A system non-equilibrium evolution method considering water action

Abstract

The application provides a system non-equilibrium evolution method considering water action, on the basis of elastic-plastic theory, water action is decomposed into elastic effective stress and plastic effective stress by considering the influence of water; the influence of water action, i.e. elastic effective stress and plastic effective stress, on three basic equations and boundary conditions is analyzed, the elastic effective stress influences the balance equation, and the plastic effective stress changes the yield criterion; the influence of water action, i.e. elastic effective stress and plastic effective stress, on the plastic residual energy norm is analyzed, the expression of the plastic residual energy norm is unchanged, and the minimum plastic residual energy principle still holds; the method is realized in a finite element framework, and the plastic residual energy norm in the deformation reinforcement theory is used to measure and evaluate the overall stability of the structure. The method provided by the application overcomes the limitation that the existing deformation reinforcement theory does not consider water action, and provides an effective way for analyzing water storage disturbance problems.

Description

Technical Field

[0001] This invention relates to the field of structural stability evaluation in geotechnical engineering, and specifically to a non-equilibrium evolution method for systems that considers the effects of water. Background Technology

[0002] Due to the combined effects of rapid valley erosion and strongly folded mountain ranges, the southwestern region generally possesses complex topographic and geological structures characterized by steep valleys, high ground stress, and complex hydrogeological conditions. This results in the geological bodies at dam sites being in a state of critical or near-critical equilibrium under natural conditions. Drastic engineering disturbances, such as water impoundment, can disrupt this critical equilibrium. Therefore, it is necessary to analyze the impact of water impoundment on the overall structural evolution from the perspective of non-equilibrium evolution.

[0003] Regarding non-equilibrium evolution methods, the existing approach is deformation-strengthening theory, whose core is the principle of minimum plastic residual energy. Its main point is that, given a fixed external load and loading path, an elastoplastic structure always evolves towards the direction of minimum plastic residual energy, even when the structure's self-supporting capacity is at its maximum and the strengthening force is at its minimum. Since its development, deformation-strengthening theory has been applied to various aspects of geotechnical engineering. However, this analysis process has not considered the influence of other disturbances such as water, i.e., the impact of water accumulation on the principle of minimum plastic residual energy. Whether deformation-strengthening theory is applicable after considering the effect of water, and whether the expression for the minimum residual energy norm holds, needs verification. Summary of the Invention

[0004] The purpose of this invention is to overcome the limitation of existing deformation and reinforcement theories that do not consider the effect of water, and to provide a non-equilibrium evolution method for systems that takes into account the effect of water.

[0005] Therefore, the above-mentioned objective of the present invention is achieved through the following technical solution:

[0006] A non-equilibrium evolution method for a system considering the effects of water includes the following steps:

[0007] S1. Based on the elastic-plastic theory, considering the influence of water, the elastic-plastic theory is extended to the pore elastic-plastic theory, in which the effect of water includes elastic effective stress and plastic effective stress.

[0008] S2. Analyze the effect of water on the elastoplastic calculation process, that is, the effect of elastic effective stress and plastic effective stress on the three basic equations and boundary conditions;

[0009] S3. Analyze the effect of water on the plastic complementary energy norm in deformation strengthening theory, that is, the effect of elastic effective stress and plastic effective stress on the plastic complementary energy norm (based on deformation strengthening theory, the plastic complementary energy norm is a generalized Lyapunov function that can be used to evaluate the non-equilibrium evolution of the system).

[0010] S4. Implement this method within the finite element framework.

[0011] While adopting the above technical solutions, the present invention may also adopt or combine the following technical solutions:

[0012] As a preferred technical solution of the present invention: In step S1, the pore elastic-plastic theory specifically states that the only driving force for the elastic deformation of the porous medium is the effective elastic stress.

[0013] σ′ ij =σ ij -αpδ ij (1)

[0014] In the formula: σ ij The total stress in component form; σ′ ij Represents the effective elastic stress in component form; δ ij Kronecker function; α is the effective elastic stress coefficient, i.e., Biot coefficient; p represents the magnitude of pore water pressure;

[0015] The only driving force for plastic deformation in porous media is the effective plastic stress:

[0016] σ″ ij =σ ij -βpδ ij (2)

[0017] In the formula: σ i ′ j β represents the effective plastic stress in component form; β represents the effective plastic stress coefficient.

[0018] In step S2, the influence of water on the elastoplastic calculation process is analyzed. The specific steps are as follows:

[0019] S21. Give the three governing equations of the structure in component form, neglecting the effect of water, including the equilibrium equation, geometric equation, constitutive relation, and yield criterion, as follows:

[0020]

[0021]

[0022]

[0023]

[0024] In the formula: f i Volume force in component form; ε ij Represents the total strain in component form; Represents elastic strain in component form; Plastic strain in component form; u i Displacement in component form; C ijkl f represents the compliance coefficient tensor; f represents the yield function.

[0025] S22. Give the displacement boundary conditions and stress boundary conditions in component form:

[0026]

[0027] In the formula: Indicates the displacement on the displacement boundary; Indicates the stress at the stress boundary; n j S represents the unit normal vector; u Indicates the displacement boundary; S t Indicates stress boundary; displacement boundary and stress boundary must satisfy S u ∪S t =S,

[0028] S23, Apply the effective stress formula σ i ′ j =σ ij -αpδ ij Substituting into the equilibrium equation (3), we can derive the equilibrium differential equation and yield condition expressed in terms of elastic effective stress, respectively:

[0029]

[0030]

[0031] In the formula: F i This represents the permeation volume force; the effective elastic stress only affects the equilibrium equations, which is equivalent to adding a permeation volume force, while the geometric equations, constitutive equations, yield conditions, and boundary conditions remain unchanged.

[0032] S24. Effective plastic stress only changes the yield state, specifically manifested in a change in the yield criterion:

[0033]

[0034] In the formula: f′ represents the new yield function.

[0035] As a preferred technical solution of the present invention: In step S3, the influence of water on the plastic residual energy norm in the deformation strengthening theory is analyzed, and the specific steps are as follows:

[0036] S31. Give the viscoelastic-plastic constitutive relations without considering the effect of water:

[0037]

[0038] In the formula: and These are the elastic strain rate and the plastic strain rate, respectively.

[0039] The plastic strain rate defined by the Duvant-Lions model is:

[0040]

[0041] In the formula: τ is the viscosity coefficient; This refers to the stress that eventually settles at the yield point after a period of time.

[0042] S311. According to the principle of maximum plastic dissipation:

[0043]

[0044] Substituting the plastic strain rate into formula (13), we get:

[0045]

[0046] In the formula: σ is a point outside the yield surface in the elastoplastic calculation; It is a point inside or on the yield surface; It is the point closest to σ among all points on the yield surface; that is... Minimize the following expression:

[0047]

[0048] S312. Construct the Lagrange function:

[0049]

[0050] In the formula: λ is the Lagrange multiplier; Equation (16) is in The necessary condition for taking an extreme value is:

[0051]

[0052] Substituting the plastic strain rate into formula (17), we get:

[0053]

[0054] S313. Assume the yield surface does not change with time, i.e., it satisfies the consistency condition:

[0055]

[0056] Substituting formula (18) into formula (19), we get:

[0057]

[0058] S32. Give the plasticity norm without considering the effect of water:

[0059]

[0060] In the formula: L is the integral of the square of the distance between two stress points over the entire structural volume, which measures the degree to which the stress beyond the yield surface deviates from the equilibrium stress;

[0061] The steps to determine the properties possessed by the plastic complementary energy norm are as follows:

[0062] S321. The plasticity norm is always non-negative.

[0063] L≥0(22)

[0064] In the formula: if and only if When the stress exceeds the yield surface, the equality holds; at this time, the structure has no stress exceeding the yield surface, and the structure is in equilibrium and stable.

[0065] S322, the first derivative of the plasticity complement norm is:

[0066]

[0067] Substituting the plastic strain rate (12), the viscoelastic-plastic constitutive relation (11), and equation (20) into formula (23) in turn, we get:

[0068]

[0069] In the formula: the second term Non-negative; the first term can be decomposed into:

[0070]

[0071] Substituting formula (25) into formula (24), we get:

[0072]

[0073] In the formula: the first derivative of the plastic complementary energy norm is always not greater than zero if and only if When the equality holds, the equality holds.

[0074] From the plastic strain rate (12), it can be seen that, This means that the plastic strain rate remains constant, and the structure will continue to flow at a constant plastic strain rate. This state is called the "limit constant evolution state".

[0075] S323, the second derivative of the plasticity complement norm is:

[0076]

[0077] Substituting the viscoelastic-plastic constitutive relation into equation (27), we get:

[0078]

[0079] In the formula: the first term can be broken down into:

[0080]

[0081] Substituting the time derivatives of formulas (29) and (12) into formula (28), we get:

[0082]

[0083] In the formula: the integrand can be transformed into:

[0084]

[0085] Differentiating formula (18) with respect to time and combining it with formula (19), we get:

[0086]

[0087] Substituting formulas (31) and (32) into formula (30), we get:

[0088]

[0089] In the formula: the second derivative of the plastic complementary energy norm is always not less than zero if and only if Right now When the equality holds, the equality holds.

[0090] S33. The effective elastic stress only affects the equilibrium equations of the structure. Its influence on the plastic complementary energy norm is determined by the following steps:

[0091] S331. The definition of the plastic residual energy norm remains unchanged, and the value of the plastic residual energy norm is still not less than zero, L≥0.

[0092] S332. The effect of effective elastic stress on the first derivative of the plastic complementary energy norm is reflected in formula (25), which yields:

[0093]

[0094] In the formula: the time derivative of the permeation volume force is zero, and the first derivative of the plastic residual energy norm is still not greater than zero.

[0095] S333. The effect of the effective elastic stress on the second derivative of the plastic complementary energy norm is reflected in formula (29), which yields:

[0096]

[0097] In the formula: the time derivative of the permeation volume force is zero, and the second derivative of the plastic residual energy norm is still not less than zero.

[0098] S34. The effective plastic stress only changes the yield criterion. Its effect on the plastic complementary energy norm is explained in the following steps:

[0099] S341. The definition of the plastic residual energy norm remains unchanged, and the value of the plastic residual energy norm is still not less than zero, L≥0.

[0100] S342. The effective plastic stress changes the yield criterion. The yield function in formulas (16) to (19) is uniformly replaced by f′. Formula (20) still holds, and the first derivative of the plastic complementary energy norm is still not greater than zero.

[0101] S343. The effective plastic stress changes the yield criterion, and formula (33) is rewritten as:

[0102]

[0103] In the formula: the second derivative of the plastic complementary energy norm is still not less than zero.

[0104] As a preferred technical solution of the present invention: In step S4, the finite element implementation of the non-equilibrium evolution method specifically includes the following steps:

[0105] S41. Determine the structural loads and boundary conditions, where the loads include the seepage volume force generated by the equivalent elastic effective stress;

[0106] S42. Calculate the total stress field under the current conditions, i.e., the effective elastic stress field σ′;

[0107] S43. Based on the elastic effective stress field σ′, considering the magnitude of the seepage water pressure, the plastic effective stress field σ″ is calculated.

[0108] S44. Substitute the effective plastic stress into the yield criterion:

[0109] If the yield function is less than or equal to zero, it indicates that the structure is in equilibrium and stable, and the plastic residual energy norm is zero.

[0110] If the yield function is greater than zero, update the elastic effective stress and perform iterative calculations until the calculation converges. Calculate the plastic residual energy norm at this point to evaluate the overall stability of the structure.

[0111] This invention provides a non-equilibrium evolution method for systems considering the effects of water. Based on elastoplastic theory, it decomposes the effects of water into elastic effective stress and plastic effective stress. The method analyzes the influence of water (i.e., elastic and plastic effective stresses) on the three fundamental equations and boundary conditions. Elastic effective stress affects the equilibrium equations, while plastic effective stress alters the yield criterion. The method also analyzes the influence of water (i.e., elastic and plastic effective stresses) on the plastic complementary energy norm. The expression for the plastic complementary energy norm remains unchanged, and the principle of minimum plastic complementary energy still holds. This method is implemented within a finite element framework, using the plastic complementary energy norm from deformation strengthening theory to measure and evaluate the overall stability of the structure. The method provided by this invention overcomes the limitation of existing deformation strengthening theories that do not consider the effects of water, providing an effective approach for analyzing water storage disturbance problems. Attached Figure Description

[0112] Figure 1 This is a flowchart illustrating the non-equilibrium evolution method for systems considering the effects of water provided by the present invention.

[0113] Figure 2 This is a schematic diagram of the internal and external stresses on the elastic-plastic iterative yield surface.

[0114] Figure 3 This is a schematic diagram illustrating the evolution of the plastic complementary energy norm.

[0115] Figure 4 This is a flowchart of the finite element implementation of the nonequilibrium evolution method. Detailed Implementation

[0116] The present invention will be described in detail with reference to the accompanying drawings and specific embodiments.

[0117] like Figure 1 As shown, a non-equilibrium evolution method for a system considering the effects of water is implemented as follows:

[0118] (1) Based on the elastic-plastic theory, considering the influence of water, the elastic-plastic theory is extended to the pore elastic-plastic theory, in which the effect of water includes elastic effective stress and plastic effective stress.

[0119] (2) Analyze the effect of water on the elastoplastic calculation process, that is, the effect of elastic effective stress and plastic effective stress on the three basic equations and boundary conditions;

[0120] (3) Analyze the effect of water on the plastic residual energy norm in deformation and strengthening theory, that is, the effect of elastic effective stress and plastic effective stress on the plastic residual energy norm;

[0121] (4) Implement the method within the finite element framework.

[0122] In step (1) above, the pore elastic-plastic theory specifically states that the only driving force for elastic deformation of porous media is the effective elastic stress.

[0123] σ′ ij =σ ij -αpδ ij (1)

[0124] In the formula: σ ij The total stress in component form; σ′ ij Represents the effective elastic stress in component form; δ ij Here, α is the Kronecker function; α is the effective elastic stress coefficient, also known as the Biot coefficient; and p represents the magnitude of the pore water pressure. The only driving force for plastic deformation in porous media is the effective plastic stress.

[0125] σ″ ij =σ ij -βpδ ij (2)

[0126] In the formula: σ′ ij β represents the effective plastic stress in component form; β represents the effective plastic stress coefficient.

[0127] In step (2) above, the influence of water on the elastoplastic calculation process is analyzed. The specific steps are as follows:

[0128] (2.1) The three governing equations of the structure, expressed in component form without considering the effect of water, are given as follows: Equilibrium equations, geometric equations, constitutive relations, and yield criteria.

[0129]

[0130]

[0131]

[0132]

[0133] In the formula: f i Volume force in component form; ε ij Represents the total strain in component form; Represents elastic strain in component form; Plastic strain in component form; u i Displacement in component form; C ijkl f represents the compliance coefficient tensor; f represents the yield function.

[0134] (2.2) The displacement boundary conditions and stress boundary conditions are given in component form:

[0135]

[0136] In the formula: Indicates the displacement on the displacement boundary; Indicates the stress at the stress boundary; n j S represents the unit normal vector; u Indicates the displacement boundary; S t Indicates stress boundary; displacement boundary and stress boundary must satisfy S u ∪S t =S,

[0137] (2.3) Apply the effective stress formula σ′ ij =σ ij -αpδ ij Substituting into the equilibrium equation (3), we can derive the equilibrium differential equation and yield condition expressed in terms of elastic effective stress, respectively:

[0138]

[0139]

[0140] In the formula: F i This represents the permeation volume force; the effective elastic stress only affects the equilibrium equations, which is equivalent to adding a permeation volume force, while the geometric equations, constitutive equations, yield conditions, and boundary conditions remain unchanged.

[0141] (2.4) The effective plastic stress only changes the yield state, specifically manifested in a change in the yield criterion:

[0142]

[0143] In the formula: f′ represents the new yield function.

[0144] like Figure 2 , Figure 3 As shown, the specific steps in step (3) above, analyzing the effect of water on the plastic residual energy norm in deformation strengthening theory, are as follows:

[0145] (3.1) The viscoelastic-plastic constitutive relations are given without considering the effect of water:

[0146]

[0147] In the formula: and These are the elastic strain rate and the plastic strain rate, respectively. The plastic strain rate defined by the Duvant-Lions model is:

[0148]

[0149] In the formula: τ is the viscosity coefficient; This refers to the stress that eventually settles on the yield point after a period of time.

[0150] (3.1.1) According to the principle of maximum plastic dissipation:

[0151]

[0152] Substituting the plastic strain rate into formula (13), we get:

[0153]

[0154] In the formula: σ is a point outside the yield surface in the elastoplastic calculation; It is a point inside or on the yield surface; It is the point closest to σ among all points on the yield surface. That is... Minimize the following expression:

[0155]

[0156] (3.1.2) Construct the Lagrange function:

[0157]

[0158] In the formula: λ is the Lagrange multiplier; Equation (16) is in The necessary condition for taking an extreme value is:

[0159]

[0160] Substituting the plastic strain rate into formula (17), we get:

[0161]

[0162] (3.1.3) Assume that the yield surface does not change with time, i.e., the consistency condition is satisfied:

[0163]

[0164] Substituting formula (18) into formula (19), we get:

[0165]

[0166] (3.2) Give the plasticity norm without considering the effect of water:

[0167]

[0168] In the formula: L is the integral of the square of the distance between two stress points over the entire structural volume, which measures the degree to which the stress beyond the yield surface deviates from the equilibrium stress.

[0169] The steps to determine the properties possessed by the plastic complementary energy norm are as follows:

[0170] (3.2.1) The plasticity norm is always non-negative:

[0171] L≥0(22)

[0172] In the formula: if and only if When the stress exceeds the yield surface, the equality holds. At this point, the structure is in equilibrium and stable, with no stress exceeding the yield surface.

[0173] (3.2.2) The first derivative of the plastic complementary energy norm is:

[0174]

[0175] Substituting the plastic strain rate (12), the viscoelastic-plastic constitutive relation (11), and equation (20) into formula (23) in turn, we get:

[0176]

[0177] In the formula: the second term Non-negative. The first term can be broken down into:

[0178]

[0179] Substituting formula (25) into formula (24), we get:

[0180]

[0181] In the formula: the first derivative of the plastic complementary energy norm is always not greater than zero if and only if When the equality holds, the equation holds. From the plastic strain rate (12), we know that... This means that the plastic strain rate remains constant, and the structure will continue to flow at a constant plastic strain rate. This state is called the "limit constant evolution state".

[0182] (3.2.3) The second derivative of the plastic complementary energy norm is:

[0183]

[0184] Substituting the viscoelastic-plastic constitutive relation into equation (27), we get:

[0185]

[0186] In the formula: the first term can be broken down into:

[0187]

[0188] Substituting the time derivatives of formulas (29) and (12) into formula (28), we get:

[0189]

[0190] In the formula: the integrand can be transformed into:

[0191]

[0192] Differentiating formula (18) with respect to time and combining it with formula (19), we get:

[0193]

[0194] Substituting formulas (31) and (32) into formula (30), we get:

[0195]

[0196] In the formula: the second derivative of the plastic complementary energy norm is always not less than zero if and only if Right now When the equality holds, the equation is true.

[0197] (3.3) The effective elastic stress only affects the equilibrium equations of the structure. Its influence on the plastic complementary energy norm is as follows:

[0198] (3.3.1) The definition of the plastic residual energy norm remains unchanged, and the value of the plastic residual energy norm is still not less than zero L≥0.

[0199] (3.3.2) The influence of the effective elastic stress on the first derivative of the plastic complementary energy norm is reflected in formula (25), which yields:

[0200]

[0201] In the formula: the time derivative of the permeation volume force is zero, and the first derivative of the plastic residual energy norm is still not greater than zero.

[0202] (3.3.3) The influence of the effective elastic stress on the second derivative of the plastic complementary energy norm is reflected in formula (29), which yields:

[0203]

[0204] In the formula: the time derivative of the permeation volume force is zero, and the second derivative of the plastic residual energy norm is still not less than zero.

[0205] (3.4) The effective plastic stress only changes the yield criterion. Its effect on the plastic complementary energy norm is as follows:

[0206] (3.4.1) The definition of the plastic residual energy norm remains unchanged, and the value of the plastic residual energy norm is still not less than zero L≥0.

[0207] (3.4.2) The effective plastic stress changes the yield criterion. The yield function in formulas (16) to (19) is uniformly replaced by f′. Formula (20) still holds, and the first derivative of the plastic complementary energy norm is still not greater than zero.

[0208] (3.4.3) The effective plastic stress changes the yield criterion, and formula (33) is rewritten as:

[0209]

[0210] In the formula: the second derivative of the plastic complementary energy norm is still not less than zero.

[0211] like Figure 4 As shown, the finite element implementation of the non-equilibrium evolution method in step (4) above includes the following steps:

[0212] S41. Determine the structural loads and boundary conditions, where the loads include the permeable volume force generated by the equivalent elastic effective stress.

[0213] S42. Calculate the total stress field under the current conditions, i.e., the elastic effective stress field σ′.

[0214] S43. Based on the elastic effective stress field σ′, considering the magnitude of the seepage water pressure, the plastic effective stress field σ″ is calculated.

[0215] S44. Substitute the effective plastic stress into the yield criterion:

[0216] If the yield function is less than or equal to zero, it indicates that the structure is in equilibrium and stable, and the plastic residual energy norm is zero.

[0217] If the yield function is greater than zero, update the elastic effective stress and perform iterative calculations until the calculation converges. Calculate the plastic residual energy norm at this point to evaluate the overall stability of the structure.

[0218] The above specific embodiments are used to explain and illustrate the present invention, and are only preferred embodiments of the present invention, not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., 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 non-equilibrium evolution method for a system considering the effects of water, characterized in that: The method includes the following steps: S1. Based on the elastic-plastic theory, considering the influence of water, the elastic-plastic theory is extended to the pore elastic-plastic theory, in which the effect of water includes elastic effective stress and plastic effective stress. S2. Analyze the effect of water on the elastoplastic calculation process, that is, the effect of elastic effective stress and plastic effective stress on the three basic equations and boundary conditions; S3. Analyze the effect of water on the plastic residual energy norm in deformation strengthening theory, that is, the effect of elastic effective stress and plastic effective stress on the plastic residual energy norm; S4. Implement this method within the finite element framework; In step S3, the influence of water on the plastic residual energy norm in the deformation strengthening theory is analyzed. The specific steps are as follows: S31. Give the viscoelastic-plastic constitutive relations without considering the effect of water: （11） In the formula: and These are the elastic strain rate and the plastic strain rate, respectively. The plastic strain rate defined by the Duvant-Lions model is: （12） In the formula: It is the viscosity coefficient; This refers to the stress that eventually settles at the yield point after a period of time. S311. According to the principle of maximum plastic dissipation: （13） Substituting the plastic strain rate into formula (13), we get: （14） In the formula: It is a point outside the yield surface in elastoplastic calculations; It is a point inside or on the yield surface; It is the distance from all points on the yield surface. The nearest point; that is Minimize the following expression: （15） S312. Construct the Lagrange function: （16） In the formula: For Lagrange multipliers; Equation (16) in The necessary condition for taking an extreme value is: （17） Substituting the plastic strain rate into formula (17), we get: （18） S313. Assume the yield surface does not change with time, i.e., it satisfies the consistency condition: （19） Substituting formula (18) into formula (19), we get: （20） S32. Give the plasticity norm without considering the effect of water: （21） In the formula: It is the integral of the square of the distance between two stress points over the entire structural volume, and measures the degree to which the stress beyond the yield surface deviates from the equilibrium stress. The steps to determine the properties possessed by the plastic complementary energy norm are as follows: S321. The plasticity complement norm is always non-negative. （22） In the formula: if and only if When the stress exceeds the yield surface, the equality holds; at this time, the structure has no stress exceeding the yield surface, and the structure is in equilibrium and stable. S322, the first derivative of the plasticity complement norm is: （23） Substituting the plastic strain rate (12), the viscoelastic-plastic constitutive relation (11), and equation (20) into formula (23) in turn, we get: （24） In the formula: the second term Non-negative; the first term is split into: （25） Substituting formula (25) into formula (24), we get: （26） In the formula: the first derivative of the plastic complementary energy norm is always not greater than zero if and only if When the equality holds, the equality holds. Due to the plastic strain rate (12). This means that the plastic strain rate remains constant, and the structure will continue to flow at a constant plastic strain rate. This state is called the "limit constant evolution state". S323, the second derivative of the plasticity complement norm is: （27） Substituting the viscoelastic-plastic constitutive relation into formula (27), we get: （28） In the formula: the first term is broken down into: （29） Substituting the time derivatives of formulas (29) and (12) into formula (28), we get: （30） In the formula: the integral is transformed into: （31） Differentiating formula (18) with respect to time and combining it with formula (19), we get: （32） Substituting formulas (31) and (32) into formula (30), we get: （33） In the formula: the second derivative of the plastic complementary energy norm is always not less than zero if and only if Right now When the equality holds, the equality holds. S33. The effective elastic stress only affects the equilibrium equations of the structure. Its influence on the plastic complementary energy norm is determined by the following steps: S331. The definition of the plasticity norm remains unchanged, and the value of the plasticity norm is still not less than zero. ; S332, The effect of effective elastic stress on the first derivative of the plastic complementary energy norm is reflected in formula (25), which gives: （34） In the formula: the time derivative of the permeation volume force is zero, and the first derivative of the plastic residual energy norm is still not greater than zero. ; S333, The effect of the effective elastic stress on the second derivative of the plastic complementary energy norm is reflected in formula (29), which gives: （35） In the formula: the time derivative of the permeation volume force is zero, and the second derivative of the plastic residual energy norm is still not less than zero. ; S34. The effective plastic stress only changes the yield criterion. Its effect on the plastic complementary energy norm is explained in the following steps: S341. The definition of the plasticity norm remains unchanged, and the value of the plasticity norm is still not less than zero. ; S342. The effective plastic stress changes the yield criterion, and the yield function in formulas (16) to (19) is uniformly replaced by... Formula (20) still holds true, and the first derivative of the plastic complementary energy norm is still not greater than zero. ; S343. The effective plastic stress changes the yield criterion, and formula (33) is rewritten as: （36） In the formula: the second derivative of the plastic complementary energy norm is still not less than zero. ; In step S4, the finite element implementation of the non-equilibrium evolution method is carried out, and the specific steps are as follows: S41. Determine the structural loads and boundary conditions, where the loads include the seepage volume force generated by the equivalent elastic effective stress; S42. Calculate the total stress field under the current conditions, i.e., the effective elastic stress field. ; S43, in an elastic effective stress field Based on this, and considering the magnitude of the seepage water pressure, the effective plastic stress field is calculated. ; S44. Substitute the effective plastic stress into the yield criterion: If the yield function is less than or equal to zero, it indicates that the structure is in equilibrium and stable, and the plastic residual energy norm is zero. If the yield function is greater than zero, update the elastic effective stress and perform iterative calculations until the calculation converges. Calculate the plastic complementary energy norm at this point to evaluate the overall stability of the structure.

2. The non-equilibrium evolution method for a system considering the effects of water according to claim 1, characterized in that: In step S1, the pore elastic-plastic theory states that the only driving force for elastic deformation in porous media is the effective elastic stress. （1） In the formula: Represents the total stress in component form; Represents the effective elastic stress in component form; The Kronecker function; The effective elastic stress coefficient is the Biot coefficient. Indicates the magnitude of pore water pressure; The only driving force for plastic deformation in porous media is the effective plastic stress: （2） In the formula: Represents the effective plastic stress in component form; β Indicates the effective stress coefficient for plasticity; In step S2, the influence of water on the elastoplastic calculation process is analyzed. The specific steps are as follows: S21. Give the three governing equations of the structure in component form, neglecting the effect of water, including the equilibrium equation, geometric equation, constitutive relation, and yield criterion, as follows: （3） （4） （5） （6） In the formula: Volume force in component form; Represents the total strain in component form; Represents elastic strain in component form; Plastic strain in component form; Displacement in component form; Represents the flexibility coefficient tensor; Represents the yield function; S22. Give the displacement boundary conditions and stress boundary conditions in component form: （7） In the formula: Indicates the displacement on the displacement boundary; This represents the stress at the stress boundary; Represents the unit normal vector; Indicates the displacement boundary; Represents stress boundaries; displacement boundaries and stress boundaries must satisfy... ; S23, Apply the effective stress formula Substituting into the equilibrium equation (3), the equilibrium differential equation and yield condition expressed in terms of elastic effective stress are derived as follows: （8） （9） In the formula: Represents the volumetric force of osmosis; The effective elastic stress only affects the equilibrium equations, which is equivalent to adding a penetrating volume force, while the geometric equations, constitutive equations, yield conditions, and boundary conditions remain unchanged. S24. Effective plastic stress only changes the yield state, specifically manifested in a change in the yield criterion: （10） In the formula: This represents the new yield function.

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