A method for predicting deformation of foundation pit excavation by fusing monitoring data

Abstract

The application discloses a kind of foundation pit excavation deformation prediction methods of fusion monitoring data, including collecting foundation pit engineering information, and establishing finite element model;Obtain the prior distribution of uncertain soil parameters;Using random sampling method obtains the initial set of sample, each sample in set contains soil parameters and initial response of foundation pit;Based on finite element model and soil parameter sample, the deformation value of foundation pit in this excavation stage is calculated, and the prediction set is obtained;Compare the predicted value with the monitoring data in this stage, and update the soil parameters;Based on the updated soil parameters, combined with finite element model, the deformation of next excavation stage is predicted, compared with the monitoring data obtained in next stage, and a new round of update is carried out until excavation is completed.The application has very important significance for the prevention and timely remedy of foundation pit excavation accident.

Description

Technical Field

[0001] This invention belongs to the field of geotechnical engineering technology, and in particular relates to a method for predicting excavation deformation of foundation pits by integrating monitoring data. Background Technology

[0002] Foundation pit excavation is a common and crucial foundation engineering project, required for high-rise buildings, subway stations, underground parking lots, and many others. However, urban areas are densely populated with buildings and complex underground pipelines, necessitating early prediction of the excavation's impact on adjacent buildings to enable timely remedial measures and ensure project safety. Currently, numerous experts and scholars have established various empirical models and numerical methods for predicting the deformation of foundation pit retaining structures and soil. However, in practical applications, the excavation response predicted by either empirical models or numerical methods still differs from on-site monitoring data. This is due to various unavoidable uncertainties in geotechnical engineering, such as the inherent uncertainties of soil parameters and the uncertainties of the computational models used.

[0003] In current foundation pit excavation construction, monitoring data related to retaining structure deformation and ground settlement behind the wall are often available. Typically, this monitoring data is only used for comparison with alarm values ​​defined by standards or specifications, and does not contribute to improving prediction accuracy. Utilizing this multi-source information and multi-type monitoring data to quantify and reduce geotechnical engineering uncertainties, and improving the accuracy of foundation pit excavation deformation prediction, has significant implications for the prevention and timely remediation of foundation pit excavation accidents. Summary of the Invention

[0004] The purpose of this invention is to provide a method for predicting the deformation of foundation pit excavation by integrating monitoring data. Based on the ensemble Kalman filter algorithm, it integrates multi-source information and staged monitoring data to quantify the uncertainty of soil parameters, making the deformation prediction of each stage of foundation pit excavation more accurate and applicable to ensuring the safety of foundation pit construction.

[0005] To achieve the above objectives, the present invention provides a method for predicting excavation deformation of foundation pits by integrating monitoring data, the method comprising the following steps:

[0006] Step 1: Collect basic information on the foundation pit excavation project and establish a corresponding finite element model as a forward calculation model for foundation pit deformation prediction.

[0007] Step 2: Select soil parameters that have a significant impact on the deformation of the foundation pit as uncertain parameters, and determine the prior distribution of unknown soil parameters based on geological reports, exploration data, and existing literature.

[0008] Step 3: Based on the prior distribution, randomly generate M sets of soil parameters to generate the initial sample set;

[0009] Step 4: Input the initial soil parameter samples of group M into the forward calculation model to calculate the deformation of the foundation pit in this stage of excavation corresponding to each input. The foundation pit deformation and soil parameter samples together constitute the prediction set.

[0010] Step 5: Obtain the on-site monitoring data of this excavation stage, compare it with the predicted value of the foundation pit deformation of this stage calculated by the forward model, and obtain the updated soil parameters and foundation pit deformation based on ensemble Kalman filtering to form an updated set; substitute the updated soil parameters into the forward calculation model to obtain the predicted value of the foundation pit deformation of the next stage.

[0011] Step 6: Based on the monitoring data obtained from subsequent excavation stages, repeat step 5 until all excavation stages are completed.

[0012] This invention discloses a method for predicting excavation deformation of foundation pits by integrating monitoring data. The method includes: collecting foundation pit engineering information and establishing a finite element model; selecting uncertain soil parameters, collecting existing data, and obtaining the prior distribution of the uncertain soil parameters; obtaining an initial set of samples using a random sampling method, where each sample (i.e., an augmented state vector) contains soil parameters and the initial response of the foundation pit; calculating the foundation pit deformation value for the current excavation stage based on the finite element model and soil parameter samples to obtain a prediction set; comparing the predicted values ​​with the monitoring data for the current stage, correcting and updating the soil parameters to obtain an updated set; and predicting the deformation for the next excavation stage based on the updated soil parameters and the finite element model, comparing the prediction with the monitoring data obtained in the next stage, and performing a new round of updates until the excavation is completed.

[0013] Furthermore, the basic information on the foundation pit engineering collected in step 1 of this invention includes the excavation width and depth, excavation sequence, continuous wall stiffness, support spacing, stiffness and prestress, soil properties, and drainage operation; a finite element model is established using commercial software as a forward model to calculate the foundation pit excavation deformation response.

[0014] Furthermore, the commercial software includes, but is not limited to, ABAQUS, PLAXIS 2D, PLAXIS 3D, MidasGTS, and ANSYS.

[0015] Furthermore, in step 2 of the present invention, based on engineering experience, parameters that have a significant impact on deformation are selected as unknown soil parameters. The prior distribution of the unknown soil parameters can be uniform distribution, normal distribution, or log-normal distribution.

[0016] Furthermore, in step 3 of this invention, Latin hypercube sampling is used to generate M sets of soil parameters. The soil parameters θ and the system state, i.e., the initial deformation value d, constitute the augmented state vector x = [d, θ]', where the symbol ' represents the transpose of the vector; the samples of the M sets of augmented state vectors x constitute the initial set. i represents the sample number, M represents the total number of samples, and i = 1, 2, ..., M.

[0017] Furthermore, in step 4 of this invention, the foundation pit deformation and original soil parameters calculated by the forward model constitute the predicted state vector. symbol This represents the predicted state vector that will be corrected in the next update step. M sets of predicted state vectors. The samples constitute the prediction set i represents the sample index, M represents the total number of samples, i = 1, 2, ..., M; the mean of this prediction set. The formula for calculating the covariance matrix P is as follows:

[0018]

[0019]

[0020] In the formula, This represents the mean of the prediction set. This represents the transpose of the mean of the prediction set; Represents the predicted state vector. denoted as the transpose of the predicted state vector; i represents the sample index, M represents the total number of samples, i = 1, 2, ..., M; P represents the covariance matrix.

[0021] Furthermore, the monitoring data obtained in step 5 of the present invention includes one or more of the following: lateral displacement of the retaining structure, horizontal displacement of the soil behind the wall, settlement of the soil behind the wall, and heave of the soil at the bottom of the pit. The predicted value is the result of finite element model calculation with the same physical quantity type as the monitoring data.

[0022] Furthermore, in step 5 of this invention, a comparison is made between the predicted value and the monitored value. The weights of the two are determined by the Kalman gain matrix K, and the calculation formula is as follows:

[0023] K = PH'(HPH' + R -1

[0024] In the formula, K represents the Kalman gain matrix; P represents the covariance matrix, which is calculated in step 4; H is the observation operator, which is intended to transform the augmented state space to the observation space, and H' represents the transpose of the observation operator; R is the observation error matrix; the superscript "-1" indicates the inverse matrix.

[0025] Each predicted state vector in the prediction set The updated state vector x is obtained after correction and update. i The calculation formula is as follows:

[0026]

[0027] In the formula, xi The updated state vector is defined as follows: i represents the sample number, i = 1, 2, ..., M, where M represents the total number of samples; K represents the Kalman gain matrix; y represents the field monitoring value; and H is the observation operator, which aims to transform the augmented state space into the observation space. Let i represent the predicted state vector, where i represents the sample number, i = 1, 2, ..., M, and M represents the total number of samples.

[0028] Furthermore, this invention uses the finite element model as the computational model and combines it with the ensemble Kalman filter method, which avoids the problem that traditional finite element model prediction methods cannot update unknown parameters, thereby improving prediction accuracy and reducing prediction uncertainty.

[0029] Compared with the prior art, the present invention has at least the following advantages:

[0030] Based on the ensemble Kalman filter algorithm, prior information and monitoring data from existing stages are integrated before the next stage of excavation of the foundation pit. This quantifies and reduces the characterization of soil uncertainty, improves the accuracy of excavation deformation prediction in subsequent stages, and achieves accurate prediction of excavation deformation. This is of great significance for the prevention and timely remediation of foundation pit excavation accidents. Attached Figure Description

[0031] Figure 1 A flowchart of a method for predicting excavation deformation of a foundation pit by integrating monitoring data provided by the present invention;

[0032] Figure 2 This is a schematic diagram of a foundation pit project provided in an embodiment of the present invention;

[0033] Figure 3 This is a schematic diagram illustrating the convergence history of soil parameters calculated using the method of this invention in an embodiment of the invention.

[0034] Figure 4 This is a comparison chart of the predicted lateral displacement values ​​of the enclosure structure using the method of the present invention, the predicted values ​​using the traditional finite element method, and the monitored values ​​in an embodiment of the present invention. Detailed Implementation

[0035] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. Note that the following description of the embodiments is merely illustrative and is not intended to limit its applicability or use, nor is the present invention limited to the following embodiments.

[0036] Reference Figure 1 The present invention provides a method for predicting the deformation of foundation pit excavation by integrating monitoring data. This method integrates existing data and monitoring data to predict and update the lateral displacement of the retaining structure in stages. Figure 2An example of a foundation pit project with seven excavation stages, affecting six layers of alternating sand and clay soil, is provided. Figure 2 The provided embodiments, in conjunction with Figure 1 The method of the present invention includes the following steps:

[0037] Step 1: Collect basic information on the foundation pit excavation project and establish a corresponding finite element model as a forward calculation model for foundation pit deformation prediction.

[0038] The basic information of the foundation pit project includes the excavation width and depth, excavation sequence, diaphragm wall stiffness, support spacing, stiffness and prestress, soil properties, and drainage operations. In this embodiment, a finite element model is established using the commercial software ABAQUS as a forward model to calculate the excavation deformation response of the foundation pit.

[0039] Step 2: Select soil parameters that have a significant impact on the deformation of the foundation pit as uncertain parameters, and determine the prior distribution of unknown soil parameters based on geological reports, exploration data, and existing literature.

[0040] In this embodiment, sand and clay were simulated using the Mohr-Coulomb model and the Cambridge model, respectively. All soil properties of the sand were defined, while for the clay, based on the influence of soil parameters on the lateral displacement of the retaining wall, the Poisson's ratio *v* and the slope of the rebound curve *κ* of three clay layers were selected as uncertain parameters, resulting in a total of six unknown parameters. In this embodiment, the prior distribution of the soil parameters followed a normal distribution, with means of 0.25 and 0.03, respectively, and coefficients of variation of 20% for both.

[0041] Step 3: Based on the prior distribution, randomly generate M sets of soil parameters to generate the initial sample set.

[0042] In this embodiment, Latin hypercube sampling is used to generate M=100 sets of soil parameters. The soil parameters θ=[κ1,v1,κ2,v2,κ3,v3], where the subscript "1" indicates the first layer of clay. The system state d is a vector composed of the lateral displacement values ​​at various positions along the depth of the retaining structure in the finite element model, and the symbol ' represents the transpose of the vector. The initial values ​​of the soil parameters θ and the system state d (here, the zero vector is simply used to indicate that the initial value is zero) constitute the augmented state vector x=[d,θ]', and the symbol ' represents the transpose of the vector. The 100 samples of x constitute the initial set. i represents the sample number, i = 1, 2, ..., M, and M represents the total number of samples, M = 100.

[0043] Step 4: Input the initial samples of soil parameters from group M into the forward calculation model to calculate the deformation of the foundation pit in this stage of excavation corresponding to each input. The foundation pit deformation and soil parameter samples together constitute the prediction set.

[0044] In this embodiment, 100 (M=100) initial soil parameter samples are input into the forward calculation model, and the lateral displacement values ​​of the retaining structure at various depth positions are calculated in parallel. The vector composed of these lateral displacement values ​​and the soil parameters constitute the predicted state vector. symbol This represents the predicted state vector that will be corrected in the next update step. 100 sets of predicted state vectors. The samples constitute the prediction set The mean of the prediction set is calculated using the following two formulas. Sum of covariance matrix P:

[0045]

[0046]

[0047] In the formula, This represents the mean of the prediction set. This represents the transpose of the mean of the prediction set; Represents the predicted state vector. denoted as the transpose of the predicted state vector; i represents the sample index, M represents the total number of samples, i = 1, 2, ..., M; P represents the covariance matrix.

[0048] Step 5: Obtain the on-site monitoring data of this excavation stage and compare it with the predicted value of the foundation pit deformation calculated by the forward model. Based on the ensemble Kalman filter, obtain the updated soil parameters and foundation pit deformation to form an updated set. Substitute the updated soil parameters into the forward calculation model to obtain the predicted value of the foundation pit deformation for the next stage.

[0049] In this embodiment, the on-site monitoring data consists of the lateral displacement y from 17 monitoring points along the depth of the enclosure structure. In step 5 of this invention, the weights of the predicted and monitored values ​​are determined by the Kalman gain matrix K, and the calculation formula is as follows:

[0050] K = PH'(HPH' + R -1

[0051] In the formula, K represents the Kalman gain matrix; P represents the covariance matrix, which is calculated in step 4; H is the observation operator, which is intended to transform the augmented state space to the observation space, and H' represents the transpose of the observation operator; R is the observation error matrix; the superscript "-1" indicates the inverse matrix.

[0052] In this embodiment, H is a dimension N d ×(N d +N θ The matrix N is given by the formula. d N represents the number of monitoring points. d =17, Nθ N represents the number of unknown soil parameters. θ =6; R is a dimension of N d ×N d The observation error matrix.

[0053] Each predicted state vector in the prediction set The updated state vector x is obtained after correction and update. i The calculation formula is as follows:

[0054]

[0055] In the formula, x i The updated state vector is defined as follows: i represents the sample number, i = 1, 2, ..., M, where M represents the total number of samples; K represents the Kalman gain matrix; y represents the field monitoring value; and H is the observation operator, which aims to transform the augmented state space into the observation space. Let i represent the predicted state vector, where i represents the sample number, i = 1, 2, ..., M, and M represents the total number of samples.

[0056] In this embodiment, M = 100, and y is a vector composed of monitoring values ​​from 17 monitoring points.

[0057] The updated soil parameters are input into the forward model, i.e. the finite element model established in step 1, to calculate the predicted deformation values ​​for the next excavation stage.

[0058] Step 6: Based on the monitoring data obtained from subsequent excavation stages, repeat step 5 until all excavation stages are completed.

[0059] Figure 3 This is a schematic diagram of the convergence history of the Poisson's ratio of the soil parameter calculated in this embodiment. As the number of iterations increases, the soil parameter gradually converges from the initial prior distribution to a smaller range, and the uncertainty decreases.

[0060] Figure 4 This paper demonstrates the lateral displacement monitoring values ​​for excavation stage 4, the lateral displacement predictions based on the prior distribution of soil parameters, and the lateral displacement predictions based on the updated soil parameters. Specifically, it involves fusing prior information and monitoring data from excavation stage 3, updating soil parameters according to steps 1-5, and obtaining the updated soil parameter distribution based on the monitoring data from excavation stage 3. This updated soil parameter sample is then substituted into the forward calculation model, i.e., the finite element model established in step 1, to obtain the lateral displacement prediction sample for excavation stage 4, and plotting the corresponding 95% confidence intervals, such as... Figure 4 As shown. Furthermore, Figure 4The paper also compares the traditional finite element method (FEM). The traditional FEM prediction is based on the prior distribution of soil parameters generated in step 3. Comparing the predictions obtained in excavation stage 4 based on the traditional FEM, the prior distribution, and the updated soil parameters, it can be seen that all three prediction confidence intervals completely cover the monitored values. Specifically, the predictions obtained by the traditional FEM are almost identical to those based on the prior distribution, and both have significantly larger confidence intervals than those based on the updated soil parameters. This indicates that the prediction method provided by this invention can quantify and reduce the characterization of soil uncertainty by fusing prior information and existing stage monitoring data, thereby improving the accuracy of excavation deformation prediction in the next stage. In contrast, the accuracy of the traditional FEM prediction is highly dependent on the prior distribution and lacks the ability to update soil parameters, thus failing to reduce prediction uncertainty and improve prediction accuracy.

[0061] The above embodiments are only used to explain and illustrate the present invention, and are not intended to limit the present invention. Any modifications and variations made to the present invention within the spirit and scope of the claims shall fall within the protection scope of the present invention.

Claims

1. A method for predicting excavation deformation of foundation pits by integrating monitoring data, characterized in that, Includes the following steps: Step 1: Collect basic information on the foundation pit excavation project and establish a finite element model as a forward calculation model for foundation pit deformation prediction; Step 2: Select soil parameters that have a significant impact on the deformation of the foundation pit as uncertain parameters, and determine the prior distribution of unknown soil parameters based on geological reports, exploration data, and existing literature. Step 3: Based on the prior distribution, randomly generate M sets of soil parameters to generate the initial sample set; Step 4: Input the initial parameter samples of M groups of samples into the forward calculation model to calculate the deformation of the foundation pit in this stage of excavation corresponding to each input group. The foundation pit deformation and soil parameter samples together constitute the prediction set. Step 5: Obtain the on-site monitoring data of this excavation stage, compare it with the predicted value of the foundation pit deformation of this stage calculated by the forward calculation model, and obtain the updated soil parameters and foundation pit deformation based on ensemble Kalman filtering to form an updated set; Substitute the updated soil parameters into the forward calculation model to obtain the predicted values ​​of the foundation pit deformation for the next stage; Step 6: Based on the monitoring data obtained from subsequent excavation stages, repeat step 5 until all excavation stages are completed. In step 4, the initial parameter samples of the M groups are input into the forward calculation model to calculate the deformation of the foundation pit at this stage of excavation for each input group. The foundation pit deformation and soil parameter samples together constitute the prediction set, which specifically includes: The predicted state vector is composed of the foundation pit deformation and soil parameter samples calculated by the forward calculation model. ,symbol M sets of predicted state vectors represent the predicted state vectors that will be corrected in the next update step. The samples constitute the prediction set , where i is the sample index, i = 1, 2, …, M, and the mean of the prediction set. Covariance Matrix The calculation formula is as follows: ； ； In the formula, This represents the mean of the prediction set. This represents the transpose of the mean of the prediction set; Represents the predicted state vector. This represents the transpose of the predicted state vector, where i represents the sample index and M represents the number of samples, i = 1, 2, …, M; Represent the covariance matrix; Step 5 involves acquiring the on-site monitoring data for this excavation stage and comparing it with the predicted values ​​of the foundation pit deformation calculated by the forward calculation model. This specifically includes: The predicted and monitored values ​​are compared, and their weights are determined by the Kalman gain matrix K, calculated as follows: ； In the formula, K represents the Kalman gain matrix; P represents the covariance matrix, which is calculated in step 4; H is the observation operator, intended to transform the augmented state space to the observation space. This indicates the transpose of the observation operator; R is the observation error matrix; the superscript "-1" indicates the inverse matrix; Each predicted state vector in the prediction set The updated state vector is obtained by correcting and updating it. The calculation formula is as follows: ； In the formula, The updated state vector is denoted by i, where i = 1, 2, …, M, and M represents the number of samples; K represents the Kalman gain matrix. Here are the field monitoring values; H is the observation operator; Let i represent the predicted state vector, where i represents the sample index, i = 1, 2, …, M, and M represents the number of samples.

2. The method for predicting excavation deformation of a foundation pit by integrating monitoring data according to claim 1, characterized in that, In step 1, the basic information of the foundation pit excavation project includes the excavation width and depth, excavation sequence, continuous wall stiffness, support spacing, stiffness and prestress, soil properties, and drainage operation. A finite element model was built using commercial software and used as a forward model to calculate the excavation deformation response of the foundation pit.

3. The method for predicting excavation deformation of a foundation pit by integrating monitoring data according to claim 2, characterized in that, The commercial software mentioned is ABAQUS, PLAXIS 2D, PLAXIS 3D, Midas GTS, or ANSYS.

4. The method for predicting excavation deformation of a foundation pit by integrating monitoring data according to claim 1, characterized in that, In step 2, the unknown soil parameters are selected based on engineering experience and have a significant impact on deformation. The prior distribution of the unknown soil parameters adopts a uniform distribution, a normal distribution, or a log-normal distribution.

5. The method for predicting excavation deformation of a foundation pit by integrating monitoring data according to claim 1, characterized in that, In step 3, based on the prior distribution, M sets of soil parameters are randomly generated to form the initial sample set, which specifically includes: Based on the prior distribution, Latin hypercube sampling is used to generate M sets of soil parameters. The soil parameters θ and the system state, i.e., the initial deformation value d, constitute the augmented state vector x = [d, θ]', where the symbol ' represents the transpose of the vector. The samples of the M sets of augmented state vectors x constitute the initial sample set. , i represents the sample number, M represents the number of samples, i = 1, 2, …, M.

6. The method for predicting excavation deformation of a foundation pit by integrating monitoring data according to claim 1, characterized in that, In step 5, the on-site monitoring data includes one or more of the following: lateral displacement of the retaining structure, horizontal displacement of the soil behind the wall, settlement of the soil behind the wall, and heave of the soil at the bottom of the pit.

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