Construction method of water-containing rock damage statistical constitutive model considering compaction deformation

Abstract

The invention discloses a construction method of a water-containing rock damage statistical constitutive model considering compaction deformation, which comprises the following steps: carrying out a uniaxial compression test on a rock sample to obtain an axial stress-axial strain curve and a demarcation point in a compaction stage and a linear elasticity stage in the axial stress-axial strain curve; a sigmoid function is introduced, and the constitutive relation of the water-containing rock in the microfracture compaction stage is constructed; acquiring a damage variable after coupling of rainfall damage and stress damage caused by rock moisture infiltration; based on a damage statistical theory, constructing a constitutive relationship between a linear elasticity stage and a damage softening stage after a microfracture compaction stage of the water-containing rock; and constructing a damage statistical constitutive model of the water-containing rock considering compaction deformation. The constitutive curve corresponding to the constitutive model well reflects the compaction characteristic, the elastic characteristic, the damage softening characteristic and other deformation characteristics of the rock mass, and high prediction precision and practical application value are shown.

Description

Technical Field

[0001] The present invention relates to the technical field of engineering structures, and in particular to a method for constructing a statistical constitutive model of water-bearing rock damage taking compaction deformation into consideration. Background Art

[0002] In 1958, Soviet scholar I.M. Kachanov [1] In the study of creep problems of metal materials, the concept of damage mechanics was proposed, and the concepts of "continuity factor" and "effective stress" were proposed. In 1971, based on the principle of irreversible process thermodynamics, French scholar J. Lemaitre [2] and JL Chaboche [3] Using the continuum mechanics method, the discipline of "damage mechanics" was proposed. On this basis, A.Dragon [4] Based on the concept of fracture surface, the brittle plastic damage characteristics of rock were studied and the corresponding continuum model was established. Since then, scholars from all over the world have adopted various research methods and proposed a large number of geometric expressions of damage variables based on different angles to describe the expression relationship between elastic constants and damage in continuum mechanics. [5] Based on the microplane theory, the relationship between macroscopic and microscopic constitutive properties is analyzed, and the process of combining microscopic mechanics with microplane theory is explained. The specific idea is to use microplanes in each step of modeling, and finally derive the microplane damage criterion of open and closed cracks characterized by damage driving force. In particular, the plastic yield criterion describing the static friction characteristics and shear dilation effect of closed cracks is established. This criterion well explains the physical and mechanical mechanism of closed crack cohesion and reasonably considers the weakening effect of cohesion during the stress process. In addition, there is J.Kemeny [6] , DOPotyondy [7] , E.Hoek [8] , Li Changchun [9] , Ling Jianming

[10] , Wu Lixin

[11] Many domestic and foreign scholars have made outstanding contributions to rock damage mechanics, laying a solid theoretical foundation for the further development of damage mechanics in the future.

[0003] Due to the effects of geological movement and tectonic stress fields, a large number of cracks, fissures and fissures of different sizes and irregular spatial distribution are formed in rocks, which play a vital role in the strength and failure mode of rock masses. Domestic and foreign scholars have conducted extensive research on the geometric morphology and physical and mechanical properties of these defects.

[12] For example, T.Kyoya, Y.Ichikawa, T.Kawamoto, etc. summarized randomly distributed cracks as isotropic damage, and then used the second-order symmetric damage tensor to describe anisotropic damage, established a geometric expression of damage variables, and extended it to the analysis process of the finite element method. Zhou Weiyuan et al.

[13] By introducing the second-order damage tensor and describing the internal connectivity of the rock mass as a continuous function, an implicit expression of the shear yield criterion for anisotropic jointed rock mass is established, and the influence of the parameters related to the second-order damage tensor on the anisotropy of rock mass yield is analyzed.

[14] Using the second-order tensor to describe the anisotropic damage inside the rock mass, a method for calculating the initial damage tensor of jointed rock mass was proposed based on the existing crack probability statistical model, and compared with other calculation methods.

[15] By defining the damage of multi-crack rock mass, a model of equivalent secondary cracks generated during crack extension was established, and then the evolution equation of fracture damage of multi-crack rock mass was explored, and the effectiveness of the model was verified through experiments.

[16] Based on statistical damage theory, a new three-dimensional damage constitutive model was established. Then, based on the Mohr-Coulomb criterion, a microelement strength function was constructed, and a damage evolution equation considering the post-peak morphology was established. The theoretical calculation results of the model are consistent with the results of conventional triaxial compression tests on gravel-bearing coarse sandstone and siltstone, revealing the damage mechanics mechanism of the phenomenon of weakening bond resistance and strengthening friction resistance during rock loading. Tao Zhenyu et al.

[17] Based on the effective field theory, the interaction between non-penetrating joints and cracks is described geometrically, and the damage constitutive equation of non-penetrating jointed rock mass under engineering conditions is derived.

[18] Using the three-dimensional model rheology-damage coupling calculation method, the stability analysis of the underground powerhouse cavern group of Jinping I Hydropower Station was carried out, and the long-term rheological deformation of the cavern was predicted.

[19] A microscopic damage mechanism model that can uniformly describe weak planes, open and closed cracks, and micropores was proposed, and a coupled constitutive model of anisotropic plasticity-damage-hydraulic fracturing of rock materials was established. On this basis, a two-dimensional numerical simulation program was written to simulate the failure behavior of heterogeneous materials.

[20] The research status of the physical and mechanical properties of rocks under low temperature and freeze-thaw cycle conditions at home and abroad, as well as the temperature, seepage characteristics and water, heat and force coupling characteristics are summarized and prospected. The temperature-seepage-stress-damage coupling model of cold zone tunnels under ventilation conditions proposed by our team is also explained. [21,22] Based on damage mechanics, a series of damage statistical constitutive models applicable to zigzag nodes were established. Li, Zhao et al.

[23] Inspired by the Ivan Wan concept, a reduced-order constitutive model with reduced degrees of freedom of the contact interface was proposed. Li et al. [24,25] A discontinuum degradation analysis model was established, and a constitutive model centered on rock fragment filling was further proposed to predict the shear behavior of discontinuum.

[26] and Simo et al.

[27] A series of empirical models were also proposed to describe the nonlinear elastic shear stress-displacement relationship of discontinuous surfaces.

[28] The rock damage variable based on crushing energy consumption was established by separating the total dissipated energy of rock; Huang Zhengjun et al.

[29] The dynamic fatigue characteristics and damage evolution laws of granite under different volume strain rates were revealed. Due to the complexity of the rock damage process, it is often difficult to accurately describe it macroscopically, and statistical analysis and nonlinear elastic analysis have to be used. Cao Wengui et al.

[30] A statistical damage constitutive model that can simulate the entire process of rock deformation was established; Zhang Chao et al.

[31] proposed a rock statistical damage characterization variable and its evolution model considering the damage strain threshold; Liang Mingchun et al.

[16] A new three-dimensional damage constitutive model considering the shear dilatancy and expansion characteristics of rock was established based on statistical damage theory.

[0004] Existing constitutive model research has focused not only on model construction and validation but also on the models' scope of applicability and limitations. This research provides important theoretical support for geotechnical engineering, helping to improve the safety and reliability of projects. However, constitutive model research still faces many challenges. Future research needs to further explore how to improve the models' predictive capabilities and accuracy to promote their application and development in geotechnical engineering.

[0005] [1]Zhang X, Lin H, Wang Y, et al. Creep damage model of rock mass undermulti-level creep load based on spatio-temporal evolution of deformationmodulus[J]. Archives of Civil and Mechanical Engineering, 2021, 21(2).

[0006] [2]Lemaitre J,Sermage J P,Desmorat R.Atwo scaledamage concept appliedto fatigue[J].International Journal of Fracture,1999,97(1-4):67-81.

[0007] [3]Chaboche J L,Maire J F.New progress in micromechanics-based CDMmodels and their application to CMCs[J].Composites Science and Technology,2001,61(15):2239-2246.

[0008] [4]Dragon A,Halm D,Désoyer T.Anisotropic damage in quasi-brittlesolids::modelling,computational issues and applications[J].Computer Methodsin Applied Mechanics and Engineering,2000,183(4):331-352.

[0009] [5]Kong L,Xie H,Li C.Coupled microplane and micromechanics model fordescribing the damage and plasticity evolution of quasi-brittle material[J].International Journal of Plasticity,2023,162.

[0010] [6]Kemeny J.The Next Step in Micromechanical Studies of RockDeformationand Failure:Experiments and Theory for More Complicated ValueProblems that Include Stress Gradient Effects[J].National Science Foundation,1991.

[0011] [7]Potyondy DO, Cundall P A.Abonded-particle model for rock[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(8):1329-1364.

[0012] [8]Hoek E, Diederichs M S. Empirical estimation of rock mass modulus[J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(2):20215.

[0013] [9] Li Changchun, Chen Li, Hao Li, et al. Microscopic damage constitutive relation of rock-like brittle materials[J]. Rock and Soil Mechanics, 1989, (2): 55-68.

[0014]

[10] Ling Jianming, Sun Jun. Rock failure criterion based on damage strain space[J]. Journal of Tongji University (Natural Science Edition), 1995, (5): 48487.

[0015]

[11] Wu Lixin, Wang Jinzhuang, Meng Shunli. Instant compression SEM study on the damage expansion law of coal and rock[J]. Chinese Journal of Rock Mechanics and Engineering, 1998, (1): 9-15.

[0016]

[12] Zhao Yangsheng. A review of the development of rock mechanics and some unsolved problems over the past century [J]. Chinese Journal of Rock Mechanics and Engineering, 2021, 40(7): 1297-1336.

[0017]

[13] Yang Qiangchen, Zhou Weiyuan. Anisotropic yield criterion for jointed rock mass based on second-order damage tensor[J]. Chinese Journal of Rock Mechanics and Engineering, 2005, (8): 1275-1282.

[0018]

[14] Wu Peng. Damage model and nonlinear elastic finite element analysis of jointed rock mass[J]. Chinese Journal of Rock Mechanics and Engineering, 1988, (3): 19202.

[0019]

[15] Xu Jingnan, Zhu Weishen, Bai Shiwei. Mechanical properties of multi-fracture rock mass under compressive shear stress: fracture damage evolution equation and experimental verification [J]. Rock and Soil Mechanics, 1994, (2): 1-12.

[0020]

[16] Liang Mingchun, Miao Shengjun, Cai Meifeng, et al. Rock damage constitutive model considering shear dilatancy and post-peak morphology [J]. Chinese Journal of Rock Mechanics and Engineering, 2021, 40(12): 2392-2401.

[0021]

[17] Li Haotao. Effective field and damage constitutive relationship of non-penetrating jointed rock mass[J]. Journal of Wuhan University of Hydraulic and Electric Engineering, 2000, (3): 5-8.

[0022]

[18] Zhu Weishen, Qi Yinping, Guo Yunhua, et al. Three-dimensional damage rheological analysis of deformation and fracture of surrounding rock of underground powerhouse of Jinping I hydropower station [J]. Chinese Journal of Rock Mechanics and Engineering, 2012, 31(5): 865-872.

[0023]

[19] Yang Qiang. Dam failure simulation and localized damage analysis of rock materials[M]. Beijing: Tsinghua University, 2009.

[0024]

[20] Chen Weizhong, Tan Xianjun, Yu Hongdan, et al. Research progress and thinking on thermal, hydraulic and mechanical properties of rock mass under low temperature and freeze-thaw environment [J]. Chinese Journal of Rock Mechanics and Engineering, 2011, 30(7): 1318-1336.

[0025]

[21] Xie SJ, Lin H, Wang YX, et al.Nonlinear shear constitutive model for peak shear-type joints based on improved Harris damage function[J].ArchCiv Mech Eng,2020,20(3).

[0026]

[22] Xie S, Lin H, Chen Y, et al. Adamage constitutive model for shearbehavior of joints based on determination of the yield point[J]. International Journal of Rock Mechanics and Mining Sciences, 2020,128.

[0027]

[23] Iwan W D.On a class of models for yielding behavior of continuous and composite systems[J].J Appl Mech,1967,34(3):612-&.

[0028]

[24] Li Y, Oh J, Mitra R, et al. A constitutive model for a laboratoryrock joint with multi-scale asperity degradation[J]. Comput Geotech, 2016,72:14151.

[0029]

[25] Li Y, Wu W, Tang Ca, et al. Predicting the shear characteristics of rock joints with asperity degradation and debris backfilling under cyclic loading conditions [J]. International Journal of Rock Mechanics and MiningSciences, 2019, 120: 108-118.

[0030]

[26] Tang Z,Xia C,Xiao S.Constitutive model for joint shear stress-displacement and analysis of dilation[J].Chin J Rock Mech Eng,2011,30(5):917-925.

[0031]

[27] Simon R,Aubertin M,Mitri H.Anon-linear constitutive model for rock joints to evaluate unstable slip;proceedings of the Vail Rocks 1999,The37th US Symposium on Rock Mechanics(USRMS),F,1999[C].American Rock MechanicsAssociation.

[0032]

[28] Miao Shengjun, Liu Zejing, Zhao Xingguang, et al. Energy dissipation and damage characteristics of Beishan granite under cyclic loading[J]. Chinese Journal of Rock Mechanics and Engineering, 2021, 40(5): 928-938.

[0033]

[29] Huang Zhengjun, Zhao Xingguang, Li Yuan, et al. Effect of volume strain rate on fatigue properties of Beishan granite[J]. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(5): 1161-1168.

[0034]

[30] Cao Wengui, Yang Shang, Zhang Chao. Statistical damage constitutive model of rock considering the change of elastic modulus[J]. Hydrogeology and Engineering Geology, 2017, 44(3): 42-48.

[0035]

[31] Zhang Chao, Yang Chuqing, Bai Yun. Research on damage evolution analysis and modeling methods of rock-like brittle materials[J]. Rock and Soil Mechanics, 2021, 42(9): 2344-2354. Summary of the Invention

[0036] Based on this, the purpose of the present invention is to provide a method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation, which demonstrates high prediction accuracy and practical application value.

[0037] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0038] The present invention provides a method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation, which comprises the following steps:

[0039] S1. Conduct a uniaxial compression test on the rock sample to obtain an axial stress-axial strain curve and a dividing point between the compaction stage and the linear elastic stage in the axial stress-axial strain curve. Based on the dividing point, the axial stress-axial strain curve is divided into an axial stress-axial strain curve corresponding to the constitutive relationship of the microcrack compaction stage and an axial stress-axial strain curve corresponding to the constitutive relationship of the rock after microcrack compaction;

[0040] S2. Introduce the sigmoid function to construct the constitutive relationship of micro-cracks and compaction stage of water-bearing rocks;

[0041] S3. Obtain the damage variable D after coupling the rainfall damage and stress damage caused by rock water infiltration. w +D l -D w D l , where D w It is the damage caused by rainfall, D l It is the damage caused by loading stress;

[0042] S4. Based on the damage statistics theory, the constitutive relations of the linear elastic stage and the damage softening stage after the micro-crack compaction stage of water-bearing rock are constructed:

[0043] σ=E ew (ε-ε m )(1-D)+σr D,(ε>ε cc ),

[0044] Among them, E ew is the value of elastic modulus E after rainfall, σ r is the residual strength, ε cc is the axial strain value corresponding to the boundary between the compaction stage and the linear elastic stage, ε m is the axial strain value corresponding to the intersection of the extension line of the linear elastic stage curve and the axis where the axial strain is located;

[0045] S5. Combine steps S2 and S4 to construct a damage statistical constitutive model of water-bearing rock considering compaction deformation.

[0046] 2. The method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation according to claim 1, wherein the constitutive relationship of the microcracks of the water-bearing rock during the compaction stage is:

[0047]

[0048] Among them, z1, z2, and z3 represent the shape parameters of the rock cavity, and E i is the initial value of the elastic modulus E, E ew is the value of the elastic modulus E after rainfall.

[0049] In one embodiment, the method of step S2 comprises the following steps:

[0050] S21. Establish the constitutive model of the nonlinear elastic growth gap closing stage in the axial stress-axial strain curve σ=f(E,ε)ε,(ε<ε cc ); where elastic modulus E = f(E,ε). In the compaction stage at the beginning of loading, due to the compaction of the initial pores, the elastic modulus of the rock mass will continue to increase, resulting in the constitutive model of the nonlinear elastic growth gap closure stage in the axial stress-axial strain curve, which can be expressed as:

[0051] σ=f(E,ε)ε,(ε<ε cc ) (1);

[0052] S22. When ε=0, the elastic modulus activation is 0, f(E,ε)=E i ,

[0053] That is, f ε＝0 (E,ε)=E i (2);

[0054] When the pores are completely closed, ε = ε cc , the elastic modulus is fully activated, and the crack closure stress σ cc satisfy

[0055] σ cc =E ew (ε cc -ε m ),

[0056] That is to say

[0057]

[0058] , at this time the elastic modulus activation degree is 1, ε cc is the axial strain value corresponding to the boundary between the compaction stage and the linear elastic stage, E ew is the value of elastic modulus E after rainfall;

[0059] S23. Introducing the sigmoid function Combining formulas (1) to (3), the specific function formula of the elastic modulus E is obtained as follows:

[0060]

[0061] S24. Substitute formula (4) into formula (1) to obtain the constitutive relationship of water-bearing rock in the microcrack compaction stage:

[0062]

[0063] In one embodiment, the method of step S4 comprises the following steps:

[0064] S41. Assume that there are N discontinuous units in the rock mass, N→∞, and the area of ​​each unit is A0. Then the total loaded area A is expressed as:

[0065] A=NA0 (5),

[0066] The rock mass load F is composed of the load σ of each unit i Summing gives:

[0067]

[0068] Among them, E ew is the value of elastic modulus E after rainfall;

[0069] S42. Assume that the number of damaged units at any time after entering the damage softening stage is q, and the number of intact units is Nq. Combining formula (5) and formula (6), the rock load F in the linear elastic stage and the damage softening stage can be calculated by the sum of the forces on the intact units and the damaged units:

[0070]

[0071] Among them, σ r Refers to residual strength;

[0072] S43. Combined with formula (7), the rock mass load F is divided by the total unit area A to obtain the expression of stress σ in the linear elastic stage and damage softening stage:

[0073]

[0074] Formula (8) can be further simplified as:

[0075]

[0076] S44. According to the Lemaitre strain equivalence theory, the damage variable D = q / N is substituted into formula (9) to construct the constitutive relationship of the linear elastic stage and the damage softening stage after the micro-crack compaction stage of water-bearing rock:

[0077] σ=E ew (ε-ε m )(1-D)+σ r D,(ε>ε cc ) (10),

[0078] Among them, ε cc is the strain at the beginning of the linear elastic stage, E ew is the value of the elastic modulus E after rainfall.

[0079] In one embodiment, the method of step S3 comprises the following steps:

[0080] S31. Based on the strain equivalence theory, the damage variable D after coupling of rainfall damage and stress damage caused by rainfall on rock mass satisfies:

[0081] D=D w +D l -D w D l (11);

[0082] S32. Rainfall damage D caused by rainfall based on elastic modulus calculation method w Expressed as:

[0083]

[0084] Among them, E ew is the value of elastic modulus E after rainfall, E d is the elastic modulus in the dry state;

[0085] S33, using the improved Harris distribution function

[0086] Obtain stress damage D l The evolution equation is:

[0087]

[0088] Among them, F a is the microscopic unit strength of rock, a and b are the model parameters of the mechanical properties of rock materials;

[0089] S34, based on the damage initiation point as the dividing point between the linear elastic stage and the damage softening stage, the yield stress σ y is the damage threshold, formula (13) can be transformed into:

[0090] F a =E ew (ε-ε m )-σ y (15),

[0091] Yield stress σ y satisfy:

[0092] σ y =E ew (ε y -ε m ) (16),

[0093] Among them, ε y is the yield stress point σ y corresponding strain;

[0094] S35. Combine formulas (14)-(16) to obtain stress damage D l The expression:

[0095]

[0096] S36. Combining formulas (11)-(12) and (17), the damage variable D after coupling of rainfall damage and stress damage caused by rainfall in rock mass is obtained:

[0097]

[0098] In one embodiment, the method of step S5 is specifically performed as follows:

[0099] Substituting formula (18) into formula (10) and combining it with formula (18), the damage statistical constitutive model of water-bearing rock considering the compression deformation in the whole process can be obtained:

[0100]

[0101] In one embodiment, after S36, the following further includes

[0102] S37. Obtain the values ​​of model parameters a and b.

[0103] In one embodiment, it is characterized in that the method of step S37 specifically operates as follows:

[0104] Based on the axial stress-axial strain curve, the peak stress point (ε p ,σ p ) is equal to 0, when ε=ε p When , the derivative of ε in formula (19) can be obtained:

[0105]

[0106] Because ε p >ε y , the coordinate value corresponding to the peak stress point (ε p ,σ p ) is substituted into formula (19) to obtain:

[0107]

[0108] Combining formulas (19) to (20), we can obtain the expressions of a and b:

[0109]

[0110] In summary, the present invention provides a method for constructing a statistical constitutive model of damage of water-bearing rock considering compaction deformation. By dividing the axial stress-axial strain curve into the axial stress-axial strain curve corresponding to the constitutive relationship of the microcrack compaction stage and the axial stress-axial strain curve corresponding to the constitutive relationship of the rock after microcrack compaction, the constitutive relationship of the microcrack compaction stage of water-bearing rock and the constitutive relationship of the linear elastic stage and the damage softening stage after the microcrack compaction stage of water-bearing rock are respectively constructed, so that the constitutive curve corresponding to the constitutive model better reflects the deformation characteristics of the rock mass such as compaction characteristics, elastic characteristics, damage softening characteristics, etc., and shows high prediction accuracy and practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0111] Figure 1 A schematic flow chart of a method for constructing a statistical constitutive model of water-bearing rock damage taking into account compaction deformation provided by an embodiment of the present invention;

[0112] Figure 2 A graph showing the relationship between axial strain and axial stress in a method for constructing a statistical constitutive model of water-bearing rock damage taking into account compaction deformation provided by an embodiment of the present invention;

[0113] Figure 3 A schematic diagram of the principle of progressive damage of rock mass under uniaxial compression provided by an embodiment of the present invention;

[0114] Figure 4A combined schematic diagram of rainfall damage and stress damage is provided for an embodiment of the present invention;

[0115] Figure 5 A schematic diagram comparing the calculated values ​​and experimental results of the constitutive model provided in an embodiment of the present invention;

[0116] Figure 6 A schematic diagram comparing the calculated values ​​of a method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation provided by an embodiment of the present invention with the calculated values ​​of other model methods. DETAILED DESCRIPTION

[0117] In order to further understand the features, technical means, specific objectives and functions achieved by the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0118] Figure 1 FIG. 1 is a flow chart of a method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation provided by an embodiment of the present invention. Figure 1 As shown in FIG, a method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation specifically includes the following steps:

[0119] S1. Conduct a uniaxial compression test on the rock sample to obtain an axial stress-axial strain curve and a dividing point between the compaction stage and the linear elastic stage in the axial stress-axial strain curve. Based on the dividing point, the axial stress-axial strain curve is divided into an axial stress-axial strain curve corresponding to the constitutive relationship of the microcrack compaction stage and an axial stress-axial strain curve corresponding to the constitutive relationship of the rock after microcrack compaction; wherein, conduct a uniaxial compression test on the rock sample, establish a first rectangular coordinate system, and obtain the axial stress-axial strain curve.

[0120] like Figure 2 As shown in Figure 1, rock failure is a progressive damage process. Based on the damage statistics theory, a constitutive model describing the mechanical behavior of rock can be effectively constructed. The typical rock stress-strain curve can be divided into four stages according to the stage characteristics:

[0121] (1) I-microcrack compaction stage (0<σ<σ cc ), due to the formation and subsequent geological effects, there are a large number of microcracks in the rock mass. As the loading occurs, these pre-existing microcracks will be continuously compacted, resulting in plastic deformation and evolution of mechanical properties. The stress is less than σ cc When the original microcracks are compacted, the mechanical properties of the rock mass are enhanced, and the slope of the σ-ε curve increases with loading; m is the axial strain value corresponding to the intersection of the extension line of the linear elastic stage curve and the axis where the axial strain is located, ε cc The stress is σcc The strain at , corresponds to the axial strain value at the junction of the compaction stage and the linear elastic stage.

[0122] (2)II-elastic stage (σ cc <σ<σ y ), in this stage, the σ-ε curve is quasi-linear, where the slope of the σ-ε curve is the rock elastic modulus E. In this process, the number of rock units that change from the non-destructive state to the damaged state is very small, so all rock units are considered to be in the non-destructive state; y When the stress is σ y The corresponding strain is the axial strain value corresponding to the inflection point when the elastic modulus begins to decay.

[0123] (3) III-damage softening stage (σ y <σ<σ p ). In this stage, the nonlinear deformation characteristics of the rock mass begin to become obvious. Compared with the previous stage, with the increase of strain ε, the stress increases nonlinearly, but the rate of increase continues to slow down. At this time, the number of rock units converted to the damaged state increases significantly; ε p The stress is σ p The strain at the time corresponds to the axial strain value corresponding to the coordinate point at the peak stress in the axial stress-axial strain curve.

[0124] (4)IV-post-peak stage (σ p <σ<σ r ). In this stage, with the increase of strain ε, stress σ drops sharply, the internal cementation of the rock mass is largely destroyed, cracks expand and penetrate throughout the rock mass, and the number of rock units in a damaged state increases greatly.

[0125] S2. The sigmoid function is introduced to describe the slow activation state of the elastic modulus of the rock mass during the compaction stage, and the constitutive relationship of the micro-crack compaction stage of water-bearing rock is constructed:

[0126]

[0127] Among them, z1, z2, and z3 represent the shape parameters of the rock cavity, and E i is the initial value of the elastic modulus E, E ew is the value of the elastic modulus E after rainfall.

[0128] like Figure 2 As shown, the method of step S2 specifically includes the following steps:

[0129] S21. Establish the constitutive model of the nonlinear elastic growth gap closing stage in the axial stress-axial strain curve σ=f(E,ε)ε,(ε<ε cc); where elastic modulus E = f(E,ε). In the compaction stage at the beginning of loading, due to the compaction of the initial pores, the elastic modulus of the rock mass will continue to increase, resulting in the constitutive model of the nonlinear elastic growth gap closure stage in the axial stress-axial strain curve, which can be expressed as:

[0130] σ=f(E,ε)ε,(ε<ε cc ) (1);

[0131] S22. When ε=0, the elastic modulus activation is 0, f(E,ε)=E i ,

[0132] That is, f ε＝0 (E,ε)=E i (2);

[0133] When the pores are completely closed, ε = ε cc , the elastic modulus is fully activated, and the crack closure stress σ cc satisfy

[0134] σ cc =E ew (ε cc -ε m ),

[0135] That is to say

[0136]

[0137] , at this time the elastic modulus activation degree is 1, ε cc is the axial strain value corresponding to the boundary between the compaction stage and the linear elastic stage, E ew is the value of elastic modulus E after rainfall;

[0138] S23. Introducing the sigmoid function Combining formulas (1) to (3), the specific function formula of the elastic modulus E is obtained as follows:

[0139]

[0140] In the present invention, the sigmoid function is often used as an activation function to describe the slowly activated state of the rock mass elastic modulus.

[0141] S24. Substitute formula (4) into formula (1) to obtain the constitutive relationship of water-bearing rock in the microcrack compaction stage:

[0142]

[0143] S3. Obtain the damage variable D after coupling the rainfall damage and stress damage caused by rock water infiltration. w +Dl -D w D l , where D w It is the damage caused by rainfall, D l It is the damage caused by loading stress.

[0144] S4. Based on the damage statistics theory, the constitutive relations of the linear elastic stage and the damage softening stage after the micro-crack compaction stage of water-bearing rock are constructed:

[0145] σ=E ew (ε-ε m )(1-D)+σ r D,(ε>ε cc ),

[0146] Among them, E ew is the value of elastic modulus E after rainfall, σ r is the residual strength, ε m It is the axial strain value corresponding to the intersection of the extension line of the linear elastic stage curve and the axis where the axial strain lies.

[0147] The method of step S4 specifically includes the following steps:

[0148] S41, such as Figure 3 As shown, it is assumed that there are N discontinuous units in the rock mass, N→∞, and the area of ​​each unit is A0, then the total loaded area A can be expressed as:

[0149] A=NA0 (5),

[0150] The rock mass load F can be obtained from the load σ of each unit i Summing gives:

[0151]

[0152] Among them, E ew is the value of the elastic modulus E after rainfall.

[0153] When the rock mass deformation is in the linear elastic stage, the relationship between stress and strain is linear elastic. In this stage, all elements are considered intact. When the rock mass deformation enters the damage softening stage, some intact elements begin to transform into failed elements.

[0154] S42. Assume that the number of damaged units at any time after entering the damage softening stage is q. Since the damaged units are converted from intact units, the number of intact units at this time is Nq. Combining formula (5) and formula (6), the rock load F in the linear elastic stage and the damage softening stage can be calculated by the sum of the forces of the intact units and the damaged units:

[0155]

[0156] Among them, σ r Refers to residual strength;

[0157] S43. Combining formula (7), dividing the rock mass load F by the total unit area A, we can obtain the expression of stress σ in the linear elastic stage and damage softening stage:

[0158]

[0159] Formula (8) can be further simplified as:

[0160]

[0161] S44. According to the Lemaitre strain equivalence theory, the damage variable D = q / N is used to describe the damage degree of the rock mass after entering the damage softening stage. Substituting it into formula (9), the damage constitutive relation of the rock mass under load can be further transformed, and then the constitutive relation of the linear elastic stage and the damage softening stage after the micro-crack compaction stage of water-bearing rock can be constructed:

[0162] σ=E ew (ε-ε m )(1-D)+σ r D,(ε>ε cc ) (10),

[0163] Among them, ε cc is the strain at the beginning of the linear elastic stage, E ew is the value of elastic modulus E after rainfall, σ r is the residual strength.

[0164] like Figure 4 As shown in Figure 1, during rainfall, the infiltration of rainwater not only weakens the cementation between internal particles but also reduces the friction between particles, seriously affecting the mechanical properties of the rock mass. Therefore, when studying the mechanical properties of rock mass under rainfall conditions, it is necessary to consider both rainfall damage caused by rainfall and stress damage caused by stress, namely the damage variable D.

[0165] The method of step S3 is specifically performed as follows:

[0166] S31. Based on the strain equivalence theory, the damage variable D after coupling of rainfall damage and stress damage caused by rainfall on rock mass satisfies:

[0167] D=D w +D l -D w D l (11),

[0168] Among them, D wIt is the damage caused by rainfall, D l It is the damage caused by loading stress.

[0169] From formula (11), we can see that when there is only stress damage in the rock mass, that is, rainfall damage D w =0, coupling damage D = D l ; When stress damage D l = 0, the coupling damage D = D w , indicating that the damage expression can be well adapted to the study of mechanical properties under rainfall conditions.

[0170] S32. Rainfall damage D caused by rainfall based on elastic modulus calculation method w It can be expressed as:

[0171]

[0172] Among them, E ew is the value of elastic modulus E after rainfall, E d is the elastic modulus in the dry state.

[0173] S33, using the improved Harris distribution function

[0174] Obtain stress damage D l The evolution equation is:

[0175]

[0176] Among them, the improved Harris distribution function is used to describe the probability density function of rock microunits, F a is the microscopic unit strength (or stress level) of rock, and a and b are the model parameters of the mechanical properties of rock materials.

[0177] S34, based on the damage initiation point as the dividing point between the linear elastic stage and the damage softening stage, the yield stress σ y is the damage threshold, formula (13) can be transformed into:

[0178] F a =E ew (ε-ε m )-σ y (15),

[0179] Yield stress σ y satisfy:

[0180] σ y =E ew (ε y -ε m ) (16),

[0181] Among them, εy is the yield stress point σ y The corresponding strain is the axial strain value corresponding to the inflection point when the elastic modulus begins to decay.

[0182] S35. Combine formulas (14)-(16) to obtain stress damage D l The expression:

[0183]

[0184] S36. Combining formulas (11)-(12) and (17), the damage variable D after coupling of rainfall damage and stress damage caused by rainfall in rock mass can be obtained:

[0185]

[0186] S5. Combine steps S2 and S4 to construct a damage statistical constitutive model of water-bearing rock considering compaction deformation.

[0187] Specifically, the method of step S5 is as follows:

[0188] Substituting formula (18) into formula (10) and combining it with formula (18), the damage statistical constitutive model of water-bearing rock considering the compression deformation in the whole process can be obtained:

[0189]

[0190] In one embodiment, after step S36, the following steps are also included:

[0191] S37. Obtain the values ​​of model parameters a and b.

[0192] The method of step S37 is specifically performed as follows:

[0193] The model parameters a and b are calculated using the "extreme value method":

[0194] Based on the axial stress-axial strain curve, the peak stress point (ε p ,σ p ) has a first-order derivative equal to 0.

[0195] That is, when ε=ε p When , the derivative of ε in formula (19) can be obtained:

[0196]

[0197] Because ε p >ε y , the coordinate value corresponding to the peak stress point (ε p ,σ p ) is substituted into formula (19) to obtain:

[0198]

[0199] Combining formulas (19) to (20), we can obtain the expressions of a and b:

[0200]

[0201] In order to verify the rationality and superiority of the proposed damage statistical constitutive model of water-bearing rock considering compaction deformation, we used formula (19) to fit the test curve to obtain the calculated value of the compaction stage. By comparing the calculated value with the test results, we found that the two are in good agreement, such as Figure 5 shown.

[0202] To further highlight the superiority of the constitutive model of the present invention, a systematic comparative analysis will be conducted. In this process, actual test results are used as the analysis object, and the advantages and disadvantages of each comparison model are evaluated by comparing the consistency between the model calculation value and the test data.

[0203] Among the selected comparison models, two models that are widely used in the field of rock mechanics are further selected: the classic Harris model and the Weibull model.

[0204] Both models do not consider the impact of the compaction stage, so they have limitations in this aspect. The expression of the classic Harris model without considering the compaction stage is:

[0205]

[0206] The Weibull model expression without considering the compaction stage is:

[0207]

[0208] Where m and θ are the material parameters in the Weibull function.

[0209] The main problem with the above two models is that they cannot accurately describe the mechanical response of the rock mass in the initial compaction stage, which may lead to a large deviation between the predicted results and the actual situation in actual engineering applications.

[0210] Furthermore, the following steps were used to compare and analyze the differences among the three different models, specifically including: (1) performing a detailed analysis of the experimental data and extracting key parameters; (2) using the model proposed in this invention as well as the Harris model and the Weibull model to perform calculations and obtain the corresponding stress-strain curves; and (3) comparing the calculated values ​​with the experimental data to evaluate the consistency of each model with the experimental data.

[0211] The comparison results of the three different models are as follows: Figure 6 As shown, the model proposed in this paper is more accurate in describing the progressive failure behavior of rock masses than the other two models, and can accurately reflect the various deformation characteristics of rock masses. It has a significant advantage in describing the compaction characteristics of rock masses, and can capture in detail the subtle differences in the changes in compaction characteristics of rock masses during stress. More importantly, the model proposed in this paper also shows high accuracy in describing the damage softening characteristics, indicating that the model proposed in this paper can effectively reflect the mechanical properties of rock masses during the damage process.

[0212] like Figure 1 As shown, in order to make the technical solution of the present invention clearer, the preferred embodiments are described below.

[0213] S1. Conduct a uniaxial compression test on the rock sample to obtain an axial stress-axial strain curve and a dividing point between the compaction stage and the linear elastic stage in the axial stress-axial strain curve. Based on the dividing point, the axial stress-axial strain curve is divided into an axial stress-axial strain curve corresponding to the constitutive relationship of the microcrack compaction stage and an axial stress-axial strain curve corresponding to the constitutive relationship of the rock after microcrack compaction;

[0214] S2. Introduce the sigmoid function to construct the constitutive relationship of micro-cracks and compaction stage of water-bearing rocks;

[0215] S3. Obtain the damage variable D after coupling the rainfall damage and stress damage caused by rock water infiltration. w +D l -D w D l , where D w It is the damage caused by rainfall, D l It is the damage caused by loading stress;

[0216] S4. Based on the damage statistics theory, the constitutive relations of the linear elastic stage and the damage softening stage after the micro-crack compaction stage of water-bearing rock are constructed:

[0217] σ=E ew (ε-ε m )(1-D)+σ r D,(ε>ε cc ),

[0218] Among them, E ew is the value of elastic modulus E after rainfall, σ r is the residual strength, ε cc is the axial strain value corresponding to the boundary between the compaction stage and the linear elastic stage, ε m is the axial strain value corresponding to the intersection of the extension line of the linear elastic stage curve and the axis where the axial strain is located;

[0219] S5. Combine steps S2 and S4 to construct a damage statistical constitutive model of water-bearing rock considering compaction deformation.

[0220] In summary, the damage statistical constitutive model of water-bearing rock considering compaction deformation of the present invention divides the axial stress-axial strain curve into the axial stress-axial strain curve corresponding to the constitutive relationship of the microcrack compaction stage and the axial stress-axial strain curve corresponding to the constitutive relationship of the rock after microcrack compaction, and respectively constructs the constitutive relationship of the microcrack compaction stage of water-bearing rock and the constitutive relationship of the linear elastic stage and the damage softening stage after the microcrack compaction stage of water-bearing rock, so that the constitutive curve corresponding to the constitutive model better reflects the deformation characteristics of the rock mass such as compaction characteristics, elastic characteristics, damage softening characteristics, etc., and shows high prediction accuracy and practical application value.

[0221] The above-described embodiments merely illustrate several embodiments of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make various modifications and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation, characterized in that: The following steps are included: S1. Conduct a uniaxial compression test on the rock sample to obtain an axial stress-axial strain curve and a dividing point between the compaction stage and the linear elastic stage in the axial stress-axial strain curve. Based on the dividing point, the axial stress-axial strain curve is divided into an axial stress-axial strain curve corresponding to the constitutive relationship of the microcrack compaction stage and an axial stress-axial strain curve corresponding to the constitutive relationship of the rock after microcrack compaction; S2. Introduce the sigmoid function to construct the constitutive relationship of micro-cracks and compaction stage of water-bearing rocks; S3. Obtain the damage variable D after coupling the rainfall damage and stress damage caused by rock water infiltration. w +D l -D w D l , where D w It is the damage caused by rainfall, D l It is the damage caused by loading stress; S4. Based on the damage statistics theory, the constitutive relations of the linear elastic stage and the damage softening stage after the micro-crack compaction stage of water-bearing rock are constructed: σ=E ew (e-e m )(1-D)+σ r D,(e>e cc ), Among them, E ew is the value of elastic modulus E after rainfall, σ r is the residual strength, ε cc is the axial strain value corresponding to the boundary between the compaction stage and the linear elastic stage, ε m is the axial strain value corresponding to the intersection of the extension line of the linear elastic stage curve and the axis where the axial strain is located; S5. Combine steps S2 and S4 to construct a damage statistical constitutive model of water-bearing rock considering compaction deformation.

2. The method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation according to claim 1, characterized in that: The constitutive relationship of the water-bearing rock in the micro-crack compaction stage is: Among them, z1, z2, and z3 represent the shape parameters of the rock cavity, and E i is the initial value of the elastic modulus E, E ew is the value of the elastic modulus E after rainfall.

3. The method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation according to claim 2, characterized in that: The method of step S2 comprises the following steps: S21. Establish the constitutive model of the nonlinear elastic growth gap closing stage in the axial stress-axial strain curve σ=f(E,ε)ε,(ε<ε cc ); where elastic modulus E = f(E,ε). In the compaction stage at the beginning of loading, due to the compaction of the initial pores, the elastic modulus of the rock mass will continue to increase, resulting in the constitutive model of the nonlinear elastic growth gap closure stage in the axial stress-axial strain curve, which can be expressed as: σ=f(E,ε)ε,(ε<ε cc ) (1); S22. When ε=0, the elastic modulus activation is 0, f(E,ε)=E i , That is, f ε＝0 (E,ε)=E i (2); When the pores are completely closed, ε = ε cc , the elastic modulus is fully activated, and the crack closure stress σ cc satisfy s cc =E ew (e cc -e m ), That is to say At this time, the elastic modulus activation degree is 1, ε cc is the axial strain value corresponding to the boundary between the compaction stage and the linear elastic stage, E ew is the value of elastic modulus E after rainfall; S23. Introducing the sigmoid function Combining formulas (1) to (3), the specific function formula of the elastic modulus E is obtained as follows: S24. Substitute formula (4) into formula (1) to obtain the constitutive relationship of water-bearing rock in the microcrack compaction stage:

4. The method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation according to claim 1, characterized in that: The method of step S4 comprises the following steps: S41. Assume that there are N discontinuous units in the rock mass, N→∞, and the area of ​​each unit is A0. Then the total loaded area A is expressed as: A=NA0 (5), The rock mass load F is composed of the load σ of each unit i Summing gives: Among them, E ew is the value of elastic modulus E after rainfall; S42. Assume that the number of damaged units at any time after entering the damage softening stage is q, and the number of intact units is Nq. Combining formula (5) and formula (6), the rock load F in the linear elastic stage and the damage softening stage can be calculated by the sum of the forces on the intact units and the damaged units: Among them, σ r Refers to residual strength; S43. Combined with formula (7), the rock mass load F is divided by the total unit area A to obtain the expression of stress σ in the linear elastic stage and damage softening stage: Formula (8) can be further simplified as: S44. According to the Lemaitre strain equivalence theory, the damage variable D = q / N is substituted into formula (9) to construct the constitutive relationship of the linear elastic stage and the damage softening stage after the micro-crack compaction stage of water-bearing rock: σ=E ew (e-e m )(1-D)+σ r D,(e>e cc ) (10), Among them, ε cc is the strain at the beginning of the linear elastic stage, E ew is the value of the elastic modulus E after rainfall.

5. The method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation according to claim 4, characterized in that: The method of step S3 comprises the following steps: S31. Based on the strain equivalence theory, the damage variable D after coupling of rainfall damage and stress damage caused by rainfall on rock mass satisfies: D=D w +D l -D w D l (11); S32. Rainfall damage D caused by rainfall based on elastic modulus calculation method w Expressed as: Among them, E ew is the value of elastic modulus E after rainfall, E d is the elastic modulus in the dry state; S33, using the improved Harris distribution function Obtain stress damage D l The evolution equation is: Among them, F a is the microscopic unit strength of rock, a and b are the model parameters of the mechanical properties of rock materials; S34, based on the damage initiation point as the dividing point between the linear elastic stage and the damage softening stage, the yield stress σ y is the damage threshold, formula (13) can be transformed into: F a =E ew (e-e m )-s y (15), Yield stress σ y satisfy: s y =E ew (e y -e m ) (16), Among them, ε y is the yield stress point σ y corresponding strain; S35. Combine formulas (14)-(16) to obtain stress damage D l The expression: S36. Combining formulas (11)-(12) and (17), the damage variable D after coupling of rainfall damage and stress damage caused by rainfall in rock mass is obtained:

6. The method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation according to claim 5, characterized in that: The method of step S5 is specifically performed as follows: Substituting formula (18) into formula (10) and combining it with formula (18), the damage statistical constitutive model of water-bearing rock considering the compression deformation in the whole process can be obtained:

7. The method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation according to claim 6, characterized in that: After S36, it also includes S37. Obtain the values ​​of model parameters a and b.

8. The method for constructing a statistical constitutive model of water-bearing rock damage considering compaction deformation according to claim 7, characterized in that: The method of step S37 is specifically performed as follows: Based on the axial stress-axial strain curve, the peak stress point (ε p ,σ p ) is equal to 0, when ε=ε p When , the derivative of ε in formula (19) can be obtained: Because ε p >ε y , the coordinate value corresponding to the peak stress point (ε p ,σ p ) is substituted into formula (19) to obtain: Combining formulas (19) to (20), we can obtain the expressions of a and b:

Images