Method for calculating shear strength parameters and method for evaluating the same

Abstract

The application discloses a shear strength parameter calculation method and an evaluation method thereof, and relates to the field of geotechnical engineering, aiming at fast and accurate shear strength parameters. The technical scheme adopted by the application is as follows: the shear strength parameter calculation method is used to calculate the cohesion and the internal friction angle according to constraint condition one and constraint condition two through at least two groups of triaxial test data. Constraint condition one: the sum of the vector distances from the tangent points of the to-be-solved failure strength line or the parallel line of the to-be-solved failure strength line to each Mohr stress circle to the to-be-solved failure strength line is 0. Constraint condition two: the sum of the distances from the tangent points of the to-be-solved failure strength line or the parallel line of the to-be-solved failure strength line to each Mohr stress circle to the to-be-solved failure strength line is minimum. The application further provides an evaluation method of the shear strength parameter calculation method, which is used to determine the cohesion and the internal friction angle according to the above method, and then to evaluate the quality through the maximum distance ratio δ. The application is used for calculating and evaluating the shear strength parameters according to the triaxial test data.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of geotechnical engineering, and particularly relates to a method for calculating shear strength parameters of cohesion c and internal friction angle and a method for quality evaluation of calculation results of shear strength parameters. BACKGROUND

[0002] Triaxial test is one of the basic methods for obtaining shear strength of rock-soil mass in geotechnical engineering. The standard theoretical method for obtaining shear strength parameters by triaxial test is as follows: three or more rock-soil mass samples are respectively subjected to different confining pressures σi3, and the axial pressure is gradually increased until the rock-soil mass sample is destroyed or deformed too much, and the corresponding axial stress σi1 is obtained, where i represents the sample number. Through the test data of each rock-soil mass sample, a Mohr stress circle can be drawn in a plane coordinate system, and a common tangent line of each Mohr stress circle can be drawn, and the failure strength line can be obtained: where the friction c and the internal friction angle are the shear strength parameters to be solved.

[0003] The number of rock-soil mass samples for obtaining shear strength by triaxial test is generally 3-5, and the corresponding number of Mohr stress circles can be drawn after the test. For example, when the number of rock-soil mass samples is three, three Mohr stress circles can be drawn in a plane coordinate system, and the common tangent line of the three Mohr stress circles is the failure strength line, as shown in Figure 1 .

[0004] Due to the differences between the rock-soil mass samples, or the test equipment and operation, etc., the Mohr stress circles obtained by each rock-soil mass sample in the same batch are difficult to have a common tangent line. When each Mohr stress circle does not have a common tangent line, and a failure strength line must be drawn to determine the values of cohesion c and internal friction angle to obtain the shear strength parameters, there is a problem that it is difficult to determine the shear strength parameters. At present, the solutions to this problem can be summarized as the following three methods, and each method has its own advantages and disadvantages.

[0005] The first method is to draw manually according to experience. This method is most commonly used in actual work, and has the advantages of fast speed, and the disadvantages that the results are related to the experience of the drawing personnel, and the results are uncertain. Even if the same triaxial test data is used, different drawing personnel may obtain different shear strength parameters.

[0006] The second method is to draw a common tangent line for each two Mohr stress circles to obtain multiple friction c and internal friction angle Data, and then average respectively. This method is not much practical application, although the only results can be obtained, and easy to operate, but the use of the method in the mathematical sense is not clear, the results are considered to have significant errors, and even wrong.

[0007] The third method is mathematical solution. The third method has many kinds, including optimal solution, least square method, nonlinear programming method, etc. The third method generally has better theoretical basis, and can also obtain unique results, but most of them are more complex, involving partial differential equations, bias analysis and other complex derivation and calculation process, and have no advantage in simplicity, so they are rarely used in practice. At the same time, the third method may obtain unreasonable results, such as c < 0 kPa or The results of this method cannot be corrected. In addition, the results obtained by this method cannot reflect the quality of the test. For example, as shown in Figure 2 and Figure 3 , the shear strength parameters obtained by mathematical solution of the two tests are exactly the same, but the triaxial test data of each test are obviously different, and the quality of the two test results is obviously different, so it is necessary to evaluate the results in order for engineers to reasonably evaluate and select. SUMMARY

[0008] In view of the problems that the results obtained by the existing method through triaxial test data to calculate the shear strength parameters are not unique, the calculation is complex, and even wrong, the present application provides a shear strength parameter calculation method, which aims to quickly and accurately determine the shear strength parameters according to the triaxial test data.

[0009] The technical scheme adopted by the present application is: a shear strength parameter calculation method, which directly calculates the cohesion c and internal friction angle n ≥ 2 and is an integer.

[0010] Constraint condition one: the sum of the vector distances from the tangent points of the to-be-solved failure strength line or the parallel line of the to-be-solved failure strength line to each Mohr stress circle to the to-be-solved failure strength line is 0. The vector distance is a distance with positive and negative directions according to the direction, and the distance from the tangent point on one side of the to-be-solved failure strength line to the to-be-solved failure strength line is defined as negative, and the distance from the tangent point on the other side of the to-be-solved failure strength line to the to-be-solved failure strength line is defined as positive, or vice versa.

[0011] Specifically, the calculation formula of constraint condition one is Wherein: σi3, σi1 are the stress values measured by the triaxial test of the i-th group of samples, unit: kPa; is the internal friction angle, unit: °; c is the cohesion, unit: kPa.

[0012] Constraint condition two: the sum of the distances from the tangent points of the sought failure strength line or parallel lines of the sought failure strength line to each Mohr stress circle to the sought failure strength line is minimum.

[0013] Specifically, the calculation formula of constraint condition two is The value of is minimum. The symbols in the calculation formula of constraint condition two are the same as before.

[0014] Further, for the cohesion c and internal friction angle obtained directly according to constraint condition one and constraint condition two, the following correction is performed: if the cohesion c < 0, the cohesion c = 0 is taken, and the internal friction angle is obtained according to constraint condition one; if the internal friction angle is greater than 90 degrees, the internal friction angle is taken, and the cohesion c is obtained according to constraint condition two.

[0015] The present application also provides an evaluation method of the shear strength parameter calculation method. The cohesion c and internal friction angle obtained according to the shear strength parameter calculation method are first determined. The cohesion c and internal friction angle obtained according to the shear strength parameter calculation method can be the cohesion c and internal friction angle obtained directly according to constraint condition one and constraint condition two, or the cohesion c and internal friction angle obtained after correction according to the above method.

[0016] The quality is then evaluated through the maximum distance ratio δ. The size of the maximum distance ratio δ is negatively correlated with the quality of the test results. The calculation formula of the maximum distance ratio δ is

[0017] The beneficial effects of the present application are that the shear strength parameters cohesion c and internal friction angle obtained by the shear strength parameter calculation method have unique values, and the calculation results have clear and reasonable mathematical meanings. The calculation formula of constraint condition one and constraint condition two proposed by the present application is simple to calculate and can be implemented through a computer. The evaluation method of the shear strength parameter calculation method proposed by the present application quantitatively evaluates the calculation results, which is convenient for engineers to reasonably evaluate and select. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 is a schematic diagram of a general method of taking values of shear strength parameters.

[0019] Figure 2 is a schematic diagram of shear strength parameters obtained through mathematical solutions of a test.

[0020] Figure 3is a schematic diagram of a test through mathematical solution to obtain the same shear strength parameter. Figure 2 is a schematic diagram of a test through mathematical solution to obtain the same shear strength parameter.

[0021] Figure 4 is a schematic diagram of a test through mathematical solution to obtain the same shear strength parameter.

[0022] Figure 5 is a schematic diagram of a test through mathematical solution to obtain the same shear strength parameter. DETAILED DESCRIPTION

[0023] The present application will be further described below in conjunction with the accompanying drawings and examples.

[0024] The shear strength parameter calculation method of the present application calculates the cohesion c and the internal friction angle wherein n≥2 and is an integer, and the value of n is generally 3, 4 or 5.

[0025] According to the triaxial test data, the Mohr stress circles can be plotted in the plane coordinate system, and the number of the Mohr stress circles is the same as the number n of the triaxial test data groups. The following takes n=2 as an example for illustration, see Figure 4 .

[0026] Constraint condition one: the sum of the vector distances from the tangent points of the to-be-solved failure strength line or the parallel line of the to-be-solved failure strength line to the to-be-solved failure strength line to each Mohr stress circle is 0. The vector distance is a distance with positive and negative directions according to the direction, and the distance from the tangent point on one side of the to-be-solved failure strength line to the to-be-solved failure strength line is defined as negative, and the distance from the tangent point on the other side of the to-be-solved failure strength line to the to-be-solved failure strength line is defined as positive, or vice versa. For example, see Figure 4 , the oblique line in the first quadrant of the x-axis and the y-axis is the to-be-solved failure strength line, and when the value of n is 2, the constraint condition 1 is: -|d1|+|d2|=0 or |d1|-|d2|=0. Specifically, the calculation formula of the constraint condition one is: wherein σi3 and σi1 are the stress values measured by the triaxial test of the i-th group of samples, in units of kPa; is the internal friction angle, in units of °; and c is the cohesion, in units of kPa.

[0027] Constraint condition two: the sum of the distances from the tangent points of the to-be-solved failure strength line or the parallel line of the to-be-solved failure strength line to the to-be-solved failure strength line to each Mohr stress circle is the minimum. The distance in the constraint condition two is a scalar. For example, the calculation formula of the constraint condition two is: , and the value of is the minimum. The symbols in the calculation formula of the constraint condition two have the same meanings as before.

[0028] The constraint condition one and the constraint condition two contain two unknowns to be solved, that is, the internal friction angle and the cohesion c, so the constraint condition one and the constraint condition two form a binary first-order equation set. By solving, the unique shear strength parameters, the cohesion c and the internal friction angle The shear strength parameter calculation method can be implemented through computer programming and has the characteristics of convenient solving.

[0029] Considering that the shear strength parameters have a certain reasonable range, the cohesion c and the internal friction angle directly calculated according to the constraint condition one and the constraint condition two may exceed the reasonable range, in order to avoid obtaining unreasonable results, the cohesion c and the internal friction angle directly calculated according to the constraint condition one and the constraint condition two are modified as follows: if the cohesion c < 0, the cohesion c = 0 is taken, and the internal friction angle is obtained according to the constraint condition one. If the internal friction angle is greater than 90 degrees, the internal friction angle is taken, and the cohesion c is obtained according to the constraint condition two.

[0030] The second subject of the present application is an evaluation method of the shear strength parameter calculation method. The cohesion c and the internal friction angle may be the cohesion c and the internal friction angle directly calculated according to the constraint condition one and the constraint condition two, or the cohesion c and the internal friction angle after the modification according to the above method. Then the quality is evaluated through the maximum distance ratio δ, and the calculation formula of the maximum distance ratio δ is

[0031] The maximum distance ratio δ serves as a basis for quantitatively evaluating the reliability of the shear strength parameter result value, and the size of the maximum distance ratio δ is negatively correlated with the quality of the test result. Only for a large number of tests, the applicant provides a segmented suggestion on the maximum distance ratio δ: when δ ≤ 0.05, the quality of the test result is excellent; when 0.05 < δ ≤ 0.15, the quality of the test result is general; and when δ > 0.15, the quality of the test result is poor, and the technical personnel need to use the shear strength parameter result value with caution.

[0032] The correctness of the present application is verified through three groups of triaxial test data as follows.

[0033] The three groups of triaxial test data are shown in Table 1, and the three groups of triaxial test data correspond to sample 1, sample 2 and sample 3 respectively. According to the three groups of triaxial test data, a Mohr stress circle is first drawn, and then a common tangent line is determined to obtain the shear strength parameters: the cohesion c = 0.21 kPa and the internal friction angle as shown in Table 1. Figure 5 .

[0034] Table 1. Triaxial test data for three groups.

[0035] Sample No. σ13(kPa) σ11(kPa) Sample 1 0.2748 1.5662 Sample 2 0.6116 2.5884 Sample 3 0.9205 3.5536

[0036] The cohesion c and internal friction angle are calculated below using the shear strength parameter calculation method of the present invention based on the three sets of triaxial test data described in Table 1.

[0037] Using the formula for constraint one, the following cohesive force c and internal friction angle that satisfy constraint one can be obtained. The corresponding values ​​are shown in Table 2.

[0038] Table 2 shows the shear strength parameters for calculations that meet constraint condition one.

[0039]

[0040] Using the formula for constraint two, calculate the cohesion c and internal friction angle for all conditions satisfying constraint one. The sum of the distances to the corresponding values ​​is shown in Table 3.

[0041] Table 3 shows the calculation formula for constraint condition two.

[0042]

[0043] As shown in Table 3, the minimum sum of distances under constraint condition two corresponds to a cohesive force c of 0.2175 kPa and an internal friction angle. The internal friction angle is 30°. To further improve the calculation accuracy, based on the above calculations, the internal friction angle is adjusted... Within the range of 29.1° to 30.9°, the above calculations were performed again using the formulas for constraint condition one and constraint condition two, and the final calculated value was determined to be: internal friction angle. Cohesion c = 0.21 kPa.

[0044] The shear strength parameters obtained by the plotting method are consistent with those directly calculated using this invention, proving the correctness of the shear strength parameter calculation method of this invention. According to the evaluation method of the shear strength parameter calculation method of this invention, the maximum distance ratio δ for the directly calculated shear strength is 0.00016. As mentioned above, since the three sets of triaxial test data are completely tangent circles, the maximum distance ratio δ should be 0. However, due to errors in reading the coordinates in the computer (the values ​​of σ13 and σ11 were read to 4 decimal places in this case), the calculation results are slightly different. However, according to the evaluation criteria, this does not affect the quality evaluation of the test results, and the test results are of excellent quality.

[0045] The invention will now be illustrated with engineering examples.

[0046] As shown in Table 4, three semi-formed rock indoor triaxial test results from a hydropower project were selected for analysis. Tests 1 and 2 were undisturbed samples, while Test 3 was a remolded sample. The remolded sample exhibited more uniform characteristics, and the results were generally of better quality. For comparative verification, two experienced staff members were invited to propose relevant test results using graphical methods and their work experience, and these results were compared with the values ​​calculated according to this invention.

[0047] Table 4. Comparison of results from three triaxial tests.

[0048]

[0049] As can be seen from Table 4, the method of the present invention has the following advantages: the experimental results are unique; the mathematical meaning of the results is clear and reasonable; and the experimental quality can be quantitatively evaluated.

Claims

1. A method for calculating shear strength parameters, characterized in that: Using n sets of triaxial test data, the cohesive force c and the internal friction angle φ are directly calculated according to constraint conditions one and two, where n≥2 and are integers. Constraint 1: The sum of the vector distances from the points of tangency between the line of failure strength to be determined or its parallels and each of the Mohr stress circles to the line of failure strength to be determined is 0. The formula for constrainment 1 is as follows: ,in: φ is the stress value determined by the triaxial test of the i-th group of specimens, in kPa; φ is the internal friction angle, in °; c is the cohesion, in kPa. Constraint 2: The sum of the distances from the points of tangency between the line of failure strength to be determined or its parallels and each Mohr stress circle is minimized. The formula for constrained condition 2 is: The minimum value is found in: φ is the stress value determined by the triaxial test of the i-th group of specimens, in kPa; φ is the internal friction angle, in °; c is the cohesion, in kPa. The cohesive force c and internal friction angle φ directly calculated according to constraint conditions one and two are then corrected as follows: if the cohesive force c < 0, take the cohesive force c = 0 and obtain the internal friction angle φ according to constraint condition one; if the internal friction angle φ > 70°, take the internal friction angle φ = 70° and obtain the cohesive force c according to constraint condition two.

2. The method for calculating shear strength parameters as described in claim 1, characterized in that: The value of n is 3, 4 or 5.

3. An evaluation method for calculating shear strength parameters, characterized in that: First, determine the cohesion c and internal friction angle φ according to the shear strength parameter calculation method described in claim 1 or 2. Then, evaluate the quality using the maximum distance ratio δ. The magnitude of the maximum distance ratio δ is negatively correlated with the quality of the test results. The formula for calculating the maximum distance ratio δ is as follows: .

4. The evaluation method for the shear strength parameter calculation method as described in claim 3, characterized in that: When δ≤0.05, the test results are of excellent quality; when 0.05<δ≤0.15, the test results are of average quality; when δ>0.15, the test results are of poor quality.

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