Method for determining weakly cemented soft rock creep rate demarcation point
Patent Information
- Application Number
- CN202311578240.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-11-23
- Publication Date
- 2026-10-27
- Estimated Expiration
- 2043-11-23
AI Technical Summary
[0026](1)本发明开展了不同含水条件下弱胶结软岩的分级蠕变试验,获取了不同含水条件下弱胶结软岩的蠕变特征和蠕变速率特征。
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Figure CN117606929B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of geotechnical engineering technology, and in particular to a method for determining the creep rate boundary point of weakly cemented soft rock. Background Technology
[0002] Large deformations and even instability in rock masses are closely related to creep. Under long-term loads, rock masses undergo instantaneous deformation and creep. When the external load on the rock mass exceeds its long-term strength, the total strain of the rock mass includes four processes: instantaneous deformation, decaying creep, constant-rate creep, and accelerated creep. When the external load on the rock mass is less than its long-term strength, the total strain of weakly cemented soft rock includes three processes: instantaneous strain, decaying creep, and constant-rate creep. Throughout the creep process, when the external load on the rock mass exceeds its long-term strength, the rock mass will eventually enter the accelerated creep stage and ultimately fail. Therefore, determining the boundary between decaying creep and constant-rate creep, as well as the boundary between constant-rate creep and accelerated creep, is a key technical challenge that the geotechnical creep constitutive model urgently needs to address, and it is of great significance to the safety and long-term stability of rock mass engineering structures. Summary of the Invention
[0003] To address the aforementioned technical problems, this invention provides a method for determining the boundary point of creep rate in weakly cemented soft rock. This method can determine the boundary point t1 between decaying creep and constant creep, as well as the boundary point t2 between constant creep and accelerated creep, providing a basis for long-term stability and safety analysis in rock mass engineering.
[0004] To solve the above-mentioned technical problems, the present invention provides the following solution:
[0005] This invention provides a method for determining the creep rate boundary point of weakly cemented soft rock, the method comprising:
[0006] S1: Conduct graded creep tests on weakly cemented soft rock to obtain creep data of weakly cemented soft rock;
[0007] S2: Plot the creep-time curve based on the creep data, obtain the creep rate-time relationship curve, and the creep characteristics and creep rate characteristics of weakly cemented soft rock under different water conditions;
[0008] S3: Based on Casagrande's approach to determining the preconsolidation pressure of soil, the creep rate curve tangent method is used to find the intersection point C of the tangent line at the maximum curvature point A of the decay creep rate curve and the steady-state creep rate curve, and the intersection point D of the tangent line at the maximum curvature point B of the acceleration creep rate curve and the steady-state creep rate curve.
[0009] S4: According to the method of finding the point of maximum curvature to obtain the intersection point, the abscissa values corresponding to the intersection point C and the intersection point D are respectively regarded as the boundary point t1 between the decay creep and the constant creep of the weakly cemented soft rock and the boundary point t2 between the constant creep and the accelerated creep.
[0010] S5: Substitute the creep rate boundary points t1 and t2 determined in steps S1 to S4 into the creep damage constitutive model, and fit the experimental data using the Trust-Region algorithm to obtain the model parameters E0, E1, η1, η2, η3, β1, β2, α1, α2, α3.
[0011] Preferably, the creep test of weakly cemented soft rock is a staged unloading confining pressure test. Specifically, the unloading creep test uses the stress control module in the advanced loading module to load the sample to the initial stress state of axial and confining pressure at a loading rate of 0.1 MPa / min and maintain it constant. Then, while keeping the axial pressure constant, the confining pressure is unloaded to a predetermined value at an unloading rate of 0.05 MPa / s, and the sample's stress state is maintained constant for approximately 50 hours before proceeding to the next stage of unloading. The confining pressure is unloaded in 5 stages, and the deviatoric stress after each stage of unloading is taken as 30%, 40%, 50%, 55%, and 60% of the uniaxial compressive strength of the rock.
[0012] Preferably, the creep rate-time curve of the present invention includes two types: steady-state creep and unsteady-state creep. The steady-state creep includes two stages: decaying creep and constant-rate creep. The unsteady-state creep includes three stages: decaying creep, constant-rate creep, and accelerated creep. By taking the first derivative of the creep curve, the creep rate-time curve of weakly cemented soft rock at different stress levels can be obtained. In the decaying creep stage, the creep rate continuously decreases, corresponding to the stage of rapid decline in the creep rate-time curve. In the constant-rate creep stage, the creep rate remains constant, corresponding to the stage of stable creep rate-time curve. In the accelerated creep stage, the creep rate continuously increases, corresponding to the stage of rapid rise in the creep rate-time curve.
[0013] Preferably, the method for determining the boundary point t1 between decaying creep and constant-rate creep, and the boundary point t2 between constant-rate creep and accelerated creep, is proposed based on Casagrande's approach to determining the preconsolidation pressure of soil. The specific steps include:
[0014] (1) When the stress level exceeds the long-term strength of the rock mass, the creep curve includes three stages: decay creep, constant creep and accelerated creep. Find the maximum curvature points A and B of the creep rate in the decay creep stage and the accelerated creep stage respectively on the creep rate-time curve. Draw the tangent AC of the maximum curvature radius of the decay creep rate curve through point A and intersect the extension of the constant creep rate curve at point C. The abscissa t1 corresponding to point C is the boundary point between the decay creep stage and the constant creep stage.
[0015] (2) Draw the tangent line BD of the maximum radius of curvature of the accelerated creep rate curve through point B and intersect the extension of the constant creep rate curve at point D. The abscissa t2 corresponding to point D is the dividing point between the constant creep stage and the accelerated creep stage.
[0016] (3) When the stress level is lower than the long-term strength of the rock mass, the creep curve includes two stages: decay creep and constant creep. At this time, it is only necessary to find the point A with the maximum curvature in the decay creep stage, draw the tangent AC of the maximum curvature radius of the decay creep rate curve through point A and intersect the extension of the constant creep rate curve at point C. The abscissa t1 corresponding to point C is the boundary point between the decay creep stage and the constant creep stage.
[0017] Preferably, the creep damage constitutive model is a six-element fractional-order damage constitutive model, and its creep equation is as follows:
[0018] When σ0 < σ s hour,
[0019]
[0020]
[0021] When σ0≥σ s hour,
[0022]
[0023] In the formula: σ0 is the level of deviatoric stress, MPa; σ s η0 represents the long-term strength of weakly cemented soft rock, in MPa; η1, η2, and η3 are the viscosity coefficients of the viscoelastic, viscous, and viscoplastic damage elements, respectively; β1 and β2 are the order of the fractional-order damage cuvette; E0 is the elastic modulus of the elastic element; E1 is the elastic modulus of the fractional-order Kelvin model; α1, α2, and α3 are the coefficients characterizing the damage correlation of rock mass materials, obtained by fitting experimental data; t1 and t2 are the boundary points between decaying creep and constant-rate creep, and between constant-rate creep and accelerated creep, respectively.
[0024] Preferably, the creep rate boundary points t1 and t2 are substituted into the creep constitutive model to obtain the model parameters. E0, E1, η1, η2, η3, β1, β2, α1, α2, α3 can be used to predict creep deformation of weakly cemented soft rock and the critical time point for creep failure of roadways under different stress levels and water content conditions.
[0025] The beneficial effects of this invention are:
[0026] (1) The present invention carried out graded creep tests on weakly cemented soft rocks under different water conditions, and obtained the creep characteristics and creep rate characteristics of weakly cemented soft rocks under different water conditions.
[0027] (2) Based on Casagrande's approach to determining the preconsolidation pressure of soil, this invention proposes a method for determining the boundary point t1 between the decaying creep stage and the constant creep stage and the boundary point t2 between the constant creep stage and the accelerated creep stage, based on the characteristics of the creep rate curve.
[0028] (3) The present invention can substitute the obtained creep rate boundary points t1 and t2 into the creep constitutive model, and fit the experimental data through the Trust-Region algorithm to obtain the model parameters E1, η1, η2, η3, β1, β2, α1, α2, α3, which can be used for creep prediction of weakly cemented soft rock and prediction of the critical time point of creep failure of roadway under different stress levels and water conditions. Attached Figure Description
[0029] Figure 1 A flowchart of a method for determining the creep rate boundary point of weakly cemented soft rock provided by the present invention;
[0030] Figure 2 The creep and creep rate curves of weakly cemented soft rock with a water content of 0% (dry state) provided for embodiments of the present invention;
[0031] Figure 3 The creep and creep rate curves of weakly cemented soft rock with a water content of 5.33% (natural state) are provided for embodiments of the present invention.
[0032] Figure 4 The creep and creep rate curves of weakly cemented soft rock with a water content of 7.05% (natural state) are provided for embodiments of the present invention.
[0033] Figure 5 The creep and creep rate curves of weakly cemented soft rock with a water content of 9.36% (natural state) are provided for the embodiments of the present invention.
[0034] Figure 6 The creep and creep rate curves of weakly cemented soft rock with a water content of 12.18% (saturated state) are provided for the embodiments of the present invention.
[0035] Figure 7 Creep curves of weakly cemented soft rock under different stress levels with a moisture content of 0% (dry state) provided for embodiments of the present invention;
[0036] Figure 8Creep curves of weakly cemented soft rock under different stress levels with a water content of 5.33% (dry state) provided for embodiments of the present invention;
[0037] Figure 9 Creep curves of weakly cemented soft rock at different stress levels with a water content of 7.05% (natural state) provided for embodiments of the present invention;
[0038] Figure 10 Creep curves of weakly cemented soft rock at different stress levels with a water content of 9.36% (natural state) provided for embodiments of the present invention;
[0039] Figure 11 Creep curves of weakly cemented soft rock under different stress levels with a water content of 12.18% (saturated state) provided for embodiments of the present invention;
[0040] Figure 12 A schematic diagram of the method for determining the creep rate boundary point is provided for embodiments of the present invention;
[0041] Figure 13 This is a graph showing the variation of t1 under different water content conditions, provided in an embodiment of the present invention.
[0042] Figure 14 This is a graph showing the variation of t2 under different water content conditions provided in an embodiment of the present invention.
[0043] Figure 15 The creep constitutive model provided for embodiments of the present invention. Detailed Implementation
[0044] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are for illustrative purposes only and are not intended to limit the scope of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.
[0045] Example 1
[0046] This invention provides a method for determining the creep rate boundary point of weakly cemented soft rock, with reference to... Figure 1 As shown, the method for determining the creep rate boundary point of the weakly cemented soft rock includes:
[0047] S1: Conduct graded loading creep tests on weakly cemented soft rock to obtain creep data of weakly cemented soft rock;
[0048] The creep data of the weakly cemented soft rock include:
[0049] The loading deviatoric stress q, time t, and axial strain ε of the specimen in the creep of weakly cemented soft rock.
[0050] S2: Based on the creep data, plot the creep-time curve and the creep rate-time curve, and analyze the creep characteristics and creep rate characteristics of weakly cemented soft rock under different water conditions.
[0051] Furthermore, the creep variable-time relationship curves for the entire creep test process are plotted. Based on the principle of linear superposition, the creep data are processed to obtain the creep variable-time relationship curves for each loading stage.
[0052] By taking the first derivative of the creep rate curve, the creep rate-time relationship curves of weakly cemented soft rock under different water content conditions and different stress levels are obtained.
[0053] S3: Based on Casagrande's approach to determining the preconsolidation pressure of soil, find the intersection point C of the tangent line at the maximum curvature point A of the decay creep rate curve and the steady-state creep rate curve, and the intersection point D of the tangent line at the maximum curvature point B of the accelerated creep rate curve and the steady-state creep rate curve.
[0054] Casagrande's approach to determining the preconsolidation pressure of soil is to plot the indoor compression curve of the sample on the e-lgp coordinate system, then find the maximum point A on the compression curve, draw a horizontal line A1 through point A, a tangent line A2, and the bisector of the angle between them A3, and finally extend the straight line segment at the bottom of the compression curve upward to intersect line A3 and point B. The x-coordinate of point B is the preconsolidation pressure to be determined.
[0055] Based on this idea, on each creep rate-time relationship curve, find the intersection point C of the tangent line at the point of maximum curvature A of the decay creep rate curve and the steady-state creep rate curve, and the intersection point D of the tangent line at the point of maximum curvature B of the acceleration creep rate curve and the steady-state creep rate curve.
[0056] S4: According to the method of finding the point of maximum curvature to obtain the intersection point, the abscissa values corresponding to the intersection point C and the intersection point D are respectively regarded as the boundary point t1 between the decay creep and the constant creep of the weakly cemented soft rock and the boundary point t2 between the constant creep and the accelerated creep.
[0057] Based on this, a method is proposed to determine the boundary point t1 between decaying creep and constant-rate creep, and the boundary point t2 between constant-rate creep and accelerated creep.
[0058] S5: Substitute the creep rate boundary points t1 and t2 determined in steps S1 to S4 into the creep damage constitutive model, and fit the experimental data using the Trust-Region algorithm to obtain the model parameters;
[0059] The creep damage constitutive model is a six-element fractional-order creep damage constitutive model, and the parameters of the creep damage constitutive model include E0, E1, η1, η2, η3, β1, β2, α1, α2, α3.
[0060] Example 2
[0061] The effectiveness of the solution is further illustrated below with specific implementation examples. The creep test of weakly cemented soft rock conducted in this invention is a graded loading creep test under different water content conditions under unloading pressure. The samples were placed in a drying oven and dried at 105℃ for 24 hours to prepare dried samples with a moisture content w=0%. The original samples were taken, and the moisture contents were measured to be 5.33% (natural moisture content), 7.05% (natural moisture content), 9.36% (natural moisture content), and 12.18% (saturated state). Using a TAW-2000 triaxial rock testing machine, a uniaxial compression test was conducted with a displacement loading speed of 0.5 mm / min. The uniaxial compressive strengths of the weakly cemented soft rock under different water content conditions were tested to be 15.03 MPa, 13.18 MPa, 11.15 MPa, 8.52 MPa, and 6.38 MPa, respectively. The unloading pressure creep test used the stress control module in the advanced loading module to load the specimen to σ at a loading rate of 0.1 MPa / min. 10 =σ 30 The initial stress state is maintained and kept constant. Subsequently, the axial compression σ is maintained. 10 After the confining pressure is reduced to a predetermined value at a constant unloading rate of 0.05 MPa / s, the stress state of the sample is kept constant for about 50 hours before proceeding to the next stage of unloading. The confining pressure is unloaded in 5 stages, and the deviatoric stress after each stage of unloading is taken as 30%, 40%, 50%, 55%, and 60% of the uniaxial compressive strength of the rock.
[0062] Based on experimental data under different water content conditions, and according to the content described in Example 1 of the present invention, the creep variable-time relationship curves for each stage under different water content conditions can be obtained (e.g., Figures 2-6 (as shown) and the creep rate-time relationship curve (as shown) Figures 7-11 (as shown);
[0063] Analyze the relationship curves of creep variable-time and creep rate-time (e.g.) Figures 2-11 As shown, the creep-time curves can be obtained, including two types: steady-state creep and unsteady-state creep. The steady-state creep curve includes two stages: decaying creep and constant-rate creep; the unsteady-state creep includes three stages: decaying creep, constant-rate creep, and accelerated creep. Instantaneous deformation occurs at the moment of loading. In the decaying creep stage, creep exhibits non-linear growth, but its growth rate gradually decreases, i.e., the creep rate gradually decreases and eventually tends to a constant. In the constant-rate creep stage, creep exhibits linear growth, and its creep rate remains at a certain value. In the accelerated creep stage, creep exhibits non-linear rapid growth, and the growth rate gradually increases, i.e., the creep rate increases rapidly.
[0064] Based on Casagrande's approach to determining the preconsolidation pressure of soil, a method is proposed to determine the boundary point t1 between decaying creep and constant-rate creep, and the boundary point t2 between constant-rate creep and accelerated creep, based on the characteristics of the creep rate curve. The specific steps are as follows:
[0065] (1) When the stress level exceeds the long-term strength of the rock mass, the creep curve includes three stages: decay creep, constant creep and accelerated creep. Find the maximum curvature points A and B of the creep rate in the decay creep stage and the accelerated creep stage respectively on the creep rate-time curve. Draw the tangent AC of the maximum curvature radius of the decay creep rate curve through point A and intersect the extension of the constant creep rate curve at point C. The abscissa t1 corresponding to point C is the boundary point between the decay creep stage and the constant creep stage.
[0066] (2) Draw the tangent line BD of the maximum radius of curvature of the accelerated creep rate curve through point B and intersect the extension of the constant creep rate curve at point D. The abscissa t2 corresponding to point D is the dividing point between the constant creep stage and the accelerated creep stage.
[0067] (3) When the stress level is lower than the long-term strength of the rock mass, the creep curve includes two stages: decay creep and constant-rate creep. In this case, it is only necessary to find the point A with the maximum curvature in the decay creep stage. Draw the tangent AC to the maximum radius of curvature of the decay creep rate curve through point A and intersect it with the extension of the constant-rate creep rate curve at point C. The x-coordinate t1 corresponding to point C is the boundary point between the decay creep stage and the constant-rate creep stage. The specific diagram is as follows: Figure 12 As shown.
[0068] Based on the above method, the boundary points t1 between decaying creep and constant creep, and t2 between constant creep and accelerated creep, for weakly cemented soft rocks under different water conditions can be determined, as shown in Table 1. The variation patterns of these boundary points (t1 and t2) are analyzed under different water conditions. Figure 13 As shown in Figure 14, it can be seen from the figure that t1 and t2 both show an increasing trend with the increase of water content; substituting the creep rate boundary points t1 and t2 into the creep damage constitutive model (as shown in Figure 14); Figure 15 As shown in Table 2, the experimental data were fitted using the Trust-Region algorithm to obtain the model parameters E0, E1, η1, η2, η3, β1, β2, α1, α2, α3.
[0069] Table 1. t1 and t2 under different water content conditions;
[0070]
[0071] Table 2. Parameters of the fractional-order creep damage model;
[0072]
[0073] In summary, the method for determining the creep rate boundary point of weakly cemented soft rock proposed in this invention can be used to predict creep deformation of weakly cemented soft rock under different stress levels and water-bearing conditions, and to predict the critical time point for creep failure of roadways.
[0074] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for determining the creep rate boundary point of weakly cemented soft rock, characterized in that, Includes the following steps: S1. Conduct graded creep tests on weakly cemented soft rock to obtain creep data of weakly cemented soft rock; S2. Based on the creep data, plot the creep-time curve, obtain the creep rate-time curve, and analyze the creep characteristics and creep rate characteristics of weakly cemented soft rock under different water conditions. S3. Based on Casagrande's approach to determining the preconsolidation pressure of soil, the creep rate curve tangent method is used to find the intersection point C of the tangent line at the maximum curvature point A of the decaying creep rate curve and the steady-state creep rate curve, and the intersection point D of the tangent line at the maximum curvature point B of the accelerating creep rate curve and the steady-state creep rate curve. S4. Based on the method of finding the intersection point by finding the point of maximum curvature, the x-coordinate values corresponding to intersection points C and D are regarded as the boundary points between the decay creep and the constant creep of the weakly cemented soft rock. t 1 and the dividing point between constant-rate creep and accelerated creep t 2; S5. Determine the creep rate boundary points identified in steps S1 to S4. t 1 and t 2. Substitute the data into the creep constitutive model and fit the experimental data using the Trust-Region algorithm to obtain the model parameters. E 0, E 1, η 1, η 2, η 3, β 1, β 2, α 1, α 2, α 3; The creep constitutive model in step S5 is: when σ 0< σ s hour, (1) (2) when σ 0≥ σ s hour, (3) In the formula: σ 0 represents the deviatoric stress level, in MPa; σ s The long-term strength of weakly cemented soft rock is MPa; η 1, η 2 and η 3 represents the viscosity coefficients of the viscoelastic, viscous, and viscoplastic damage elements, respectively. β 1 and β 2 represents the order of fractional-order damage to the sticky pot; E 0 represents the elastic modulus of the elastic element; E 1 represents the elastic modulus of the fractional-order Kelvin model; α 1, α 2 and α 3 are coefficients characterizing the damage correlation of rock mass materials, obtained by fitting experimental data; t 1 and t 2 represents the boundary between decaying creep and constant-rate creep, and the boundary between constant-rate creep and accelerated creep, respectively.
2. The method for determining the creep rate boundary point of weakly cemented soft rock according to claim 1, characterized in that, The graded creep test of weakly cemented soft rock described in step S1 is a graded unloading confining pressure test. The specific scheme is as follows: the unloading confining pressure creep test uses the stress control module in the advanced loading module to load the sample to the initial stress state of axial pressure and confining pressure at a loading rate of 0.1 MPa / s and keep it constant; then, keeping the axial pressure constant, the confining pressure is unloaded to a predetermined value at an unloading rate of 0.05 MPa / s and the stress state of the sample is kept constant for 50 h before proceeding to the next unloading stage; the confining pressure is unloaded in 5 stages, and the deviatoric stress after each unloading stage is taken as 30%, 40%, 50%, 55% and 60% of the uniaxial compressive strength of the rock.
3. The method for determining the creep rate boundary point of weakly cemented soft rock according to claim 1, characterized in that, The creep-time curve mentioned in step S2 includes two types: steady-state creep and unsteady-state creep. The steady-state creep curve includes two stages: decaying creep and constant-rate creep. The unsteady-state creep includes three stages: decaying creep, constant-rate creep, and accelerated creep. Taking the first derivative of the creep curve yields the creep rate curves of weakly cemented soft rock under different water content and stress levels. In the decaying creep stage, the creep rate continuously decreases, corresponding to the rapid decline stage of the creep rate-time curve. In the constant-rate creep stage, the creep rate remains constant, corresponding to the stable creep rate-time curve. In the accelerated creep stage, the creep rate continuously increases, corresponding to the rapid rise stage of the creep rate-time curve.
4. The method for determining the creep rate boundary point of weakly cemented soft rock according to claim 1, characterized in that, The Casagrande method for determining the preconsolidation pressure of soil in step S3 is as follows: First, plot the indoor compression curve of the sample on the e-lgp coordinate system; then find the point A with the largest curvature on the compression curve, draw a horizontal line A1, a tangent A2, and the bisector A3 of the angle between them through point A; finally, extend the straight line segment at the bottom of the compression curve upward to intersect line A3 at point B, and the x-coordinate of point B is the preconsolidation pressure to be determined.
5. The method for determining the creep rate boundary point of weakly cemented soft rock according to claim 4, characterized in that, Step S4 t 1, t The specific steps in step 2 are as follows: When the stress level exceeds the long-term strength of the rock mass, the creep curve includes three stages: decaying creep, constant-rate creep, and accelerated creep. On the creep rate versus time curve, find the points A and B where the curvature of the creep rate is maximum in the decaying creep stage and the accelerated creep stage, respectively. Draw a tangent AC to the radius corresponding to the maximum curvature of the decaying creep rate curve through point A, intersecting the extension of the constant-rate creep rate curve at point C. The x-coordinate of point C is... t Point 1 is the dividing point between the decaying creep stage and the constant-rate creep stage; similarly, draw the tangent line BD from point B to the radius corresponding to the maximum curvature of the accelerated creep rate curve, intersecting the extension of the constant-rate creep rate curve at point D. The x-coordinate of point D is... t 2 represents the boundary between the constant-rate creep stage and the accelerated creep stage. When the stress level is lower than the long-term strength of the rock mass, the creep curve includes two stages: decaying creep and constant-rate creep. In this case, it is only necessary to find the point A with the maximum curvature in the decaying creep stage. Draw the tangent AC to the radius corresponding to the maximum curvature of the decaying creep rate curve through point A, and intersect it with the extension of the constant-rate creep rate curve at point C. The x-coordinate of point C is... t 1 is the dividing point between the decay creep stage and the constant-rate creep stage.
6. The method for determining the creep rate boundary point of weakly cemented soft rock according to claim 1, characterized in that, The creep rate threshold mentioned in step S5 t 1 and t 2. It can be used to predict creep of weakly cemented soft rock and the critical time point for creep failure of roadways under different stress levels and water content conditions.