Generalized effective stress calculation method considering thermal-chemical action and application thereof

Abstract

The invention discloses a generalized effective stress calculation method considering a thermal-chemical effect and application of the generalized effective stress calculation method, and belongs to the technical field of geotechnical engineering.The generalized effective stress calculation method fully considers the influence of temperature and pollutant concentration on soil-water interaction on the basis of thermodynamics and conservation equations; the thermodynamic stress of liquid phases in a solid phase, a macroscopic pore and a microscopic pore of the double-porosity geotechnical material is accurately determined, and thermal pressurization related to temperature and generalized osmotic pressure related to pollutant concentration are fused into a liquid phase thermodynamic stress equation. On the basis, the method for calculating the generalized effective stress of the double-porosity geotechnical material considering the environmental load is successfully exported. By applying the generalized effective stress calculation method, the deformation behavior of the clay under the mechanical, thermal and chemical coupling loading condition is predicted, a solid theoretical foundation is built for the design of an anti-seepage buffer barrier in geotechnical engineering and the safety evaluation of geological environment engineering, and the method has important application value and practical significance.

Description

Technical Field

[0001] The present invention belongs to the technical field of geotechnical engineering, and particularly relates to a calculation method of generalized effective stress considering thermo-chemical effects and its application in predicting soil deformation. Background Art

[0002] In many environmental geotechnical engineering projects, soil is not only subjected to external mechanical loads, but the solute concentration and temperature inside the soil may also change significantly at the same time. For example, in the geological disposal system of high-level radioactive waste, the heat released by nuclear reactions will not only change the temperature of the buffer material, but also the pollutant transport will change the internal pollutant concentration of the buffer material; the heat released by the biochemical reaction of the landfill will not only change the compacted clay cushion, and the upper part of the cushion is usually exposed to the leachate environment with a certain concentration. The changes in soil temperature and pore solution concentration will change the internal physical and chemical processes of the soil-water system, making the hydraulic, mechanical properties and deformation evolution laws of the soil under the combined action of mechanical loads, temperature and permeating solution significantly different from the working conditions with only mechanical loads. To accurately predict the changes in soil hydraulic and mechanical properties and deformation evolution laws under complex environmental conditions, it is necessary to calculate the numerical values of temperature and chemical loads, which has very important theoretical and practical significance for the performance analysis and sustainable design of many geological structures.

[0003] From existing research, it can be seen that currently, for the generalized effective stress method and constitutive relationship of active clay, temperature effects or chemical effects are mostly considered separately, and they are often established based on macroscopic parameters, lacking the support of microscopic mechanisms. At the same time, it remains to be further verified whether it is appropriate to use the effective stress formula and constitutive relationship applicable to traditional single-pore geotechnical materials to describe the mechanical behavior and strength changes of geotechnical materials with dual-pore or even multi-pore structural characteristics. In addition, establishing a generalized effective stress method considering pore structure characteristics can overcome the limitations of traditional single-pore models in describing cross-scale stress-strain coupling mechanical behavior and cross-scale mass exchange chemical behavior, and has a clearer physical basis and wider applicability. Summary of the Invention

[0004] Aiming at the deficiencies of the existing effective stress calculation method that cannot simultaneously consider thermal and chemical effects and the micro-macro and microscopic pore structure characteristics of soil, the present invention innovatively proposes a calculation method of generalized effective stress based on thermodynamic principles and fully considering environmental impacts and pore structure characteristics. This method can be widely applied to various engineering fields and scientific research scenarios involving effective stress calculations under the action of complex environmental factors, providing a more perfect and scientific solution for accurately analyzing and evaluating the stress state in related systems.

[0005] The object of the present invention can be achieved by the following technical solutions:

[0006] A generalized effective stress calculation method considering thermo-chemical effects, comprising the following steps:

[0007] Step 1: After substituting the chemical potential expressions of the soil skeleton, macroscopic liquid phase, and microscopic liquid phase into the stress expressions of the solid phase, free liquid phase, and adsorbed liquid phase;

[0008] Under the assumptions that the macroscopic pores are not affected by the electric field; the microscopic pores are affected by the electric field, and the microscale pore water activity affected by the solute is close to 1, adjust the thermodynamic pressures of the fluids in the macroscopic and microscopic pores to:

[0009]

[0010] where; n, n M and n m respectively represent the total porosity, macroscopic porosity, and microscopic porosity; δ ij is the Kronecker symbol, p represents the pore water pressure caused by the mechanical load in the macroscopic pore space; p MT represents the thermally induced pore water pressure in the macroscopic pore space; p ml represents the pore water pressure caused by the mechanical load in the microscopic pore space; p mT represents the thermally induced pore water pressure in the microscopic pore space, p r represents the reference pressure;

[0011] Step 2: The average pore water pressure and the measured pore water pressure satisfy:

[0012] p lp = p lR + V 0 RTln(a wlR / a wlp ) - ρ *lw Ω l = p lR + Π D - ρ *lw Ω l = p lR + Π(14)

[0013] In the formula, p lp represents the average pore water pressure; p lR represents the pressure of the equilibrium solution, and also represents the measured pore water pressure; V 0 represents the mole fraction of water; R represents the universal gas constant; T represents the absolute temperature; a wlR represents the activity of the solvent water inside the equilibrium solution; a wlp represents the activity of the solvent water in the pore solution; ρ *lw represents the mass density of pure water; ρ *lw Ω l represents the surface force; ΠD represents the Donnan osmotic pressure; Π represents the generalized osmotic pressure;

[0014] Step 3. Under the condition that the assumption ρ M = ρ m = ρ w holds, combining with formula (14) to obtain the following relationship between the pore water pressure in the microscopic pores and the pore water pressure in the equilibrium solution:

[0015] p ml = p + Π D - ρ w Ω l (16)

[0016] Set the reference pressure and the soil background concentration to zero, and assume that the contributions of temperature to the macroscopic and microscopic pore fluid pressures are equal to obtain the total stress equation. According to the total stress equation, the generalized effective stress is:

[0017]

[0018] In the formula, b represents the Biot coefficient, and numerically it is equal to 1 - K b / K m .

[0019] As a further solution of the present invention, the calculation formula of the Donnan osmotic pressure is:

[0020]

[0021] In the formula, c fix represents the fixed charge density of the soil skeleton, and the calculation formula is c fix = 10·α·CEC·G s ·(1 - n), where CEC represents the cation exchange capacity, with the unit of mmol / 100g, α represents the effective coefficient of CEC, and G s represents the specific gravity of the soil, and c represents the concentration of the pollutant, in units of molar concentration.

[0022] As a further solution of the present invention, the calculation formula of the surface force is expressed as:

[0023] In the formula, n mr is the microscopic porosity under the reference state, and n m is the microscopic porosity under specific load and concentration conditions.

[0024] As a further solution of the present invention, the n mr is determined by conducting a mercury intrusion test on the deionized water-saturated soil under unloaded or low-loaded conditions. The microscopic porosity n under specific load and concentration conditions mDetermined by mercury intrusion test under specific conditions.

[0025] The present invention also discloses the application of the above-mentioned calculation method of generalized effective stress considering thermo-chemical effects in predicting the deformation behavior of clay.

[0026] Advantages of the present invention:

[0027] 1. The calculation method of the present invention can comprehensively consider the influence of mechanical, temperature and chemical triple loads on the consolidation deformation of soil, providing a more accurate tool for predicting the deformation of soil under multiple environmental conditions. By emphasizing the dependence of active clay on mechanical load, soil temperature and solute concentration changes, the calculation method of the present invention can quantitatively describe the influence of physical and chemical actions on the evolution laws of soil hydraulic and mechanical properties.

[0028] 2. The calculation method of the present invention particularly emphasizes the dual pore structure characteristics of active clay, which is crucial for understanding and predicting the behavior of soil under different environmental conditions.

[0029] 3. The calculation method of the present invention can predict the deformation evolution law of soil under complex environmental conditions, which has important theoretical and practical significance for the performance analysis and sustainable design of geological structures.

[0030] 4. The calculation method of the present invention shows superiority in describing the compression deformation of soil under environmental loads, and can accurately predict the volume change of soil under different temperature and chemical environments.

[0031] 5. The present invention provides new theoretical support for the stability analysis of soil in environmental engineering such as high-level radioactive waste geological disposal systems and landfills, and helps to improve the safety and stability of geotechnical structures. Description of the drawings

[0032] The present invention will be further described below with reference to the drawings.

[0033] Figure 1 Relationship between void ratio and effective stress of Wyoming bentonite during the swelling deformation process at an environmental temperature of 25 °C: a) Terzaghi effective stress; b) generalized effective stress;

[0034] Figure 2 Relationship between void ratio and effective stress of Wyoming bentonite during the swelling deformation process at an environmental temperature of 50 °C: a) Terzaghi effective stress; b) generalized effective stress;

[0035] Figure 3 Relationship between void ratio and effective stress of Wyoming bentonite during the swelling deformation process at an environmental temperature of 75 °C: a) Terzaghi effective stress; b) generalized effective stress;

[0036] Figure 4 Relationship between void ratio and effective stress of Wyoming bentonite during the compression deformation process at an ambient temperature of 20 °C: a) Terzaghi effective stress; b) generalized effective stress;

[0037] Figure 5 Relationship between void ratio and effective stress of Wyoming bentonite during the compression deformation process at an ambient temperature of 40 °C: a) Terzaghi effective stress; b) generalized effective stress;

[0038] Figure 6 Relationship between void ratio and effective stress of Wyoming bentonite during the compression deformation process at an ambient temperature of 60 °C: a) Terzaghi effective stress; b) generalized effective stress. Specific implementation mode

[0039] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to 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 creative efforts shall fall within the protection scope of the present invention.

[0040] A calculation method for generalized effective stress considering thermo-chemical effects includes the following steps:

[0041] Determine the thermodynamic stress expressions of the solid phase, free liquid phase, and adsorbed liquid phase respectively;

[0042] The expressions of the three are respectively:

[0043]

[0044] In the formula, and respectively represent the thermodynamic pressure tensors of the solid phase, macroscopic pore liquid phase, and microscopic pore liquid phase; σ″ ij is the intergranular stress tensor of the soil; μ s , μ M and μ m respectively represent the chemical potentials of the solid phase, macroscopic pore liquid phase, and microscopic pore liquid phase; ρ s , ρ M and ρ m respectively represent the densities of the solid phase, macroscopic pore liquid phase, and microscopic pore liquid phase; n, n M and n m respectively represent the total porosity, macroscopic porosity, and microscopic porosity; δij is the Kronecker symbol;

[0045] It can be clearly seen from Formulas (1) to (3) that the chemical potentials of the solid phase, the macro-pore liquid phase, and the micro-pore liquid phase play a crucial role in determining the stresses of each phase. Considering the previous research results, when considering the influence of the external environment, the chemical potentials of the soil skeleton, the macro-liquid phase, and the micro-liquid phase can be expressed as follows:

[0046]

[0047] In the formula, K b represents the elastic modulus of the saturated medium; K m represents the elastic modulus of soil particles; p M represents the macro-liquid phase pressure; p r represents the reference pressure; p m represents the micro-liquid phase pressure; ω M represents the chemical osmotic efficiency coefficient of the macro-structure; ω m represents the chemical osmotic efficiency coefficient of the micro-structure; M w represents the molar mass of water; a Mc represents the water activity of the macro-liquid phase; a mc represents the water activity of the micro-liquid phase; T represents the absolute temperature;

[0048] When the temperature of the soil mass changes, thermal pore water pressure will be generated in the macro and micro pore spaces. At this time, the pore fluid pressures at the macro and micro scales can be further written as:

[0049] p M = p + p MT (7)

[0050] p m = p ml + p mT (8)

[0051] In the formula, p represents the pore water pressure caused by mechanical loads in the macro pore space; p MT represents the thermally induced pore water pressure in the macro pore space; p ml represents the pore water pressure caused by mechanical loads in the micro pore space; p mT represents the thermally induced pore water pressure in the micro pore space.

[0052] Substituting Formulas (4), (5), and (6) into Formulas (1), (2), and (3) respectively, we can obtain:

[0053]

[0054] Assume that the macro pores are not affected by the electric field; the micro pores are affected by the electric field. It is considered that when only macro pores exist, the soil mass does not have the semi-permeable membrane property, that is, the reflection coefficient ω of this part MIs equal to zero. On the contrary, the pore water within the micro-pores is all affected by the electric field. Therefore, it can be considered that the electric double layers of the part containing only micro-pores are completely overlapped, with ideal semi-permeable membrane properties, that is, the reflection coefficient ω m Is 1. In addition, combining with the water activity values provided by Montes-H et al., it is considered that the water activity of the micro-scale pore water affected by the solute is close to 1. Based on these assumptions, and combining formulas (10) and (11) at the same time, the thermodynamic pressures of the fluids within the macro-pores and micro-pores are readjusted as:

[0055]

[0056]

[0057] Although the chemical terms are eliminated in formulas (12) and (13), the contributions of the chemical action and the electrification of the soil body to the chemical potential and the inter-granular stress of the soil body are not ignored, but are all reflected in the pore water pressure corresponding to the micro-pores.

[0058] The average pore water pressure and the measured pore water pressure satisfy:

[0059] p lp = p lR + V 0 RT ln(a wlR / a wlp ) - ρ *lw Ω l = p lR + Π D - ρ *lw Ω l = p lR + Π(14)

[0060] In the formula, p lp Represents the average pore water pressure; p lR Represents the pressure of the equilibrium solution, and also represents the measured pore water pressure; V 0 Represents the mole fraction of water; R represents the universal gas constant; T represents the absolute temperature; a wlR Represents the activity of the solvent water inside the equilibrium solution; a wlp Represents the activity of the solvent water in the pore solution; ρ *lw Represents the mass density of pure water; ρ *lw Ω l Represents the surface force; Π D Represents the Donnan osmotic pressure; Π represents the generalized osmotic pressure, which mainly reflects the osmotic pressure difference between the pore water and the equilibrium solution.

[0061] The calculation formula for the Donnan osmotic pressure is:

[0062]

[0063] In the formula, c fix represents the fixed charge density of the soil skeleton, reflecting the total amount of fixed charges in the soil per unit volume. The calculation formula is c fix = 10·α·CEC·G s ·(1 - n), where CEC represents the cation exchange capacity, with the unit of mmol / 100g, α represents the effective coefficient of CEC, and G s represents the specific gravity of the soil. In addition, c represents the concentration of the pollutant, in molar concentration units.

[0064] To simplify the calculation, it is considered that the density of the bound water in the microscopic pores is equal to the density of the free water, both equal to the density of the free water, that is, ρ M = ρ m = ρ w .

[0065] Based on this assumption, and combined with formula (14), it can be known that the following relationship is satisfied between the pore water pressure in the microscopic pores and the pore water pressure in the equilibrium solution:

[0066] p ml = p + Π D - ρ w Ω l (16)

[0067] The calculation formula of the surface force is expressed as:

[0068]

[0069] In the formula, n mr is the microscopic porosity under the reference state, mainly determined by mercury intrusion tests on deionized water-saturated soil under unloaded or low-loaded conditions. In addition, the microscopic porosity n m under specific load and concentration conditions is mainly determined by mercury intrusion tests under specific conditions.

[0070] To simplify the calculation process, the reference pressure and the soil background concentration are set to zero. When the reference pressure and the soil background concentration are zero, the corresponding forces are added to obtain the total stress formula:

[0071]

[0072] When it is assumed that the contributions of temperature to the macroscopic and microscopic pore fluid pressures are equal, that is:

[0073] p MT = p mT = p T

[0074] The total stress equation can be further expressed as:

[0075]

[0076] Through Equation (19), the final form of the generalized effective stress method can be expressed as:

[0077]

[0078] where b represents the Biot coefficient, which is numerically equal to 1 - K b / K m .

[0079] Adopt the thermal pore water pressure proposed by Ghaaowd et al. (2015):

[0080]

[0081] where p' represents the average effective consolidation pressure; e 0 represents the initial void ratio of the soil mass; λ represents the slope of the compression curve.

[0082] In order to study the influence of thermo-chemical action on the mechanical properties of compacted Wyoming bentonite, Liang Weiyun (2021) carried out swelling and compression deformation tests under different concentrations, temperatures and dry densities. At the same time, mercury intrusion tests were used to explore the changes in pore structure. Table 1 lists the soil property parameters of the Wyoming bentonite used in the tests.

[0083] Table 1

[0084]

[0085] The calculation formula for the slope of the compression curve is:

[0086]

[0087] where I p is the plasticity index; e 0 is the initial void ratio.

[0088] Take 0.2 μm as the critical value of macro and micropores. Using this critical value, the macro void ratio of bentonite with a dry density of 1.7 g / cm 3 is 0.18. The micro void ratio is obtained by subtracting the macro void ratio from the total void ratio. The initial micro porosity value is used as the micro parameter of the equation.

[0089] Simulation of swelling deformation of compacted bentonite specimens under different environmental conditions.

[0090] The initial dry density of the Wyoming bentonite used in the swelling deformation test is 1.7 g / cm 3 , and the tests are mainly carried out at three environmental temperatures of 25, 50 and 75 °C.

[0091] Figure 1 , Figure 2 and Figure 3 respectively show the relationships between the void ratio and the Terzaghi effective stress σ' and the generalized effective stress σ” under different temperature and chemical load conditions during the swelling deformation process. It can be seen that when using the Terzaghi effective stress to describe the soil deformation, the effective stress-void ratio relationship curves under different concentrations are completely different. When using the generalized effective stress considering the environmental impact to describe the soil deformation, regardless of the external environment, there is a unique correlation between the generalized effective stress σ” and the saturated void ratio of Wyoming bentonite. The unique correspondence between the generalized effective stress σ” and the saturated void ratio of Wyoming bentonite can not only prove the effectiveness of the generalized effective stress method, but also illustrate the superiority of the generalized effective stress method proposed in the present invention in describing the deformation evolution law of soil under complex environmental conditions.

[0092] Simulation of the compression deformation of compacted bentonite specimens under different environmental conditions.

[0093] The initial dry density of the Wyoming bentonite used in the compression deformation test is 1.7 g / cm 3 , and the tests are mainly carried out at three environmental temperatures of 20, 40 and 60 °C.

[0094] Figure 4 , Figure 5 and Figure 6 respectively give the relationship curves between the effective stress and the saturated void ratio e during the process of using the Terzaghi effective stress σ' and the generalized effective stress σ” to describe the soil compression deformation at temperatures of 20 °C, 40 °C and 60 °C. From Figure 4 , Figure 5 and Figure 6 it can be seen that the Terzaghi effective stress σ' cannot uniformly describe the deformation evolution law of soil under different temperature and concentration conditions in semi-logarithmic coordinates. However, the generalized effective stress σ” considering the influence of temperature and chemical action can uniformly describe the compression deformation evolution law of soil under different environmental conditions, which once again illustrates the superiority of the generalized effective stress method proposed in the present invention.

[0095] The above content is only an example and explanation of the present invention. Those skilled in the art of this technology can make various modifications or supplements to the described specific embodiments or use similar methods to replace them. As long as they do not deviate from the invention or exceed the scope defined by this claim book, they should all belong to the protection scope of the present invention.

Claims

1. A generalized effective stress calculation method considering thermal-chemical effects, characterized in that: The steps include: Step 1: Substitute the chemical potential expressions of soil skeleton, macroscopic liquid phase and microscopic liquid phase into the stress expressions of solid phase, free liquid phase and adsorbed liquid phase; Under the assumption that the macroscopic pores are not affected by the electric field; Under the condition that the microscopic pores are affected by the electric field and the water activity of the microscopic pores affected by the solute is close to 1, the thermodynamic pressure of the fluid in the macroscopic pores and microscopic pores is adjusted to: in; n、n M and n m represents the total porosity, macro porosity and micro porosity respectively; δ ij is the Kronecker symbol, p represents the pore water pressure caused by mechanical load in the macroscopic pore space; p MT represents the thermally induced pore water pressure in the macroscopic pore space; p ml represents the pore water pressure caused by mechanical load in microscopic pore space; p mT represents the thermally induced pore water pressure in the microscopic pore space, p r Indicates the reference pressure; Step 2: The average pore water pressure and the measured pore water pressure meet the following conditions: p lp =p lR +V0RT ln(a wlR / a wlp )-r *lw Oh l =p lR +P D -r *hv Oh l =p lR +P(14) In the formula, p lp represents the average pore water pressure; p lR represents the pressure of the equilibrium solution, and also represents the measured pore water pressure; V0 represents the mole fraction of water; R represents the universal gas constant; T represents the absolute temperature; a wlR Represents the activity of the solvent water inside the equilibrium solution; a wlp represents the activity of solvent water in the pore solution; ρ *lw Represents the mass density of pure water; ρ *lw Ω l represents the surface force; Π D represents Donnan osmotic pressure; Π represents generalized osmotic pressure; Step 3: Assume that ρ M =ρ M =ρ w Under the condition that , the pore water pressure in the microscopic pores and the pore water pressure in the equilibrium solution satisfy the following relationship by combining formula (14): p ml =p+Π D -r w Oh l (16) The reference pressure and soil background concentration are set to zero, and the contribution of temperature to the macroscopic and microscopic pore fluid pressures is assumed to be equal, and the total stress equation is obtained. The generalized effective stress is obtained according to the total stress equation: In the formula, b represents the Biot coefficient, which is numerically equal to 1-K b / K m .

2. A generalized effective stress calculation method considering thermal-chemical effects according to claim 1, characterized in that: The calculation formula of the Donnan osmotic pressure is: In the formula, c fix represents the fixed charge density of the soil skeleton, calculated as c fix =10·α·CEC·G s (1-n), where CEC is the cation exchange capacity in mmol / 100g, α is the effective coefficient of CEC, and G s represents the specific gravity of the soil, and c represents the concentration of the pollutant in molar concentration.

3. A generalized effective stress calculation method considering thermal-chemical effects according to claim 1, characterized in that: The calculation formula of surface force is expressed as: Where n mr is the microscopic porosity in the reference state, n m Microporosity at specific load and concentration conditions.

4. A generalized effective stress calculation method considering thermal-chemical effects according to claim 3, characterized in that: The mr The microscopic porosity n under specific load and concentration conditions is determined by mercury injection test on deionized water saturated soil under no load or low load conditions. m Determined by mercury injection test under specific conditions.

5. Application of a generalized effective stress calculation method considering thermo-chemical effects according to any one of claims 1 to 4 in the prediction of clay deformation behavior.

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