A method for constructing a nonlinear unified constitutive model for shear failure of rock structural planes

Abstract

The present invention discloses a method for constructing a nonlinear unified constitutive model of shear failure of rock structural surface, which comprises the following steps: performing a shear test on an artificial structural surface sample to obtain a shear stress-shear displacement curve; obtaining a shear stiffness k in the peak shear type shear stress-shear displacement curve; s , peak stress τ p , residual stress τ r and the initial shear stiffness k in the shear stress-shear displacement curve of sliding failure si , peak stress τ p , residual stress τ r ; Establish the corresponding function of the shear stress-shear displacement curve to obtain the nonlinear unified constitutive model of shear failure of rock structure surface. The present invention establishes the corresponding function of the unified constitutive model of the shear stress-shear displacement curve, and in the positive infinite limit of x, the variable u is converted into the ultimate strength τ u The nonlinear unified constitutive model of shear failure of rock structural surface is obtained by substitution, which can effectively predict the shear stress-shear displacement curves of peak shear type and sliding failure type.

Description

Technical Field

[0001] The invention relates to the field of engineering technology, and in particular to a method for constructing a nonlinear unified constitutive model of shear failure of a rock structural surface. Background Art

[0002] Rock mass is a readily available, high-strength natural material that has been extensively transformed into engineered structures (e.g., tunnels, underground powerhouses at hydroelectric power stations, and geological storage reservoirs) to meet specific industrial needs. [1] .

[0003] Generally speaking, the behavior of rock masses in surface and near-surface engineering projects is controlled by the shear strength of structural surfaces such as joints, bedding, cleavage, fissures, shear fractures, and faults that are widely developed in the rock mass. [2-4] .

[0004] Shear failure along the structural surface is one of the most common forms of failure in rock slopes, dam foundations, surface and underground excavations, and geothermal water reservoirs, which can cause casualties, construction delays, and even irreparable damage to the engineering application itself. [5，6] Therefore, a deep understanding of the shear deformation characteristics of rock structural surfaces can provide targeted prevention and control strategies for geotechnical engineering.

[0005] The shear constitutive model describing the shear stress-shear displacement behavior is the basis for evaluating the deformation of the structural surface and is also one of the most important factors in evaluating the mechanical properties of rock materials. [7] As the research progressed, experts gradually realized that both pre-peak deformation and post-peak deformation (i.e., the complete stress-displacement relationship) should be considered comprehensively in shear constitutive modeling. In the past few decades, a series of linear models, nonlinear models, and elastoplastic incremental models have been developed. [7，8] To characterize the shear characteristics of rock structural surfaces. The full shear stress-shear displacement curves of rock structural surfaces vary in shape and are difficult to describe with simple mathematical models. Existing models mostly use piecewise functions to represent them. Saeb and Amadei [9] The Goodman model was extended to the deformation of the entire rock mass structure surface (including the pre-peak area and the post-peak area), and a trilinear segmented stress-displacement model was established for the first time. However, this model is only an idealized treatment of the actual shear curve, and a large number of shear tests [10，11] It is proved that both the pre-peak region and the post-peak region show obvious nonlinear characteristics. Lin et al.

[12] Based on statistical damage theory, a two-stage damage constitutive model with yield point as the dividing point was proposed. Simon et al.

[13] A complete stress-displacement surface model considering the post-peak softening characteristics of the structural surface was established, which uses an exponential function to describe the comprehensive process of shear deformation. Li and Zhao

[14] Based on Iwan model

[15] , a piecewise reduced-order constitutive model with peak points and residual points as dividing points was proposed, which effectively improved the efficiency of numerical simulation.

[0006] Due to the complexity of the mechanical properties of rock materials, the establishment of a model suitable for progressive shear failure of rock structures is not yet mature.

[16] . Although the efficiency and reliability of these pioneering models have been verified, there are inherent limitations in the application of these methods, such as complex formula expressions, many input variables, and complex parameter determination. In addition, the inappropriate expression of the shear component, the particularly strong applicability, and the overly extensive back-analysis of experimental results are also their shortcomings. Finally, these models all require the artificial introduction of stress thresholds to process the complete shear stress-shear displacement curve in sections. The determination of residual points and yield points relies heavily on visual inspection and expert knowledge, which inevitably introduces subjectivity. In addition, the dispersion of experimental data may complicate the process of locating the yield point and residual point. Unfortunately, there is no standard that stipulates how to determine these points, and there are still few reports on this to date.

[0007] Therefore, it is urgent to propose a nonlinear unified constitutive model that can respond to the shear failure of rock structural surfaces.

[0008] References:

[0009] [1] Feng P, Dai F, Shuai K, Wei M.Dynamic mechanical behaviors of pre-fractured sandstone with noncoplanar and unparallel flaws.Mech Mater.2022;166:104219.doi:https: / / doi.org / 10.1016 / j.mechmat.2022.104219.

[0010] [2]Lu CP, Liu B, Liu B, Liu Y, Wang HY, Zhang H. Anatomy of mining-inducedfault slip and a triggered rockburst. Bull Eng Geol Environ. 2019;78(7):5147-60.doi:10.1007 / s10064-019-01464-8.

[0011] [3]Tarasov BG,Sadovskii VM,Sadovskaya OV,Cassidy MJ,RandolphMF.Modelling the static stress–strain state around the fan-structure in theshear rupture head.Appl Math Model.2018;57:268-79.doi:https: / / doi.org / 10.1016 / j.apm.2018.01.020.

[0012] [4]Fan X,Yang Z,Li K.Effects of the lining structure on mechanicaland fracturing behaviors of four-arc shaped tunnels in a jointed rock massunder uniaxial compression.Theor Appl Fract Mec.2021;112:102887.doi:https: / / doi.org / 10.1016 / j.tafmec.2020.102887.

[0013] [5]Wang F,Xia K,Yao W,Wang S,Wang C,Xiu Z.Slip behavior of rough rockdiscontinuity under high velocity impact:Experiments and models.Int J RockMech Min Sci 2021;144:104831.doi:https: / / doi.org / 10.1016 / j.ijrmms.2021.104831.

[0014] [6]Xiang Z,Wang H,Xu W,Xie W-c.Experimental study on hydro-mechanicalbehaviour of anisotropic columnar jointed rock-like specimens.Rock Mech RockEng.2020;53(12):5781-94.doi:10.1007 / s00603-020-02245-6.

[0015] [7]Zhou JK,Chen XD.Stress-strain behavior and statistical continuousdamage model of cement mortar under high strain rates.J Mater Civil Eng.2013;25(1):120-30.doi:10.1061 / (asce)mt.1943-5533.0000570.

[0016] [8]Xie SJ,Lin H,Chen YF,Yong R,Xiong W,Du SG.A damage constitutivemodel for shear behavior of joints based on determination of the yieldpoint.Int J Rock Mech Min Sci 2020;128.doi:10.1016 / j.ijrmms.2020.104269.

[0017] [9]Saeb S,Amadei B.Modelling rock joints under shear and normalloading.Int J Rock Mech Min Sci 1992;29(3):267-78.doi:https: / / doi.org / 10.1016 / 0148-9062(92)93660-C.

[0018]

[10] Xie S,Lin H,Cheng C,Chen Y,Wang Y,Zhao Y et al.Shear strengthmodel of joints based on Gaussian smoothing method and macro-microroughness.Comput Geotech.2022;143:104605.doi:https: / / doi.org / 10.1016 / j.compgeo.2021.104605.

[0019]

[11] Grasselli G,Egger P.Constitutive law for the shear strength ofrock joints based on three-dimensional surface parameters.Int J Rock Mech MinSci2003;40(1):25-40.doi:https: / / doi.org / 10.1016 / S1365-1609(02)00101-6.

[0020]

[12] Lin H,Xie S,Yong R,Chen Y,Du S.An empirical statisticalconstitutive relationship for rock joint shearing considering scale effect.CrMecanique.2019.doi:https: / / doi.org / 10.1016 / j.crme.2019.08.001.

[0021]

[13] Simon R,Aubertin M,Mitri H,editors.A non-linear constitutivemodel for rock joints to evaluate unstable slip.Vail Rocks 1999,The 37th USSymposium on Rock Mechanics(USRMS);1999:American Rock Mechanics Association.

[0022]

[14] Li Y,Zhao T.A reduced-order constitutive model and discretizationstrategy for shearing behavior of rock joints.Comput Geotech.2021;137:104268.doi:https: / / doi.org / 10.1016 / j.compgeo.2021.104268.

[0023]

[15] Iwan WD.A distributed-element model for hysteresis and its steady-state dynamic response.J Appl Mech.1966;33(4):893-900.doi:10.1115 / 1.3625199.

[0024]

[16] Gao W, Chen Summary of the invention

[0025] Based on this, the purpose of the present invention is to provide a method for constructing a nonlinear unified constitutive model of shear failure of rock structural surfaces, classify typical shear stress-shear displacement curves, and establish a nonlinear unified constitutive model that can respond to two types of shear curves of rock structural surfaces on the basis of meeting the basic requirements of the shear curves of rock structural surfaces.

[0026] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0027] The present invention provides a method for constructing a nonlinear unified constitutive model of shear failure of rock structural planes, which comprises the following steps:

[0028] Carry out shear test on artificial structure surface specimens to obtain shear stress-shear displacement curve;

[0029] The obtained shear stress-shear displacement curve is classified into a peak shear type shear stress-shear displacement curve and a sliding failure type shear stress-shear displacement curve, and the shear stiffness k in the peak shear type shear stress-shear displacement curve is obtained. s , peak stress τ p , residual stress τ r and the initial shear stiffness k in the shear stress-shear displacement curve of sliding failure si , peak stress τ p , residual stress τ r ; Among them, the residual stress τ r The stable value is defined as the ultimate strength τ u ;

[0030] Establish the corresponding function of shear stress-shear displacement curve Obtaining a nonlinear unified constitutive model for shear failure of rock structures Among them, β, r, and η are preset parameters, and all are greater than 0.

[0031] In one embodiment, the method of step S130 includes:

[0032] Step S131, establishing the corresponding function of the unified constitutive model of the shear stress-shear displacement curve: Among them, β, r, η, and u are preset parameters, and all are greater than 0;

[0033] Step S132: when x=0, y=0, and in the positive infinite limit of x, y approaches u, the variable u is converted to the value of u Substitute the nonlinear unified constitutive model of rock structural plane shear failure Among them, β, r, and η are preset parameters, and all are greater than 0.

[0034] In one embodiment, after step S130, the following step is further included:

[0035] Step S140: Obtain a nonlinear unified constitutive model corresponding to the peak shear stress-shear displacement curve based on the known shear stress-shear displacement curve Nonlinear unified constitutive model corresponding to shear stress-shear displacement curve of sliding failure

[0036] In one embodiment, when a nonlinear unified constitutive model corresponding to a peak shear stress-shear displacement curve is obtained based on a known shear stress-shear displacement curve, When the method of step S140 comprises the following steps:

[0037] Based on the known shear stress-shear displacement curve and test data, the ultimate strength τ is obtained u Get value;

[0038] The test data before the peak point satisfies the formula ①: τ=k si δ r ;

[0039] Taking the logarithm of both sides of equation ①, we get equation ②: lnτ=rlnδ+lnk si ;

[0040] make Will Substituting into formula ②, we get formula ③: Y = rX + Z;

[0041] The pre-peak shear test data was converted into the form of lnτ-lnδ, and then a linear fit was performed. The slope of the fitting line was the parameter r, and the intercept was the parameter lnk. si , get the parameters r and k si The value of .

[0042] In one embodiment, when a nonlinear unified constitutive model corresponding to a peak shear stress-shear displacement curve is obtained based on a known shear stress-shear displacement curve, When the method of step S140 further comprises the following steps:

[0043] By formula Get formula ④:

[0044] Take the logarithm of both sides of formula ④ to get formula ⑤:

[0045] Taking the quadratic logarithm on both sides of formula ⑤ simplifies it to formula ⑥:

[0046] make Then formula ⑥ is transformed into a linear expression, and the values ​​of parameters β and η can be obtained by linear fitting the experimental data of the post-peak stage;

[0047] τ u , r, k si , β, and η are substituted into the nonlinear unified constitutive model corresponding to the peak shear stress-shear displacement curve After that, the nonlinear unified constitutive model expression corresponding to the complete peak shear stress-shear displacement curve is obtained.

[0048] In one embodiment, the ultimate strength τ u =39.802MPa, parameters r and k si The values ​​of are 1.2197 and 58.431 respectively, and the parameters β and η are 0.312 and 7.104 respectively.

[0049] In one embodiment, when the nonlinear unified constitutive model corresponding to the sliding failure shear stress-shear displacement curve is obtained based on the known shear stress-shear displacement curve, When the method of step S140 comprises the following steps:

[0050] Based on the known shear stress-shear displacement curve and test data, the ultimate strength τ is obtained u Get value;

[0051] Let parameter k si is 0, the formula Simplified to formula ⑦:

[0052] Simplify formula ⑦ to formula ⑧:

[0053] Taking the quadratic logarithm on both sides of formula ⑧ simplifies it to formula ⑨:

[0054] make Considering lnδ as the independent variable X, lnβ as the intercept Z, and parameter η as the slope of the line, formula ⑨ is transformed into a linear expression Q=ηX+Z. Then, the experimental data of the post-peak stage are transformed into data in the form of QX according to the operation rules of Q and X. After linear fitting, the values ​​of parameters β and η are obtained by back calculation.

[0055] τ u , k si , β, and η are substituted into the nonlinear unified constitutive model corresponding to the peak shear stress-shear displacement curve After that, the nonlinear unified constitutive model expression corresponding to the complete sliding failure shear stress-shear displacement curve is obtained.

[0056] In one embodiment, before step S110, the following step is also included:

[0057] Step S100: preparing an artificial structure surface sample.

[0058] In one embodiment, after step S130, the following step is further included:

[0059] Step S150: Substitute the structural plane shear test data into the nonlinear unified constitutive model of rock structural plane shear failure to verify the validity of the nonlinear unified constitutive model of rock structural plane shear failure.

[0060] In one embodiment, by the equation and Verify the validity of the nonlinear unified constitutive model for shear failure of rock structure surface, where τ i,test and τ i,model are the test results and model results respectively, τ ave is the average value of each test data, N is the number of test results, R 2 It is a statistical measure of the correlation between N groups of experimental results and model results, and RMSE is a measure of the degree of difference between the experimental results and the model results.

[0061] In summary, the method for constructing a nonlinear unified constitutive model of shear failure of rock structural surfaces provided by the present invention establishes a corresponding function of the unified constitutive model of the shear stress-shear displacement curve, and in the positive infinite limit of x, the variable u is converted into the ultimate strength τ u By replacing the original model, a nonlinear unified constitutive model of shear failure of rock structural surface is obtained, which can effectively predict the shear stress-shear displacement curves of peak shear type and sliding failure type. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 A schematic flow chart of a method for constructing a nonlinear unified constitutive model for shear failure of a rock structural surface provided by an embodiment of the present invention;

[0063] Figure 2a A schematic diagram of shear stress-shear displacement curves corresponding to test results of shear failure of different artificial structural surfaces provided in an embodiment of the present invention;

[0064] Figure 2b A schematic diagram of a shear stress-shear displacement curve corresponding to a peak shear type provided in an embodiment of the present invention;

[0065] Figure 2c A schematic diagram of a shear stress-shear displacement curve corresponding to the sliding failure type provided in an embodiment of the present invention;

[0066] Figure 3 A schematic diagram of a full shear stress-shear displacement curve of a marble toothed structure surface provided by an embodiment of the present invention;

[0067] Figure 4a A schematic diagram of a typical full shear stress-shear displacement curve provided in an embodiment of the present invention;

[0068] Figure 4b A schematic diagram of the linear fitting results corresponding to the experimental data of the post-peak extraction stage provided in an embodiment of the present invention;

[0069] Figure 4c A comparison diagram of the model curve and the test results provided by the embodiment of the present invention;

[0070] Figure 5a A schematic diagram of a sliding failure type shear stress-shear displacement curve corresponding to a marble serrated structure surface provided by an embodiment of the present invention;

[0071] Figure 5b A schematic diagram of a sliding failure type shear stress-shear displacement curve corresponding to a natural rough structure surface of granite (DS), quartzite (JS), and a natural rough structure surface of sandstone (KS) provided in an embodiment of the present invention;

[0072] Figure 5cA schematic diagram of a sliding failure type shear stress-shear displacement curve corresponding to an artificial rough structure surface provided in an embodiment of the present invention;

[0073] Figure 5d A schematic diagram of a sliding failure shear stress-shear displacement curve corresponding to an artificial straight structural surface provided in an embodiment of the present invention;

[0074] Figure 6a A schematic diagram of a peak shear stress-shear displacement curve corresponding to a marble serrated structure surface provided by an embodiment of the present invention;

[0075] Figure 6b A schematic diagram of a peak shear type shear stress-shear displacement curve corresponding to a natural rough structure surface of granite (DS), quartzite (JS), and a natural rough structure surface of sandstone (KS) provided in an embodiment of the present invention;

[0076] Figure 6c A schematic diagram of a peak shear stress-shear displacement curve corresponding to an artificial rough structure surface provided in an embodiment of the present invention;

[0077] Figure 6d A schematic diagram of a peak shear stress-shear displacement curve corresponding to an artificial straight structural surface provided in an embodiment of the present invention;

[0078] Figure 7 Schematic diagram of the manufacturing process and direct shear test of the artificial structure surface specimen provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0079] In order to further understand the features, technical means, specific objectives and functions of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0080] Figure 1 is a flow chart of a method for constructing a nonlinear unified constitutive model of shear failure of a rock structural surface provided by an embodiment of the present invention, such as Figure 1 As shown in FIG. 1 , the method for constructing the nonlinear unified constitutive model of shear failure of the rock structure surface specifically includes the following steps:

[0081] Step S110, performing a shear test on the artificial structure surface sample to obtain a shear stress-shear displacement curve; performing a shear test on the artificial structure surface sample according to the ISRM suggested method recorded in Muralha J, Grasselli G, Tatone B, Blümel M, Chryssanthakis P, Yujing J. ISRM Suggested Method for Laboratory Determination of the Shear Strength of Rock Joints: Revised Version. Rock Mech Rock Eng. 2014; 47(1): 291-302. doi: 10.1007 / s00603-013-0519-z., performing a shear test on the artificial structure surface sample using a RYL-600 shear rheometer, and obtaining shear stress-shear displacement curves corresponding to different artificial structure surface samples; during the shear test, taking photos to record the original morphology and failure morphology characteristics of each artificial structure surface sample, and then observing the shear failure mode of each artificial structure surface sample through the photos.

[0082] In one embodiment, before step S110, the method further includes:

[0083] Step S100, making an artificial structural surface sample; in this embodiment, an artificial toothed structural surface sample made of cement mortar is used to simulate the geometric characteristics of a natural structural surface. The size of the artificial structural surface sample is 100mm*100mm*100mm (length*width*height), the sawtooth undulation angles are 0°, 10°, 30°, and 45°, and the normal stresses are 0.4, 1.2, 1.6, and 2.0MPa, respectively. The method for making the above-mentioned artificial structural surface sample can be realized by those skilled in the art using existing technologies. Specifically, Figure 7 As shown, cement mortar is placed in a steel mold by pouring and vibrating, and finally solidified to form artificial structural surface specimens with sawtooth undulation angles of 0°, 10°, 30°, and 45° respectively.

[0084] Step S120: classify the obtained shear stress-shear displacement curve into a peak shear type shear stress-shear displacement curve and a sliding failure type shear stress-shear displacement curve, and obtain the shear stiffness k in the peak shear type shear stress-shear displacement curve. s , peak stress τ p , residual stress τ r and the initial shear stiffness k in the shear stress-shear displacement curve of sliding failure si , peak stress τ p , residual stress τ r ; Among them, the residual stress τr The stable value is defined as the ultimate strength τ u , the hardening curve in the peak shear type shear stress-shear displacement curve did not decrease significantly, and the softening curve in the sliding failure type shear stress-shear displacement curve decreased significantly.

[0085] like Figure 2a to Figure 2c As shown in the figure, by analyzing the obtained shear stress-shear displacement curve, it can be known that the shear failure modes of the structural surfaces corresponding to different sawtooth undulation angles are similar. By analyzing the fracture characteristics of the artificial structural surfaces corresponding to different sawtooth undulation angles, it can be concluded that the shear failure modes of the artificial structural surface samples are mainly tooth damage and wear damage. These two failure modes are also reflected in the shear curve, corresponding to the peak shear type shear stress-shear displacement curve and the sliding damage type shear stress-shear displacement curve, respectively.

[0086] Both toothing failure and wear failure are determined by the structural surface morphology and stress state. For relatively smooth structural surface specimens or structural surface specimens with low normal stress, it is easier to slide along the serrated surface during the shear process, resulting in wear failure, otherwise it will be damaged by toothing. With the increase of normal stress, the failure mode changes from wear failure to toothing failure. Taking the shear stress-shear displacement curve corresponding to the toothed structural surface specimen with θ=10° as an example, under the normal pressure of 0.4MPa, the shear stress-shear displacement curve belongs to the sliding failure type, and the residual stress is close to the peak stress; while the peak shear type shear stress-shear displacement curve will show an obvious stress drop in the post-peak stage after the normal stress increases. At this time, the peak stress τ p The residual stress τ r In contrast, the shear stress-shear displacement curve of sliding failure only includes the climbing stage and the sliding stage, τ p and τ r There is almost no difference. To facilitate the establishment of the subsequent constitutive model, the residual stress τ r The stable value is defined as the ultimate strength τ u .

[0087] Step S130: Establishing the corresponding function of the shear stress-shear displacement curve Obtaining a nonlinear unified constitutive model for shear failure of rock structures Among them, β, r, and η are preset parameters, and all are greater than 0.

[0088] In one embodiment, the method of step S130 includes:

[0089] Step S131, establishing the corresponding function of the unified constitutive model of the shear stress-shear displacement curve: Among them, β, r, η, and u are preset parameters, and all are greater than 0.

[0090] Although the shear stress-shear displacement curve corresponding to the artificial structure surface sample is affected by many factors, the overall performance is similar to Figure 2a to Figure 2c Similarly, the nonlinear model in the prior art can only reflect the sliding failure type or peak shear type curve, and a constitutive model that can uniformly describe the shear stress-shear displacement relationship of the sliding failure type and the peak shear type is still missing.

[0091] A good shear constitutive model must have mathematical properties similar to those of the measured shear curves. Figure 2a to Figure 2c From the curve change trend, it can be seen that the constitutive model that can uniformly describe the shear stress-shear displacement relationship of sliding failure type and peak shear type must meet the following requirements:

[0092] (1) When the model curve passes through the origin of the coordinate system, that is, when the shear displacement is 0, the shear stress is also 0;

[0093] (2) The model curve is quasi-linear during initial loading and slightly convex when the shear displacement is large;

[0094] (3) At the end of loading, the shear stress tends to be stable as the shear displacement increases, that is, the total shear stress-displacement curve has an asymptote.

[0095] The existing model expressions can be roughly divided into power function type and exponential function type. The most special feature of the power function type is that the function curve passes through the origin of the coordinate system, while a feature of the exponential function is that there are asymptotes. Considering the above three requirements, the power function and the exponential function are multiplied to derive a new function that has the advantages of both functions.

[0096] Step S132: When x=0, y=0, and in the positive infinite limit of x, y approaches u, so the variable u can be expressed by the limit strength τ u Substitute the nonlinear unified constitutive model of rock structural plane shear failure Among them, β, r, and η are preset parameters, and all are greater than 0.

[0097] In one embodiment, after step S130, the following step is further included:

[0098] Step S140: Obtain a nonlinear unified constitutive model corresponding to the peak shear stress-shear displacement curve based on the known shear stress-shear displacement curve Nonlinear unified constitutive model corresponding to shear stress-shear displacement curve of sliding failure Among them, the literature Zhou H, Cheng GT, Zhu Y, Chen J, Lu JJ, Cui GJ et al. Experimental study of shear deformation characteristics of marbledentate joints. Rock Soil Mech. 2019; 40(3): 852-60. doi: 10.16285 / j.rsm.2017.0964. records the known shear stress-shear displacement curve.

[0099] In engineering applications, "curve fitting" is often used to determine the parameters of mathematical models that match test data. When the sum of the squares of the deviations between the test points and the fitting curve is minimized, the fitting effect is best. This process is called regression analysis, which is also the method for determining the model parameter values ​​in the present invention.

[0100] like Figure 3 As shown in the figure, taking the typical full shear stress-shear displacement curve in the literature Zhou H, Cheng GT, Zhu Y, Chen J, Lu JJ, Cui GJ et al. Experimental study of shear deformation characteristics of marbledentate joints. Rock Soil Mech. 2019; 40(3): 852-60. doi: 10.16285 / j.rsm.2017.0964. as an example, the solution process of the model parameters is explained.

[0101] Specifically, when the nonlinear unified constitutive model corresponding to the peak shear stress-shear displacement curve is obtained based on the known shear stress-shear displacement curve When the method of step S140 comprises the following steps:

[0102] Based on the known shear stress-shear displacement curve and test data, the ultimate strength τ is obtained u In this embodiment, the typical full shear stress-shear displacement curve in the literature Zhou H, Cheng GT, Zhu Y, Chen J, Lu JJ, Cui GJ et al. Experimental study of shear deformation characteristics of marbledentate joints. Rock Soil Mech. 2019; 40(3): 852-60. doi: 10.16285 / j.rsm.2017.0964 is taken as an example, τu =39.802MPa;

[0103] The test data before the peak point satisfies the formula ①: τ=k si δ r ; Compared with the post-peak stage, the shear displacement in the pre-peak stage is smaller, The influence of -βδ is small, that is, η ≈0,e 0 =1;

[0104] Taking the logarithm of both sides of equation ①, we get equation ②: lnτ=rlnδ+lnk si ;

[0105] make Will Substituting into formula ②, we get formula ③: Y = rX + Z;

[0106] The pre-peak shear test data was converted into the form of lnτ-lnδ, and then a linear fit was performed. The slope of the fitting line was the parameter r, and the intercept was the parameter lnk. si , and then obtain the parameters r and k si In this embodiment, if Figure 4a As shown in the literature, taking the typical full shear stress-shear displacement curve in Zhou H, Cheng GT, Zhu Y, Chen J, Lu JJ, Cui GJ et al. Experimental study of shear deformation characteristics of marbledentate joints. Rock Soil Mech. 2019; 40(3): 852-60. doi: 10.16285 / j.rsm.2017.0964 as an example, the parameters r and k si The values ​​are 1.2197 and 58.431 respectively;

[0107] By formula Get formula ④: The geometry of the post-peak region of the full shear stress-shear displacement curve is mainly determined by the formula The exponential term in Control, so the experimental data of the post-peak stage are selected to solve the parameters β and η;

[0108] Take the logarithm of both sides of formula ④ to get formula ⑤:

[0109] Taking the quadratic logarithm on both sides of formula ⑤ simplifies it to formula ⑥:

[0110] make Then formula ⑥ is transformed into a linear expression, and the values ​​of parameters β and η can be obtained by linear fitting the experimental data of the post-peak stage; in this embodiment, Figure 4b As shown in the literature Zhou H, Cheng GT, Zhu Y, Chen J, Lu JJ, Cui GJ et al. Experimental study of sheardeformation characteristics of marbledentate joints. Rock Soil Mech. 2019; 40(3): 852-60. doi: 10.16285 / j.rsm.2017.0964., the parameters β and η are 0.312 and 7.104 respectively;

[0111] τ u , r, k si , β, and η are substituted into the nonlinear unified constitutive model corresponding to the peak shear stress-shear displacement curve After that, the nonlinear unified constitutive model expression corresponding to the complete peak shear stress-shear displacement curve is obtained. The model curve is compared with the experimental results in the literature Zhou H, Cheng GT, Zhu Y, Chen J, Lu JJ, Cui GJ et al. Experimental study of sheardeformation characteristics of marbledentate joints. Rock Soil Mech. 2019; 40(3): 852-60. doi: 10.16285 / j.rsm.2017.0964. Figure 4c shown.

[0112] When the nonlinear unified constitutive model corresponding to the sliding failure shear stress-shear displacement curve is obtained based on the known shear stress-shear displacement curve When the method of step S140 comprises the following steps:

[0113] Based on the known shear stress-shear displacement curve and test data, the ultimate strength τ is obtained u Get value;

[0114] Let parameter k si is 0, the formula Simplified to formula ⑦:

[0115] Simplify formula ⑦ to formula ⑧:

[0116] Taking the quadratic logarithm on both sides of formula ⑧ simplifies it to formula ⑨:

[0117] make Considering lnδ as the independent variable X, lnβ as the intercept Z, and parameter η as the slope of the line, formula ⑨ is transformed into a linear expression Q=ηX+Z. Then, the experimental data of the post-peak stage is transformed into data in the form of QX according to the operation rules of Q and X. After linear fitting, the values ​​of parameters β and η can be obtained by back calculation. In this embodiment, Figure 4b As shown in the literature Zhou H, Cheng GT, Zhu Y, Chen J, Lu JJ, Cui GJ et al. Experimental study of shear deformation characteristics of marbledentate joints. Rock Soil Mech. 2019; 40(3): 852-60. doi: 10.16285 / j.rsm.2017.0964., the parameters β and η are 0.312 and 7.104 respectively;

[0118] τ u , k si , β, and η are substituted into the nonlinear unified constitutive model corresponding to the peak shear stress-shear displacement curve After that, the nonlinear unified constitutive model expression corresponding to the complete sliding failure shear stress-shear displacement curve is obtained.

[0119] It is worth noting that each parameter in the nonlinear unified constitutive model of the present invention can be determined by the above method, but it is more convenient to solve using the planning and solving function of software such as Origin or Excel.

[0120] In one embodiment, after step S130, the following step is further included:

[0121] Step S150: Substitute the structural plane shear test data into the nonlinear unified constitutive model of rock structural plane shear failure to verify the validity of the nonlinear unified constitutive model of rock structural plane shear failure.

[0122] In order to verify the effectiveness and applicability of the proposed model, some statistical indicators are used. The root mean square error (RMSE) between the predicted value and the measured value, the coefficient of determination (R 2 ) can well evaluate the prediction performance of the nonlinear unified constitutive model of the present invention, such as RMSE and R2 The expression and To verify the validity of the nonlinear unified constitutive model of rock structural surface shear failure, where τ i,test and τ i,model are the test results and model results respectively, τ ave is the average value of each test data, N is the number of test results, R 2 It is a statistical measure of the correlation between N groups of experimental results and model results. RMSE is a measure of the degree of difference between the experimental results and the model results. A larger R 2 The small RMSE value shows that the nonlinear unified constitutive model of the present invention has great predictability.

[0123] (1) Sliding failure type

[0124] The present invention selects shear test data of marble serrated surface, granite natural rough surface (DS), quartzite (JS), sandstone natural rough surface (KS), artificial rough surface and artificial straight surface for verification.

[0125] Among them, the marble dentate structure surface is recorded in the literature Zhou H, Cheng GT, Zhu Y, Chen J, Lu JJ, Cui GJ et al. Experimental study of shear deformation characteristics of marble dentate joints. Rock Soil Mech. 2019; 40(3): 852-60. doi: 10.16285 / j.rsm.2017.0964.

[0126] The natural roughness surface of granite (DS), quartzite (JS), and sandstone (KS) are recorded in the literature Singh HK, Basu A. A comparison between the shear behavior of'real'natural rock discontinuities and their replicas. Rock Mech Rock Eng. 2018; 51(1): 329-40. doi: 10.1007 / s00603-017-1334-8.

[0127] The artificial rough structure surface is recorded in the literature Tang ZC, Zhang ZF, Zuo CQ, Jiao YY. Peak shearstrength criterion for mismatched rock joints: Revisiting JRC-JMCcriterion. Int J Rock Mech Min Sci 2021; 147: 104894. doi: https: / / doi.org / 10.1016 / j.ijrmms.2021.104894.

[0128] Artificial straight structural surfaces are recorded in the literature Wu Q, Xu Y, Tang H, Fang K, Jiang Y, Liu C et al. Investigation on the shear properties of discontinuities at the interface between different rock types in the Badong formation, China. Eng Geol. 2018; 245: 280-91. doi: https: / / doi.org / 10.1016 / j.enggeo.2018.09.002.

[0129] Granite, marble, sandstone and artificial structural surfaces represent igneous rocks, metamorphic rocks, sedimentary rocks and rock-like materials, respectively, covering all sources of current structural surface samples. Figures 5a to 5d For comparison between the model curve and the test results, the expressions and statistics of each test are shown in Table 1. The prediction curve of the nonlinear unified constitutive model of the present invention is in good agreement with the test results, indicating that the nonlinear unified constitutive model of the present invention has a good ability to reproduce the shear mechanical behavior corresponding to the sliding failure of different structural surfaces. The statistical results in Table 1 show that, except for the JS7 specimen (σ n =0.45MPa,R 2 <0.95), the results obtained by the nonlinear unified constitutive model of the present invention are all close to 0.99, and the RMSE value is small.

[0130] Table 1 Model expressions and statistical indicators

[0131]

[0132] (2) Peak shear type

[0133] In the same way, the literature Zhou H, Cheng GT, Zhu Y, Chen J, Lu JJ, Cui GJ et al. shear behavior of'real'natural rockdiscontinuities and their replicas.Rock Mech Rock Eng.2018;51(1):329-40.doi:10.1007 / s00603-017-1334-8.,Tang ZC,Zhang ZF,Zuo CQ,Jiao YY.Peak shearstrength criterion for mismatched rock joints:Revisiting JRC-JMCcriterion.Int J Rock Mech Min Sci 2021; 147: 104894. doi: https: / / doi.org / 10.1016 / j.ijrmms.2021.104894., Wu Q, Xu Y, Tang H, Fang K, Jiang Y, Liu C et al. Investigation on the shear properties of discontinuities at the interface between different rock types in the Badong formation, China. Eng Geol. 2018; 245: 280-91. doi: https: / / doi.org / 10.1016 / j.enggeo.2018.09.002. The softening shear deformation curves are used for verification. Following the same steps as the sliding failure type, the corresponding test results are substituted into the nonlinear unified constitutive model solution expression of the present invention, which need not be repeated here.

[0134] like Figure 6a-6d As shown in the figure, after comparing the model curve with the experimental results, the present invention found that the theoretical curve is consistent with the experimental results, and R 2All of them are greater than 0.95, indicating that the nonlinear unified constitutive model of the present invention has a good ability to reproduce the shear mechanical behaviors corresponding to the peak shear of different structural surfaces.

[0135] In summary, the method for constructing a nonlinear unified constitutive model of shear failure of rock structural surfaces of the present invention establishes a corresponding function of the unified constitutive model of the shear stress-shear displacement curve, and in the positive infinite limit of x, the variable u is converted into the ultimate strength τ u By replacing the original model, a nonlinear unified constitutive model of shear failure of rock structural surface is obtained, which can effectively predict the shear stress-shear displacement curves of peak shear type and sliding failure type.

[0136] The above-described embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the attached claims.

Claims

1. A method for constructing a nonlinear unified constitutive model for shear failure of rock structural surfaces, characterized in that: The steps include: Step S110, performing a shear test on the artificial structure surface sample to obtain a shear stress-shear displacement curve; Step S120: classify the obtained shear stress-shear displacement curve into a peak shear type shear stress-shear displacement curve and a sliding failure type shear stress-shear displacement curve, and obtain the shear stiffness k in the peak shear type shear stress-shear displacement curve. s , peak stress τ p , residual stress τ r and the initial shear stiffness k in the shear stress-shear displacement curve of sliding failure si , peak stress τ p , residual stress τ r ; Among them, the residual stress τ r The stable value is defined as the ultimate strength τ u ; Step S130: Establishing the corresponding function of the shear stress-shear displacement curve Obtaining a nonlinear unified constitutive model for shear failure of rock structures Among them, β, r, and η are preset parameters, and all are greater than 0; Step S140: Obtain a nonlinear unified constitutive model corresponding to the peak shear stress-shear displacement curve based on the known shear stress-shear displacement curve Nonlinear unified constitutive model corresponding to shear stress-shear displacement curve of sliding failure The method of step S130 specifically includes the following operations: Step S131, establishing the corresponding function of the unified constitutive model of the shear stress-shear displacement curve: Among them, β, r, η, and u are preset parameters, and all are greater than 0; Step S132: when x=0, y=0, and in the positive infinite limit of x, y approaches u, the variable u is converted to the value of u Substitute the nonlinear unified constitutive model of rock structural plane shear failure Among them, β, r, and η are preset parameters, and all are greater than 0; When the nonlinear unified constitutive model corresponding to the peak shear type shear stress-shear displacement curve is obtained based on the known shear stress-shear displacement curve When the method of step S140 comprises the following steps: Based on the known shear stress-shear displacement curve and test data, the ultimate strength τ is obtained u Get value; The test data before the peak point satisfies the formula ①: τ=k si δ r ; Taking the logarithm of both sides of equation ①, we get equation ②: lnτ=rlnδ+lnk si ; make Will Substituting into formula ②, we get formula ③: Y = rX + Z; The pre-peak shear test data was converted into the form of lnτ-lnδ, and then a linear fit was performed. The slope of the fitting line was the parameter r, and the intercept was the parameter lnk. si , get the parameters r and k si The value of .

2. The method for constructing a nonlinear unified constitutive model of shear failure of rock structure surface according to claim 1, characterized in that: When the nonlinear unified constitutive model corresponding to the peak shear type shear stress-shear displacement curve is obtained based on the known shear stress-shear displacement curve When the method of step S140 further comprises the following steps: By formula Get formula ④: Take the logarithm of both sides of formula ④ to get formula ⑤: Taking the quadratic logarithm on both sides of formula ⑤ simplifies it to formula ⑥: make Then formula ⑥ is transformed into a linear expression, and the values ​​of parameters β and η can be obtained by linear fitting the experimental data of the post-peak stage; τ u , r, k si , β, and η are substituted into the nonlinear unified constitutive model corresponding to the peak shear stress-shear displacement curve After that, the nonlinear unified constitutive model expression corresponding to the complete peak shear stress-shear displacement curve is obtained.

3. The method for constructing a nonlinear unified constitutive model of shear failure of rock structure surface according to claim 2, characterized in that: The ultimate strength τ u =39.802MPa, parameters r and k si The values ​​of are 1.2197 and 58.431 respectively, and the parameters β and η are 0.312 and 7.104 respectively.

4. The method for constructing a nonlinear unified constitutive model of shear failure of rock structure surface according to claim 1, characterized in that: When the nonlinear unified constitutive model corresponding to the sliding failure shear stress-shear displacement curve is obtained based on the known shear stress-shear displacement curve When the method of step S140 comprises the following steps: Based on the known shear stress-shear displacement curve and test data, the ultimate strength τ is obtained u Get value; Let parameter k si is 0, the formula Simplified to formula ⑦: Simplify formula ⑦ to formula ⑧: Taking the quadratic logarithm on both sides of formula ⑧ simplifies it to formula ⑨: make Considering lnδ as the independent variable X, lnβ as the intercept Z, and parameter η as the slope of the line, formula ⑨ is transformed into a linear expression Q=ηX+Z. Then, the experimental data of the post-peak stage are transformed into data in the form of QX according to the operation rules of Q and X. After linear fitting, the values ​​of parameters β and η are obtained by back calculation. τ u , k si , β, and η are substituted into the nonlinear unified constitutive model corresponding to the peak shear stress-shear displacement curve After that, the nonlinear unified constitutive model expression corresponding to the complete sliding failure shear stress-shear displacement curve is obtained.

5. The method for constructing a nonlinear unified constitutive model of shear failure of rock structural plane according to claim 1, characterized in that: Before step S110, the method further includes: Step S100: preparing an artificial structure surface sample.

6. The method for constructing a nonlinear unified constitutive model of shear failure of rock structural plane according to claim 1, characterized in that: After step S130, the following steps are also included: Step S150: Substitute the structural plane shear test data into the nonlinear unified constitutive model of rock structural plane shear failure to verify the validity of the nonlinear unified constitutive model of rock structural plane shear failure.

7. The method for constructing a nonlinear unified constitutive model of shear failure of rock structural plane according to claim 6, characterized in that: Through the equation and Verify the validity of the nonlinear unified constitutive model for shear failure of rock structure surface, where τ i,test and τ i,model are the test results and model results respectively, τ ave is the average value of each test data, N is the number of test results, R 2 It is a statistical measure of the correlation between N groups of experimental results and model results, and RMSE is a measure of the degree of difference between the experimental results and the model results.

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