Rapid intelligent prediction method for deformation of deep foundation pit in soft soil area

Abstract

The invention discloses a rapid intelligent prediction method for deformation of a deep foundation pit in a soft soil area. The intelligent prediction method comprises the following steps that different soft soil stratum small strain hardening (HSS) model parameters are randomly generated through a Monte Carlo algorithm, finite element software PLAXIS is used for simulating the foundation pit excavation process, and deep foundation pit deformation conditions under different stratum conditions are obtained; gathering parameters of the soil body HSS model, the maximum lateral displacement of the foundation pit enclosure structure, the maximum settlement of the ground outside the pit and the maximum sagging moment of the enclosure wall towards the interior of the pit into a deformation database of the deep foundation pit in the soft soil area; an artificial neural network (ANN) method is introduced, the relation between the HSS model parameters of the soft soil area and the deformation of the deep foundation pit is established, and rapid and intelligent prediction of the deformation of the deep foundation pit in the soft soil area is achieved. According to the technical scheme, the Monte Carlo algorithm and the ANN algorithm are combined in the foundation pit deformation prediction method, simulation and processing of a large amount of foundation pit deformation data can be achieved, and powerful reference is provided for rapid prediction of deformation of the deep foundation pit in the soft soil area in actual engineering.

Description

Technical Field

[0001] The invention relates to the field of underground space development, and in particular to a method for rapid intelligent prediction of deformation of deep foundation pits in soft soil areas. Background Art

[0002] In recent years, urban construction and development have faced many problems such as insufficient land and resource constraints. The development and utilization of urban underground space can provide new ideas for urban construction and open up new channels. The utilization of shallow underground space in soft soil cities such as Shanghai is becoming increasingly saturated, and the rational development and utilization of deep underground space has become particularly urgent. Large-scale underground space development, such as the construction of subway stations, underground commercial centers, underground parking lots, underground substations, underground sewage treatment facilities and other facilities are closely related to foundation pit engineering. However, the high density of buildings in cities and the complexity of underground pipelines pose great challenges to the construction of foundation pits. The excavation of foundation pit engineering is prone to cause deformation of the surrounding environment. These deformations will have a great impact on the complex urban environment, causing cracking or even damage to the surrounding structures, thereby affecting the normal use of the structures. Therefore, as people begin to pay attention to and attach importance to the environmental deformation caused by foundation pit engineering, the design of foundation pit engineering has gradually shifted from strength control to deformation control. In order to better design the foundation pit, it is crucial to accurately predict the deformation of the soil around the foundation pit.

[0003] At present, the methods commonly used to analyze the impact of foundation pit excavation on the surrounding environment mainly include empirical analysis methods and numerical simulation methods. Many scholars have proposed a series of empirical analysis methods for foundation pit deformation based on a large amount of foundation pit monitoring data and local foundation pit engineering experience. These empirical methods can be effectively used in local foundation pit engineering design and construction, but they also have certain limitations, such as a small scope of application and the need for a certain number of foundation pit engineering samples. Numerical simulation methods are gradually being used in foundation pit deformation analysis. This method can simulate site information based on on-site survey data, and can predict the deformation of each construction stage during foundation pit excavation separately, and the prediction results are also relatively accurate. In addition to conventional empirical analysis methods and finite element numerical simulation methods, some scholars have applied regression analysis methods, neural network methods, etc. to the field of underground engineering, but not many of them are directly used to analyze and predict foundation pit deformation. The regression analysis method uses a large amount of historical data to find the functional relationship between variables.

[0004] Foundation pit engineering also faces a major problem, namely the uncertainty of soil parameters. This property may bring risks to the project, and the traditional safety factor method often cannot reflect the impact of uncertainty. Summary of the invention

[0005] The purpose of the present invention is to propose a method for generating a deep foundation pit database based on the Monte Carlo algorithm for the deformation of deep foundation pits in soft soil areas, and on this basis, to propose a fast intelligent prediction method for the deformation of deep foundation pits in soft soil areas based on artificial neural networks, so as to solve the problem that the deformation of deep foundation pits in soft soil areas is difficult to predict, and to create favorable conditions for the subsequent development of underground space.

[0006] To this end, the present invention adopts the following technical solutions:

[0007] A rapid intelligent prediction method for deformation of deep foundation pits in soft soil areas, characterized by comprising the following steps:

[0008] Step 1: Randomly generate soil parameter data of deep foundation pit in soft soil area by Monte Carlo algorithm;

[0009] Step 2: Establish a finite element model based on the generated deep foundation pit data to simulate the foundation pit excavation process;

[0010] Step 3: Collect and record the deformation during the simulated foundation pit excavation process, and summarize the soil small strain hardening (HSS) model parameters, the maximum lateral displacement of the foundation pit retaining structure, the maximum surface settlement outside the pit, and the maximum positive bending moment of the retaining wall toward the pit into the deep foundation pit deformation database in soft soil areas;

[0011] Step 4: Use artificial neural network method to establish the relationship between HSS model parameters and foundation pit deformation;

[0012] Step 5: Under the premise of ensuring the prediction accuracy, the structure of the artificial neural network model is simplified by changing the number of hidden layers and the number of neurons in the hidden layers, and the formula of HSS model parameters and foundation pit deformation is obtained. This formula is used to realize the rapid and intelligent prediction of deep foundation pit deformation in soft soil areas.

[0013] Furthermore, in step 1, the process of randomly generating soil parameter data of deep foundation pit in soft soil area by Monte Carlo algorithm is as follows:

[0014] According to the mechanical parameters of the soft soil in layers ③ and ④ in Shanghai, namely the soft clay in Shanghai, as the random input variables of the Monte Carlo model, the mechanical parameters of the soft clay include the effective cohesion c', the effective internal friction angle Reference tangent modulus Reference secant modulus Loading and unloading modulus and dynamic shear initial modulus Considering that the physical and mechanical parameters of the soil in the passive zone of the foundation pit have a great influence on the deformation of the foundation pit, reinforcing the passive zone of the foundation pit is also a common method to control the deformation of the foundation pit. Therefore, the mechanical parameters of the ⑤1 layer of soil in Shanghai are also used as random input variables of the Monte Carlo model.

[0015] Assume that all random input variables conform to normal distribution; effective cohesion c' and effective internal friction angle of soil The standard deviation and coefficient of variation of come from the test results, which can be the test results published in the literature; since the coefficient of variation of the effective cohesion of soil is large and the value of the effective cohesion is small, if the normal distribution is used alone, the value of the effective cohesion may be less than 0. Therefore, the effective cohesion c' adopts a truncated normal distribution, and the lower limit of the truncation is set to 0kPa; assuming that the random input variable and The value of is within ±30% of the mean, with a confidence level of 95%. The corresponding standard deviation and coefficient of variation can be obtained by consulting the corresponding table of confidence intervals and confidence levels.

[0016] In step 1, in order to determine the sampling times of the Monte Carlo algorithm, balance the computational efficiency and the accuracy of the calculation results, the sampling times are determined in an incremental scheme, and the mean and standard deviation of the random sampling results are compared. Finally, a sampling scheme of 1000 times is selected as more reasonable.

[0017] Furthermore, the specific process of establishing the artificial neural network model in step 4 is as follows: The accuracy indicator during training is the mean square error:

[0018]

[0019] Where: y i To calculate the target value, y i ' is the calculated value. The Momentum-SGD algorithm is used to update the weights. The SGD algorithm only considers a single loss function to calculate the corresponding gradient in the iterative calculation:

[0020]

[0021] Where: w t+1 is the updated weight value, w t is the unupdated weight, is the gradient function of the weight, α is the learning rate, a momentum can be defined during implementation, and then the new speed is used instead of the original gradient direction to update, which can be expressed by the following formula:

[0022]

[0023] Where: v t+1 is the updated velocity value, v t is the unupdated velocity value, β is the introduced momentum, which is generally taken as β = 0.9, and Lr is the learning rate, which can be taken as Lr = 0.005. Formula (2) is expressed as follows after Momentum optimization:

[0024] w t+1 =w t -v t+1 (4)

[0025] A simple mathematical model of a single neuron can be viewed as a nonlinear function that transforms a set of input variables x i (i=1, ..., m) is converted into output variables, that is, the values ​​of neurons:

[0026]

[0027] Where: a is the calculation result input to the activation function, x i is the input variable, w i is the weight, b is the bias, and m is the number of input variables. Generally speaking, the bias b is regarded as the weight w i The special case of , the value of x0 corresponding to the additional input is set to +1, simplifying equation (6) to the following form:

[0028]

[0029] Then, the activation function g is used to calculate a and give the unit output n. The hyperbolic tangent function is selected as the activation function because its function graph passes through the origin and has a faster convergence speed. Its function formula is as follows:

[0030]

[0031] The input layer uses the HSS model parameters as the variable x, which can be expressed as N 0 , which is an n×d input matrix, n is the number of parameters and d is the number of samples. The weight and bias matrices can be represented as W k =[n k , n k-1 ] and B=[n k ,1],n k is the number of neurons in the kth hidden layer. All parameters also need to be normalized:

[0032]

[0033] Where: x n is the normalized variable, x min and x max are the minimum and maximum values ​​of variable x respectively. The hidden layer neurons can be calculated according to the following formula:

[0034]

[0035] Where: W 01 and B 01are the weight matrix and bias matrix between the input layer and the hidden layer respectively. Meanwhile, the output layer can be expressed as:

[0036]

[0037] Where: Y m，max and Y m，min are the maximum values ​​of the predicted parameters, the subscript m is used to indicate that the data are measured values, p is used to indicate that the data are predicted values, and k is the number of output variables. 12 and B 12 are the weight matrix and bias matrix between the hidden layer and the output layer, respectively.

[0038] Compared with the prior art, the beneficial effects of the present invention are: the problem of insufficient deformation data of deep foundation pits in soft soil areas is solved by the Monte Carlo algorithm; the artificial neural network model is introduced to make full use of the accumulated large-scale foundation pit deformation database, forming a fast and accurate deep foundation pit deformation rapid intelligent prediction method in soft soil areas, which can avoid the time and economic costs caused by a large number of complex geotechnical tests, improve the predictability of foundation pit deformation in actual projects, and is conducive to further underground space development. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a schematic diagram of the process of the rapid intelligent prediction method of deep foundation pit deformation in soft soil areas of the present invention.

[0040] Figure 2 The mean and standard deviation graphs for different sampling times.

[0041] Figure 3 This is the two-dimensional finite element model diagram of the foundation pit.

[0042] Figure 4 This is the error change diagram of the model training process.

[0043] Figure 5-a The following is a comparison chart of the maximum lateral displacement of the case enclosure structure.

[0044] Figure 5-b This is a comparison chart of the maximum surface settlement outside the case pit. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. In practical applications, various changes can be made to them in form and details without departing from the spirit and scope of the present invention.

[0046] Step 1: The Monte Carlo algorithm is used to randomly generate soil parameter data of deep foundation pits in soft soil areas, and some mechanical parameters of soft soil layers ③ and ④ in Shanghai, namely Shanghai soft clay, are used as random input variables of the model. Considering that the physical and mechanical parameters of the soil in the passive zone of the foundation pit have a great influence on the deformation of the foundation pit, reinforcing the passive zone of the foundation pit is also a common method to control the deformation of the foundation pit. Therefore, some mechanical parameters of the soil layer ⑤1 are used as random input variables of the model.

[0047] Assume that all random input variables conform to normal distribution. The effective cohesion c' and effective internal friction angle of soil The standard deviation and coefficient of variation come from the results of a large number of experiments by scholars. It is worth noting that since the coefficient of variation of the effective cohesion c' of soil is large and the value of the effective cohesion c' is small, if the normal distribution is used alone, the value of the effective cohesion c' may be less than 0. Therefore, a truncated normal distribution is used for the effective cohesion c', and the lower limit of the truncation is set to 0kPa. Assuming that the random input variable and The value of is within the range of ±30% of the mean, with a confidence level of 95%. By querying the corresponding table of confidence intervals and confidence levels, the corresponding standard deviation and coefficient of variation can be obtained, such as Figure 2 Shown are the mean and standard deviation for different sampling numbers, with the sampling number being determined to be 1000.

[0048] Step 2: Use PLAXIS software to build a finite element model based on the generated foundation pit data to simulate the foundation pit excavation process: Figure 3 As shown in the figure, the model is a 15-node plane strain model with a length of 178m and a width of 45m. The minimum distance between the retaining wall and the side boundary of the model is 3-5 times the wall embedding depth; the minimum distance between the bottom of the retaining wall and the bottom boundary of the model is approximately the length of the wall. The underground continuous wall is simulated using a 5-node two-dimensional plate element, and the internal support is simulated using a 2-node point-to-point anchor element. The layout of the underground continuous wall and horizontal support is simulated according to the actual layout of the project. The underground continuous wall uses C30 concrete with an elastic modulus of 30GPa; the internal support uses steel support with an elastic modulus of 200GPa.

[0049] Step 3: Collect and record the deformation during the foundation pit excavation process, and summarize the soil HSS model parameters, the maximum lateral displacement of the foundation pit retaining structure, the maximum surface settlement outside the pit, and the maximum positive bending moment of the retaining wall toward the pit into the deep foundation pit deformation database in soft soil areas;

[0050] Step 4: Use artificial neural network method to establish the relationship between HSS model parameters and foundation pit deformation. During the training period, the accuracy index uses mean square error, such as Figure 4 Shown is the changing trend of the mean square error during the training process:

[0051]

[0052] Where: y i To calculate the target value, y i ' is the calculated value. The Momentum-SGD algorithm is used to update the weights. The SGD algorithm only considers a single loss function to calculate the corresponding gradient in the iterative calculation:

[0053]

[0054] Where: w t+1 is the updated weight value, w t is the unupdated weight, is the gradient function of the weight, α is the learning rate, a momentum can be defined during implementation, and then the new speed is used instead of the original gradient direction to update, which can be expressed by the following formula:

[0055]

[0056] Where: v t+1 is the updated velocity value, v t is the unupdated velocity value, β is the introduced momentum, which is generally taken as β = 0.9, and Lr is the learning rate. In this study, Lr = 0.005 is taken. Formula (3) is expressed as follows after Momentum optimization:

[0057] w t+1 =w t -v t+1 (4)

[0058] A simple mathematical model of a single neuron can be viewed as a nonlinear function that transforms a set of input variables x i (i=1, ..., m) is converted into the output variable n, which is the value of the neuron:

[0059]

[0060] Where: a is the calculation result input to the activation function, x i is the input variable, w i is the weight, b is the bias, and m is the number of input variables. Generally speaking, the bias b is regarded as the weight w i The special case of , the value of x0 corresponding to the additional input is set to +1, simplifying equation (6) to the following form:

[0061]

[0062] Then, the activation function g is used to calculate a and give the unit output n. The hyperbolic tangent function is selected as the activation function, and its function formula is as follows:

[0063]

[0064] The input layer uses the HSS model parameters as the variable x, which can be expressed as N 0 , which is an n×d input matrix, n is the number of parameters and d is the number of samples. The weight and bias matrices can be represented as W k =[n k , n k-1 ] and B=[n k ,1],n k is the number of neurons in the kth hidden layer. All parameters also need to be normalized:

[0065]

[0066] Where: x n is the normalized variable, x min and x max are the minimum and maximum values ​​of variable x respectively. The hidden layer neurons are calculated according to the following formula:

[0067]

[0068] Where: W 01 and B 01 are the weight matrix and bias matrix between the input layer and the hidden layer respectively. The output layer can be expressed as:

[0069]

[0070] Where: Y m，max and Y m，min are the maximum values ​​of the predicted parameters, the subscript m is used to indicate that the data are measured values, p is used to indicate that the data are predicted values, and k is the number of output variables. 12 and B 12 are the weight matrix and bias matrix between the hidden layer and the output layer respectively. Figure 4 The figure shows the error change during the model training process. The optimal value is obtained after 6600 iterations, and the mean square error value is the smallest at this time.

[0071] Step 5: By comparing the prediction accuracy, while ensuring the prediction accuracy, by changing the number of hidden layers and the number of neurons in the hidden layer, simplifying the artificial neural network model structure, a single hidden layer structure with three neurons is obtained, and the formula of HSS model parameters and foundation pit deformation is further derived. Substituting the known HSS model parameters into the formula can realize the rapid intelligent prediction of deep foundation pit deformation in soft soil areas. Figure 5-a and Figure 5-b The figure shows the effect of foundation pit deformation prediction, which shows the predicted values ​​of the maximum displacement and maximum settlement of the foundation pit.

[0072] The above is the embodiment of the present invention. The technical solution of the present invention is not limited to the above specific embodiment, and all technical variations made according to the technical solution of the present invention fall within the protection scope of the present invention.

Claims

1. A rapid intelligent prediction method for deep foundation pit deformation in soft soil areas, characterized in that The following steps are involved: Step 1: Randomly generate soil parameter data of deep foundation pit in soft soil area by Monte Carlo algorithm; Step 2: Establish a finite element model based on the generated deep foundation pit data to simulate the foundation pit excavation process; Step 3: Collect and record the deformation during the simulated foundation pit excavation process, and summarize the soil HSS model parameters, the maximum lateral displacement of the foundation pit retaining structure, the maximum surface settlement outside the pit, and the maximum positive bending moment of the retaining wall toward the pit into the deep foundation pit deformation database in the soft soil area; Step 4: Use artificial neural network method to establish the relationship between HSS model parameters and foundation pit deformation; Step 5: Simplify the artificial neural network model structure, obtain the formula of HSS model parameters and foundation pit deformation, and use this formula to realize rapid and intelligent prediction of deep foundation pit deformation in soft soil areas.

2. The rapid intelligent prediction method for deep foundation pit deformation in soft soil areas according to claim 1 is characterized in that In step 1, the process of randomly generating soil parameter data of deep foundation pit in soft soil area by Monte Carlo algorithm is as follows: According to the mechanical parameters of the soft soil in layers ③ and ④ in Shanghai, namely the soft clay in Shanghai, as the random input variables of the Monte Carlo model, the mechanical parameters of the soft clay include the effective cohesion c', the effective internal friction angle Reference tangent modulus Reference secant modulus Loading and unloading modulus and dynamic shear initial modulus The mechanical parameters of layer ⑤1 of the soil in Shanghai are also used as random input variables of the Monte Carlo model.

3. The rapid intelligent prediction method for deformation of deep foundation pits in soft soil areas according to claim 2 is characterized in that Assume that all random input variables conform to normal distribution; effective cohesion c' and effective internal friction angle of soil The standard deviation and coefficient of variation are derived from the experimental results; the effective cohesion c' adopts a truncated normal distribution with the lower limit set to 0 kPa; it is assumed that the random input variable and The value is within ±30% of the mean with a confidence level of 95%.

4. The rapid intelligent prediction method for deformation of deep foundation pits in soft soil areas according to claim 2 is characterized in that In step 1, the sampling times of the Monte Carlo algorithm are determined by balancing the computational efficiency and the accuracy of the results. The sampling times are determined in an incremental scheme. The mean and standard deviation of the random sampling results are compared, and the sampling times are selected as 1000 times.

5. The rapid intelligent prediction method for deformation of deep foundation pits in soft soil areas according to claim 1 is characterized in that The accuracy indicator during the training of the artificial neural network model in step 4 is the mean square error: Where: y i To calculate the target value, y i ' is the calculated value; The Momentum-SGD algorithm is used to update the weights. The SGD algorithm only considers a single loss function to calculate the corresponding gradient in the iterative calculation: Where: w t+1 is the updated weight value, w t is the unupdated weight, is the gradient function of the weight, α is the learning rate, a momentum is defined during implementation, and then the new speed is used instead of the original gradient direction to update, which is expressed by the following formula: Where: v t+1 is the updated velocity value, v t is the unupdated velocity value, β is the introduced momentum, Lr is the learning rate, and formula (2) is expressed as follows after Momentum optimization: w t+1 =w t -v t+1 (4) A simple mathematical model of a single neuron is viewed as a nonlinear function that transforms a set of input variables x i (i=1,…,m) is converted into output variables, that is, the values ​​of neurons: Where: a is the calculation result input to the activation function, x i is the input variable, w i is the weight, b is the bias, and m is the number of input variables; The bias b is considered as the weight w i As a special case, equation (5) is simplified to the following form: Subsequently, the activation function g is used to calculate a to give the unit output n; the hyperbolic tangent function is selected as the activation function, and its function formula is as follows: The input layer uses the HSS model parameter x, denoted as N 0 , which is an n×d input matrix, n is the number of parameters, d is the number of samples; the weight and bias matrices are denoted as W k =[n k , n k-1 ] and B=[n k ,1],n k is the number of neurons in the kth hidden layer; All parameters are also normalized: Where: x n is the normalized variable, x min and x max are the minimum and maximum values ​​of the variable x respectively; The hidden layer neurons are calculated according to the following formula: Where: W 01 and B 01 are the weight matrix and bias matrix between the input layer and the hidden layer respectively; Meanwhile, the output layer is expressed as: Where: Y m，max and Y m，min are the maximum values ​​of the predicted parameters, the subscript m is used to indicate that the data are measured values, p is used to indicate that the data are predicted values, k is the number of output variables, and W 12 and B 12 are the weight matrix and bias matrix between the hidden layer and the output layer, respectively.

6. The rapid intelligent prediction method for deformation of deep foundation pits in soft soil areas according to claim 1 is characterized in that In step five, the structure of the artificial neural network model is simplified by changing the number of hidden layers and the number of neurons in the hidden layers.

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