A method for predicting the strength of a soft-hard composite rock mass

Abstract

The present invention discloses a method for predicting the strength of a hard-soft composite rock mass, including obtaining the rock mechanical parameters of the hard-soft composite rock mass and the confining pressure of the bedding plane of the hard-soft composite rock mass in the target area; when calculating the strength of the bedding plane of the hard-soft composite rock mass in the target area with an inclination angle θ = 45° to 75°, calculating the strength of the hard-soft composite rock mass in the target area according to the uniaxial compressive strength; when calculating the strength of the bedding plane of the target area with an inclination angle θ = 0° to 45° and 75° to 90°, directly proceeding to the next step; obtaining the uniaxial compressive strength when the inclination angle θ of the target bedding plane is 0°, the maximum principal stress when the inclination angle θ of the bedding plane is 15°, and the maximum principal stress when the inclination angle θ of the bedding plane is 30°; calculating to obtain a correction coefficient; and calculating the strength of the bedding plane of the hard-soft composite rock mass in the target area according to the correction coefficient and the confining pressure. The method for the strength of the hard-soft composite rock mass of the present invention is more accurate, has a wider application, and considers more factors.

Description

Technical Field

[0001] The present invention relates to a method for predicting the strength of a hard - soft composite rock mass, belonging to the technical field of geotechnical engineering. Background Art

[0002] The hard - soft interbedded rock mass is a common type of heterogeneous rock mass in engineering geological conditions. The existence of bedding planes and soft rock layers often leads to its failure under relatively low external load conditions, thus triggering geological disasters or engineering accidents. Exploring the influence laws of adverse factors such as soft rock layers and bedding planes on the mechanical properties of hard - soft interbedded rock masses and familiarizing with the loading and failure behaviors of hard - soft interbedded rock masses are beneficial for predicting and evaluating the potential risks of relevant geological conditions in actual engineering projects and disaster prevention and control, so as to carry out targeted construction operations.

[0003] There are many influencing factors for the mechanical properties and failure behaviors of hard - soft interbedded rock masses, such as the dip angle of bedding planes, rock layer thickness, and the strength of soft rock layers, etc. The angle formed between the bedding and the load direction often determines whether the final failure mode of the hard - soft interbedded rock mass is tensile fracture, shear fracture, or a composite fracture mode. Shear - sliding failure along the bedding plane is the main unique failure characteristic of hard - soft interbedded rock masses, which is common in hard - soft interbedded rock masses with a bedding plane dip angle of 15° - 75°. In addition, the thickness and mechanical properties of the soft rock layer will also affect the final failure mode of the hard - soft interbedded rock mass, which not only depends on the physical properties and geometric conditions of the soft rock itself, but also is affected by the adjacent hard rock layers. As an important part of the layered structure, hard rock often makes an in - negligible contribution to the final failure result, which is often easily overlooked in previous studies. Hard - soft interbedded rock masses will have various failure behaviors under adverse loads. With the change of the bedding plane dip angle, its failure may be caused by the failure of the rock layer matrix or the cracking of the bedding plane. For different failure types, the internal related inducing factors are different. Obviously, the cracking along the bedding plane depends on the bonding performance of the bedding plane, while the failure of the rock layer matrix depends on its own mechanical properties.

[0004] In summary, developing an improved method for predicting the strength of hard - soft composite rock masses has important theoretical guiding significance for the stability assessment of hard - soft alternating rock masses, and the content of the present invention can also well provide relevant guiding work for the engineering of hard - soft composite rock masses. Summary of the Invention

[0005] In order to overcome the defects existing in the prior art, the present invention aims to provide a method for predicting the strength of a hard - soft composite rock mass.

[0006] The technical solution provided by the present invention to solve the above - mentioned technical problems is: a method for predicting the strength of a hard - soft composite rock mass, comprising the following steps:

[0007] Step 1. Obtain the rock mechanical parameters of the hard-soft composite rock mass and the confining pressure σ3 of the bedding plane of the hard-soft composite rock mass in the target area;

[0008] Step 2. Calculate the strength of the bedding plane of the hard-soft composite rock mass in the target area with an inclination angle θ = 45° - 75°. Then, adopt the slip failure criterion to calculate the strength of the hard-soft composite rock mass in the target area according to the confining pressure σ3; calculate the strength of the bedding plane of the target area with an inclination angle θ = 0° - 45° and 75° - 90°, and then directly proceed to the next step;

[0009] Step 3. Obtain the uniaxial compressive strength σ c(0°) of the bedding plane with an inclination angle θ = 0° in the hard-soft composite rock mass in the target area through on-site tests, the maximum principal stress σ 1(15°) of the bedding plane with an inclination angle θ = 15°, and the maximum principal stress σ 1(30°) of the bedding plane with an inclination angle θ = 30°;

[0010] Step 4. Calculate and obtain the correction coefficient A and n / k according to the maximum principal stress σ 1(15°) of the bedding plane with an inclination angle θ = 15° and the maximum principal stress σ 1(30°) of the bedding plane with an inclination angle θ = 30°;

[0011] Step 5. Calculate the strength of the bedding plane of the hard-soft composite rock mass in the target area according to the uniaxial compressive strength σ c(0°) of the bedding plane with an inclination angle θ = 0°, the confining pressure σ3, the correction coefficient A, and n / k.

[0012] A further technical solution is that the rock mechanical parameters include cohesion c w , friction angle

[0013] A further technical solution is that in Step 1, the confining pressure σ3 of the underground target area is directly measured by using an underground pressure sensor.

[0014] A further technical solution is that the formula for calculating the strength of the hard-soft composite rock mass in the target area in Step 2 is:

[0015]

[0016] In the formula: c w is cohesion; is the friction angle; θ is the inclination angle; σ३ is the confining pressure; σ1 is the maximum principal stress.

[0017] A further technical solution is that the specific process of Step 3 is:

[0018] First, prepare the specimens. Take rock blocks with bedding planes from core drillings or exploratory trenches at different directional angles to obtain specimens with bedding plane inclination angles of θ = 0°, 15°, and 30° respectively.

[0019] Then, place the specimens at the center of the bearing plate of the testing machine, ensure that both end faces of the specimens are in uniform contact with the upper and lower pressure plates of the testing machine, and load the specimens at a loading rate of 0.5 - 1.0 Mpa per second until the specimens are damaged, and record the failure load.

[0020] Thus, calculate the uniaxial compressive strengths σ c(0°) , σ c(15°) , and σ c(30°) when the bedding plane inclination angles θ are 0°, 15°, and 30° respectively.

[0021] When the specific confining pressure σ3 = 0, the magnitudes of the uniaxial compressive strength σ c(15°) at the bedding plane inclination angle θ = 15° and the uniaxial compressive strength σ c(30°) at the bedding plane inclination angle θ = 30° are respectively the maximum principal stresses σ 1(15°) at the bedding plane inclination angle θ = 15° and the maximum principal stress σ 1(30°) at the bedding plane inclination angle θ = 30°. 1(15°) and the maximum principal stress σ 1(30°) .

[0022] A further technical solution is that the calculation formula for the uniaxial compressive strength is:

[0023]

[0024] In the formula: σ c is the uniaxial compressive strength of the rock, P is the maximum failure load, and A is the cross-sectional area of the specimen perpendicular to the loading direction.

[0025]

[0025] A further technical solution is that the calculation formula in Step 4 includes:

[0026]

[0027] In the formula: σ c(0°) is the uniaxial compressive strength at the bedding plane inclination angle θ = 0°; σ 1(15°) is the maximum principal stress at the bedding plane inclination angle θ = 15°; σ 1(30°) is the maximum principal stress at the bedding plane inclination angle θ = 30°; σ3 is the confining pressure; A and n / k are both correction factors. 1(30°) 1(30°) for the maximum principal stress at the bedding plane inclination angle θ = 30°; σ3 is the confining pressure; A and n / k are both correction factors.

[0028] A further technical solution is that the calculation formula in Step 4 is:

[0029]

[0030] In the formula: σ 1(θ) is the maximum principal stress at the bedding plane inclination angle θ; σ is the maximum principal stress at the bedding plane inclination angle θ; σc(0°) is the uniaxial compressive strength when the dip angle θ of the bedding plane is 0°; σ3 is the confining pressure; both A and n / k are correction factors.

[0031] The present invention has the following beneficial effects: The strength model of the present invention introduces a modification factor A to further correct the Tien-Kuo strength model. The strength prediction error range of the hard-soft composite rock mass is 5%. It can well predict the strength for the hard-soft composite rock mass project. Therefore, the strength method of the hard-soft composite rock mass of the present invention is more accurate, more widely applicable, and considers more factors. Description of the Drawings

[0032] Figure 1 It is a coordinate system definition diagram of the hard-soft interlayered rock mass. Detailed Embodiment

[0033] The technical solution of the present invention will be clearly and completely described below with reference to the drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0034] The calculation formula in the present invention is obtained through the following steps:

[0035] A. First, establish the Tien-Kuo strength model based on the defects shown by the Jaeger strength criterion in determining the strength of layered rock masses;

[0036] This criterion is the strength segmented according to different failure modes of rock samples;

[0037] When the rock undergoes shear sliding failure along the bedding plane, its strength expression is:

[0038]

[0039] In the formula: c w and are the cohesion and friction angle of the bedding plane respectively, and can be determined through compression tests.

[0040] When the failure of the rock is caused by the failure of the rock formation matrix, its strength expression is:

[0041]

[0042] In the formula: σ 1(0°) and σ 1(θ) are the maximum principal stress when the dip angle θ of the bedding plane is 0° and the maximum principal stress when the dip angle θ of the bedding plane is 0° respectively.

[0043] k is the strength ratio of the specimen with vertical bedding to the specimen with horizontal bedding, expressed as:

[0044]

[0045] When the shear failure of the interbedded specimen with hard and soft layers occurs along the bedding plane, according to the single weak plane principle proposed by Jaeger, the strength expression as shown in Equation (1) can be obtained. When the failure of the specimen is caused by the failure of the rock mass matrix, the elastic constitutive relationship of the interbedded rock mass with hard and soft layers can be expressed by the transverse isotropic constitutive model.

[0046] As Figure 1 shown, the linear elastic constitutive relationship of the interbedded specimen with hard and soft layers in the local coordinate system is expressed in matrix form:

[0047]

[0048] In the formula: E and E′ are the elastic moduli parallel and perpendicular to the transverse isotropic plane respectively, G′ is the shear modulus in the direction normal to the transverse isotropic plane, υ and υ′ are the material Poisson's ratios in the corresponding directions when stressed. Correspondingly, the constitutive equation in the global coordinate system is expressed as:

[0049]

[0050] The relevant quantities K 11 , K 12 ……K 66 in the above compliance matrix can be obtained by coordinate transformation of the corresponding quantities in the local coordinate system. In the compression state, the stress matrix of the interbedded specimen can be written in the following form:

[0051]

[0052] In the formula: S1 is the deviatoric stress tensor, and;

[0053] S1 = σ1 - σ3 (7)

[0054] Combined with Equation (5), it can be known that the axial strain related to the deviatoric stress can be expressed as:

[0055] ε yy = K 22 S1 (8)

[0056] In the formula,

[0057]

[0058] In the compression state, when the strain of the rock mass matrix exceeds its maximum strain, the failure of the interbedded rock mass with hard and soft layers occurs.

[0059] According to the maximum principal strain criterion, the stress-strain relationship of the interbedded rock samples with the bedding plane dip angle θ can be expressed as:

[0060] ε yf =K 22 S 1(β) (10)

[0061] The strain ε of the rock sample at failure yf is independent of the bedding plane dip angle and is affected by the confining pressure. Therefore, when determining the strength of the rock sample at a certain bedding plane dip angle, it is easy to obtain the strength of the rock sample at any bedding plane dip angle. Taking the strength of the rock sample with a horizontal bedding plane dip angle as a comparison, the strength ratio is obtained;

[0062]

[0063] If we let

[0064] E′=E (0°) ,E=E (90°) (12)

[0065] k=E (0°) / E (90°) =S 1(0°) / S 1(90°) (13)

[0066]

[0067] the expression shown in Equation (2) can be obtained, that is, the strength expression for the matrix failure of layered rock masses in the Tien-Kuo strength model.

[0068] The Tien-Kuo strength model is a strength theoretical expression based on elastic theory. However, rock materials often have non-linear characteristics. Based on this realistic situation, many scholars have proposed strength criteria that can reflect the non-linear variation of rock strength. For example, You Mingqing gave a parabolic criterion for predicting rock strength based on a large amount of experimental data and theoretical research, that is;

[0069]

[0070] Its display expression is:

[0071]

[0072] In the formula, σ c is the uniaxial compressive strength, and this formula can be further written in the following form:

[0073] σ1 - σ3=σ c +2(σ3σ c ) 0.5 (17)

[0074] When failure of the rock matrix occurs in the hard-soft interbedded rock mass, the non-linear characteristics of the matrix should be considered in the strength estimation. Therefore, Equation (2) can be rewritten as:

[0075]

[0076] Since the hard-soft interbedded rock mass also has anisotropic characteristics, a coefficient A is introduced in Equation (17), which is a constant related to the anisotropic characteristics of the hard-soft interbedded rock mass.

[0077] Equation (17) is the improved strength criterion considering the non-linear characteristics of the rock, which is applicable to the failure type caused by the cracking of the rock matrix. The Tien-Kuo strength model is a piecewise strength criterion obtained according to different failure types, and the improved criterion still follows this basic criterion.

[0078] When the dip angle θ of the bedding plane is 45° - 75°, the slip failure criterion, i.e., Equation (1), is adopted. The cohesion c w and friction angle of a specific dip angle θ of the bedding plane are obtained through tests. Then, the confining pressure σ3 is obtained, and the strength values of other angles between θ = 45° and 75° can be calculated according to Equation (1).

[0079] When the dip angle θ of the bedding plane is 0° - 45° and 75° - 90°, the modified Tien-Kuo strength criterion, i.e., Equation (2), is adopted. The uniaxial compressive strength σ c(0°) when the dip angle θ of the bedding plane in the hard-soft composite bedding plane is 0° is obtained through tests. When selecting typical values of θ = 15° and 30°, the maximum principal stresses σ 1(15°) and σ 1(30°) of the bedding plane dip angles θ = 15° and 30° in the failure criterion are obtained through in-situ tests. Assuming a certain confining pressure σ3 value, substituting it into Equation (18), and then obtaining the equations according to Equations (19) and (20). Further, the correction coefficient A and n / k are obtained according to Equations (19) and (20). Then, according to the correction coefficient A and n / k, the dip angle θ of the bedding plane, and the uniaxial compressive strength σ c(0°) of the bedding plane dip angle θ = 0°, the compressive strength of the hard-soft composite rock mass with other bedding plane dip angles θ = 0° - 45° and 75° - 90° under a certain confining pressure σ3 value is calculated.

[0080] When the dip angle θ of the bedding plane is 15° or 30°, the failure of the specimen is caused by the failure of the rock matrix. Since sin 4 15° = 0.0045 and sin 4 30° = 0.0625, sin 4 θ / k decreases exponentially, and Equation (18) can be simplified to

[0081]

[0082] A method for predicting the strength of a hard-soft composite rock mass according to the present invention comprises the following steps:

[0083] Step 1: Obtain the rock mechanical parameters (cohesion c w , friction angle ) of the hard-soft composite rock mass and the confining pressure σ3 of the bedding plane of the hard-soft composite rock mass in the target area;

[0084] Among them, the confining pressure σ3 of the underground target area is directly measured by using an underground pressure sensor.

[0085] Step 2: When calculating the strength of the bedding plane dip angle θ = 45° - 75° in the hard-soft composite rock mass in the target area, adopt the slip failure criterion, and calculate the strength of the hard-soft composite rock mass in the target area according to formula (1) and the confining pressure σ3;

[0086] When calculating the strength of the bedding plane angle θ = 0° - 45° and 75° - 90° in the target area, directly proceed to the next step;

[0087] Step 3: Obtain the uniaxial compressive strength σ c(0°) of the bedding plane dip angle θ = 0° in the hard-soft composite rock mass in the target area, the maximum principal stress σ 1(15°) of the bedding plane dip angle θ = 15°, and the maximum principal stress σ 1(30°) of the bedding plane dip angle θ = 30°;

[0088] First, prepare specimens. Take rock blocks of the bedding plane from drill cores or adits in different direction angles so that the specimens with bedding plane dip angles of θ = 0°, 15°, and 30° are obtained. According to the regulations, the standard specimen is a cylinder with a diameter of 50 mm and a height of 100 mm. The processing accuracy of the specimen needs to meet the relevant requirements of the International Society for Rock Mechanics (ISRM).

[0089] Then place the specimen at the center of the loading plate of the testing machine, ensure that both end faces of the specimen are in uniform contact with the upper and lower loading plates of the testing machine, load the specimen at a loading speed of 0.5 - 1.0 Mpa per second until the specimen fails, and record the failure load.

[0090] Calculate the uniaxial compressive strength of the rock according to the following formula.

[0091]

[0092] In the formula: σ c is the uniaxial compressive strength of the rock (Mpa), P is the maximum failure load (N), and A is the cross-sectional area of the specimen perpendicular to the loading direction (mm 2 );

[0093] Thus, the uniaxial compressive strengths σ c(0°) , σ c(15°) and σ c(30°) are calculated when the bedding plane dip angle θ = 0°, 15° and 30°. In the failure criterion, when the specific confining pressure σ3 = 0, the uniaxial compressive strength σ c(15°) when the bedding plane dip angle θ = 15° and the uniaxial compressive strength σ c(30°) when the bedding plane dip angle θ = 30° are respectively the maximum principal stresses σ 1(15°) when the bedding plane dip angle θ = 15° and the maximum principal stress σ 1(30°) .

[0094] Step Four: According to formula (19) and formula (20), under the condition of specific σ3 = 0, the maximum principal stress σ 1(15°) when the bedding plane dip angle θ = 15° and the maximum principal stress σ 1(30°) when the bedding plane dip angle θ = 30° are calculated to obtain the correction coefficient A and n / k;

[0095] Step Five: According to formula (18), the uniaxial compressive strength σ c(0°) when the bedding plane dip angle θ = 0°, the confining pressure σ3 of the target area, the correction coefficient A and n / k, the strength of the bedding plane of the hard-soft composite rock mass in the target area is calculated.

[0096] As mentioned above, it is not any form of limitation to the present invention. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to equivalent embodiments of equivalent changes within the scope of the technical solution of the present invention by using the technical content disclosed above. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention all fall within the scope of the technical solution of the present invention.

Claims

1. A method for predicting the strength of a soft-hard composite rock mass, characterized in that, It includes the following steps: Step 1: Obtain the rock mechanics parameters of the hard-soft composite rock mass and the confining pressure of the bedding plane of the hard-soft composite rock mass in the target area σ 3; Step 2. Calculate the inclination angle of the bedding plane of the hard-soft composite rock mass in the target area θ If the strength is 45°~75°, the sliding failure criterion is adopted, and the strength of the hard-soft composite rock mass in the target area is calculated according to the confining pressure σ 3 Calculate the inclination angle of the bedding plane of the hard-soft composite rock mass in the target area θ If the strength is within the range of 0° to 45° and 75° to 90°, proceed directly to the next step; Step 3. Obtain the dip angle of bedding planes in the hard-soft composite rock mass in the target area through in-situ tests θ = The uniaxial compressive strength at 0° σ c(0°) , the dip angle of bedding planes θ = The maximum principal stress at 15° σ 1(15°) and the dip angle of bedding planes θ = The maximum principal stress at 30° σ 1(30°) ; Step 4. Calculate the correction factor based on the maximum principal stress at the bedding plane dip angle θ = of 15° σ 1(15°) and the maximum principal stress at the bedding plane dip angle θ = of 30° σ 1(30°) to obtain the correction factor A and n / k ; Step 5. According to the dip angle of the bedding plane θ = uniaxial compressive strength at 0° σ c(0°) , confining pressure σ 3. Correction factor A and n / k calculate the strength of the bedding plane of the hard-soft composite rock mass in the target area.

2. The strength prediction method of a soft-hard composite rock mass according to claim 1, characterized in that The rock mechanical parameters include cohesion c w , friction angle φ w .

3. A strength prediction method for a soft-hard composite rock mass according to claim 1, characterized in that In the first step, the confining pressure of the underground target area is directly measured by using an underground pressure sensor σ 3.

4. A strength prediction method for a soft-hard composite rock mass according to claim 2, characterized in that The formula for calculating the strength of the hard and soft composite rock mass in the target area in the second step is: Wherein: c w is the cohesion; φ w is the friction angle; θ is the inclination angle; σ 3 is the confining pressure; σ 1 is the maximum principal stress.

5. The strength prediction method for a soft-hard composite rock mass according to claim 1, characterized in that, The specific process of the third step is: First, prepare the specimens. Take rock blocks on the bedding plane from drill cores or adits and trenches at different directional angles to obtain specimens with bedding plane inclination angles of θ = 0°, 15°, and 30°; Then place the specimen at the center of the bearing plate of the testing machine, ensure that both end faces of the specimen are in uniform contact with the upper and lower pressure plates of the testing machine, load the specimen at a loading speed of 0.5 - 1.0 Mpa per second until the specimen fails, and record the failure load; Thus, the dip angle of the bedding plane is calculated θ to obtain the uniaxial compressive strengths at 0 degrees, 15 degrees, and 30 degrees σ c(0°) , σ c(15°) and σ c(30°) ; Apply a specific confining pressure σ When 3 = 0, the dip angle of the bedding plane θ = The uniaxial compressive strength at 15° σ c(15°) And the dip angle of the bedding plane θ = The uniaxial compressive strength at 30° σ c(30°) The magnitudes of are respectively the maximum principal stress at the dip angle of the bedding plane θ = At 15° σ 1(15°) And the dip angle of the bedding plane θ = The maximum principal stress at 30° σ 1(30°) .

6. The strength prediction method for a soft-hard composite rock mass according to claim 5, characterized in that, The calculation formula for the uniaxial compressive strength is: In the formula: σ c is the uniaxial compressive strength of the rock, P is the maximum failure load, A is the cross-sectional area of the specimen perpendicular to the loading direction.

7. A strength prediction method for a soft-hard composite rock mass according to claim 1, characterized in that The calculation formulas in the fourth step include: Wherein: σ c(0°) is the dip angle of the bedding plane θ = is the uniaxial compressive strength at 0°; σ 1(15°) is the dip angle of the bedding plane θ is the maximum principal stress at = 15°; σ 1(30°) is the dip angle of the bedding plane θ = is the maximum principal stress at 30°; σ 3 is the confining pressure; A and n / k are both correction factors.

8. A method for predicting the strength of a soft-hard composite rock mass according to claim 1, characterized in that, The calculation formula in the fourth step is: Wherein: σ 1(θ) is the dip angle of the bedding plane θ and is the maximum principal stress at this time; σ c(0°) is the dip angle of the bedding plane θ = and is the uniaxial compressive strength at 0°; σ 3 is the confining pressure; A and n / k are both correction factors.

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