Foundation pit temperature field-seepage-stress field coupling calculation method based on dynamic grid

Abstract

The invention relates to a dynamic grid-based foundation pit temperature field-seepage-stress field coupling calculation method, which comprises the following steps of: establishing a nonlinear dynamic bidirectional coupling constitutive relationship of a temperature field, a seepage field and a stress field containing a two-dimensional foundation pit cofferdam, and obtaining a three-field full coupling equation set; in combination with a GPU acceleration solver, solving the three-field full-coupling equation set by adopting a sub-domain decoupling-asynchronous iteration strategy; and performing real-time early warning on the cofferdam construction period according to a solving result. The method has the advantages that compared with a traditional linear model, the precision of the established three-field full-coupling equation set is improved, and the interaction influence relation of three fields can be well simulated.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical simulation, and more specifically, it relates to a coupled calculation method for the foundation pit temperature field - seepage - stress field based on dynamic grids. Background Art

[0002] Traditional numerical analysis methods have bottlenecks in aspects such as calculation efficiency, grid adaptability, and constitutive model accuracy, restricting the accurate prediction ability of engineering disasters. Existing limitations include: 1) In terms of grid division. In engineering, static uniform grids (such as the fixed layered grid method) are mostly used, which are difficult to adapt to local high-gradient regions caused by the coupled action of multiple physical fields such as the surrounding rock damage area and seepage mutation zone during the construction process. 2) In terms of calculation efficiency. The traditional finite element method adopts a CPU cluster parallel strategy (such as the MPI multi-node architecture), but there are still defects such as large memory consumption and high communication latency when dealing with large-scale cofferdam problems. And its single physical field solution architecture fails to solve the data exchange bottleneck in the multi-field coupling iteration process, resulting in limited speedup. 3) In terms of constitutive models. Existing cofferdam analyses mostly adopt the ideal elastic-plastic model or the Drucker-Prager criterion, which are difficult to accurately characterize the nonlinear strength attenuation and permeability mutation characteristics during the unloading process of deep rock masses. Although the improved Burger model can reflect viscoelastic-plastic characteristics, it does not establish a dynamic association with the damage variable, resulting in convergence difficulties in the multi-field coupling equations. Summary of the Invention

[0003] The purpose of the present invention is to propose a coupled calculation method for the foundation pit temperature field - seepage - stress field based on dynamic grids in view of the deficiencies of the existing technology.

[0004] In the first aspect, a coupled calculation method for the foundation pit temperature field - seepage - stress field based on dynamic grids is provided, including:

[0005] S1. Establish a non-linear dynamic two-way coupled constitutive relationship of the temperature field, seepage field, and stress field of a two-dimensional foundation pit cofferdam, and obtain a full-coupled system of equations for the three fields;

[0006] S2. Combine a GPU-accelerated solver and use a domain decomposition - asynchronous iteration strategy to solve the full-coupled system of equations for the three fields;

[0007] S3. According to the solution results, conduct real-time early warning for the cofferdam construction period.

[0008] Preferably, S1 includes:

[0009] S101. Establish a non-linear dynamic two-way coupled constitutive relationship between the temperature field and seepage field of a two-dimensional foundation pit cofferdam;

[0010] S102. Establish a non-linear dynamic two-way coupled constitutive relationship between the temperature field and stress field of a two-dimensional foundation pit cofferdam;

[0011] S103. Establish the constitutive relationship of nonlinear dynamic two-way coupling between the seepage field and the stress field of the two-dimensional foundation pit cofferdam;

[0012] S104. According to S101 - S103, establish the fully coupled three-field equations.

[0013] Preferably, in S101, during the temperature-seepage coupling process, introduce a nonlinear permeability model, and apply temperature power-law correction and stress exponential decay.

[0014] Preferably, in S102, during the temperature-stress coupling process, introduce a damage-dependent thermal conductivity model to quantify the influence of damage evolution on the heat transfer path.

[0015] Preferably, in S103, during the seepage-stress coupling process, introduce a non-Darcy seepage strain model to characterize the sudden change phenomenon of seepage strain driven by temperature gradient through cross terms.

[0016] Preferably, in S2, during the spatial domain decomposition, adaptively divide the subdomains according to the field variable gradients.

[0017] Preferably, in S2, in terms of asynchronous iteration of time steps, apply the implicit Crank-Nicolson format, explicit RK-4 format, and quasi-static update to the temperature field, seepage field, and stress field respectively.

[0018] In the second aspect, a foundation pit temperature field-seepage-stress field coupling calculation system based on dynamic grids is provided for executing any of the methods in the first aspect, including:

[0019] A building module, configured to establish the constitutive relationship of nonlinear dynamic two-way coupling between the temperature field, seepage field, and stress field of the two-dimensional foundation pit cofferdam, and obtain the fully coupled three-field equations;

[0020] A solving module, configured to solve the fully coupled three-field equations by adopting a domain decomposition-asynchronous iteration strategy in combination with a GPU-accelerated solver;

[0021] An early warning module, configured to perform real-time early warning on the construction period of the cofferdam according to the solving results.

[0022] In the third aspect, a computer storage medium is provided, in which a computer program is stored; when the computer program runs on a computer, the computer is enabled to execute any of the methods in the first aspect.

[0023] In the fourth aspect, an electronic device is provided, including:

[0024] A memory, configured to store the computer program;

[0025] A processor is used to execute the computer program to implement any method as described in the first aspect.

[0026] The beneficial effects of the present invention are:

[0027] 1. When the temperature gradient is large, the present invention introduces a nonlinear permeability model into the temperature-seepage coupling, applies temperature power law correction and stress exponential attenuation, and improves the accuracy compared with the traditional linear model; when the hydraulic gradient is large, the seepage-stress coupling introduces a non-Darcy seepage strain model, and the seepage strain mutation phenomenon driven by the temperature gradient is characterized by cross terms, which can better simulate the interactive influence relationship between the two; in the process of temperature-stress coupling, a damage-dependent thermal conductivity model is introduced to quantify the influence of damage evolution on the heat transfer path, which can better simulate the dynamic influence of high temperature zone temperature on thermal stress.

[0028] 2. In the spatial domain decomposition, the present invention adaptively divides the subdomains according to the gradient of the field variables to improve the load balancing degree of the model; and in terms of asynchronous iteration of the time step, the present invention applies the implicit Crank-Nicolson format, the explicit RK-4 format and the quasi-static update to the temperature field, the seepage field and the stress field respectively; in terms of computing performance, GPU heterogeneous acceleration is adopted, and GPU shared memory is used to optimize sparse matrix storage.

[0029] 3. The present invention adopts self-optimization of support parameters based on the gradient descent method to reduce the material cost of cofferdam lining; and can provide real-time warning and dynamically update the risk identification response time of the monitoring data-driven model during the construction period. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 Schematic diagram of the three-field coupling model of the two-dimensional foundation pit cofferdam provided for this application;

[0031] Figure 2 Schematic diagram of the coupling calculation process provided for this application. DETAILED DESCRIPTION

[0032] The present invention is further described below in conjunction with embodiments. The description of the following embodiments is only used to help understand the present invention. It should be noted that for ordinary persons in the art, without departing from the principle of the present invention, the present invention can also be modified in some ways, and these improvements and modifications also fall within the scope of protection of the claims of the present invention.

[0033] Embodiment 1:

[0034] To overcome the deficiencies of numerical software in the multi-field coupling problem of cofferdams, this application provides a calculation method that can relatively quickly perform the coupling calculation of temperature-seepage-stress of cofferdams. It should be noted that there are large gradients in the temperature field, seepage field, and stress field around the cofferdam. To more generally describe the three-field coupling of cofferdam engineering, the influence between fields is considered to be non-linear in the following text.

[0035] Specifically, the coupling calculation method of the foundation pit temperature field-seepage-stress field based on dynamic grids provided by this application includes:

[0036] S1. Establish a non-linear dynamic two-way coupling constitutive relationship including the temperature field, seepage field, and stress field of a two-dimensional foundation pit cofferdam, and obtain a fully coupled equation set for the three fields.

[0037] Specifically, S1 includes:

[0038] S101. Establish a non-linear dynamic two-way coupling constitutive relationship between the temperature field and seepage field of a two-dimensional foundation pit cofferdam.

[0039] Specifically, the non-linear dynamic two-way coupling constitutive relationship between the temperature field and seepage field includes the influence of the temperature field on the seepage field and the influence of the seepage field on the temperature field. The influence of the temperature field on the seepage field includes that temperature affects the permeability coefficient of the soil isolated by the cofferdam and temperature affects the viscosity of the fluid. And, in the process of temperature-seepage coupling in this application, a non-linear permeability model is introduced, and temperature power-law correction and stress exponential decay are applied.

[0040] Among them, the influence of temperature on the permeability coefficient of the soil isolated by the cofferdam is expressed as:

[0041] K(T) = K0[1 + β KT (T - T0) + γ KT (T - T0) 2 (1)

[0042] Where β KT and γ KT are both temperature correction coefficients, T0 represents the initial temperature, T is the temperature field at time t and coordinates (x, y), and K0 is the initial permeability coefficient of the soil.

[0043] The influence of temperature on the viscosity of the fluid is expressed as:

[0044]

[0045] μ Among them, μ0 is the initial fluid viscosity, and λ

[0046] is the Arrhenius-type temperature influence factor. μ is the fluid viscosity at temperature T. In addition, the influence of the seepage field on the temperature field is reflected in the convection-diffusion coupling, which is expressed as:

[0047]

[0048] where is the Darcy seepage field, ρ is the density of the soil mass, and c p is the heat capacity of the soil mass, and ρ ω and c pω are both convection constants. represents the gradient of the temperature field, and represents the divergence of the temperature field gradient.

[0049] S102. Establish the constitutive relationship of the non - linear dynamic two - way coupling between the temperature field and the stress field of the two - dimensional foundation pit cofferdam.

[0050] The constitutive relationship of the non - linear dynamic two - way coupling between the temperature field and the stress field includes the influence of the temperature field on the stress field and the influence of the stress field on the temperature field. Moreover, during the temperature - stress coupling process, a damage - dependent thermal conductivity model is introduced to quantify the influence of damage evolution on the heat transfer path.

[0051] Specifically, the influence of the temperature field on the stress field is manifested as the non - linear influence of temperature on stress (thermal strain), and the formula is:

[0052]

[0053] where T c represents the critical temperature, that is, the thermal strain saturation threshold, and α T is the thermal strain constant, and tanh() is the hyperbolic tangent function.

[0054] The influence of the stress field on the temperature field is manifested as the modification of the fracture thermal conductivity, and the formula is:

[0055]

[0056] where σ c represents the stress - sensitive threshold of the thermal conductivity, k0 is the initial thermal conductivity of the soil mass, β k is the thermal conductivity calculation constant, σ is the stress tensor of the soil mass, and ||σ|| represents the norm of the tensor σ.

[0057] S103. Establish the constitutive relationship of the non - linear dynamic two - way coupling between the seepage field and the stress field of the two - dimensional foundation pit cofferdam.

[0058] The constitutive relationship of the non - linear dynamic two - way coupling between the seepage field and the stress field includes the influence of the seepage field on the stress field and the influence of the stress field on the seepage field. Moreover, in this application, during the seepage - stress coupling process, a non - Darcy seepage strain model is introduced to describe the sudden change phenomenon of seepage strain driven by the temperature gradient through the cross - term.

[0059] Specifically, the influence of the seepage field on the stress field is manifested as the non-linear seepage expansion effect, and the formula is:

[0060] ε H (H) = α H sign(H - H0)·(H - H0) n (6)

[0061] where H0(x, y) represents the initial water head value of the soil mass at the coordinates (x, y), and α H is the calculation constant of seepage strain, n = 1.3 is the non-linear index of seepage strain, and sign() is the sign function.

[0062] The influence of the stress field on the seepage field is manifested as porosity-stress coupling, and the formula is:

[0063]

[0064] where σ0 represents the porosity stress sensitivity threshold, and β φ is the calculation constant of porosity, φ0 is the initial porosity, K0 is the initial permeability coefficient, and m = 2.5 is the Kozeny-Carman equation index.

[0065] S104. According to S101 - S103, establish the fully coupled equations of the three fields.

[0066] Among them, the formula of the temperature field is:

[0067]

[0068] where Q T is the external heat source.

[0069] The formula of the seepage field is:

[0070]

[0071] where Q H is the external flow rate, S s is the soil water storage rate, and β F is the water head correction coefficient.

[0072] The formula of the stress field is:

[0073]

[0074] where C is the non-linear stiffness tensor considering damage:

[0075]

[0076] where δ ij is the Kronecker symbol, and δ is only valid when i = j ij= 1, and in other cases, δ ij = 0, where v is the Poisson's ratio of the soil mass.

[0077] S2. Combine with a GPU-accelerated solver and use a domain decomposition-asynchronous iteration strategy to solve the three-field fully coupled equations.

[0078] S3. Based on the solution results, conduct real-time warning for the construction period of the cofferdam.

[0079] Embodiment 2:

[0080] Based on Embodiment 1, Embodiment 2 of the present application provides a more specific coupling calculation method for the foundation pit temperature field-seepage-stress field based on dynamic grids, including:

[0081] S1. Establish a non-linear dynamic two-way coupling constitutive relationship for the temperature field, seepage field, and stress field of a two-dimensional foundation pit cofferdam, and obtain the three-field fully coupled equations.

[0082] Exemplarily, apply the three-field coupling model obtained in S1 to an actual cofferdam project, and establish a two-dimensional plane strain numerical model as follows Figure 1 shown, where the origin of the oxy coordinate system is taken at the ground surface directly above the cofferdam. The outer boundary dimensions of the model are h1, h2, a, b, c, d respectively. The total head of the ground surface outside the foundation pit excavation is constantly H1, and the temperature is constantly T1. The total head of the ground surface at the bottom of the foundation pit is constantly H2, and the temperature is constantly T2. The outer boundaries of the foundation pit model are all impermeable boundaries and heat insulation boundaries. The total head of the ground surface is constantly H0, and the temperature is constantly T0. The total head and initial temperature in the soil mass are respectively assumed to be H1 and T1, and it is assumed that the displacement of the model boundary is constantly 0. Among them Figure 1 is the left half part model in the symmetric foundation pit plane strain problem, so the right boundary of the model is the axis of symmetry, which is also an impermeable boundary and a heat insulation boundary. The permeability coefficients of the soil and the surrounding rock are ks1 and ks2 respectively, and the thermal conductivity coefficients of the soil and the surrounding rock are ka1 and ka2 respectively. Since ks2 << ks1, it is assumed that the surface of the cofferdam is all impermeable.

[0083] In addition, Figure 1 The coupling characteristics in are shown in Table 1, and the model parameter selection is shown in Table 2.

[0084] Table 1 Explanation table of coupling characteristics

[0085]

[0086] Table 2 Table of model parameter values

[0087]

[0088]

[0089] S2. Combine with the GPU-accelerated solver, and adopt the domain decomposition-asynchronous iteration strategy to solve the three-field fully coupled equations.

[0090] In the spatial domain decomposition, after each iteration, the gradients of the three fields of the model are made dimensionless, and the proportion of the stress field gradient is calculated. Then, the global computational grid is updated as a whole according to this proportion, and the total number of grids is kept unchanged during the update process, so as to improve the model load balance while ensuring the model's computing power. The stress field proportion after each iteration is as follows:

[0091]

[0092] where respectively represent the magnitudes of the gradients of the temperature field, seepage field and stress field during a certain iteration process, and Φ(x, y) represents the stress field gradient division weight at a specific position during a certain iteration process.

[0093] In terms of the asynchronous iteration of time steps, the implicit Crank-Nicolson format, explicit RK-4 format and quasi-static update are respectively applied to the temperature field, seepage field and stress field:

[0094] Implicit Crank-Nicolson format update of the temperature field: Construct the implicit differential equation of the gradient at the same point in the current iteration and the next iteration, and then solve the implicit differential equation through the built-in ode45() stiffness function in matlab.

[0095] Explicit RK-4 format update of the seepage field: Estimate the state of the next time step by weighted average of the gradients in four stages according to the current iteration status of a certain area.

[0096] Quasi-static update of the stress field: That is, as Figure 2 shown, at a certain iteration step, first calculate the seepage field and temperature field, then calculate the stress field, and then continue to calculate the mutual influence of the three, and then enter the next iteration step. That is, when calculating a certain field alone, assume that the other two fields are instantaneously unchanged, which is the quasi-static iterative update.

[0097] In terms of computing performance, GPU heterogeneous acceleration is adopted, and the sparse matrix storage is optimized by using the shared memory of the CPU and GPU. The CPU is responsible for processing the control logic and task scheduling, and the GPU is responsible for executing parallel computing-intensive tasks, so that the two work together to optimize the overall performance.

[0098] S3. According to the final solution result, give an early warning to the final high stress field area during the cofferdam construction period considering the three-field coupling, and carry out reinforcement pretreatment.

[0099] In S3, the self-optimization of the support parameters based on the gradient descent method in this application can make full use of the performance of the support by means of the intelligent mutual matching of the support materials and structural forms in the model library through the final results of the three-field coupling calculation, reduce the material cost of the cofferdam lining, and can give real-time warnings to monitor the dynamic update risk identification response time of the model during the construction period.

[0100] It should be noted that the same or similar parts in this embodiment and Embodiment 1 can be referred to each other and will not be elaborated in this application.

[0101] Embodiment 3:

[0102] Based on Embodiment 2, Embodiment 3 of this application provides a coupled calculation system for the foundation pit temperature field-seepage-stress field based on dynamic grids, including:

[0103] A building module for building a non-linear dynamic two-way coupled constitutive relationship including the temperature field, seepage field and stress field of a two-dimensional foundation pit cofferdam, and obtaining a full-coupling equation set for the three fields;

[0104] A solving module for solving the full-coupling equation set of the three fields by adopting a domain decomposition-asynchronous iteration strategy in combination with a GPU acceleration solver;

[0105] A warning module for giving real-time warnings to the cofferdam construction period according to the solving results.

[0106] It should be noted that the system provided in this embodiment is the system corresponding to the method provided in Embodiment 2. Therefore, the same or similar parts in this embodiment and Embodiment 2 can be referred to each other and will not be elaborated in this application.

Claims

1. A coupled calculation method for the temperature field - seepage - stress field of a foundation pit based on a dynamic grid, characterized in that Including: S1. Establish a non-linear dynamic two-way coupling constitutive relationship including the temperature field, seepage field and stress field of a two-dimensional foundation pit cofferdam, and obtain a fully coupled three-field equation set; S2. Combine a GPU-accelerated solver and adopt a domain decomposition-asynchronous iteration strategy to solve the fully coupled three-field equation set; S3. Based on the solution results, conduct real-time warning during the construction period of the cofferdam.

2. The coupled calculation method of foundation pit temperature field-seepage-stress field based on dynamic grid according to claim 1, wherein, S1 includes: S101. Establish a non-linear dynamic two-way coupling constitutive relationship between the temperature field and seepage field of a two-dimensional foundation pit cofferdam; S102. Establish a non-linear dynamic two-way coupling constitutive relationship between the temperature field and stress field of a two-dimensional foundation pit cofferdam; S103. Establish a non-linear dynamic two-way coupling constitutive relationship between the seepage field and stress field of a two-dimensional foundation pit cofferdam; S104. Based on S101 - S103, establish a fully coupled three-field equation set.

3. The coupled calculation method of foundation pit temperature field-seepage-stress field based on dynamic grid according to claim 2, characterized in that In S101, during the temperature-seepage coupling process, introduce a non-linear permeability model and apply temperature power-law correction and stress exponential decay.

4. The coupled calculation method of foundation pit temperature field-seepage-stress field based on dynamic grid according to claim 3, characterized in that, In S102, during the temperature-stress coupling process, introduce a damage-dependent thermal conductivity model to quantify the influence of damage evolution on the heat transfer path.

5. The coupled calculation method of foundation pit temperature field-seepage-stress field based on dynamic grid according to claim 4, wherein In S103, during the seepage-stress coupling process, introduce a non-Darcy seepage strain model to depict the sudden change phenomenon of seepage strain driven by temperature gradient through cross terms.

6. The coupled calculation method of foundation pit temperature field - seepage - stress field based on dynamic grid according to claim 5, characterized in that In S2, during the spatial domain decomposition, adaptively divide sub-domains according to the field variable gradient.

7. The coupled calculation method of foundation pit temperature field - seepage - stress field based on dynamic grid according to claim 6, characterized in that In S2, in terms of time-step asynchronous iteration, apply the implicit Crank-Nicolson format, explicit RK-4 format and quasi-static update to the temperature field, seepage field and stress field respectively.

8. A coupled calculation system for the temperature field - seepage - stress field of a foundation pit based on a dynamic grid, characterized in that, Used to execute the method according to any one of claims 1 to 7, including: A building module, used to establish a non-linear dynamic two-way coupling constitutive relationship including the temperature field, seepage field and stress field of a two-dimensional foundation pit cofferdam, and obtain a fully coupled three-field equation set; A solving module, used to combine a GPU-accelerated solver and adopt a domain decomposition-asynchronous iteration strategy to solve the fully coupled three-field equation set; A warning module, used to conduct real-time warning during the construction period of the cofferdam based on the solution results.

9. A computer storage medium, characterized in that, The computer storage medium stores a computer program; when the computer program runs on a computer, the computer is enabled to execute the method according to any one of claims 1 to 7.

10. An electronic device, characterized in that, Including: A memory, used to store the computer program; A processor, used to execute the computer program to implement the method according to any one of claims 1 to 7.

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