Strength prediction method based on cohesionless soil damage specific strength theory

Abstract

The invention discloses a cohesionless soil damage ratio strength theory-based strength prediction method, which comprises the following steps of: establishing a strength criterion general expression of cohesionless soil in a triaxial compression stress state on the basis of a strain decomposition hypothesis and a unit energy consumption rate extreme value calculation model; converting the principal stress into a generalized stress parameter, and substituting the generalized stress parameter into a general expression of the strength criterion to obtain a generalized stress form of the strength criterion; establishing a damage ratio expression based on cohesionless soil strength envelope surface characteristics, and determining a corresponding empirical coefficient according to the cohesionless soil type to obtain an optimized strength criterion; and substituting the stress parameter of the target cohesionless soil into the optimized strength criterion, calculating to obtain a strength prediction value of the cohesionless soil, and verifying the prediction precision in combination with true triaxial test data. According to the method, low, medium and high full confining pressure ranges are covered, the plastic flow characteristics and the internal friction angle change rule of the cohesionless soil are accurately reflected, and high-precision strength prediction of the cohesionless soil under the complex stress condition is achieved.

Description

Technical Field

[0001] This invention relates to the field of strength prediction technology for geotechnical engineering materials, and in particular to a strength prediction method based on the damage ratio strength theory of cohesionless soil. Background Technology

[0002] Cohesion-free soils, including desert sand, river sand, beach sand, gravel, and coarse-grained soils, are widely distributed in nature and are common foundation materials or structural materials in construction fields such as water conservancy, civil engineering, transportation, and offshore engineering. With the continuous expansion of engineering construction scale, cohesion-free soils are often subjected to complex true triaxial and high confining pressure stress states. Accurate prediction of their strength characteristics and failure patterns has become a key issue in ensuring the safety and stability of engineering projects.

[0003] Currently, the strength criteria for isotropic cohesionless soils widely used in engineering, such as the Mohr-Coulomb single shear criterion, the Lade-Duncan criterion, and the SMP criterion, are mainly based on experimental data under medium to low confining pressure conditions. These criteria have certain applicability under conventional stress levels, but their theoretical models have inherent limitations: First, their failure envelope is open in the meridional plane and cannot be closed, meaning that these theories cannot describe the plastic flow phenomena that may occur in materials under extremely high hydrostatic pressure; second, these criteria usually assume that the internal friction angle is constant, or only consider the influence of the intermediate principal stress coefficient, failing to fully reflect the complex law of the internal friction angle changing with the mean principal stress and the minimum principal stress. Therefore, the accuracy and applicability are challenged when predicting the soil strength under high confining pressure and true triaxial complex stress states.

[0004] On the other hand, research findings from the fields of concrete and rock mechanics have provided insights into understanding the behavior of soil under high stress. Experiments show that lightweight aggregate concrete undergoes plastic flow failure under high lateral pressure and triaxial isobaric stress, with its failure envelope closing on the hydrostatic pressure axis. Similarly, deep rocks also exhibit significant plastic deformation characteristics under high confining pressure. These phenomena suggest that, under high confining pressure sufficient to suppress brittle failure, the failure mechanism of cohesionless soils is likely to shift from shear slip to plastic flow, and its strength envelope should be a smooth spatial surface closed on the hydrostatic pressure axis.

[0005] In terms of theoretical development, researchers have proposed a damage ratio strength theory based on strain decomposition models and unit cell relative energy dissipation rate extreme value calculation models. This theory aims to unify the description of material failure laws and has been successfully applied to the multiaxial strength prediction of materials such as concrete and asphalt mixtures. By introducing the damage ratio parameter, this theory can effectively reflect the difference between tensile and compressive strengths of materials and the influence of stress state on strength.

[0006] However, directly applying this theory to cohesionless soils remains challenging. Existing damage ratio expressions typically include numerous empirical coefficients, resulting in complex models. Furthermore, they lack a targeted and simplified theoretical characterization of the key mechanical behavior unique to cohesionless soils—the tendency towards plastic flow under high hydrostatic pressure, leading to failure surface closure. Therefore, developing a novel strength theory and prediction method that can accurately describe the strength and failure characteristics of cohesionless soils from low to high confining pressure, and even under triaxial isobaric conditions, with a concise form and clearly defined physical meanings for its parameters, has become an urgent technical problem to be solved in this field. Summary of the Invention

[0007] The purpose of this invention is to provide a strength prediction method based on the damage ratio strength theory of cohesionless soil, covering the entire range of low, medium and high confining pressure, accurately reflecting the plastic flow characteristics and internal friction angle variation law of cohesionless soil, solving the problems of inaccurate prediction under high confining pressure and insufficient consideration of the influence of multiple stress factors in existing criteria, and realizing high-precision strength prediction of cohesionless soil under complex stress conditions.

[0008] To achieve the above objectives, the present invention provides the following solution: A strength prediction method based on the damage specific strength theory of cohesionless soil, the method comprising the following steps: S1. Constructing a theoretical framework for the damage specific strength of cohesionless soil: Based on the strain decomposition assumption and the unit volume energy dissipation rate extreme value calculation model, a general expression for the strength criterion of cohesionless soil under triaxial compressive stress is established. S2, Establish stress parameter transformation relationship: Convert principal stresses into generalized stress parameters, substitute them into the generalized expression of strength criterion to obtain the generalized stress form of strength criterion; S3, Determine the expression for the damage ratio variable and empirical coefficients: Establish the expression for the damage ratio based on the strength envelope characteristics of cohesionless soil, and determine the corresponding empirical coefficients according to the type of cohesionless soil to obtain the optimized strength criterion; S4, Strength Prediction and Verification: Substitute the stress parameters of the target cohesionless soil into the optimized strength criterion to calculate the predicted strength value of the cohesionless soil, and verify the prediction accuracy by combining true triaxial test data.

[0009] Furthermore, in S1, the strain decomposition assumption is as follows: it is assumed that the total longitudinal strain and the total transverse strain of cohesionless soil are both decomposed into elastic strain and inelastic strain, as expressed below: (1) (2) In the formula, ε is the total longitudinal strain, ε e For longitudinal elastic strain, ε ine ε' is the longitudinal inelastic strain; ε′ is the transverse total strain.e For transverse elastic strain, ε′ ine For transverse inelastic strain; where ε′ and ε′ are... e and ε′ ine They are represented as follows: (3) In the formula, v is the lateral deformation coefficient, v0 is Poisson's ratio, and v r This represents the damage deformation coefficient of the inelastic strain portion.

[0010] Furthermore, in S1, the derivation process of the unit cell energy dissipation rate extreme value calculation model is as follows: Treating the cohesionless soil as an isotropic material, and using inelastic principal strain as the main energy dissipation mechanism in the failure process, the unit cell energy dissipation rate calculation model is... for: (4) In the formula, σ i Let i = 1, 2, 3 be the nominal principal stresses of the element at the start of failure, σ1 be the maximum principal stress, σ2 be the intermediate principal stress, and σ3 be the minimum principal stress. Let t be the inelastic principal strain rate; The expression for the inelastic principal strain rate is derived by combining the strain decomposition relationship. After substituting it into the calculation model formula (4) for the energy dissipation rate of the unit volume, the strength criterion constraint condition is introduced by the Lagrange multiplier method: (9) The general expression for the strength criterion is obtained as follows: (13) In the formula, v D,c The pressure damage ratio.

[0011] Furthermore, the generalized stress parameters in S2 include the mean principal stress, generalized shear stress, and Lode angle; converting the principal stresses into generalized stress parameters includes converting the principal stresses into the mean principal stress. p Generalized shear stress q The Lode angle represents the triaxial intensity. (14) In the formula, σ1, σ2, and σ3 are the principal stresses of the element, and σ1>σ2>σ3>0.

[0012] Furthermore, in S2, substituting the general expression for the strength criterion yields the generalized stress form of the strength criterion, specifically including: Substituting equation (14) into equation (13), we obtain the generalized stress form corresponding to equation (13): (15) In the formula,q For generalized shear stress, p For the mean principal stress, v D,c The pressure damage ratio.

[0013] Furthermore, in S3, the strength envelope characteristics of cohesive-free soil include closed, smooth, and outwardly convex surfaces, and the damage ratio monotonically decreases with hydrostatic stress; the damage ratio expression is a four-empirical-coefficient damage ratio expression.

[0014] Furthermore, in S3, the expression for the four empirical coefficient damage ratio is as follows: (16) In the formula, p is the mean principal stress. i For Lode angle, a 1. a 2. a 3. a 4 is the empirical coefficient; where ( p - a 1) The term reflects the intersection of the meridian and the hydrostatic stress axis at... a 1, and p = a At 1 o'clock, v D ,c It converges to 0.5. a The value of 2 affects the convexity of the deviated plane. a 2. a 3 and a 4 Reflecting Lode Angle i The resulting slope change pattern, and The term has the property of being continuously differentiable.

[0015] Furthermore, in S3, the method for determining the empirical coefficient is as follows: when p = a Meridians at different Lode angles intersect at the same point. a 1. a 3 and a 4 represents (19) parameter a 1- a 4. The details of the value selection method are as follows: Preliminary determination is made based on the test data along the tension / compression meridian. A 1. B 1. A 2. B 2 takes a value, and A 1. B 1. A 2 and BThe value of 2 must ensure that the tension / compression meridian intersects the hydrostatic stress axis at the same point; A 1. B 1. A 2 and B Substituting the value of 2 into equation (19) yields a 1. Value; a The value of 2 is closely related to whether the deviated plane is convex; 1 < a 2≤1.5, adjusted to simplify calculation. a The value of 2 satisfies the convexity of the partial plane; a Substituting the value of 2 into equation (19) yields a 3 and a 4. Values.

[0016] Furthermore, the empirical coefficients determined based on the type of cohesive soil are specifically selected as follows: When the non-cohesive soil is Monterey sand, Santa Monica Beach sand, or aeolian sand: a 1 = 3000 a 2 = 1.18 a 3 = -0.000129 a 4 = 0.000014; When the non-cohesive soil is gravel: a 1 = 4000 a 2 = 1.18 a 3 = -0.000156 a 4 = 0.00001; When the non-cohesive soil is granular: a 1 = 5000 a 2 = 1.07 a 3 = -0.00015 a 4 = 0.000008; When the non-cohesive soil is coarse-grained: a 1 = 11200 a 2 = 1.1, a 3 = -0.00006 a 4 = 0.000003.

[0017] Furthermore, step S4 also includes the calculation of the internal friction angle. f b The relationship with the intermediate principal stress coefficient b is derived through the following formula: different b Experimental internal friction angle at value f b The definition of is: (twenty two) intermediate principal stress coefficient b The value is: (twenty three) Substituting equations (22) and (23) into the expression for the soil damage ratio strength criterion, and rearranging, we obtain the corresponding strength criterion. f b about b The implicit functional relationship is: (twenty four) In the formula .

[0018] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: The strength prediction method based on the damage ratio strength theory of cohesionless soil provided by the present invention (1) constructs the damage ratio strength theory of cohesionless soil based on the strain decomposition model and the unit energy dissipation rate extreme value calculation model; (2) based on the assumption that the triaxial failure envelope of cohesionless soil is closed and smooth and convex, and that the damage ratio decreases monotonically with the increase of hydrostatic pressure, proposes a four-empirical coefficient damage ratio expression reflecting the high-pressure plastic flow failure law of cohesionless soil; (3) verifies and compares the applicable range and calculation accuracy of the damage ratio strength theory with other commonly used cohesionless soil strength criteria using existing experimental results of the true triaxial strength of various cohesionless soils, and explores the variation law of internal friction angle. The present invention has the following beneficial effects: Covering the entire confining pressure range: Through the design of a closed and smooth strength envelope surface, it accurately reflects the brittle shear failure of cohesionless soil under low confining pressure and the plastic flow failure characteristics under high confining pressure, solving the limitation of traditional criteria that are only applicable to low and medium confining pressure; High prediction accuracy: Considering the combined effects of mean principal stress, intermediate principal stress and Lode angle, the stress-strength relationship is quantified by the four empirical coefficient damage ratio expression. The prediction results are verified by various cohesionless soil true triaxial tests and have a high degree of agreement with the measured data. Highly practical: It provides recommended empirical coefficient values ​​for different types of cohesionless soils, clarifies the complete process of stress parameter conversion, strength calculation and internal friction angle derivation, and can be directly applied to strength prediction in engineering design; The theoretical system is comprehensive: it is constructed based on the principle of strain decomposition and extreme energy dissipation rate, and has rigorous logic. It can reflect the dynamic change law of internal friction angle with intermediate principal stress coefficient and mean principal stress, providing theoretical support for the study of mechanical properties of cohesionless soil. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart of the strength prediction method based on the damage ratio strength theory of cohesionless soil according to the present invention; Figure 2 The three-dimensional strength envelope surfaces corresponding to the theoretical damage ratio strength of each material under the four empirical coefficient recommended values ​​shown in Table 1 of the embodiments of the present invention are as follows: (a) is the three-dimensional strength envelope surface corresponding to Monterey sand, Santa Monica Beach sand or aeolian sand, (b) is the three-dimensional strength envelope surface corresponding to gravel, (c) is the three-dimensional strength envelope surface corresponding to granular soil, and (d) is the three-dimensional strength envelope surface corresponding to coarse-grained soil. Figure 3 This is a schematic diagram showing the variation of the compressive meridian and compressive damage ratio of cohesive soil with hydrostatic pressure in an embodiment of the present invention. (a) shows the variation for Monterey sand, Santa Monica Beach sand, or aeolian sand; (b) shows the variation for gravel; (c) shows the variation for granular soil; and (d) shows the variation for coarse-grained soil. Figure 4 This is a schematic diagram of the tensile and compressive meridians of the damage specific strength theory in an embodiment of the present invention, wherein (a) is the meridian corresponding to Monterey sand, Santa Monica Beach sand or aeolian sand, (b) is the meridian corresponding to gravel, (c) is the meridian corresponding to granular soil, and (d) is the meridian corresponding to coarse-grained soil. Figure 5 This is a schematic diagram of the theoretical deflection plane of the damage specific strength in an embodiment of the present invention, wherein (a) is the deflection plane corresponding to Monterey sand, (b) is the deflection plane corresponding to Santa Monica Beach sand, (c) is the deflection plane corresponding to aeolian sand, (d) is the deflection plane corresponding to gravel, (e) is the deflection plane corresponding to granular soil, and (f) is the deflection plane corresponding to coarse-grained soil. Figure 6 The non-cohesive soil in this embodiment of the invention f b ~ b A schematic diagram comparing the relationship and the damage-to-strength criterion, where (a) represents the Monterey sand corresponding to... f b ~ b Relationship, (b) is the relationship between gravel and... f b~ b Relationship, (c) represents the relationship between granular soil and soil. f b ~ b Relationship, (d) represents the relationship between coarse-grained soil and... f b ~ b relation; Figure 7 The diagram shows a comparison of the tensile and compressive meridians corresponding to each strength criterion. (a) is the meridian corresponding to Monterey sand, (b) is the meridian corresponding to Santa Monica Beach sand, (c) is the meridian corresponding to aeolian sand, (d) is the meridian corresponding to gravel, (e) is the meridian corresponding to granular soil, and (f) is the meridian corresponding to coarse-grained soil. Figure 8 The diagram shows the comparison of the deflection planes corresponding to each strength criterion, where (a) is the deflection plane corresponding to Monterey sand, (b) is the deflection plane corresponding to Santa Monica Beach sand, (c) is the deflection plane corresponding to aeolian sand, (d) is the deflection plane corresponding to gravel, (e) is the deflection plane corresponding to granular soil, and (f) is the deflection plane corresponding to coarse-grained soil. Figure 9 For the prediction of various strength criteria for cohesionless soil f b ~ b A schematic diagram comparing the relationship curves with experimental results, where (a) represents the relationship curves corresponding to Monterey sand. f b ~ b Relationship, (b) is the relationship between gravel and... f b ~ b Relationship, (c) represents the relationship between granular soil and soil. f b ~ b Relationship, (d) represents the relationship between coarse-grained soil and... f b ~ b relation. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] This invention constructs a damage ratio strength theory for cohesionless soils based on a strain decomposition model and a unit volume energy dissipation rate extreme value calculation model. Based on the assumptions that the triaxial isobaric failure envelope of cohesionless soils is closed, smooth, and convex, and that the damage ratio decreases with hydrostatic stress, a four-empirical coefficient expression for the damage ratio variable is proposed. The deviated planar failure curve of this theory is a smooth, convex curvilinear triangle, and the failure curves on the meridional plane are smooth and intersect at a single point at the triaxial isobaric stress, reflecting the plastic flow law of cohesionless soils under high confining pressure and triaxial isobaric stress. Subsequently, the effectiveness of this criterion is verified using true triaxial strength data of cohesionless soils such as sand, gravel, and coarse-grained soils. Finally, the proposed damage ratio criterion is compared with the Mohr-Coulomb criterion, Lade-Duncan criterion, and SMP criterion. The results show that the damage ratio strength theory has high calculation accuracy and reflects the variation of the inviscid internal friction angle with the intermediate principal stress coefficient, average principal stress, and minimum principal stress. The other criteria are mainly applied to low and medium confining compressive stress levels, with the corresponding meridian pressure ends open, the internal friction angle remaining unchanged, or only considering the influence of the intermediate principal stress coefficient.

[0023] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0024] like Figure 1 As shown, the strength prediction method based on the damage specific strength theory of cohesionless soil provided by this invention includes the following steps: S1. Constructing a theoretical framework for the damage specific strength of cohesionless soil: Based on the strain decomposition assumption and the unit volume energy dissipation rate extreme value calculation model, a general expression for the strength criterion of cohesionless soil under triaxial compressive stress is established. S2, Establish stress parameter transformation relationship: Convert principal stresses into generalized stress parameters, substitute them into the generalized expression of strength criterion to obtain the generalized stress form of strength criterion; S3, Determine the expression for the damage ratio variable and empirical coefficients: Establish the expression for the damage ratio based on the strength envelope characteristics of cohesionless soil, and determine the corresponding empirical coefficients according to the type of cohesionless soil to obtain the optimized strength criterion; S4, Strength Prediction and Verification: Substitute the stress parameters of the target cohesionless soil into the optimized strength criterion to calculate the predicted strength value of the cohesionless soil, and verify the prediction accuracy by combining true triaxial test data.

[0025] The specific steps of the strength prediction method based on the damage specific strength theory of cohesionless soil described in this invention are analyzed as follows: 1. Damage specific strength theory 1.1 Basic Assumptions Under small deformation conditions, cohesionless soil under triaxial compressive stress is considered a continuous body, exhibiting both longitudinal and transverse strains. Analogous to the strain decomposition method used for cohesive friction materials, it is assumed that the total longitudinal and transverse strains of cohesionless soil can also be decomposed into elastic and inelastic strains, i.e. (1) (2) In the formula, e For the total longitudinal strain, e e For longitudinal elastic strain, e ine It is a longitudinal inelastic strain; e' For the total transverse strain, e' e For transverse elastic strain, e' ine This represents transverse inelastic strain. e' , e' e and e' ine They are respectively represented as (3) In the formula, v The lateral deformation coefficient is... v 0 represents Poisson's ratio. v r This represents the damage deformation coefficient of the inelastic strain portion.

[0026] 1.2 Theoretical Construction Treating cohesionless soil as an isotropic material, and considering the inelastic principal strain induced under load as the main energy dissipation mechanism during failure, the calculation model for the energy dissipation rate of the element is as follows. for (4) In the formula, s i ( i =1,2,3) represents the nominal principal stresses of the element at the start of failure, where σ1 is the maximum principal stress, σ2 is the intermediate principal stress, and σ3 is the minimum principal stress. for t Inelastic principal strain rate at time t.

[0027] Combining equations (1), (2), and (3), the triaxial constitutive relation of isotropic cohesionless soil at failure can be expressed as follows: (5) In the formula, g For the destruction process tThe ratio of the secant modulus to the elastic modulus of cohesive soil. Inelastic principal strain. e ine,i ( t ) represents (6) According to equation (6), the inelastic principal strain rate It can be represented as (7) In the formula, for g right t The derivative of . Substituting equation (7) into (4), we obtain the expression for the energy dissipation rate of cohesive soil at failure as follows: (8) Let the strength criterion expression be (9) The strength criterion shown in equation (9) is the constraint condition that equation (4) must satisfy during the failure process, then we have (10) In the formula, λ is the Lagrange multiplier. The derivation yields... (11) In the formula, C = λE c g 2 C 0 / g, ( C 0 is a constant. From the fact that the uniaxial strength of cohesionless soil is 0, the general expression for triaxial strength theory can be obtained as follows: (12) When the stresses in the three principal stress directions of an isotropic material are both tensile or compressive stresses, the damage deformation coefficient v r Equivalent to pressure damage ratio v D,c Since cohesionless soil can only withstand triaxial compressive stress, equation (12) can be rewritten as follows: (13) 1.3 Damage ratio expression and empirical coefficient For soil materials, the mean principal stress is generally used. p Generalized shear stress q Lode angle represents triaxial strength, principal stress, and mean principal stress. p and generalized shear stress q The conversion relationships are as follows: (14) Substituting equation (14) into equation (13), we obtain the generalized stress form corresponding to equation (13): (15) Based on the strength envelope characteristics of cohesive soil under triaxial compression, and referring to the strength envelope of ordinary concrete and asphalt mixture, the following three assumptions are proposed: (1) The pressure end of the failure envelope is closed due to the plastic flow failure of the material, and the meridian intersects the hydrostatic stress axis at a certain point; (2) The damage ratio under the same Lode angle decreases monotonically with the increase of hydrostatic stress, and the damage ratio under different Lode angles decreases to the same value; (3) The strength envelope of cohesive soil is smooth and basically convex.

[0028] Define compressive stress as positive and tensile stress as negative; at this point, the Lode angle corresponding to the tensile meridian is... i It is 60°, corresponding to the Lode angle of the meridian. i The value is 0°. To meet the above basic assumptions, this invention proposes the following expression for the damage ratio using four empirical coefficients: (16) In the formula a 1- a 4 is an empirical coefficient. p - a 1) The term reflects the intersection of the meridian and the hydrostatic stress axis at... a 1, and p = a At 1 o'clock, v D It converges to 0.5; a The value of 2 affects the convexity of the deviated plane. a 2. a 3 and a 4 Reflecting Lode Angle i The resulting slope change pattern, and The term has the advantages of continuity and differentiability. According to equation (16), the corresponding compressive damage ratios for Lode angles of 0° and 60° are respectively: (17) Equation (17) can be expressed as: (18) In the formula, ;when p = a Meridians at different Lode angles intersect at the same point, i.e., vD, 0°= vD, 60°, therefore a 1. a 3 and a 4 can be represented as: (19) From equations (17) to (19), the parameters a 1- a 4. The details of the method for determining the value are as follows: (1) The value is initially determined based on the test data on the tension and compression meridian. A 1. B 1. A 2. B 2. Take a value, note A 1. B 1. A 2 and B 2. The value should be chosen so that the tension / compression meridian intersects the hydrostatic stress axis at the same point; (2) A 1. B 1. A 2 and B Substituting the value of 2 into equation (19) yields a 1. Value; (3) a The value of 2 is closely related to whether the deviated plane is convex; 1 < a 2≤1.5, to simplify calculations, we take the value of 1.5 first. a 2 = 1.5, adjust a 2. The value satisfies the convexity of the partial plane; (4) a Substituting the value of 2 into equation (19) yields a 3 and a 4. Values.

[0029] Based on triaxial test data of Monterey sand, Santa Monica Beach sand, Aeolian sand, gravel, granular soil, and coarse-grained soil, the empirical coefficient values ​​recommended in this paper are shown in Table 1. Figure 2 shows the three-dimensional strength envelope surfaces corresponding to the theoretical damage-to-strength ratios of each material under the four recommended empirical coefficient values ​​shown in Table 1. It can be seen that, except for the origin, the three-dimensional failure envelope surfaces of each material are smooth and convex.

[0030] Table 1. Values ​​of the four empirical coefficients for the damage ratio variable.

[0031] Isotropic cohesionless soil subjected to triaxial compressive load ( s 1> s 2> s When 3>0), the damage deformation coefficient v r Equivalent to pressure damage ratio v D,c Combining equation (6), the inelastic strain at failure of cohesive soil is: (20) Therefore, the inelastic volumetric strain of cohesionless soil is (twenty one) In the formula p >0; due to g It is the ratio of secant modulus to elastic modulus, so when the material fails... g <1. When v D,c When >0.5, <0, exhibiting inelastic volume expansion; when v D,c When σ = 0.5, the plastic volumetric strain =0, which indicates that the inelastic volume remains unchanged.

[0032] Figure 3 The figure shows the variation of the compressive meridian and the compressive damage ratio of cohesionless soil with hydrostatic pressure. Combining Figure 3 and Equation (21), it can be seen that: (1) the damage ratio parameter v D,c Reflecting the inelastic volume change law of cohesionless soil, v D,c A value greater than 0.5 indicates that the inelastic volume expansion of the cohesionless soil is significant. Under high confining pressure, the damage ratio parameter decreases to 0.5, which reduces the inelastic volume expansion until it remains constant, resulting in the cohesionless soil exhibiting characteristics of plastic flow. (2) According to the strength characteristics of lightweight aggregates, when the generalized shear stress q When the value reaches its peak, the cohesiveless soil enters a state of high confining pressure plastic flow, at which point the damage ratio parameter corresponding to equation (16) is [value missing]. In addition, triaxial isobaric ( s 1= s 2= s 3= a 1) Substituting the stress state into the equation, the triaxial isobaric damage ratio parameter for cohesionless soil is taken as: Various types of non-cohesive soils and The values ​​are shown in Table 2.

[0033] Table 2. Reference values ​​of damage ratio parameters for cohesionless soil under typical stress states.

[0034] 1.4 Explanation of Damage Ratio Verification This invention addresses cohesive friction materials such as ordinary concrete, fiber-reinforced concrete, and cast iron, and verifies the damage ratio values ​​using experimental results of stress-strain curves under typical stress states obtained by existing scholars. In fact, longitudinal and transverse strain testing of cohesive soil under load is not easy, making the verification of the damage ratio values ​​for cohesive soil under typical stress states difficult. This is because the strain decomposition assumption originates from cohesive friction materials, and can only indirectly demonstrate the rationality of the strain decomposition assumption and damage ratio values ​​for cohesive soil.

[0035] 2. Theoretical Verification and Comparison 2.1 Comparison with experimental data 2.1.1 True triaxial strength The variation law of tensile and compressive meridian and deviatoric plane strength under different mean principal stresses corresponding to the damage specific strength theory is compared with the triaxial strength test data of Monterey sand, Santa Monica Beach sand, Aeolian sand, gravel, granular soil, and coarse-grained soil. Figure 5 and Figure 4 As can be seen from the figure: (1) The meridian predicted by the damage specific strength theory at the origin coincides with the octahedral normal stress. p When axes intersect, the corresponding cohesive soils do not possess uniaxial strength due to the lack of cohesion. p When smaller, on the meridian q Value follows p The value increases approximately linearly with the increase of , at which point the failure mode of cohesionless soil is the traditional brittle shear failure; when q After the value reaches its peak, the non-cohesive clay enters a high-pressure plastic flow state; p When the value decreases to 0, the corresponding non-cohesive soil is in a triaxial isobaric plastic flow state.

[0036] (2) The failure envelope curves predicted by the damage ratio strength theory, such as the tensile and compressive meridian and the deviated plane under different average principal stresses, are basically consistent with the variation law of the measured strength of various cohesionless soils, and reasonably reflect their true triaxial strength characteristics.

[0037] 2.1.2 Angle of Internal Friction The internal friction angle is a commonly used strength parameter in soil mechanics. Experimental results show that it varies with the intermediate principal stress coefficient. b The values ​​are related. Different b Experimental internal friction angle at value f b The definition of (twenty two) intermediate principal stress coefficient b Value (twenty three) Substituting equations (22) and (23) into the expression for the soil damage ratio strength criterion, and rearranging, we can obtain the corresponding strength criterion. f b about b The implicit functional relation is (twenty four) In the formula .

[0038] From equation (24), it can be seen that the damage specific strength criterion corresponds to f b and b and p All are related, that is, also related to any principal stress. s i Related. Different p or s Damage specific strength criterion prediction under 3 conditions f b ~ b For a comparison of experimental data with Monterey sand, gravel, granular soil, and coarse-grained soil, see [link to relevant data]. Figure 6 ,Depend on Figure 6 visible: (1) etc. p or s Under condition 3, with the intermediate principal stress coefficient b The increase in the value of the internal friction angle predicted by the damage strength criterion... f b The value first increases and then decreases, reaching its maximum. f b value corresponding b The value is between 0.25 and 0.75.

[0039] (2) etc. b Under the condition of damage-to-strength criterion, the internal friction angle predicted f b The value varies with stress p or s It decreases as 3 increases.

[0040] (3) From the overall trend of change, the damage specific strength criterion predicts... f b ~ b The value relationship is in good agreement with the experimental results of Monterey sand, gravel and coarse soil, and reasonably reflects the variation law of internal friction angle of the above-mentioned non-cohesive soil.

[0041] 2.2 Comparison with other criteria 2.2.1 True triaxial strength The damage specific strength theory for cohesionless soil is compared and analyzed with other commonly used strength theories, such as the Mohr-Coulomb single shear criterion, the Lade-Duncan criterion, and the SMP criterion. The expressions, number of parameters, and parameter determination methods for each criterion are shown in Table 3. A comparison of the meridian and eccentric plane variation patterns corresponding to each strength criterion with experimental data is shown in Table 3. Figure 7 and Figure 8 The results of the accuracy comparison for each criterion are shown in Table 4. As can be seen from the figures: (1) The Mohr-Coulomb single shear criterion does not consider the influence of intermediate principal stress. When predicting the true triaxial strength of various cohesive soil materials, the theoretical results are obviously conservative. However, the damage ratio strength theory, the Lade-Duncan criterion and the SMP criterion are in good agreement with the test data of various cohesive soils.

[0042] (2) All the tensile and compressive meridians of each criterion intersect at the origin of the coordinate axis, which reflects the mechanical properties of cohesive soil that does not have cohesion and therefore does not have uniaxial strength.

[0043] (3) The meridians shown by the damage ratio strength theory intersect with the average principal stress axis pressure end, predicting that the cohesionless soil has the characteristics of triaxial isobaric plastic flow state, while the meridian pressure ends of the other criteria are all open, making the cohesionless bearing capacity under triaxial high pressure and triaxial isobaric states increasingly higher.

[0044] Table 3. Expressions of strength criteria by other scholars

[0045] Table 3 shows the expression for the Lade-Duncan criterion. middle, I 1 is the first invariant of the stress tensor; I3 It is the third invariant of the stress tensor; k f For parameters to be determined; the expression for the SMP criterion. middle, I 1 is the first invariant of the stress tensor; I 2 is the second invariant of the stress tensor; I 3 is the third invariant of the stress tensor; C For parameters to be determined, the internal friction angle can be used. f Sure.

[0046] Table 4 Comparison of Calculation Accuracy of Various Strength Criteria

[0047] 2.2.2 Angle of Internal Friction The Mohr-Coulomb single shear criterion does not consider the influence of the intermediate principal stress, therefore it assumes that the internal friction angle and the intermediate principal stress coefficient are related. bValues ​​are irrelevant; for the Mohr-Coulomb criterion, we have: (25) In the formula, f 0 is b= The internal friction angle of the material at 0°.

[0048] Substituting equations (22) and (23) into the de-Duncan criterion expression and rearranging, we can obtain the corresponding criterion expression. f b about b The implicit functional relation is (26) Substituting equations (22) and (23) into the expression for the P criterion and rearranging, we can obtain the corresponding criterion. f b about b The implicit functional relation is (27) From equations (26) and (27), it can be seen that the Lade-Duncan criterion and the SMP criterion predict... f b Value only with b related, p or s The change in 3 does not affect either of them. f b ~ b Relationship curve.

[0049] different p or s The damage ratio predicted by the three criteria: specific strength criterion, Mohr-Coulomb criterion, Lade-Duncan criterion, and SMP criterion. f b ~ b The relationship curve is compared with experimental data for Monterey sand, gravel, and granular soil. Figure 9 ,Depend on Figure 9 visible: (1) etc. p or wait s Under three conditions, the damage ratio criterion, Lade-Duncan criterion, and SMP criterion predict the following: f b along with b The value increases first and then decreases; etc. b Under the condition, the damage ratio criterion predicts f b The value varies with stress p or sThe value decreases with the increase of 3, while the Lade-Duncan and SMP criteria predict... f b The value remains unchanged.

[0050] (2) The SMP criterion and the Mohr-Coulomb criterion correspond to f b ~ b The relationship curve is b = 0 and b = Intersection at 1 point. Although the SMP criterion takes into account the influence of the intermediate principal stress, the overall results are still quite different from the experimental results of various cohesive soils.

[0051] (3) Overall, for various types of non-cohesive soils, different p or s Damage specific strength criterion prediction under 3 conditions f b ~ b The relationship curve better reflects the changing patterns of the experimental results.

[0052] In summary, this invention, based on the strain decomposition assumption and the unit volume energy dissipation rate extreme value calculation model, constructs a damage specific strength theory for cohesionless soils, proposes a four-empirical coefficient damage ratio variable expression, and recommends empirical coefficient values ​​for each type of cohesionless soil. The three-dimensional envelope surface corresponding to the damage specific strength theory has smooth, convex geometric characteristics, with both the zero-stress end and the high-pressure stress end of the envelope surface closed. This reflects the traditional brittle shear failure under low confining pressure, while under high confining pressure, the decrease in the damage ratio parameter leads to a decrease in inelastic volume expansion until it remains constant, resulting in the cohesionless soil exhibiting plastic flow characteristics. The damage ratio parameter index for cohesionless soils under different failure modes is quantified: high confining pressure plastic flow (0.69≤...). ≤1.05) and triaxial isobaric plastic flow ( = 0.5). Through analysis of the triaxial strength and internal friction angle test results of various cohesionless soils, and comparison with the Mohr-Coulomb criterion, Lade-Duncan criterion, and SMP criterion, the damage ratio strength theory has high accuracy and reflects the variation law of the internal friction angle of cohesionless soil with the intermediate principal stress coefficient, mean principal stress, and minimum principal stress.

[0053] The present invention also provides an electronic device comprising one or more processors; a memory; and one or more application programs, wherein the one or more application programs are stored in the memory and configured to be executed by the one or more processors, and the one or more application programs are configured to perform the strength prediction method based on the damage specific strength theory of cohesive soil as described above.

[0054] Of course, those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.). The program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The storage medium can be a memory, magnetic disk, optical disk, etc.

[0055] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A strength prediction method based on the damage specific strength theory of cohesionless soil, characterized in that, Includes the following steps: S1. Constructing a theoretical framework for the damage specific strength of cohesionless soil: Based on the strain decomposition assumption and the unit volume energy dissipation rate extreme value calculation model, a general expression for the strength criterion of cohesionless soil under triaxial compressive stress is established. S2, Establish stress parameter transformation relationship: Convert principal stresses into generalized stress parameters, substitute them into the generalized expression of strength criterion to obtain the generalized stress form of strength criterion; S3, Determine the expression for the damage ratio variable and empirical coefficients: Establish the expression for the damage ratio based on the strength envelope characteristics of cohesionless soil, and determine the corresponding empirical coefficients according to the type of cohesionless soil to obtain the optimized strength criterion; S4, Strength Prediction and Verification: Substitute the stress parameters of the target cohesionless soil into the optimized strength criterion to calculate the predicted strength value of the cohesionless soil, and verify the prediction accuracy by combining true triaxial test data.

2. The strength prediction method based on the damage specific strength theory of cohesionless soil according to claim 1, characterized in that, In S1, the strain decomposition assumption is as follows: it is assumed that the total longitudinal strain and the total transverse strain of cohesionless soil are both decomposed into elastic strain and inelastic strain, as expressed below: (1) (2) In the formula, ε is the total longitudinal strain, ε e For longitudinal elastic strain, ε ine ε' is the longitudinal inelastic strain; ε′ is the transverse total strain. e For transverse elastic strain, ε′ ine For transverse inelastic strain; where ε′ and ε′ are... e and ε′ ine They are represented as follows: (3) In the formula, v is the lateral deformation coefficient, v0 is Poisson's ratio, and v r This represents the damage deformation coefficient of the inelastic strain portion.

3. The strength prediction method based on the damage specific strength theory of cohesionless soil according to claim 2, characterized in that, In S1, the derivation process of the unit cell energy dissipation rate extreme value calculation model is as follows: Treating the cohesionless soil as an isotropic material, and using inelastic principal strain as the main energy dissipation mechanism in the failure process, the unit cell energy dissipation rate calculation model is... for: (4) In the formula, σ i Let i = 1, 2, 3, be the nominal principal stresses of the element at the start of failure, σ1 be the maximum principal stress, σ2 be the intermediate principal stress, and σ3 be the minimum principal stress. Let t be the inelastic principal strain rate; The expression for the inelastic principal strain rate is derived by combining the strain decomposition relationship. After substituting it into the calculation model formula (4) for the energy dissipation rate of the unit volume, the strength criterion constraint condition is introduced by the Lagrange multiplier method: （9） The general expression for the strength criterion is obtained as follows: (13) In the formula, v D,c The pressure damage ratio.

4. The strength prediction method based on the damage specific strength theory of cohesionless soil according to claim 3, characterized in that, The generalized stress parameters in S2 include the average principal stress, generalized shear stress, and Lode angle. Converting principal stresses to generalized stress parameters includes converting principal stresses to mean principal stresses. p Generalized shear stress q The Lode angle represents the triaxial intensity. (14) In the formula, σ1 is the maximum principal stress, σ2 is the intermediate principal stress, and σ3 is the minimum principal stress.

5. The strength prediction method based on the damage specific strength theory of cohesionless soil according to claim 4, characterized in that, In S2, substituting the general expression for the strength criterion yields the generalized stress form of the strength criterion, specifically including: Substituting equation (14) into equation (13), we obtain the generalized stress form corresponding to equation (13): (15) In the formula, q For generalized shear stress, p For the mean principal stress, v D,c The pressure damage ratio.

6. The strength prediction method based on the damage specific strength theory of cohesionless soil according to claim 5, characterized in that, In S3, the strength envelope characteristics of cohesive soil include closed, smooth, and convex surfaces, and the damage ratio decreases monotonically with hydrostatic stress; the damage ratio expression is a four-empirical coefficient damage ratio expression.

7. The strength prediction method based on the damage specific strength theory of cohesionless soil according to claim 6, characterized in that, In S3, the expression for the four empirical coefficient damage ratio is as follows: (16) In the formula, p is the mean principal stress. θ For Lode angle, a 1. a 2. a 3. a 4 is the empirical coefficient; where ( p - a 1) The term reflects the intersection of the meridian and the hydrostatic stress axis at... a 1, and p = a At 1 o'clock, v D ,c It converges to 0.

5. a The value of 2 affects the convexity of the deviated plane. a 2. a 3 and a 4 Reflecting Lode Angle θ The resulting slope change pattern, and The term has the property of being continuously differentiable.

8. The strength prediction method based on the damage specific strength theory of cohesionless soil according to claim 7, characterized in that, In S3, the method for determining the empirical coefficient is as follows: when p = a Meridians at different Lode angles intersect at the same point. a 1. a 3 and a 4 represents (19) parameter a 1- a 4. The details of the value selection method are as follows: Preliminary determination is made based on the test data along the tension / compression meridian. A 1. B 1. A 2. B 2 takes a value, and A 1. B 1. A 2 and B The value of 2 must ensure that the tension / compression meridian intersects the hydrostatic stress axis at the same point; A 1. B 1. A 2 and B Substituting the value of 2 into equation (19) yields a 1. Value; a The value of 2 is closely related to whether the deviated plane is convex; 1 < a 2≤1.5, adjusted to simplify calculation. a The value of 2 satisfies the convexity of the partial plane; a Substituting the value of 2 into equation (19) yields a 3 and a 4. Values.

9. The strength prediction method based on the damage specific strength theory of cohesionless soil according to claim 8, characterized in that, The empirical coefficients determined based on the type of cohesive soil are specifically chosen as follows: When the non-cohesive soil is Monterey sand, Santa Monica Beach sand, or aeolian sand: a 1 = 3000 a 2 = 1.18 a 3 = -0.000129 a 4 = 0.000014; When the non-cohesive soil is gravel: a 1 = 4000 a 2 = 1.18 a 3 = -0.000156 a 4 = 0.00001; When the non-cohesive soil is granular: a 1 = 5000 a 2 = 1.07 a 3 = -0.00015 a 4 = 0.000008; When the non-cohesive soil is coarse-grained: a 1 = 11200 a 2 = 1.1, a 3 = -0.00006 a 4 = 0.000003.

10. The strength prediction method based on the damage specific strength theory of cohesionless soil according to claim 8, characterized in that, S4 also includes the calculation of the internal friction angle. φ b The relationship with the intermediate principal stress coefficient b is derived through the following formula: different b Experimental internal friction angle at value φ b The definition of is: (22) intermediate principal stress coefficient b The value is: (23) Substituting equations (22) and (23) into the expression for the soil damage ratio strength criterion, and rearranging, we obtain the corresponding strength criterion. φ b about b The implicit functional relationship is: (24) In the formula, .

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