Stress state graph equivalent method based on rock failure curved surface

Abstract

The invention discloses a stress state graph equivalent method based on a rock failure curved surface, and the method comprises the steps: 1, building a coordinate system OXYZ, and building a pi axis in the coordinate system OXYZ; 2, marking a complex stress state coordinate point P 'in the coordinate system OXYZ in the step 1; 3, making a pi plane circle of the complex stress state point P'; step 4, performing stress state graph equivalence; and S3, finding a position with a maximum coordinate component value on the pi plane circle of the complex stress state point P'in the step S3, marking a coordinate point of the position as a bidirectional equal stress feature point P on the pi plane circle, and enabling the stress state of the bidirectional equal stress feature point P to be equivalent to the stress state of the complex stress state P '. According to the method, the modes of rock failure curved surface drawing, graph point drawing and coordinate picking are adopted, complex calculation is not involved in the process, and application of engineering field personnel is facilitated.

Description

Technical Field

[0001] The invention belongs to the technical field of tunnel monitoring, and in particular relates to a stress state graphic equivalence method based on rock failure surfaces. Background Art

[0002] For deep rock projects such as tunnels, dams, caverns, etc., the ground stress state of the rock mass at the project site is extremely complex, which is manifested in the variability and discreteness of the direction and magnitude of the principal stress. At the same time, during the excavation of the project, the stress state change process of the surrounding rock is also extremely complex, including the constant change in the direction and magnitude of the principal stress. Therefore, in the process of designing the project support parameters or formulating prevention and control measures, it is necessary to obtain rock samples on site, conduct indoor rock strength tests and numerical simulation calculations, and design reasonable support parameters and prevention and control measures based on the test and calculation results, so as to avoid deformation and instability, collapse or rock burst disasters in the surrounding rock of the project, and ensure the safe construction of the project.

[0003] There are two types of indoor strength tests for rocks: conventional triaxial compression test and true triaxial compression test. The stresses in the three directions of the true triaxial compression test are not equal, which can better reflect the actual stress conditions of the surrounding rock at the project site. However, since the two confining pressures of the true triaxial test are not equal, the test workload is large, time-consuming, and the test cost is high. Therefore, in general, laboratories use conventional triaxial compression tests to approximate true triaxial compression tests, and directly apply the results of conventional triaxial compression tests to numerical simulation calculations and field parameter design. This results in the inability of laboratory test data to reflect the actual stress conditions of the surrounding rock at the project site, and it is also impossible to determine the ductile / brittle failure mode of the rock. Therefore, engineering applications have a certain degree of approximation and experience.

[0004] In order to solve this problem, a lower test cost and a small number of tests are used to reflect the actual stress conditions of the surrounding rock at the project site. The complex stress state of the true triaxial test of rock needs to be equivalent to the stress state of the conventional triaxial test of rock. There is no mature equivalent method at present. The relevant stress tensor transformation method mainly establishes the matrix of coordinate system change, and obtains the stress state before and after the transformation according to the matrix operation. This process is only the transformation of the stress tensor in different coordinate systems. The whole calculation process is complicated, and does not consider the equivalence of stress states with physical significance, nor does it consider the actual concerns of the project, such as the destructive strength value, energy size, surrounding rock stress value, etc., so the engineering practicability is poor. Summary of the invention

[0005] The purpose of the present invention is to provide a stress state graphical equivalence method based on rock failure surface, which adopts the method of drawing rock failure surface, graphically plotting points and picking coordinates. The process does not involve complex calculations and is convenient for application by engineering site personnel.

[0006] The present invention adopts the following technical solution: a stress state graphical equivalent method based on rock failure surface, comprising the following steps:

[0007] Step 1: Establish the coordinate system OXYZ and establish the π axis in the coordinate system OXYZ:

[0008] Define the straight line x=y=z in the coordinate system OXYZ as the π axis;

[0009] Step 2: Mark the coordinate point P' of the complex stress state of rock in the coordinate system OXYZ in step 1:

[0010] The three principal stress values ​​of the complex stress state coordinate point P′ are P′ a , P′ b , P′ c ; The three coordinate components of the coordinate point P′ are equal to its three principal stress values ​​P′ a , P′ b , P′ c ; Execute step 3 or determine the state of the rock;

[0011] Step 3: Make a π plane circle of the complex stress state point P′:

[0012] Taking the vertical distance from the coordinate point P' to the π axis as the radius, rotate the coordinate point P' around the π axis for one circle, and its trajectory forms a π plane circle of the complex stress state point P';

[0013] Step 4: Stress state graphical equivalence:

[0014] On the π plane circle of the complex stress state point P′ in step 3, find the position with the maximum value of a certain coordinate component, mark the coordinate point of this position, which is the bidirectional isostress characteristic point P on the π plane circle. The stress state of the bidirectional isostress characteristic point P is equivalent to the stress state of the complex stress state P′;

[0015] Pick up the three coordinate components of the bidirectional isostress characteristic point P, which are P a , P b , P c , the values ​​of the three coordinate components are equal to the three principal stress values ​​of the bidirectional isostress characteristic point P, and the two minor principal stress values ​​of the three principal stresses are equal, that is, P a >P b =P c .

[0016] Furthermore, in step 2, the process of determining the state of the rock is as follows:

[0017] Step S1, establish the coordinate points of the principal stress state during conventional triaxial compression failure in the coordinate system OXYZ:

[0018] Conventional triaxial compression tests are used to measure the principal stress state of rock at different confining pressure levels when it reaches failure. One principal stress state corresponds to three coordinate points in the coordinate system OXYZ, and the three coordinate points are three bidirectional isostress characteristic points. Three bidirectional isostress characteristic points under each confining pressure level are obtained. The three bidirectional isostress characteristic points are on the same circle and divide the circle into three equal parts.

[0019] Step S2, making π plane circles at various confining pressure levels:

[0020] For each of the three bidirectional isostress characteristic points under each confining pressure level, two adjacent bidirectional isostress characteristic points are connected by arcs in sequence, and all of them are enclosed to form a π plane circle; each π plane circle is perpendicular to the π axis, and the center of the circle is located on the π axis; each confining pressure level obtains the π plane circle under the confining pressure level;

[0021] Step S3: Establish rock failure surface:

[0022] The two π plane circles of each adjacent confining pressure level in step S2 are connected by a smooth curved surface to form a nearly conical curved surface that is extremely symmetrical about the π axis, and the curved surface is the rock failure curved surface; any two different points on the circumference of each same π plane circle belong to the equivalent stress state;

[0023] Step S4: rock damage judgment under complex stress state:

[0024] When the coordinate point of P′ is within the rock failure surface in step S3, it indicates that the rock has not reached failure under the complex stress state P′; when the coordinate point of P′ falls on the rock failure surface, it indicates that the rock has reached failure under the complex stress state P′; when the coordinate point of P′ falls outside the rock failure surface, it indicates that the rock has been overloaded under the complex stress state P′ obtained by numerical calculation.

[0025] The present invention also discloses a method for distinguishing rock failure modes under complex stress states, based on the above-mentioned stress state graphical equivalent method based on rock failure surfaces, and further comprising the following after step 4:

[0026] Step 5: Determine the conversion pressure σ of the rock sample 3,t :

[0027] The minimum confining pressure for rock to undergo ductile deformation failure is defined as the rock transformation pressure σ 3,t ;

[0028] Step 6: The two minor principal stress values ​​P of the bidirectional isostress characteristic point P in step 4 are b or P c and rock conversion pressure σ 3,t Compare, when P b =Pc ≥σ 3,t When P b =P c <σ 3,t When the stress state P′ is complex, the rock will experience brittle fracture failure mode.

[0029] The present invention also discloses a method for establishing a rock failure surface, comprising the following steps:

[0030] Step A1: Establish the π axis in the coordinate system OXYZ:

[0031] Define the straight line x=y=z in the coordinate system OXYZ as the π axis;

[0032] Step A2: Establish the coordinate points of the conventional triaxial compression failure principal stress state in the coordinate system OXYZ:

[0033] Conventional triaxial compression tests are used to measure the principal stress state of rock at different confining pressure levels when it reaches failure. One principal stress state corresponds to three coordinate points in the coordinate system OXYZ, and the three coordinate points are three bidirectional isostress characteristic points. Three bidirectional isostress characteristic points under each confining pressure level are obtained.

[0034] Step A3: Make a π plane circle:

[0035] For each of the three bidirectional isostress characteristic points under the confining pressure level, arcs are connected to two adjacent bidirectional isostress characteristic points, all of which are enclosed to form a π plane circle; each π plane circle is perpendicular to the π axis, and the center of each circle is located on the π axis;

[0036] Step A4: Create rock failure surface:

[0037] Each adjacent π plane circle in step 3 is connected by a smooth surface to form a nearly conical surface that is extremely symmetrical about the π axis, which is the rock failure surface; any two different points on the circumference of the same π plane circle belong to the equivalent stress state.

[0038] The beneficial effects of the present invention are: 1. Drawing the rock failure surface and performing point drawing and coordinate picking operations avoids tedious coordinate rotation calculations, is simple to operate, and is highly practical in engineering sites. 2. Only the value attribute of the stress state tensor is equivalent, and there is no need to consider the direction attribute of the stress state tensor. This is very consistent with the surrounding rock collapse damage, rock burst energy release, and surrounding rock pressure that are the focus of engineering sites, and has broad prospects for promotion and application. 3. Through stress state equivalence, conventional triaxial compression tests of rock can be used to replace true triaxial compression tests of rock. On the premise of ensuring the accuracy of the test results, the experimental workload is effectively reduced, the test cost is reduced, and the economy is good. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic diagram of principal stress space coordinate system and π axis;

[0040] Figure 2 It is a schematic diagram of the characteristic points of π-plane circle and bidirectional equal stress;

[0041] Figure 3 It is a schematic diagram of bidirectional isostress characteristic points, π plane circle, and rock failure surface;

[0042] Figure 4 It is a schematic diagram of coordinate components of bidirectional isostress characteristic points;

[0043] Figure 5 Schematic diagram of the coordinate system rotation of the complex stress state point on the π plane circle. DETAILED DESCRIPTION

[0044] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] The invention discloses a stress state graphic equivalence method based on rock failure surface, which is applicable to isotropic homogeneous rock medium and a mechanical model in which no plastic deformation occurs in the elastic stage before the rock reaches strength.

[0046] This method does not involve specific strength theory, but only relies on conventional triaxial compression test data of rock. It draws the rock failure surface in the principal stress space coordinate system and performs point drawing and coordinate picking to perform stress state equivalence. It is a graphical method and does not involve complex calculation process. The workload of stress state equivalence is small, which is convenient for application by engineering site personnel.

[0047] This method uses the rotation of the principal stress space coordinate system in the process of implementing the stress state equivalence. The rotation of the coordinate system does not change the value attributes of the stress state tensor, such as the stress tensor invariant, or the modulus of the vector, the energy density based on the stress state, the intensity or the stress value, but only changes the directional attributes of the stress state tensor. Therefore, this method adopts the equivalence of the value attributes of the stress state, which improves the simplicity of engineering application.

[0048] In the specific implementation process of the stress state graphical equivalent method based on rock failure surface of the present invention, the terms are explained as follows:

[0049] "Coordinate system" refers to the principal stress space coordinate system;

[0050] "Complex stress state" refers to any stress state other than the three bidirectional isostress characteristic points on the π plane circle;

[0051] "Stress state equivalence" means that the value properties of the stress state are equivalent.

[0052] The present invention provides a stress state graphical equivalence method based on rock failure surface, comprising the following steps:

[0053] Step 1: Establish the coordinate system OXYZ and establish the π axis in the coordinate system OXYZ:

[0054] Define the straight line x=y=z in the coordinate system OXYZ as the π axis; Figure 1 a in.

[0055] Step 2: Mark the coordinate point P' of the complex stress state of rock in the coordinate system OXYZ in step 1:

[0056] The stress state obtained by field stress test, numerical calculation, true triaxial compression test stress test and other methods has two smaller principal stresses that are not equal, so it is generally a complex stress state. The three principal stress values ​​of the complex stress state coordinate point P' are P' a , P′ b , P′ c ; The three coordinate components of the coordinate point P′ are equal to its three principal stress values ​​P′ a , P′ b , P′ c ; Execute step 3 or determine the state of the rock;

[0057] Step 3: Make a π plane circle of the complex stress state point P′:

[0058] Taking the vertical distance from the coordinate point P' to the π axis as the radius, rotate the coordinate point P' around the π axis for one circle, and its trajectory forms a π plane circle of the complex stress state point P';

[0059] Step 4: Stress state graphical equivalence:

[0060] On the π plane circle of the complex stress state point P′ in step 3, a 3D computer-aided software can be used to move the mouse on the circle and display the coordinate components on the π plane circle in real time, find the position with the largest coordinate component value, mark the coordinate point of the position, which is the bidirectional isostress characteristic point P on the π plane circle. The stress state of the bidirectional isostress characteristic point P is equivalent to the stress state of the complex stress state P′;

[0061] Pick up the three coordinate components of the bidirectional isostress characteristic point P with the mouse, which are P a , P b , P c , the values ​​of the three coordinate components are equal to the three principal stress values ​​of the bidirectional isostress characteristic point P, and the two minor principal stress values ​​of the three principal stresses are equal, that is, P a >P b =P cOnly by adopting the equivalent bidirectional isostatic stress state can the Mohr-Coulomb criterion be used to verify the strength failure and draw the Mohr circle, and the result is the same as that of the complex stress state P′.

[0062] Furthermore, in step 2, the process of determining the state of the rock is as follows:

[0063] Step S1, establish the coordinate points of the conventional triaxial compression failure principal stress state in the coordinate system OXYZ:

[0064] Conventional triaxial compression tests are used to measure the principal stress states of rock at different confining pressure levels when it reaches failure. One principal stress state corresponds to three coordinate points in the coordinate system OXYZ, and the three coordinate points are three bidirectional isostress characteristic points; each confining pressure level obtains three bidirectional isostress characteristic points under the confining pressure level; each confining pressure level obtains three bidirectional isostress characteristic points under the confining pressure level;

[0065] Step S2, making π plane circles at various confining pressure levels:

[0066] For each of the three bidirectional isostress characteristic points under each confining pressure level, two adjacent bidirectional isostress characteristic points are connected by arcs in sequence, and all of them are enclosed to form a π plane circle; each π plane circle is perpendicular to the π axis, and the center of the circle is located on the π axis; each confining pressure level obtains the π plane circle under the confining pressure level;

[0067] Step S3: Establish rock failure surface:

[0068] The two π plane circles of each adjacent confining pressure level in step S2 are connected by a smooth curved surface to form a nearly conical curved surface that is extremely symmetrical about the π axis, and the curved surface is the rock failure curved surface; any two different points on the circumference of each same π plane circle belong to the equivalent stress state;

[0069] Step S4: rock damage judgment under complex stress state:

[0070] When the coordinate point of P′ is within the rock failure surface in step S3, it indicates that the rock has not reached failure under the complex stress state P′; when the coordinate point of P′ falls on the rock failure surface, it indicates that the rock has reached failure under the complex stress state P′; when the coordinate point of P′ falls outside the rock failure surface, it indicates that the rock has been overloaded under the complex stress state P′ obtained by numerical calculation, and the overload stress needs to be reversed.

[0071] The present invention also discloses a method for distinguishing rock failure modes under complex stress states, based on the above-mentioned stress state graphical equivalent method based on rock failure surfaces, and further includes the following after step 4:

[0072] Step 5: Determine the conversion pressure σ of the rock sample 3,t :

[0073] According to the results of triaxial compression tests of rocks under different confining pressures, the rock samples after compression tests under each confining pressure level were taken out to observe their failure modes: if the rock sample broke into multiple pieces, it was a brittle fracture failure mode; if the rock test remained intact and only showed obvious shape deformation, it was a ductile deformation failure mode. For all rock samples with ductile deformation failure modes, the minimum confining pressure for rock to undergo ductile deformation failure was defined as the rock conversion pressure σ 3,t ;

[0074] Step 6: The two minor principal stress values ​​P of the bidirectional isostress characteristic point P in step 4 are b and P c and rock conversion pressure σ 3,t Compare, when P b =P c ≥σ 3,t When the complex stress state P′ occurs in ductile deformation failure mode, b =P c <σ 3,t When the complex stress state P′ occurs in a brittle fracture failure mode, different support designs need to be carried out according to the different failure modes of the rock to ensure the safety of the project.

[0075] The present invention also discloses a method for establishing a rock failure surface, comprising the following steps:

[0076] Step A1: Establish the π axis in the coordinate system OXYZ:

[0077] Define the straight line x=y=z in the coordinate system OXYZ as the π axis;

[0078] Step A2: Establish the coordinate points of the conventional triaxial compression failure principal stress state in the coordinate system OXYZ:

[0079] Conventional triaxial compression tests are used to measure the principal stress state of rock at different confining pressure levels when it reaches failure. One principal stress state corresponds to three coordinate points in the coordinate system OXYZ, and the three coordinate points are three bidirectional isostress characteristic points. Three bidirectional isostress characteristic points under each confining pressure level are obtained.

[0080] Step A3: Make a π plane circle:

[0081] For each of the three bidirectional isostress characteristic points under the confining pressure level, arcs are connected to two adjacent bidirectional isostress characteristic points, all of which are enclosed to form a π plane circle; each π plane circle is perpendicular to the π axis, and the center of each circle is located on the π axis;

[0082] Step A4: Create rock failure surface:

[0083] Each adjacent π plane circle in step 3 is connected by a smooth surface to form a nearly conical surface that is extremely symmetrical about the π axis, which is the rock failure surface; any two different points on the circumference of the same π plane circle belong to the equivalent stress state.

[0084] The invention provides a stress state graphical equivalence method based on rock failure surface, and its inference process is as follows:

[0085] 1. Conduct conventional triaxial compression tests on rocks under different confining pressure levels:

[0086] Rock samples were obtained from the project site and made into standard cylindrical specimens with a size of 5 cm × 10 cm. Several groups of conventional triaxial compression tests with different confining pressure levels were carried out on the standard rock specimens. 3,i , i=1,2…, and obtain the confining pressure σ 3,i The corresponding triaxial compression strength of rock σ 1,i When conducting a conventional triaxial compression test, the confining pressure σ 3,i The design principle is: when the rock uniaxial compressive strength R c Between 30MPa and 60MPa, the confining pressure σ 3,i The uniaxial compressive strength R increases by 2.5MPa step by step. c Between 60MPa and 120MPa, the confining pressure σ 3,i The uniaxial compressive strength R increases by 5MPa step by step. c Greater than 120MPa, confining pressure level σ 3,i The strength of triaxial compression under different confining pressures was obtained by increasing the pressure by 10 MPa.

[0087] 2. Determine the transformation pressure σ of rock 3,t :

[0088] According to the strength of triaxial compression under different confining pressures, each group of confining pressure σ 3,i The rock samples after the failure are taken out from the sample chamber of the test equipment, and the failure mode of each group of rock samples is determined: if the rock sample is broken into multiple pieces, it is determined to be a brittle fracture failure mode, such as Figure 1 As shown; if the rock specimen remains intact and only shows obvious shape deformation, such as drum shape, it is judged as ductile deformation failure mode.

[0089] According to rock mechanics theory, as the confining pressure σ 3,i As the rock failure mode increases, the rock failure will change from brittle fracture failure mode to ductile deformation failure mode. The critical confining pressure for the rock to change from brittle fracture failure mode to ductile deformation failure mode is defined as the conversion pressure σ 3,t .

[0090] Assume that the maximum confining pressure corresponding to the brittle fracture failure mode of rock is σ 3,i , then the minimum confining pressure for rock to undergo ductile deformation failure mode is σ 3,i+1 , the real conversion pressure of rock σ 3,t Between 3,i and σ 3,i+1 Between, that is, σ 3,i ≤σ 3,t ≤σ 3,i+1 In the present invention, the conversion pressure σ of the rock is 3,t Approximately determined as σ 3,t =σ 3,i+1 , that is, the minimum confining pressure on the side corresponding to the ductile deformation failure mode. This method of approximately determining the rock conversion pressure has a satisfactory safety factor for the prediction of high-stress hard rock rockbursts and the design of safety prevention and control measures parameters, and therefore meets the requirements of actual engineering applications.

[0091] 3. Establish rock failure surface in coordinate system OXYZ:

[0092] 3.1. Establish the π axis:

[0093] Establish a coordinate system, the coordinate points (x, y, z) in the coordinate system represent the principal stress state of the rock σ 1 , σ 2 , σ 3 .

[0094] The straight line in the coordinate system: x = y = z is defined as the π axis, also called the isoclinic axis or the hydrostatic pressure axis, such as Figure 3 The geometric characteristics of the π axis: it passes through the origin O and has equal angles with the three coordinate axes X, Y, and Z, that is, θ x =θ y =θ z , the isoclinic axis is named after it; when the coordinate system rotates around the π axis by any angle, the π axis of the original coordinate system is also the π axis of the new coordinate system, that is, during the rotation of the coordinate system around the π axis, the π axis remains unchanged. The physical meaning of the π axis: at the coordinate point on the π axis, the corresponding three coordinate components are equal, indicating that the principal stresses in the three directions of the rock are equal, that is, σ 1 =σ 2 =σ 3 , which is similar to the hydrostatic pressure state, and the hydrostatic pressure axis is named after it.

[0095] 3.2. Establish the coordinate points of the conventional triaxial compression failure stress state in the coordinate system:

[0096] According to the conventional triaxial compression test of rock, the corresponding stress state σ when the rock is compressed to failure at different confining pressure levels is obtained 1,i , σ 3,i , σ3,i , establish its coordinate points as follows:

[0097] The first group of tests: confining pressure is σ 3,1 The principal stress state is σ 1,1 , σ 3,1 , σ 3,1 ;

[0098] The second test group: confining pressure is σ 3,2 The principal stress state is σ 1,2 , σ 3,2 , σ 3,2 ;

[0099]

[0100] The i-th group of tests: the confining pressure is σ 3,i The principal stress state is σ 1,i , σ 3,i , σ 3,i ;

[0101] The i+1 group of tests: the confining pressure is σ 3,i+1 The principal stress state is σ 1,i+1 , σ 3,i+1 , σ 3,i+1 ;

[0102] Then, all the principal stress state points are used to establish the coordinate points in the coordinate system. The method is: for each group of test results, assume that the three stress states σ of the i-th group of tests 1,i , σ 3,i , σ 3,i , which are set in turn as the three coordinate components in the coordinate system. Therefore, the stress state of each set of test results corresponds to the three coordinate points A in the coordinate system. i , A i ′、A i ″, the coordinate components of each coordinate point are:

[0103]

[0104] The details are as follows:

[0105] Coordinate points of principal stress states for the first group of tests:

[0106]

[0107] Coordinate points of principal stress states for the second group of tests:

[0108]

[0109] The principal stress state coordinate points of the i-th group of tests are as follows: Figure 3 and Figure 4 :

[0110]

[0111] The principal stress state coordinate points of the i+1 group of tests are as follows: Figure 4 and Figure 5 :

[0112]

[0113] 3.3. Make a π plane circle in the coordinate system:

[0114] In each group of experiments, assuming that the i-th group of experiments has 3 coordinate points A in the coordinate system i , A i ′、A i ″, these three coordinate points are connected in pairs to form three arcs with central angles of 120°. The three arcs form a circle. The π axis is perpendicular to the circle and passes through the center of the circle. The circle is defined as the π plane circle. According to this method, the π plane circles of all groups, i.e., the test results of i=1,2…, are made.

[0115] For each π plane circle, taking the i-th group of test results as an example, there are A i , A i ′、A i ″Three points, the coordinate values ​​of these three points are different, but the coordinate components have the property of sequential rotation. According to the requirements of the present invention applicable to isotropic rock media, these three points correspond to the same stress state: all of them are confining pressure σ 3,i The stress state of the conventional triaxial compression failure, these three special points are defined as: biaxial iso-stress characteristic points. Figure 2 and Figure 3 shown.

[0116] Corresponding to the stress state of the same conventional triaxial compression failure, the stress state point corresponds to three bidirectional equal stress characteristic points on the same π plane circle in the coordinate system. The corresponding geometric meanings of the three coordinate components of each characteristic point are: corresponding to the coordinate axis closest to the characteristic point, its coordinate component value is the corresponding coordinate component of all coordinate points on the π plane circle where it is located, corresponding to the two coordinate axes farthest from the characteristic point, its two coordinate component values ​​are equal and are both the minimum values ​​of the corresponding coordinate components of all coordinate points on the π plane circle where it is located. Figure 4 shown.

[0117] According to the geometric characteristics of the π axis in 3.1: the coordinate system is fixed around π. Therefore, by rotating the coordinate system OXYZ around π, the complex stress state point C on the same π plane circle can be transformed into the bidirectional isostress characteristic point position C' in the new coordinate system X'Y'Z''. Figure 5 shown.

[0118] For two different complex stress state points D and E on the same π plane circle, by rotating the coordinate system OXYZ around the π axis to obtain the new coordinate system OX′Y′Z′, the point D in the original coordinate system OXYZ can be transformed into the point D′ in the new coordinate system, and the coordinate value of the point D′ in the new coordinate system OX′Y′Z′ is equal to the coordinate value of the point E in the original coordinate system OXYZ, indicating that the stress states of D′ and E are equivalent. In addition, the two points D′ and D are originally the same point, but the coordinates in different coordinate systems are different, so the two points belong to the same stress state. Therefore, the two complex stress state points D and E are equivalent. Therefore, any two different points on the same π plane circle belong to equivalent stress states. In particular, the stress states of the three bidirectional isostress characteristic points on the same π plane circle are equivalent to each other. In addition to the equivalent value attributes, the directional attributes are also equivalent. This is because, when the stress state is established as a coordinate point in step 3.2, three coordinate points are established for the stress state of the same conventional triaxial compression failure. These three coordinate points are the three bidirectional isostress characteristic points on the π plane circle.

[0119] 3.4. Establish rock failure surface:

[0120] All two adjacent π plane circles in the coordinate system are connected by smooth surfaces to form a nearly conical surface that is extremely symmetrical about the π axis. This surface is defined as the rock failure surface. Each stress state corresponds to a π plane circle, so many conventional triaxial compression tests with different confining pressure levels correspond to many π plane circles. The adjacent here refers to the two adjacent confining pressure levels after the two groups of confining pressure level values ​​are sorted from small to large, and the π plane circles corresponding to these two adjacent confining pressure levels are also adjacent. The physical meaning of the rock failure surface: the stress state point located inside the surface indicates that the rock has not reached the failure state; the stress state point located on the surface indicates that the rock is in a critical state of failure; the stress state point located outside the surface indicates that the rock exceeds the failure state, which is impossible in reality. This virtual situation of exceeding the failure state may only occur for simulation results such as numerical calculations.

[0121] Since the rock failure surface is formed by smoothly connecting all π plane circles, according to the method in 3.2, the stress state of all points on the same π plane circle of the point falling on the rock failure surface or the point inside the surface is equivalent.

[0122] 4. Equivalent method for complex stress state:

[0123] Three-dimensional computer-aided software, such as CAD and Rhino, is used to establish the rock failure surface in the coordinate system.

[0124] For the complex stress state point P′ in the coordinate system, its three principal stress values ​​are: P′ a, P′ b , P′ c , draw a π plane circle passing through point P′.

[0125] On the π plane circle where point P′ is located, mark the position of the bidirectional isostress characteristic point P and pick up the coordinates of point P, which is (P a , P b , P c ), and P a >P b =P c The stress state corresponding to this coordinate value is equivalent to the actual stress state at point P′. Replacing the stress state at point P′ with the coordinates of P can make the complex stress state of rock equivalent to the bidirectional isostress state of conventional triaxial compression, which has stronger engineering applicability.

[0126] True triaxial compression test of rock with two unequal confining pressures σ 2 and σ 3 , whose stress state is generally σ 1 >σ 2 >σ 3 , which is a typical complex stress state. In the test design process, due to the two variable factors of confining pressure, a large number of test conditions may be required, the test workload is large, and the true triaxial test is expensive. Therefore, true triaxial compression tests are rarely used in practice, but conventional triaxial compression tests are used to approximate true triaxial compression tests. This approximation process is only based on the engineering error allowance requirements and lacks theoretical support of rock mechanics.

[0127] The complex stress state of the true triaxial compression test of rock is equivalent to the bidirectional iso-stress state of the conventional triaxial compression test, which has the advantage of being simple and practical for practical engineering applications that only consider the rock stress state value attribute. Through the equivalence of the stress state, it is possible to effectively avoid the true triaxial compression test of rock and use the conventional triaxial compression test of rock to reduce the cost of engineering tests. The error size of the test results is supported by the rock mechanics theory, and the promotion and application value is high.

Claims

1. A stress state graphical equivalent method based on rock failure surface, characterized in that: The steps include: Step 1: Establish a coordinate system OXYZ, and establish a π axis in the coordinate system OXYZ: Define the straight line x=y=z in the coordinate system OXYZ as the π axis; Step 2: Mark the coordinate point P of the complex stress state of rock in the coordinate system OXYZ in step 1 ′ : The complex stress state coordinate point P ′ The three principal stress values ​​are P ′ a , P ′ b , P ′ c ;P ′ The three coordinate components of the coordinate point are equal to its three principal stress values ​​P ′ a , P ′ b , P ′ c ; Execute step 3 or determine the state of the rock; Step 3: Make complex stress state point P ′ The π plane circle: P ′ The vertical distance from the coordinate point to the π axis is the radius, and P ′ The coordinate point rotates around the π axis, and its trajectory forms a complex stress state point P ′ The π plane circle; Step 4: Stress state graphical equivalence: The complex stress state point P in step 3 ′ On the π plane circle, find the position where a certain coordinate component has the largest value, mark the coordinate point of the position, and use it as the bidirectional isostress characteristic point P on the π plane circle. The stress state of the bidirectional isostress characteristic point P is different from the complex stress state P ′ The stress state is equivalent to Pick up the three coordinate components of the bidirectional isostress characteristic point P, which are P a , P b , P c , the values ​​of the three coordinate components are equal to the three principal stress values ​​of the bidirectional isostress characteristic point P, and the two minor principal stress values ​​of the three principal stresses are equal, that is, P a >P b =P c .

2. A stress state graphical equivalent method based on rock failure surface according to claim 1, characterized in that: In step 2, the process of determining the state of the rock is as follows: Step S1, establishing the coordinate points of the principal stress state during conventional triaxial compression failure in the coordinate system OXYZ: A conventional triaxial compression test is used to measure the principal stress state of the rock when it reaches failure at different confining pressure levels. One principal stress state corresponds to three coordinate points in the coordinate system OXYZ, and the three coordinate points are three bidirectional isostress characteristic points. Each confining pressure level obtains three bidirectional isostress characteristic points at the confining pressure level. Step S2, making π plane circles at various confining pressure levels: For each of the three bidirectional isostress characteristic points under each confining pressure level, two adjacent bidirectional isostress characteristic points are connected by arcs in sequence, and all of them are enclosed to form a π plane circle; each of the π plane circles is perpendicular to the π axis, and the center of the circle is located on the π axis; each confining pressure level obtains a π plane circle under the confining pressure level; Step S3: Establish rock failure surface: The two π plane circles of each adjacent confining pressure level in step S2 are connected by a smooth curved surface to form a nearly conical curved surface that is extremely symmetrical about the π axis, and the curved surface is a rock failure curved surface; any two different points on the circumference of each of the same π plane circles belong to an equivalent stress state; Step S4: rock damage judgment under complex stress state: When P ′ The coordinate point is within the rock failure surface in step S3, indicating that the rock is in a complex stress state P ′ The state has not reached destruction; when P ′ The coordinate point falls on the rock failure surface, indicating that the rock is in a complex stress state P ′ When P ′ The coordinate point falls outside the rock failure surface, indicating that the rock is in the complex stress state P obtained by numerical calculation. ′ An overload occurred in the state.

3. A method for distinguishing rock failure modes under complex stress states, characterized in that: Based on the stress state graphical equivalent method based on rock failure surface described in claim 1, after step 4, it also includes the following: Step 5: Determine the conversion pressure σ of the rock sample 3,t : The minimum confining pressure for rock to undergo ductile deformation failure is defined as the rock transformation pressure σ 3,t ; Step 6: The two minor principal stress values ​​P of the bidirectional isostress characteristic point P in step 4 are b or P c and rock conversion pressure σ 3,t Compare, when P b =P c ≥σ 3,t When the complex stress state P ′ The rock under the condition of ductile deformation failure mode occurs when P b =P c <σ 3,t When the complex stress state P ′ The rock below undergoes brittle fracture failure mode.

4. A method for establishing a rock failure surface, characterized in that: The steps include: Step A1: Establish the π axis in the coordinate system OXYZ: Define the straight line x=y=z in the coordinate system OXYZ as the π axis; Step A2: Establish the coordinate points of the conventional triaxial compression failure principal stress state in the coordinate system OXYZ: A conventional triaxial compression test is used to measure the principal stress state of the rock when it reaches failure at different confining pressure levels. One principal stress state corresponds to three coordinate points in the coordinate system OXYZ, and the three coordinate points are three bidirectional isostress characteristic points. Each confining pressure level obtains three bidirectional isostress characteristic points at the confining pressure level. Step A3: Make a π plane circle: For three bidirectional isostress characteristic points under each confining pressure level, arcs are connected to two adjacent bidirectional isostress characteristic points to form a π plane circle; each π plane circle is perpendicular to the π axis, and the center of each circle is located on the π axis; Step A4: Create rock failure surface: Each adjacent two π plane circles in the step three are connected by a smooth curved surface to form a nearly conical curved surface that is extremely symmetrical about the π axis, and the curved surface is a rock failure surface; any two different points on the circumference of the same π plane circle belong to an equivalent stress state.

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