S3.

[0027] Based on the three types of integral characteristic values ​​obtained above (i.e., the baseline integral characteristic value S0 without soil arching effect, the integral characteristic value S1 of the stratum characteristic curve of the left active gate, and the integral characteristic value S2 of the stratum characteristic curve of the right active gate), the soil arching effect degradation rate η is constructed to complete the quantitative prediction of the degree of soil arching effect degradation. The soil arching effect degradation rate η is a dimensionless index used to quantitatively characterize the degree of soil arching effect degradation under the sequential excavation of dual-track tunnels. The calculation formula is as follows: The soil arching effect degradation rate η ranges from 0 to 1. Its physical meaning is as follows: when η = 0, it indicates that subsequent tunnel excavation did not trigger soil arching effect degradation, and the soil arching effect formed by the preceding excavation remains intact; the closer η is to 1, the more significant the soil arching effect degradation caused by subsequent excavation, and the closer the soil arching effect formed by the preceding excavation is to complete loss. Based on the soil arching effect degradation rate η, a quantitative prediction of the degree of soil arching effect degradation in the double-door test can be achieved. The prediction results can be directly used for indoor simulation of the evolution law of soil arching effect under sequential excavation of two tunnels, realizing the accurate conversion from monitoring data of the double-door test to quantitative prediction of the degree of soil arching effect degradation.

[0028] like Figure 5 As shown in the diagram, the schematic diagram of the formation characteristic curve fitting results in this embodiment uses the normalized displacement ξ as the abscissa and the soil arching ratio ρ(ξ) as the ordinate, fully presenting the curve fitting effect and the final prediction result. The circular scatter points in the diagram represent the monitoring data scatter points of the double-door test under the initial tunnel excavation condition, and the square scatter points represent the monitoring data scatter points of the double-door test under the subsequent tunnel excavation condition. The red curve and gray curve in the diagram represent the two optimal formation characteristic curve fitting lines ρ output after optimization by the physical-guided neural network, respectively. 1opt (ξ1) and ρ 2opt (ξ2). From Figure 5 As can be seen, the fitted curve closely matches the scatter plot of the experimental monitoring data, directly verifying the high-precision fitting capability of the method of this invention for formation characteristic curves. In this embodiment, the maximum normalized displacement ξ over the entire monitoring period under both sets of conditions is... max =0.25, the limiting soil arching ratio ρ of the stratum characteristic curve above the left-side active gate 2. ult1 =0.20, the limiting soil arching ratio ρ of the stratum characteristic curve above the right-side active gate 3. ult2 =0.31. After adopting the calculation process described in this embodiment, the calculated baseline integral characteristic value without soil arching effect S0=0.2500, the integral characteristic value of the stratum characteristic curve of the left movable gate S1=0.0451, and the integral characteristic value of the stratum characteristic curve of the right movable gate S2=0.0832. The final calculated soil arching effect degradation rate η is η=0.1861. This value indicates that under the two working conditions in this embodiment, the secondary excavation of the subsequent tunnel only caused a slight degradation of the soil arching effect, and the soil arching effect formed by the initial excavation remained good overall.

[0029] This invention addresses the engineering challenge of quantitatively characterizing the secondary degradation of the soil arching effect caused by sequential excavation of dual-track tunnels. It proposes a method for predicting the soil arching effect degradation rate that deeply integrates physical mechanisms and data-driven approaches. The method uses monitoring data from graded excavation under a dual-gate test as input. After discretization and vectorization, parameter vectors corresponding to the preceding and subsequent excavations are obtained. Analytical expressions for the left and right side strata characteristic curves with physical boundary constraints are constructed. A five-layer physical-guided neural network is used to intelligently fit the parameters and optimize the curves. Finally, the soil arching effect degradation rate is calculated using the full-cycle bearing capacity integral characteristic value. This forms a complete technical system from experimental data processing, physical model construction, intelligent fitting optimization to quantitative prediction of the degradation rate, providing an interpretable and quantifiable path for accurately assessing the degree of soil arching effect degradation under sequential excavation of dual-track tunnels. Compared with existing technologies, this invention overcomes the core limitations of traditional soil arching effect analysis, which relies solely on a single feature point, is prone to distortion in pure data fitting, and cannot quantitatively characterize secondary unloading degradation. It simultaneously possesses the reliability of physical mechanisms and the high accuracy of data-driven approaches. On the one hand, by constraining the actual mechanical process of soil arching effect formation and degradation, a stratigraphic characteristic curve and boundary conditions with clear physical meaning are established, ensuring that the prediction results conform to the basic laws of geotechnical mechanics and avoiding extrapolation distortion caused by unconstrained fitting. On the other hand, through a physically guided neural network with multiple physical constraints and a comprehensive loss function, experimental monitoring data are transformed into precise learning of stratigraphic characteristic curves and degradation patterns. This method can achieve quantitative and continuous prediction of the degree of soil arching effect degradation under sequential excavation of dual-track tunnels, providing more scientific, accurate, and reliable technical support for stratigraphic disturbance control, existing structure protection, and risk assessment during urban tunnel underpass construction.

Claims

1. A method for predicting the degradation rate of soil arching effect based on stratigraphic characteristic curves, applied to a scenario of sequential excavation of a dual-track tunnel simulated by a double-door test, characterized in that... Includes the following steps: S1, the monitoring data of the double-door test staged excavation are discretized and vectorized to construct the parameter vector X1=[δ] corresponding to the left movable door of the tunnel excavation. 1i P 1i ] The parameter vector X2=[δ] corresponding to the right-side movable door of the subsequent tunnel excavation 2j P 2j ] Calculate the soil arch ratio corresponding to the left and right movable doors respectively. and and normalized displacement and ;where δ 1i P represents the measured downward displacement of the left movable gate in the i-th monitoring step. 1i δ represents the measured vertical earth pressure above the i-th monitoring step of the left-side movable gate. 2j P represents the measured downward displacement of the right-side active gate in the j-th monitoring step. 2j P0 represents the measured vertical earth pressure above the right-side movable door at the j-th monitoring step, and B represents the width of the movable door. S2, construct analytical expressions for the stratigraphic characteristic curves above the left and right active gates respectively. and It also clarifies the initial boundary condition ρ(ξ=0)=1 and the ultimate stability boundary condition ρ(ξ=ξ) that the stratigraphic characteristic curve must satisfy during the evolution of the soil arching effect. max ) = ρ ult ;where ρ ult1 and ρ ult2 These are the limiting soil arching ratios of the left and right stratigraphic characteristic curves, respectively, representing the steady-state value of the soil arching ratio when the soil arching effect is completely stable. and K1 and K2 are the linear attenuation coefficients of the characteristic curves of the left and right strata, respectively, representing the intensity of the linear attenuation of the soil arching rate with displacement; K1 and K2 are the nonlinear evolution rate coefficients of the characteristic curves of the left and right strata, respectively, representing the rate at which the soil arching effect adjusts rapidly with displacement. S3. Construct a physical-guided neural network, inputting the parameter vectors X1 and X2, and combining the analytical expressions ρ1(ξ1) and ρ2(ξ2) of the formation characteristic curve and the physical boundary conditions as physical prior constraints. The network parameters are iteratively optimized through a comprehensive loss function, outputting the optimal fitting parameters a of the formation characteristic curve. 1opt k 1opt a 2opt k 2opt Analytical expression of optimal formation characteristic curve ρ 1opt ( ξ 1) and ρ 2opt ( ξ 2); S4, based on the analytical expression of the optimal formation characteristic curve ρ 1opt ( ξ 1) and ρ 2opt ( ξ 2) Calculate the baseline integral eigenvalue S0 without soil arching effect, the integral eigenvalue S1 of the characteristic curve of the strata with the left active gate, and the integral eigenvalue S2 of the characteristic curve of the strata with the right active gate, respectively, to construct the soil arching effect degradation rate. This allows for the quantitative prediction of the degree of degradation of the soil arching effect.

2. The method for predicting the degradation rate of soil arching effect based on stratigraphic characteristic curves according to claim 1, characterized in that, In step S1, the discrete displacement interval Δδ1 of the left movable door and the discrete displacement interval Δδ2 of the right movable door are determined according to the graded downward step size of the double movable door test, and the displacement node δ of the i-th monitoring step of the left movable door is... 1i =iΔδ1, where i is a natural number between 1 and m, and m is the total number of monitoring steps for the left active gate; The displacement node δ of the j-th monitoring step of the right-side active gate 2j =jΔδ2, where j is a natural number between 1 and n, and n is the total number of monitoring steps for the right-side active gate.

3. The method for predicting the degradation rate of soil arching effect based on stratigraphic characteristic curves according to claim 1, characterized in that, In step S3, the physical guidance neural network is a five-layer fully connected network architecture, including an input layer, a physical feature encoding layer, a nonlinear mapping fitting layer, a feature compression and smoothing layer, and an output layer.

4. The method for predicting the degradation rate of soil arching effect based on stratigraphic characteristic curves according to claim 3, characterized in that, The physical feature encoding layer has 64 neurons, adopts a fully connected structure, and uses Gaussian error linear unit (GELU) as the activation function to extract the basic combined features of the input variables.

5. The method for predicting the degradation rate of soil arching effect based on stratigraphic characteristic curves according to claim 3, characterized in that, The nonlinear mapping fitting layer has 128 neurons, adopts a fully connected structure, and uses Gaussian error linear unit (GELU) as the activation function to capture the nonlinear relationship of the formation characteristic curve.

6. The method for predicting the degradation rate of soil arching effect based on stratigraphic characteristic curves according to claim 1, characterized in that, In step S3, the comprehensive loss function is... Where w1, w2, and w3 are the weight coefficients of the three types of loss functions, respectively. L is the loss function for data fitting. phys Let L be the physical boundary constraint loss function. reg For parametric regularization loss function: Data fitting loss function The mean squared error loss is calculated using the following formula: , where m is the total number of monitored steps for the left movable door and n is the total number of monitored steps for the right movable door; ρ1(ξ1) is the calculated soil arching ratio at normalized displacement ξ1, expressed as the analytical expression of the optimal stratigraphic characteristic curve on the left movable gate. ρ1(ξ1) is the measured soil arching ratio at normalized displacement ξ1 of the left movable gate. ρ 2opt ( ξ 2) is the calculated soil arching ratio at normalized displacement ξ2, which is the analytical expression of the optimal stratum characteristic curve on the right movable gate. ρ2(ξ2) is the measured soil arching ratio at normalized displacement ξ2 of the right movable gate. Physical boundary constraint loss function L phys The calculation formula is ρ is used to constrain the model output to satisfy the initial boundary conditions and the ultimate stability boundary conditions; where ρ 1opt (ξ1=0) and ρ 2opt (ξ2=0) represent the predicted soil arching ratios of the optimal stratigraphic characteristic curves when the normalized displacements ξ1 and ξ2 are 0, respectively. 1max and ξ 2max ρ represents the maximum normalized displacement of the left and right movable doors, respectively. 1opt (ξ1=ξ) 1max ) and ρ 2opt (ξ2=ξ) 2max ρ represents the predicted soil arching ratio at the maximum displacement for the optimal stratigraphic characteristic curves of the left and right movable gates, respectively. ult1 and ρ ult2 These are the limiting soil arching ratios of the characteristic curves of the strata on the left and right sides, respectively. Parametric regularization loss function L reg The L2 regularization loss is calculated using the following formula: This is used to constrain the range of values ​​for the parameters to be fitted, preventing the network from overfitting. In the formula... This is an L2 norm operation.

7. The method for predicting the degradation rate of soil arching effect based on stratigraphic characteristic curves according to claim 1, characterized in that, Step S3 further includes: setting a preset loss threshold τ, and outputting the analytical expression of the optimal formation characteristic curve when the comprehensive loss function Loss≤τ. ρ 1opt ( ξ 1) and ρ 2opt ( ξ 2) When Loss>τ, update the weights and bias parameters of each layer of the network and retrain until the comprehensive loss function meets the threshold requirement.

8. The method for predicting the degradation rate of soil arching effect based on stratigraphic characteristic curves according to claim 1, characterized in that, In step S4 The analytical expression of the optimal stratigraphic characteristic curve on the left movable gate ρ 1opt ( ξ 1) For Analytical expression of the optimal formation characteristic curve on the right-side active gate ρ 2opt ( ξ 2) For ; The soil-arch-free benchmark integral eigenvalue S 0 corresponds to the baseline working condition where the soil arching effect is completely absent and the soil arching ratio is always equal to 1. The calculation formula is: The integral characteristic value of the stratigraphic characteristic curve of the left-side movable gate S 1. Based on the full-cycle bearing characteristics of the soil arching effect under the preceding tunnel excavation condition, and the optimal fitting parameters output in step S3, the following parameters are used. a 1opt , k 1opt Analytical expression of the optimal formation characteristic curve above the left active gate ρ 1opt ( ξ 1) Calculation, the calculation formula is: In the formula ρ ult1 The limiting soil arching ratio is the characteristic curve of the strata above the left-side movable gate; a 1opt , k 1opt The optimal fitting parameters for the left-side stratigraphic feature curve output in step S3; The integral characteristic value of the right-side active gate stratigraphic characteristic curve S 2. Based on the full-cycle bearing characteristics of the soil arching effect under the subsequent tunnel excavation conditions, and the optimal fitting parameters output in step S3, the following parameters are used to determine the optimal fitting parameters. a 2opt , k 2opt Analytical expression of the optimal formation characteristic curve above the right-side active gate ρ 2opt ( ξ 2) Calculation, the calculation formula is: 。

Images