Method for establishing hydraulic-mechanical-chemical full coupling influenced by fixed charges of clay body and application of hydraulic-mechanical-chemical full coupling

Abstract

The invention discloses a water-force-chemical full coupling establishment method influenced by fixed charges of clay and application, and relates to the technical field of environmental geotechnical engineering.The method comprises the following steps that Donna seepage pressure controlled by the fixed charges is introduced into a soil deformation control equation on the basis of a stress balance equation and mass conservation of pore fluid and pollutants; establishing a generalized effective stress formula; by establishing a generalized consolidation equation and a generalized Darcy law considering the fixed charge influence, the coupling behavior of the water-force-chemical full coupling equation of the saturated soil layer in the refuse landfill situation is accurately depicted. The water-force-chemical full coupling equation comprehensively considers the effect of the key element of the fixed charge on the saturated soil layer, and can accurately estimate the pore water pressure change, the sedimentation situation and the solute transport situation of the saturated soil layer under different fixed charge conditions; and scientific basis and technical support are provided for design and operation evaluation of the refuse landfill barrier.

Description

Technical Field

[0001] The present invention relates to the technical field of environmental geotechnical engineering, and particularly relates to a method for establishing a fully coupled hydro-mechanical-chemical process affected by the fixed charge of a clay body and its application. Background Art

[0002] Compacted clay is a key component of the anti-seepage and pollution isolation barrier in landfills and is crucial for the safe and stable operation of landfills. The fixed charges on the surface of clay minerals form a double-layer structure, endowing it with semi-permeable membrane characteristics, regulating various physical, chemical, and biological processes centered around ion transfer and exchange, and at the same time restricting the movement of charged pollutant ions. In the actual engineering environment, the compacted clay liner may be simultaneously affected by complex mechanical loads and leachate, which may strengthen or weaken the retardation effect of the semi-permeable membrane clay on pollutant ions, thereby changing the migration law of pollutants. Therefore, exploring the multi-physical field coupling process under the influence of fixed charges can not only accurately calculate the migration and transformation rate of pollutants, but also effectively evaluate the service performance and service life of landfills.

[0003] A large number of studies have been carried out on existing hydro-mechanical-chemical coupled pollutant transport models and fruitful results have been achieved. However, it is worth noting that these models are either not fully coupled or only coupled in some aspects. At the same time, these models generally ignore the potential influence of the consolidation charge on the surface of clay minerals on the hydro-mechanical-chemical coupling process. As is well known, the amount of surface charge of clay minerals directly determines the strength of the semi-permeable membrane characteristics of clay. In other words, the chemosmotic flow, chemosmosis-induced consolidation, and degree of chemical consolidation controlled by the characteristics of the clay membrane are all regulated by the amount of fixed charge on the surface of clay particles. However, the existing coupling equations do not fully consider the influence of fixed charges. Therefore, there is an urgent need to improve the existing coupling equations to fully consider the influence of soil fixed charges on the multi-physical field coupling effect. This helps to accurately predict the pollutant transport process inside the compacted clay liner, thereby providing theoretical support for practical engineering.

[0004] Therefore, it is crucial to carry out research on the fully coupled hydro-mechanical-chemical equations considering the influence of fixed charges and, based on this, explore the pollutant migration law within the clay liner. With the rapid development of modern industry and the increasing frequency of human activities, environmental pollution problems have become increasingly prominent, extremely severe and complex. In particular, the potential risks brought by soil pollution continue to intensify, and the damage to the ecological environment and human health is becoming increasingly serious. At the same time, in many environmental protection projects and land resource development and utilization projects, the clay liner, as an important pollution barrier and control medium, the research on its mechanism of action on pollutant migration is not yet sufficient. Conducting in-depth and systematic research on the relevant fully coupled equations considering the influence of fixed charges and the exploration of the pollutant migration law within the clay liner is of extremely crucial strategic significance for scientifically and accurately predicting the pollutant diffusion trend and effectively formulating pollution prevention and control strategies. This not only helps to deepen the understanding of the action principle of the clay liner in environmental governance, optimize pollution prevention and control measures, but also provides a solid theoretical basis and technical support for the reasonable planning and development of land resources in polluted areas and the precise design and efficient implementation of environmental protection projects, ultimately achieving the important goal of environmental protection and pollution reduction, with undeniable theoretical value and extremely significant engineering practical significance. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for establishing a fully coupled hydro-mechanical-chemical model affected by the fixed charges of clay bodies and its application, accurately construct this fully coupled equation, deeply analyze the interaction details and internal logic of multi-physical fields of clay bodies in complex and changeable environments, clearly reveal the evolution law of the physical and chemical processes inside clay bodies and their interaction paths, accurately determine the specific influencing factors and action degrees of the fixed charges of clay bodies, and innovatively propose an effective mode and key indicators for comprehensively, scientifically and accurately evaluating the service performance of clay liners based on this coupled equation, providing a reliable theoretical basis and technical support for the related engineering applications of clay bodies.

[0006] The purpose of the present invention can be achieved through the following technical solutions:

[0007] A method for establishing a fully coupled hydro-mechanical-chemical model affected by the fixed charges of clay bodies, comprising the following steps:

[0008] Based on the stress equilibrium equation, the mass conservation of pore fluid and pollutants, introduce the Donna osmotic pressure controlled by fixed charges into the soil deformation control equation to establish a generalized effective stress formula:

[0009]

[0010] In the formula, σ' g represents the generalized effective stress; σ z represents the vertical total stress; u represents the excess pore water pressure; n represents the soil porosity; Π DDenote the Donna osmotic pressure; ρ f Denote the pore water density; Ω denotes the surface force potential of the pore water; n0 denotes the initial porosity of the soil mass; Π denotes the generalized osmotic pressure; the subscript r denotes the reference state.

[0011] As a further aspect of the present invention: The calculation formula of the Donna osmotic pressure is expressed as:

[0012]

[0013] In the formula, R is the universal gas constant, T represents the absolute temperature; cfix is the fixed charge density, and the calculation formula is cfix = 10·CEC·Gs·(1 - n); c represents the concentration of pollutants inside the pores.

[0014] As a further aspect of the present invention: Based on the generalized Hooke's law, establish the calculation formula for the relationship between the generalized effective stress and strain:

[0015] dσ' gij =C ijlk dε kl (5)

[0016] In the formula, dσ' gij represents the increment of the generalized effective stress tensor; C ijkl is the elastic stiffness matrix; dσ kl is the increment of the total strain tensor;

[0017] Expand the first term in the formula to get:

[0018] C ijkl dε kl =λdε kk δ ij +2μdε ij (6)

[0019] In the formula, δ ij is the Kronecker symbol; λ and μ are the Lame coefficients, and their expressions are respectively:

[0020]

[0021]

[0022] In the formula, ν is the Poisson's ratio; E is the elastic modulus; G is the shear modulus.

[0023] As a further aspect of the present invention: It can be seen from formulas (5) and (6) that the stress-strain relationship in the vertical direction is expressed as:

[0024] dσ z =λdε z +2μdεz (9)

[0025] Meanwhile, the vertical displacement and strain satisfy:

[0026]

[0027] where w z is the displacement in the z direction;

[0028] Substituting equations (3), (9), and (10) into the stress equilibrium equation, the soil deformation control equation is obtained and expressed as;

[0029]

[0030] As a further solution of the present invention: establish the pore fluid continuity equation, expressed as:

[0031]

[0032] where v f is the absolute velocity of the pore fluid;

[0033] When the soil porosity does not change with depth and the pore fluid density is constant, the pore fluid continuity equation is expressed as:

[0034]

[0035] The change in soil porosity is described using the generalized effective stress, and the formula is:

[0036] n = n0 - Δn = n0 - m v σ' g (14)

[0037] where m v is the coefficient of volume change caused by the load;

[0038] The relationship between the porosity and time is:

[0039]

[0040] By taking the mathematical derivative of equation (4) and substituting the obtained derivative result into equation (15), we get:

[0041]

[0042] where ζ is a concentration-related coefficient, and for simplicity of calculation, its calculation formula is written as:

[0043]

[0044] As a further solution of the present invention: the coefficient of volume change m caused by chemical loadc Coefficient of volume change m caused by mechanical load v Satisfy:

[0045] m c = nζm v (18)

[0046] It can be seen from formulas (17) and (18) that formula (16) is re-expressed as:

[0047]

[0048] The seepage velocity of pore fluid is expressed as:

[0049] v f = v r + v s (20)

[0050] In the formula, v r represents the seepage velocity of pore fluid relative to the soil skeleton; v s represents the soil particle velocity.

[0051] As a further solution of the present invention: The calculation formulas of the seepage velocity v r of pore fluid relative to the soil skeleton and the soil particle velocity v s are respectively expressed as:

[0052]

[0053]

[0054] In the formula, v represents the Darcy velocity; under the combined influence of mechanical load and pollutant concentration, the generalized Darcy velocity of pore fluid is expressed as:

[0055]

[0056] In the formula, v u and v π respectively represent the Darcy velocities under pore water pressure and chemical osmotic pressure; k c represents the chemical osmotic coefficient of pore water, which satisfies k c = ωζk h ; γ w represents the unit weight of pore water; ω is the chemical osmotic efficiency coefficient of clay; k h represents the hydraulic conductivity coefficient, and the relationship between the hydraulic conductivity coefficient and the initial hydraulic conductivity coefficient satisfies:

[0057]

[0058] In the formula, k h0 is the initial hydraulic conductivity coefficient;

[0059] Substitute formulas (19) and (23) into formula (13), and the expression of the pore fluid flow control equation can be obtained, that is:

[0060]

[0061] The pore water flow control equation (25) includes the coefficient of soil volume change m c related to the charged characteristics of the soil and the chemosmotic coefficient k c .

[0062] As a further solution of the present invention: The pollutant transport control equation mainly considers the mass conservation on the solid and liquid phases. Among them, the mass conservation of pollutants inside the pore fluid is:

[0063]

[0064] In the formula, Y represents the source-sink term of pollutants; J f represents the pollutant flux inside the pore fluid;

[0065] The pollutant flux J f inside the pore fluid is expressed as:

[0066] J f = J a + J D (27)

[0067] In the formula, Ja represents the convective flux of pollutants; J D represents the diffusion flux of pollutants; among them, the calculation formula of the convective flux Ja of pollutants is:

[0068]

[0069] The calculation formula of the diffusion flux J D of pollutants is:

[0070]

[0071] In the formula, Dc is the hydrodynamic dispersion coefficient; D0 is the diffusion coefficient of pollutants in the free solution; αL is the longitudinal dispersion factor; τ represents the soil tortuosity factor, τ = n m , and m is an empirical parameter.

[0072] As a further solution of the present invention: Substitute formulas (27)-(29) into formula (26), and the control equation describing the transport of pollutants inside the pore fluid can be obtained:

[0073]

[0074] The mass conservation of pollutants in the solid phase medium is written as:

[0075]

[0076] Where S is the mass of pollutants adsorbed by clay particles; J s is the pollutant flux inside the solid phase medium; for the convenience of calculation, it is assumed that the soil adsorption mode follows the linear Freundlich adsorption mode, then the calculation formula for the mass of pollutants adsorbed by clay particles is:

[0077] S = K d c (32)

[0078] The pollutant flux J in the solid phase s is expressed as:

[0079] J s = (1 - n)v s ρ s S(33)

[0080] Substituting formulas (22), (32) and (33) into formula (31), the pollutant transport control equation in the solid medium is obtained:

[0081]

[0082] Assuming that the source terms in the adsorption and desorption processes are the same, combining formulas (30) and (34) gives the final control equation for pollutant transport, that is:

[0083]

[0084] Formulas (11), (25) and (35) jointly constitute a fully coupled hydro-mechanical-chemical pollutant transport model considering the influence of fixed charges. The control equation of this model covers three main variables: vertical displacement, excess pore water pressure and pollutant concentration; in addition, the joint of the coupling parameters n, k, v and Dc related to mechanical loads and pollutant concentrations realizes the full coupling of the control equation.

[0085] Application of the method for establishing a fully coupled hydro-mechanical-chemical coupling affected by fixed charges in clay bodies, application in the study of the coupled response of clay liners in landfills and the service performance of liners.

[0086] Advantages of the present invention:

[0087] Enhancing the effectiveness of landfill barriers: By establishing a generalized consolidation equation and a generalized Darcy's law considering the influence of fixed charges, an accurate description of the coupled behavior of the fully coupled hydro-mechanical-chemical equation in saturated soil layers under landfill conditions has been achieved. This fully coupled hydro-mechanical-chemical equation comprehensively considers the role of fixed charges, a key factor, on saturated soil layers, and can accurately predict the pore water pressure changes, settlement trends, and solute transport conditions in saturated soil layers under different fixed charge conditions, providing a scientific basis and technical support for the design and operation evaluation of landfill barriers. By optimizing the design scheme and operation strategy with this model, the effectiveness and stability of landfill barriers can be improved, ensuring the safe operation of landfills.

[0088] Deeply analyzing the action mechanism of landfill barriers: With the construction of a generalized consolidation equation and a generalized Darcy's law considering the influence of fixed charges, the present invention deeply explores the action principle and change process of the saturated soil layer barrier in landfills. This model incorporates the influence of fixed charges on pore water pressure, solute transport, etc., and can accurately predict the dynamic changes of saturated soil layers under the coupled action of the fully coupled hydro-mechanical-chemical equation, providing early warnings and predictions of barrier performance changes. Through the research and analysis of the characteristics of saturated soil layers, targeted barrier optimization measures can be formulated to reduce the risk of landfill leachate leakage and environmental pollution losses, providing a scientific basis and technical guarantee for the maintenance and management of landfill barriers.

[0089] Optimizing the design and operation of landfills: The present invention focuses on the research of the coupled problem of the fully coupled hydro-mechanical-chemical equation in landfills and optimizes the design and operation planning of landfills. By establishing a hydro-mechanical-chemical coupling equation considering the influence of fixed charges, the influence of fixed charges on the mechanical properties of saturated soil layers, solute transport laws, and pore water pressure distribution is analyzed, and then the selection of clay materials, landfill structure design, and leachate drainage system planning in landfills are optimized. With optimized design and operation, the economy and engineering practicability of landfills are improved, the project construction and operation costs are reduced, and the overall efficiency and sustainability of landfills are enhanced. Description of the Drawings

[0090] The present invention will be further described below in conjunction with the drawings.

[0091] Figure 1 It is the distribution law of pore water pressure with depth under the influence of different fixed charges.

[0092] Figure 2 It is the curve of the change law of soil settlement under the influence of different fixed charges.

[0093] Figure 3 It is the curve of the change law of the pollutant concentration inside the cushion with depth under different fixed charge conditions.

[0094] Figure 4 The evolution law of the accumulated concentration of pollutants at the bottom of the cushion layer with time under different fixed charge conditions.

[0095] Figure 5 The variation curve of the breakthrough depth of pollutants under different fixed charge conditions.

[0096] Figure 6 The variation curve of the breakthrough time of pollutants under different fixed charge conditions. Specific implementation manners

[0097] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without making creative efforts belong to the scope of protection of the present invention.

[0098] Refer to Figures 1 to 6 As shown, the method for establishing the fully coupled hydro-mechanical-chemical coupling affected by the fixed charge of the clay body includes the following steps:

[0099] Establishment of the coupling equation

[0100] During the establishment of the multi-physical field coupling equation, the following assumptions are made: The soil body is a homogeneous and isotropic saturated soil body; the pore water flow conforms to Darcy's law, including the Darcy flow and the chemo-osmotic flow process; the pollutant transport satisfies Fick's law; the soil body deformation is a linear elastic small deformation; the external load is applied instantaneously; the deformation of the cushion soil body, the pore water flow, and the pollutant transport only occur in the vertical direction. The soil body deformation control equation is mainly based on the stress equilibrium equation, and the stress equilibrium equation can be expressed as:

[0101]

[0102] In the formula, σ z is the total stress; f is the body force, and its expression is:

[0103] f = [nρ f +(1 - n)ρ s g (2)

[0104] In the formula, g is the acceleration due to gravity.

[0105] Based on the stress equilibrium equation, the mass conservation of pore fluid and pollutants, the Donna osmotic pressure controlled by the fixed charge is introduced into the soil body deformation control equation to establish the generalized effective stress formula:

[0106]

[0107] where, σ' g represents the generalized effective stress; σ z represents the vertical total stress; u represents the excess pore water pressure; n represents the soil porosity; Π D represents the Donna osmotic pressure; ρ f represents the pore water density; Ω represents the surface force potential of the pore water; n0 represents the initial soil porosity; Π represents the generalized osmotic pressure; the subscript r represents the reference state.

[0108] The calculation formula of the Donna osmotic pressure is expressed as:

[0109]

[0110] where, R is the universal gas constant, T represents the absolute temperature; cfix is the fixed charge density; the calculation formula is cfix = 10·CEC·Gs·(1 - n); c represents the concentration of pollutants inside the pores.

[0111] Since the generalized effective stress formula established in the patent covers both mechanical and chemical loading mechanisms, the elastic deformation process during the force-chemical loading process can be uniformly described by the generalized effective stress. At the same time, it is considered that the relationship between the generalized effective stress and strain still satisfies the generalized Hooke's law. Then, the calculation formula for the relationship between the generalized effective stress and strain at this time:

[0112] dσ' gij = C ijlk dε kl (5)

[0113] where, dσ' gij represents the increment of the generalized effective stress tensor; C ijkl is the elastic stiffness matrix; dσ kl is the increment of the total strain tensor;

[0114] Expanding the first term in the formula gives:

[0115] Ci jkl dε kl = λdε kk δi j + 2μdεi j (6)

[0116] where, δ ij is the Kronecker symbol; λ, μ are the Lame coefficients, and their expressions are respectively:

[0117]

[0118]

[0119] Where ν is the Poisson's ratio; E is the elastic modulus; G is the shear modulus.

[0120] As can be seen from Eqs. (5) and (6), the stress-strain relationship in the vertical direction is expressed as:

[0121] dσ z = λdε z + 2μdε z (9)

[0122] Meanwhile, the relationship between the vertical displacement and the strain satisfies:

[0123]

[0124] Where w z is the displacement in the z direction;

[0125] Substituting Eqs. (3), (9) and (10) into the stress equilibrium equation (1), the soil deformation control equation is obtained and expressed as:

[0126]

[0127] The fourth term in the deformation control equation mainly reflects the contribution of the chemical load.

[0128] The pore fluid flow control equation is mainly based on the pore fluid continuity equation, and the pore fluid continuity equation can be expressed as:

[0129]

[0130] Where v f is the absolute velocity of the pore fluid;

[0131] When the soil porosity does not change with depth and the pore fluid density is constant, the pore fluid continuity equation is expressed as:

[0132]

[0133] The change of soil porosity is described by the generalized effective stress, and the formula is:

[0134] n = n0 - Δn = n0 - m v σ' g (14)

[0135] Where m v is the volume change coefficient caused by the load;

[0136] The relationship between the change of porosity with time is:

[0137]

[0138] By performing mathematical differentiation on Equation (4) and substituting the resulting derivative into Equation (15), we obtain:

[0139]

[0140] In the formula, ζ is a concentration-related coefficient, and for the sake of simplicity in calculation, its calculation formula is written as:

[0141]

[0142] The coefficient of volume change m caused by chemical loading c is the same as the coefficient of volume change m caused by mechanical loading v and satisfies:

[0143] m c = nζm v (18)

[0144] From Equations (17) and (18), it can be seen that Equation (16) is re-expressed as:

[0145]

[0146] The seepage velocity of pore fluid is expressed as:

[0147] v f = v r + v s (20)

[0148] In the formula, v r represents the flow velocity of pore fluid relative to the soil skeleton; v s represents the soil particle velocity.

[0149] The v r of the flow velocity of pore fluid relative to the soil skeleton and the soil particle velocity v s are respectively expressed by the calculation formulas as:

[0150]

[0151]

[0152] In the formula, v represents the Darcy velocity; under the combined influence of mechanical loading and pollutant concentration, the generalized Darcy velocity of pore fluid is expressed as:

[0153]

[0154] In the formula, v u and v π respectively represent the Darcy velocities under pore water pressure and chemical osmotic pressure; k c represents the chemical osmotic coefficient of pore water, and it satisfies k with the hydraulic conductivityc = ωζk h ; γ w represents the unit weight of pore water; ω is the chemical osmotic efficiency coefficient of clay; k h represents the hydraulic conductivity, and the relationship between the hydraulic conductivity and the initial hydraulic conductivity satisfies:

[0155]

[0156] In the formula, k h0 is the initial hydraulic conductivity;

[0157] Substituting formulas (19) and (23) into formula (13), the expression of the pore fluid flow control equation can be obtained, that is:

[0158]

[0159] The pore water flow control equation (25) includes the coefficient of soil volume change m c related to the charged characteristics of the soil and the chemical osmotic coefficient k c .

[0160] The pollutant transport control equation mainly considers the mass conservation on the solid and liquid phases. Among them, the mass conservation of pollutants in the pore fluid is:

[0161]

[0162] In the formula, Y represents the source-sink term of pollutants; J f represents the pollutant flux inside the pore fluid;

[0163] The pollutant flux J f inside the pore fluid is expressed as:

[0164] J f = J a + J D (27)

[0165] In the formula, Ja represents the convective flux of pollutants; J D represents the diffusion flux of pollutants; among them, the calculation formula of the convective flux Ja of pollutants is:

[0166]

[0167] The diffusion flux J D of pollutants is calculated as:

[0168]

[0169] where Dc is the hydrodynamic dispersion coefficient; D0 is the diffusion coefficient of the pollutant in the free solution; αL is the longitudinal dispersion factor; τ represents the tortuosity factor of the soil mass, τ = n m , m is an empirical parameter, generally taking a value of 2.

[0170] Substituting formulas (27)-(29) into formula (26), the governing equation describing the transport of pollutants within the pore fluid is obtained:

[0171]

[0172] The mass conservation of pollutants in the solid phase medium is written as:

[0173]

[0174] where S is the mass of the pollutant adsorbed by the clay particles; J s is the pollutant flux within the solid phase medium; for the convenience of calculation, assuming that the soil adsorption mode follows the linear Freundlich adsorption mode, the calculation formula for the mass of the pollutant adsorbed by the clay particles is:

[0175] S = K d c (32)

[0176] The pollutant flux J s in the solid phase is expressed as:

[0177] J s = (1 - n)v s ρ s S(33)

[0178] Substituting formulas (22), (32), and (33) into formula (31), the governing equation for the transport of pollutants in the solid medium is obtained:

[0179]

[0180] Assuming that the source terms in the adsorption and desorption processes are the same, combining formulas (30) and (34) gives the final governing equation for pollutant transport, that is:

[0181]

[0182] Equations (11), (25) and (35) jointly constitute a fully coupled hydro-mechanical-chemical pollutant transport model considering the influence of fixed charges. The governing equations of this model cover three main variables: vertical displacement, excess pore water pressure, and pollutant concentration. In addition, the joint implementation of the coupling parameters n, k, v, and Dc related to mechanical loads and pollutant concentrations realizes the full coupling of the governing equations. At the same time, a remarkable feature of this model is its ability to consider the influence of the charged state of the soil itself on the distribution of excess pore pressure, settlement deformation, and pollutant transport, thus more accurately simulating the dynamic response of charged soil under the coupling action of multiple physical fields.

[0183] The influence of chemical loads on clay mainly stems from its surface fixed charges. It can be said that the degree to which the coupling equations are affected by chemical loads mainly depends on the strength of the charged characteristics of the soil. At the same time, the quantity of clay surface fixed charges can be measured by the cation exchange capacity (CEC). Bentonite usually has a relatively high cation exchange capacity, generally in the range of 70 - 140 mmol / 100g. In contrast, the cation exchange capacity of kaolin is relatively low, generally around 3 - 15 mmol / 100g. It should be noted that in actual compacted clay liners, the content of bentonite is relatively low. He Jun et al. found through research on the soil near the Changshankou landfill in Wuhan that the clay around the landfill is mainly composed of kaolin. Therefore, in this scheme, the cation exchange capacity CEC of the clay is fixed at 10, 20, 40, and 70 mmol / 100g, and numerical calculations are carried out.

[0184] A 1-meter-thick clay liner is selected for modeling, and the influence of body forces and mechanical dispersion is ignored during the numerical solution process. At the same time, sodium chloride is selected as the characteristic pollutant, and it is assumed that at the initial moment, the concentration of sodium chloride in the clay liner is zero, that is, u(z, 0) = 0 kPa, c(z, 0) = 0 kg / m3 (0 ≤ z ≤ L, L = 1m). In addition, the lower boundary of the compacted clay liner is defined as a Cauchy boundary, assuming that the lower boundary is between a permeable and an impermeable boundary. At this time, u(L, t) = 0 kPa.

[0185] Table 2 Parameters used in numerical calculations

[0186]

[0187]

[0188] Influence of the quantity of fixed charges on the numerical calculation results of the coupling equations

[0189] I. Influence of fixed charges on pore water pressure

[0190] Figure 1Pore water pressure distributions for simulation periods of 0.1 year, 1.0 year, 10 years, and 50 years. During the 0.1-year simulation period, when the CEC value is 10 or 20 mmol / 100 g, the pore water pressure in the compacted clay layer is positive. While near the upper boundary of the compacted clay layer with CEC values of 40 and 70 mmol / 100 g, negative pore water pressure appears. As the simulation time increases, the positive pore water pressure rapidly transforms into negative pore water pressure. During the 10-year simulation period, when the CEC value is 10 or 20 mmol / 100 g, the pore water pressure in the compacted clay layer almost returns to 0 kPa. For the compacted clay layer with CEC values of 40 and 70 mmol / 100 g, even during the 50-year simulation period, the pore water pressure does not return to 0 kPa. The formation of negative pore water pressure is related to chemo-osmotic consolidation. The greater the fixed charge adsorbed on the soil surface, the more significant the chemo-osmotic effect. Under the condition of the same solute concentration, as the CEC value increases, due to the enhancement of chemo-osmotic action, the negative pore water pressure increases and the dissipation time prolongs. The chemo-osmotic effect will be further analyzed from the perspective of soil layer settlement in the next section.

[0191] II. Influence of Fixed Charge on Settlement Evolution

[0192] Figure 2 Shows the evolution process of clay layer settlement under different fixed charge conditions. Mechanical load-induced consolidation, chemo-osmotic consolidation, and the total settlement of the clay layer. As the simulation time prolongs, due to mechanical consolidation and chemo-osmotic consolidation, the settlement deformation of the soil mass develops rapidly. After about 1 year, the settlement deformation of the soil mass reaches the maximum value. However, with the transport of solutes, the chemo-osmotic consolidation gradually decreases, which is opposite to the settlement direction, resulting in the dissipation of negative pore pressure. At the same time, due to the reduction of chemo-osmotic consolidation degree, the soil mass settlement shows a rebound phenomenon. When the solute distribution in the pore fluid of the compacted clay layer reaches a stable state, the settlement of the compacted clay layer begins to tend to be stable. In addition, the peak value of soil mass settlement increases with the increase of CEC, which is consistent with the evolution result of negative pore water pressure (see Figure 1 as shown).

[0193] III. Influence of Fixed Charge on the Law of Pollutant Migration

[0194] Figure 3 Shows the variation law of solute concentration with depth under different CEC conditions. During the 10-year simulation time, the influence of fixed charge on the solute concentration distribution is not obvious. As the simulation time prolongs, the influence of CEC on the solute concentration distribution becomes more and more obvious. The influence of fixed charge on the solute concentration distribution is also reflected in Figure 4 as shown in. Figure 4The cumulative solute concentration changes at a depth of 0.99 m in the clay layer under different fixed charge conditions. At the initial stage of the simulation, the cumulative solute concentrations under different CEC conditions are relatively low. The cumulative solute concentration increases with the extension of the simulation time, and the cumulative solute concentration in the clay layer with a larger CEC value is lower. During the 200-year simulation period, the cumulative solute concentration in the compacted clay layer with a CEC value of 10 mmol / 100 g is 9.20 kg, which is 5.32 times higher than that in the compacted clay layer with a CEC value of 70 mmol / 100 g. The solute concentration distribution is related to chemo-osmotic consolidation and chemo-osmotic flow. Due to chemo-osmotic consolidation, the porosity decreases, and the convection and diffusion effects weaken. The results show that with the increase of the CEC value, the solute transport rate slows down. At the same time, with the increase of the CEC value, the chemo-osmotic flow (opposite to the solute migration direction) increases, further slowing down the solute migration speed. This model well reveals the influence of fixed charge on the barrier characteristics of the compacted clay layer, which cannot be reflected by other chemo-hydro-mechanical coupling models.

[0195] IV. Influence of Soil Charge Quantity on Pollutant Breakthrough Depth

[0196] Figure 4 The evolution of the breakthrough depth with time under different CEC conditions is shown. At the initial stage of the simulation, the influence of CEC on the breakthrough depth is not obvious. With the extension of the simulation time, as the CEC value increases, the breakthrough depth gradually decreases. With the increase of the simulation time, the influence of CEC on the breakthrough depth becomes more obvious. The results show that the barrier characteristics of the saturated soil layer are enhanced with the increase of CEC. The simulation results are consistent with engineering practice, that is, the barrier characteristics of the saturated soil layer are enhanced with the increase of the bentonite content, which cannot be simulated by the current chemo-hydro-mechanical coupling models.

[0197] Figure 5 The evolution of the breakthrough time with CEC is shown. With the increase of CEC, the breakthrough time is significantly prolonged. When CEC increases from 10 to 20 mmol / 100 g, the breakthrough time is 24.9 - 25.5 years. When CEC increases from 10 mmol / 100 g to 70 mmol / 100 g, the breakthrough time increases from 24.9 years to 38.1 years, an increase of 50.3%. The research results emphasize the influence of fixed charge on the barrier behavior of the saturated soil layer.

[0198] This invention has important theoretical and practical significance for the design and management of landfills, optimizing the structure of clay liners, and improving their ability to resist pollutant migration.

[0199] Application of the method for establishing a fully coupled hydro-mechanical-chemical model affected by the fixed charge of clay bodies, and its application in the study of the coupled response and service performance of clay liners in landfills.

[0200] The above has described in detail an embodiment of the present invention, but the above content is only a preferred embodiment of the present invention and cannot be considered as limiting the scope of implementation of the present invention. All equivalent changes and improvements made in accordance with the scope of the application of the present invention shall still fall within the scope covered by the patent of the present invention.

Claims

1. A method for establishing a fully coupled hydro-mechanical-chemical method for the effect of fixed charges on clay bodies, characterized in that: The following steps are involved: Based on the stress balance equation, pore fluid and pollutant mass conservation, the Donna seepage pressure controlled by fixed charge is introduced into the soil deformation control equation, and the generalized effective stress formula is established: In the formula, σ' g represents the generalized effective stress; σ z represents the vertical total stress; u represents the excess pore water pressure; n represents the soil porosity; Π D represents Donna osmotic pressure; ρ f represents the pore water density; Ω represents the surface force potential of pore water; n0 represents the initial porosity of soil; Π represents the generalized osmotic pressure; and the subscript r represents the reference state.

2. The method for establishing the hydro-mechanical-chemical full coupling of the fixed charge influence of clay bodies according to claim 1, characterized in that: The Donna osmotic pressure calculation formula is expressed as: Where R is the universal gas constant, T represents the absolute temperature, cfix represents the fixed charge density, and the calculation formula is cfix=10·CEC·Gs·(1-n). c represents the pollutant concentration inside the pores.

3. The method for establishing the hydro-mechanical-chemical full coupling of the fixed charge influence of clay bodies according to claim 1, characterized in that: Based on the generalized Hooke's law, the calculation formula of the generalized effective stress and strain relationship is established: dσ' gij =C ijlk dε kl (5) In the formula, dσ' gij Expressed as the increment of the generalized effective stress tensor; C ijkl is the elastic stiffness matrix; dσ kl is the increment of the total strain tensor; Expand the first term in the formula to get: Ci jkl dε kl Zλdε kk δi j +2µday j (6) In the formula, δ ij is the Kronecker symbol; λ and μ are the Lame coefficients, and their expressions are: Where ν is Poisson's ratio, E is elastic modulus, and G is shear modulus.

4. The method for establishing the hydro-mechanical-chemical full coupling of the fixed charge influence of clay bodies according to claim 3, characterized in that: From formulas (5) and (6), it can be seen that the stress-strain relationship in the vertical direction is expressed as: ds z =λde z +2μdε z (9) At the same time, the vertical displacement and strain satisfy: In the formula, w z is the displacement in the z direction; Substituting formulas (3), (9) and (10) into the stress equilibrium equation, the soil deformation control equation is obtained, which is expressed as; 5. The method for establishing the hydro-mechanical-chemical full coupling of the fixed charge influence of clay bodies according to claim 4, characterized in that: The continuity equation of pore fluid is established and expressed as: Where v f is the absolute velocity of pore fluid; When the soil porosity does not change with depth and the pore fluid density is constant, the pore fluid continuity equation is expressed as: The generalized effective stress is used to describe the change of soil porosity, and the formula is: n=n0-Δn=n0-m v in g (14) In the formula, m v is the volume change coefficient caused by load; The relationship between porosity and time is: By mathematically deriving formula (4) and substituting the derivative result into formula (15), we get: In the formula, ζ is a coefficient related to concentration. For the convenience of calculation, its calculation formula is written as:

6. The method for establishing the hydro-mechanical-chemical full coupling of the fixed charge influence of clay bodies according to claim 5, characterized in that: Volume change coefficient due to chemical loading m c Volume change coefficient caused by mechanical load m v satisfy: m c =nζm v (18) From formulas (17) and (18), we can see that formula (16) can be re-expressed as: The penetration rate of pore fluid is expressed as: v f =v r +v s (20) In the formula, v r represents the velocity of pore fluid relative to the soil skeleton; v s Represents the soil particle velocity.

7. The method for establishing the hydro-mechanical-chemical full coupling of the fixed charge influence of clay bodies according to claim 6, characterized in that: The velocity of pore fluid relative to the soil skeleton v r and soil particle velocity v s The calculation formulas are expressed as follows: Where v represents the Darcy velocity. Under the combined influence of mechanical load and pollutant concentration, the generalized Darcy velocity of pore fluid is expressed as: In the formula, v u 、v π represents the Darcy velocity under pore water pressure and chemical osmotic pressure respectively; k c represents the chemical permeability coefficient of pore water, which satisfies the k c =ωζk h ; γ w represents the density of pore water; ω is the clay chemical penetration efficiency coefficient; k h represents the hydraulic conductivity coefficient, where the hydraulic conductivity coefficient and the initial hydraulic conductivity coefficient satisfy: In the formula, k h0 is the initial hydraulic conductivity; Substituting formula (19) and (23) into formula (13), the expression of the pore fluid flow control equation is obtained, namely: The governing equation for pore water flow (25) includes the soil volume variation coefficient m related to the electrical properties of the soil. c and the chemical permeability coefficient k c .

8. The method for establishing the hydro-mechanical-chemical full coupling of the fixed charge influence of clay bodies according to claim 7, characterized in that: The control equation of pollutant transport mainly considers the mass conservation in the solid and liquid phases, among which the mass conservation of pollutants in the pore fluid is: Where Y represents the source and sink of pollutants; J f represents the contaminant flux inside the pore fluid; Pollutant flux inside pore fluid J f It is expressed as: I f =J a +J D (27) Where, Ja represents the convection flux of pollutants; J D represents the diffusion flux of pollutants; the calculation formula of pollutant convection flux Ja is: Diffusion flux of pollutants J D The calculation formula is: Where Dc is the hydrodynamic diffusion coefficient; D0 is the diffusion coefficient of the pollutant in the free solution; αL is the longitudinal diffusion factor; τ represents the soil bending factor, τ = n m , m is an empirical parameter.

9. The method for establishing the hydro-mechanical-chemical full coupling of the fixed charge influence of clay bodies according to claim 8, characterized in that: Substituting equations (27)-(29) into equation (26) yields the governing equations describing the contaminant transport within the pore fluid: The mass conservation of pollutants in solid media can be written as: Where S is the mass of pollutants adsorbed by clay particles; J s is the pollutant flux inside the solid medium; for the convenience of calculation, it is assumed that the soil adsorption mode obeys the linear warm adsorption mode, and the calculation formula for the pollutant mass adsorbed by clay particles is: S=K d c (32) Pollutant flux in the solid phase J s It is expressed as: J s =(1-n)v s ρ s S(33) Substituting equations (22), (32) and (33) into equation (31) yields the control equation for pollutant transport in solid media: The source terms in the adsorption and desorption processes are the same. Combining equations (30) and (34) gives the final control equation for pollutant transport, namely: Formulas (11), (25) and (35) jointly constitute a fully coupled hydraulic-mechanical-chemical pollutant transport model considering the influence of fixed charges. The control equations of this model cover the three main variables: vertical displacement, excess pore water pressure and pollutant concentration. In addition, the combination of coupling parameters n, k, v and Dc related to mechanical load and pollutant concentration realizes the full coupling of the control equations.

10. Application of the method for establishing the full coupling of hydro-mechanical-chemical effects on the fixed charge of clay bodies, characterized in that: Application in the study of coupled response of landfill clay cushion and service performance of cushion.

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