Rock strain softening constitutive model construction method
By constructing a constitutive model for rock strain softening, the problem of fitting existing models is solved, and an accurate description of the post-failure stage of rock is achieved, along with simplified data import, thus improving the efficiency of engineering calculations.
Patent Information
- Application Number
- CN202511122645.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-08-12
- Publication Date
- 2025-10-31
AI Technical Summary
Existing constitutive models of rock failure processes are difficult to fit accurately, especially in the post-failure stage, and there are difficulties in importing these models into numerical software, resulting in significant differences between the calculated results and the actual situation.
A method for constructing a rock strain softening constitutive model is adopted. By determining the axial stress-axial strain curve of the rock, dividing it into multiple straight lines, calculating the axial cumulative plastic strain and cohesion, and importing the data into the strain softening model of FLAC3D software, a simplified rock strain softening constitutive model is constructed.
It achieves accurate fitting of the nonlinear strain softening process of rocks, simplifies the data import process, and improves the efficiency of practical engineering calculations.
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Figure CN120871297A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of rock mechanics, and more particularly to a method for constructing a constitutive model of rock strain softening. Background Technology
[0002] Numerous indoor rock tests have yielded full stress-strain curves indicating that the rock failure process can be divided into four stages: microfracture compaction, elasticity, stable fracture propagation, unstable fracture propagation, and post-failure. Figure 2 As shown, commonly used elastic constitutive models and the traditional Mohr-coulomb constitutive model are difficult to fit the rock characteristics in the post-failure stage, and strain softening constitutive models are required to represent them.
[0003] Ideal strain softening constitutive models often use a straight line to describe the evolution of post-peak intensity parameters, which can easily lead to discrepancies between simulation results and actual values. Non-ideal strain softening constitutive models typically employ functional expressions derived through fitting and derivation, a method that suffers from drawbacks such as complexity and poor versatility. Furthermore, importing these constitutive models into numerical software presents certain difficulties. Summary of the Invention
[0004] To address the aforementioned shortcomings in existing technologies, this invention provides a method for constructing a rock strain softening constitutive model. This model can effectively fit the nonlinear strain softening process exhibited by rocks after reaching peak strength in actual experiments. Furthermore, it allows for relatively simple importation of experimental data from small rock samples into FLAC. 3D The software is designed to be used for calculations in actual working conditions such as slope stability and tunnel excavation.
[0005] To achieve the above objectives, the technical solution adopted by this invention is: a method for constructing a rock strain softening constitutive model, comprising the following steps:
[0006] Curve determination: Determine the measured axial stress-axial strain curve of the rock to be fitted;
[0007] Curve division: Based on engineering requirements, the post-peak strain softening curve of the rock axial stress-axial strain curve is divided into j segments, and each segment is simplified to a straight line.
[0008] Parameter definition: Based on the partitioning results, the axial strain and axial stress of the peak strength are denoted as... And the axial strain and axial stress at the right endpoint of each segment divided into j segments are recorded as follows: and ,in, Let represent the axial strain at point j. This represents the axial stress at point j. This represents the axial stress at the peak strength point. This represents the axial strain at the peak strength point;
[0009] Calculation of axial cumulative plastic strain: Based on the axial stress and axial strain at the peak strength and the axial stress and axial strain at the right end of each segment, the axial cumulative plastic strain at each point is calculated.
[0010] Cohesion calculation: Calculate the cohesion at each point based on the cumulative axial plastic strain;
[0011] Model construction: The axial cumulative plastic strain and cohesion at each point are imported into FLAC in tabular form. 3D In the software, the constitutive model of rock strain softening is constructed.
[0012] Furthermore, the expression for the axial cumulative plastic strain is as follows:
[0013] ;
[0014] in, This represents the axial cumulative plastic strain at point j. Indicates the first Axial cumulative plastic strain at a point Indicates the elastic modulus. This represents the axial stress at point j. Indicates the first Axial stress at a point Let represent the axial strain at point j. Indicates the first Axial strain at a point.
[0015] Furthermore, the expression for the cohesive force is as follows:
[0016] ;
[0017] ;
[0018] in, Denotes the cohesive force at point j. Indicates the first Axial stress at a point Indicates the elastic modulus. This represents the axial cumulative plastic strain at point j. Indicates the first Axial cumulative plastic strain at a point Let represent the axial strain at point j. Indicates the first Axial strain at a point Indicates confining pressure. Indicates the angle of internal friction. Indicates process parameters.
[0019] Furthermore, the axial cumulative plastic strain and cohesion at each point are imported into FLAC in tabular form. 3D Specifically, in the software:
[0020] The cumulative axial plastic strain and cohesion at each point are calculated using a fish table. Import to FLAC in the form of 3D The software's built-in strain softening model is used to construct a constitutive model for rock strain softening. This represents the axial cumulative plastic strain at point j. Let j represent the cohesive force at point j.
[0021] The beneficial effects of this invention are:
[0022] (1) This invention can consider both ideal linear strain softening constitutive relation curves and nonlinear strain softening constitutive relation curves. Furthermore, fitting nonlinear curves is relatively simple, which to some extent solves the problems of complexity, limitations and poor fitting effect of the previous single equation fitting method.
[0023] (2) The axial cumulative plastic strain-cohesion fish function import method adopted in this invention is very compatible with FLAC. 3D The software's built-in strain softening model simplifies the process of converting measured data into a software model, thereby improving the efficiency of practical engineering calculations. Attached Figure Description
[0024] Figure 1 This is a flowchart of the method of the present invention.
[0025] Figure 2 This is a schematic diagram of the full stress-strain curve of rock and commonly used constitutive models.
[0026] Figure 3 A schematic diagram of the constitutive curve for ideal strain softening.
[0027] Figure 4 This is a schematic diagram of the constitutive curve and simplified curve for non-ideal strain softening.
[0028] Figure 5 This is a schematic diagram of the axial stress-axial strain curves of rock obtained from actual measurement, segmentation, and simulation.
[0029] Figure 6 FLAC used for calculation 3D Schematic diagram of the model. Detailed Implementation
[0030] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.
[0031] Example
[0032] Based on the background technology, this invention makes certain modifications to previous research. Under the assumption that the internal friction angle does not change and there is no shear dilatation during the strain softening stage, a rock strain softening constitutive model is derived using geometric relationships and the idea of substituting straight lines for curves. This rock strain softening constitutive model can be imported into FLAC in the form of axially accumulated plastic deformation-cohesion. 3D The built-in strain softening constitutive model in the software simplifies the process of converting measured data to numerical software. The principle of this invention is as follows:
[0033] Assuming that the stress state at every point after rock softening conforms to the Mohr-coulomb yield criterion, and The yield surface then takes the form of:
[0034]
[0035]
[0036] Where σ1 represents the maximum principal stress, σ2 represents the intermediate principal stress, σ3 represents the minimum principal stress, ε represents strain, c represents cohesion, and φ represents the angle of internal friction. =0 represents the expression for the yield surface, and Nφ represents the process parameters.
[0037] Studies show that the cohesion of rock gradually decreases during the strain softening stage, while the internal friction angle remains almost unchanged, so Nφ can be considered a constant. Since the confining pressure σ3 remains constant, the rock cohesion during the strain softening stage is only a function of σ1(ε), i.e.:
[0038]
[0039] In the construction of general strain softening constitutive models, different strain softening parameters are often used to replace the strain ε. FLAC 3D The strain softening parameter used is the equivalent axial cumulative plastic strain ε. p Its defining formula is:
[0040]
[0041]
[0042]
[0043] Where, ε ip (i = 1,3) corresponds to σ i The plastic principal strain components of (i = 1,3), where ψ represents the dilatation angle. Represents the equivalent axial cumulative plastic strain. Indicates process parameters.
[0044] When the shear expansion angle ψ = 0, by combining equations (4) to (6), we can obtain:
[0045]
[0046] Equation (7) shows that, without considering shear dilatation, the axial plastic strain ε can be used. 1p instead of epsilon p That is, the degree of weakening of cohesion is determined by ε. 1p If we decide, then equation (3) can be transformed into:
[0047]
[0048] in, Let j represent the cohesive force at point j.
[0049] Equation 8 shows that, in determining σ1(ε) 1p After that, the corresponding c(ε) can be obtained. 1p Based on this, using the calculated i points [ , c( Create the Fish function and import it into FLAC. 3D A strain softening constitutive model can then be constructed. The problem then becomes solving for the axial plastic strain ε during the strain softening stage. 1p The functional relationship between the axial compression σ1 and the axial compression σ1.
[0050] In plasticity mechanics, it is often assumed that the unloading process of rock is linearly elastic, meaning that the slope of the unloading path at any stage after the peak is the elastic modulus E0, and the unloading path intersects the horizontal axis at a point, which in the σ1-ε1 coordinate system represents the axial cumulative plastic strain ε. 1p Under any confining pressure σ3, plot the ideal strain softening constitutive curve and the unloading path at any point, as shown below. Figure 3 As shown.
[0051] Figure 3 In the diagram, OAC represents the stress-strain curve of the ideal strain softening constitutive curve, with point A... The peak point is at point B. Unload, intersecting the horizontal axis at point D. It can be known from simple geometric relationships that... The formula for calculating the axial cumulative plastic strain at that time is:
[0052]
[0053] in, This represents the axial cumulative plastic strain at point j. , Both represent the length of a line segment, and their practical meaning is as follows: Figure 3 As shown, This represents the axial stress at point 0 (peak strength point). This represents the axial stress at point 1. This represents the axial strain at point 1. This represents the axial strain at point 0 (peak strength point).
[0054] Equation (9) is the axial plastic strain ε 1p The functional relationship between the axial compression σ1 and the axial compression σ1. When a equals zero in equation (9), the material does not soften and is an ideal elastoplastic body. This case can be regarded as a special case of the strain softening model. Thus, the ideal strain softening constitutive curve in FLAC 3D The implementation process is derivation complete, that is: for any strain softening constitutive model, first divide it into i (i > 0) points, calculate the axial cumulative plastic strain corresponding to each point according to equation (9), then calculate the weakened cohesion corresponding to each point according to equation (8), and finally convert the data into [ , c( Importing FLAC into FLAC using the Fish function in the form of )] 3D middle.
[0055] The above derivation is based on an ideal model where the post-peak stress-strain curve is linear. However, many measured data show that the post-peak strain curve is not linear. Therefore, referring to the previous method of "substituting a straight line for a curve", equation (9) is modified. The post-peak curve is divided into segments j (j > 0), where j = 0 corresponds to the peak point, such as Figure 4 As shown.
[0056] The coordinates of the right endpoint of segment j are Ignoring the intervals between paragraphs, corresponding This represents the axial cumulative plastic strain of that segment. The derivation has already been completed in equation (9). Taking the second curve segment as an example, the subsequent derivation will be carried out from... Figure 3 It can be known The formula for calculation is:
[0057]
[0058] Therefore, we can know that the j-th (j > 0) segment corresponds to for:
[0059]
[0060] Combining equations (8) and (11), the cohesive force at the right endpoint of segment j (j > 0) is:
[0061]
[0062] in, Denotes the cohesive force at point j. Indicates the first Axial stress at a point For process parameters, Indicates the elastic modulus. This represents the axial cumulative plastic strain at point j. Indicates the first Axial cumulative plastic strain at a point Let represent the axial strain at point j. Indicates the first Axial strain at a point It indicates confining pressure.
[0063] The post-peak stage is divided into j segments. The axial cumulative plastic strain and weakened cohesion are calculated sequentially using equations (11) and (12). The data are then presented in [...]. , c( Importing FLAC into FLAC using the Fish function in the form of )] 3D In this way, FLAC can be implemented. 3D The constitutive curve for non-ideal strain softening is constructed, and the model accuracy is proportional to the value of j. When j → ∞, it is theoretically possible to fit softening curves of arbitrary shapes.
[0064] like Figure 1 As shown, this invention provides a method for constructing a constitutive model of rock strain softening, the implementation method of which is as follows:
[0065] Curve determination: Determine the measured axial stress-axial strain curve of the rock to be fitted;
[0066] In this embodiment, the axial stress-axial strain curve of the rock is typically obtained through multiple sets of triaxial rock tests. Here, we select the axial stress-axial strain curve of a specific rock, such as... Figure 5 As shown. Some basic parameters used in the calculation are: confining pressure σ3 is 30 MPa, Poisson's ratio υ is 0.3, and internal friction angle φ is 50°.
[0067] Curve division: Based on engineering requirements, the post-peak strain softening curve of the rock axial stress-axial strain curve is divided into j segments, and each segment is simplified to a straight line.
[0068] In this embodiment, the method of substituting straight lines for curves is used to divide the post-peak strain softening curve of the selected rock axial stress-axial strain curve into 5 segments, such as... Figure 5 As shown.
[0069] Parameter definition: Based on the partitioning results, the axial strain and axial stress of the peak strength are denoted as... And the axial stress and axial strain at the right endpoint of each segment divided into j segments are recorded as follows: and ;
[0070] In this embodiment, a total of 5 segments are divided, so there are 6 axial stress-axial strain points, as shown in Table 1. Table 1 is a table of axial stress-axial strain corresponding to the right side of each segment of the peak intensity and post-peak curve.
[0071] Table 1
[0072]
[0073] Calculation of axial cumulative plastic strain: Based on the elastic model, the axial stress and axial strain at the peak strength, and the axial stress and axial strain at the right end of each segment, the axial cumulative plastic strain at each point is calculated.
[0074] In this embodiment, the elastic modulus E0 approximates the slope of the elastic phase, according to Figure 4 The measured curve yielded an E0 of approximately 35.149 GPa. The axial cumulative plastic strain at point j... The calculation formula is: ,in, This represents the axial cumulative plastic strain at point j. Indicates the first Axial cumulative plastic strain at a point Indicates the elastic modulus. This represents the axial stress at point j. Indicates the first Axial stress at a point Let represent the axial strain at point j. Indicates the first Axial strain at a point.
[0075] In this embodiment, the axial cumulative plastic strain at each point is calculated. As shown in Table 2, Table 2 is a table of axial cumulative plastic strain at each point.
[0076] Table 2
[0077]
[0078] Cohesion calculation: Calculate the cohesion at each point based on the cumulative axial plastic strain;
[0079] In this embodiment, the cohesion at each point is calculated based on the internal friction angle, elastic modulus, axial stress, confining pressure, axial strain, and the axial cumulative plastic strain obtained above.
[0080] The cohesive force c at point j ( The calculation formula is: When using the above formula, you should first use formula N. φ N is calculated as (1+sinφ) / (1-sinφ). φ Since the internal friction angle φ in this case is 50°, N φ Approximately 7.549. Among them, Denotes the cohesive force at point j. Indicates the first Axial stress at a point For process parameters, Indicates the elastic modulus. This represents the axial cumulative plastic strain at point j. Indicates the first Axial cumulative plastic strain at a point Let represent the axial strain at point j. Indicates the first Axial strain at a point Indicates any confining pressure. This represents the internal friction angle.
[0081] The cohesive force c at each point was calculated. As shown in Table 3, Table 3 is a table of axial cumulative plastic strain at each point.
[0082] Table 3
[0083]
[0084] Model construction: The axial cumulative plastic strain and cohesion at each point are imported into FLAC in tabular form. 3D The software constructs a rock strain softening constitutive model, which can be used for calculations such as rock slope stability, tunnel surrounding rock deformation, and dislocation amount in active fault zones. Specifically:
[0085] The cumulative axial plastic strain and cohesion at each point are calculated using a fish table. Import to FLAC in the form of 3D The software's built-in strain softening model is used to construct a constitutive model for rock strain softening. This represents the axial cumulative plastic strain at point j. Let j represent the cohesive force at point j.
[0086] In this embodiment, the axial cumulative plastic strain and the cohesive force corresponding to each point are used as... Import to FLAC in the form of 3D In the software's built-in strain softening model, a standard triaxial rock specimen with a diameter of 50 mm and a height of 100 mm is constructed, such as... Figure 6 As shown. A confining pressure of 30 MPa was applied to the side of the cylinder, and velocity boundary conditions were applied to both sides. After continuous adjustments to achieve a realistic triaxial environment, the resulting axial stress-axial strain curves are shown below. Figure 5 As shown, the results are quite close to the actual measurements.
Claims
1. A method for constructing a constitutive model for rock strain softening, characterized in that, Includes the following steps: Curve determination: Determine the measured axial stress-axial strain curve of the rock to be fitted; Curve division: Based on engineering requirements, the post-peak strain softening curve of the rock axial stress-axial strain curve is divided into j segments, and each segment is simplified to a straight line. Parameter definition: Based on the partitioning results, the axial strain and axial stress of the peak strength are denoted as... And the axial strain and axial stress at the right endpoint of each segment divided into j segments are recorded as follows: and ,in, Let represent the axial strain at point j. This represents the axial stress at point j. This represents the axial stress at the peak strength point. This represents the axial strain at the peak strength point; Calculation of axial cumulative plastic strain: Based on the axial stress and axial strain at the peak strength and the axial stress and axial strain at the right end of each segment, the axial cumulative plastic strain at each point is calculated. Cohesion calculation: Calculate the cohesion at each point based on the cumulative axial plastic strain; Model construction: The axial cumulative plastic strain and cohesion at each point are imported into FLAC in tabular form. 3D Within the software, the constitutive model for rock strain softening is constructed.
2. The method for constructing a rock strain softening constitutive model according to claim 1, characterized in that, The expression for the axial cumulative plastic strain is as follows: ； in, This represents the axial cumulative plastic strain at point j. Indicates the first Axial cumulative plastic strain at a point Indicates the elastic modulus. This represents the axial stress at point j. Indicates the first Axial stress at a point Let represent the axial strain at point j. Indicates the first Axial strain at a point.
3. The method for constructing a rock strain softening constitutive model according to claim 1, characterized in that, The expression for the cohesive force is as follows: ； ； in, Denotes the cohesive force at point j. Indicates the first Axial stress at a point Indicates the elastic modulus. This represents the axial cumulative plastic strain at point j. Indicates the first Axial cumulative plastic strain at a point Let represent the axial strain at point j. Indicates the first Axial strain at a point Indicates confining pressure. Indicates the angle of internal friction. Indicates process parameters.
4. The method for constructing a rock strain softening constitutive model according to claim 1, characterized in that, Import the axial cumulative plastic strain and cohesion at each point into FLAC in tabular form. 3D Specifically, in the software: The cumulative axial plastic strain and cohesion at each point are calculated using a fish table. Import to FLAC in the form of 3D The software's built-in strain softening model is used to construct a constitutive model for rock strain softening. This represents the axial cumulative plastic strain at point j. Let j represent the cohesive force at point j.