CN115270407A - Shear strength parameter calculation method and evaluation method thereof - Google Patents
Shear strength parameter calculation method and evaluation method thereof Download PDFInfo
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Abstract
The invention discloses a shear strength parameter calculation method and an evaluation method thereof, relates to the field of geotechnical engineering, and aims to quickly and accurately calculate shear strength parameters. The technical scheme adopted by the invention is as follows: the shear strength parameter calculation method calculates cohesive force and an internal friction angle according to a constraint condition I and a constraint condition II through at least two groups of triaxial test data. Constraint one: the sum of vector distances from the tangent point of the parallel line of the to-be-determined failure strength line or the to-be-determined failure strength line and each molar stress circle to the to-be-determined failure strength line is 0. Constraint two: the sum of the distances from the tangent point of the parallel line of the line or lines of the strength of damage to be solved and each molar stress circle to the line or lines of the strength of damage to be solved is the smallest. The invention also provides an evaluation method of the shear strength parameter calculation method, which comprises the steps of determining the cohesive force and the internal friction angle according to the method, and then carrying out quality evaluation through the maximum distance ratio delta. The method is used for calculating and evaluating the shear strength parameters according to the triaxial test data.
Description
Technical Field
The invention relates to the field of geotechnical engineering, in particular to a method for calculating the cohesive force c and the internal friction angle of shear strength parameters through triaxial test data
And a method for evaluating the quality of the result value of the shear strength parameter calculation.
Background
The triaxial test is one of basic methods for acquiring the shear strength of a rock-soil body in geotechnical engineering. The standard theoretical method for obtaining the shear strength parameter by the triaxial test is as follows: different confining pressures sigma i3 are respectively adopted for three or more rock-soil body samples, the axial pressure is gradually increased until the rock-soil body samples are damaged or deformed too much, corresponding axial stress sigma i1 at the moment is obtained, wherein i represents a sample number, a molar stress circle can be drawn in a plane coordinate system through test data of each rock-soil body sample, and a common tangent line of each molar stress circle is drawn again, so that a damage intensity line can be obtained:
wherein the friction force c and the internal friction angle
I.e. the required shear strength parameter.
The rock-soil body samples with the shear strength obtained by the triaxial test are generally 3-5, and the corresponding number of molar stress circles can be drawn after the test. For example, when there are three rock-soil body samples, three molar stress circles can be drawn in a plane coordinate system, and common tangents of the three molar stress circles are failure strength lines, as shown in fig. 1.
Due to the difference of each rock-soil body sample, or the reasons of test equipment, operation and the like, the molar stress circles obtained by each rock-soil body sample in the same batch are difficult to have a common tangent. When each molar stress circle has no common tangent line, a failure strength line must be drawn to obtain the shear strength parameter so as to determine the cohesive force c and the internal friction angle
The problem of difficult determination of the shear strength parameters exists. At present, the solution of the problem can be summarized into the following three methods, and the three methods have own advantages and disadvantages.
The first method is to manually draw based on experience. The method is most commonly used in actual work, has the advantages of high speed and uncertain result value due to the fact that the result value is related to experience of drawing personnel, and different shearing strength parameters can be obtained if the drawing personnel are different according to the same triaxial test data.
The second method is to make a common tangent line for every two mol stress circles to obtain a plurality of friction forces c and internal friction angles
The data were averaged separately. The method has few practical applications, can obtain a unique result value, is simple and convenient to operate, but the method used for value taking is not clear in mathematical meaning, and the result value is considered to have obvious errors or even errors.
The third method is a mathematical solution. The third method has multiple types, including an optimal solution method, a least square method, a nonlinear programming method and the like. The third method has good theoretical basis and can obtain only result value, but has large valueThe method is complex, involves complex derivation calculation processes such as partial differential equations, deviation analysis and the like, has no advantage in the aspect of simplicity, and is rarely used in practice. At the same time, the third method may give significantly unreasonable results, for example c < 0kPa or
For such a result value, this type of method cannot make relevant corrections. In addition, the results obtained by the method have the problem that the quality of the test cannot be reflected. For example, in two tests, as shown in fig. 2 and fig. 3, the shear strength parameters obtained by the two tests through the mathematical solution are completely the same, but the respective triaxial test data are obviously different, and the quality of the two tests is obviously different, so that it is necessary to evaluate the result value for the engineer to reasonably evaluate and select.
Disclosure of Invention
Aiming at the problems of non-unique result value, complex calculation and even error of the shear strength parameter calculation through triaxial test data according to the existing method, the invention firstly provides a shear strength parameter calculation method, aiming at quickly and accurately determining the shear strength parameter according to the triaxial test data.
The technical scheme adopted by the invention is as follows: the shear strength parameter calculation method directly calculates cohesive force c and internal friction angle according to constraint condition I and constraint condition II through n groups of triaxial test data
n is not less than 2 and is an integer.
Constraint one: the sum of vector distances from the tangent point of the parallel line of the to-be-determined failure strength line or the to-be-determined failure strength line and each molar stress circle to the to-be-determined failure strength line is 0. The vector distance is a distance having positive and negative values according to the direction, and the distance from the tangent point on one side of the line of the failure strength to be obtained to the line of the failure strength to be obtained is defined as negative, and the distance from the tangent point on the other side of the line of the failure strength to be obtained to the line of the failure strength to be obtained is defined as positive, or vice versa.
Specifically, the method comprises the following steps: the calculation formula of the constraint condition one is
Wherein: the sigma i3 and the sigma i1 are stress values measured by the triaxial test of the ith group of samples, and the unit is kPa;
is the internal friction angle, in degrees; c is cohesion in kPa.
Constraint two: the sum of the distances from the tangent point of the parallel line of the line or lines of the strength of damage to be solved and each molar stress circle to the line or lines of the strength of damage to be solved is the smallest.
Specifically, the method comprises the following steps: the second constraint is calculated as
The value of (a) is minimal. The sign meaning in the formula of constraint two is the same as before.
Further, the method comprises the following steps: for cohesive force c and internal friction angle directly calculated according to constraint condition one and constraint condition two
The following modifications were made: if the cohesive force c is less than 0, taking the cohesive force c =0, and obtaining an internal friction angle according to a constraint condition I
If internal friction angle
Taking the internal friction angle
And acquiring the cohesive force c according to the constraint condition II.
The invention also provides an evaluation method of the shear strength parameter calculation method, which calculates according to the shear strength parameterMethod for determining cohesion c and internal friction angle
The cohesive force c and the internal friction angle can be directly calculated according to the constraint condition I and the constraint condition II
The cohesive force c and the internal friction angle after correction in the above-described manner may be used
And then, carrying out quality evaluation through a maximum distance ratio delta, wherein the magnitude of the maximum distance ratio delta and the quality of the test result are in a negative correlation relationship, and the calculation formula of the maximum distance ratio delta is
For example: when delta is less than or equal to 0.05, the test result quality is excellent; when delta is more than 0.05 and less than or equal to 0.15, the quality of the test result is general; when delta is greater than 0.15, the quality of the test results is poor.
The beneficial effects of the invention are: shear strength parameter cohesive force c and internal friction angle obtained by shear strength parameter calculation method
The value of (A) is unique, and the mathematical meaning of the calculation result is clear and reasonable. The calculation formulas of the constraint condition I and the constraint condition II are simple to calculate and can be implemented by a computer. The evaluation method of the shear strength parameter calculation method provided by the invention carries out quantitative evaluation on the calculation result, and is convenient for engineers to reasonably evaluate and select.
Drawings
Fig. 1 is a schematic diagram of a general method of shear strength parameter evaluation.
FIG. 2 is a schematic representation of the shear strength parameters obtained experimentally by a mathematical solution.
Fig. 3 is a diagram illustrating an experiment in which the same shear strength parameter as that of fig. 2 is obtained by a mathematical solution.
Fig. 4 is an auxiliary explanatory schematic diagram of a constraint condition one of the shear strength parameter calculation method of the present invention.
Fig. 5 is a molar stress circle and its common tangent line of a comparative example of the present invention.
Detailed Description
The invention is further illustrated by the following figures and examples.
According to the shear strength parameter calculation method, the cohesive force c and the internal friction angle are calculated according to the constraint condition I and the constraint condition II through n groups of triaxial test data
Wherein n is an integer greater than or equal to 2, and the value of n is generally 3, 4 or 5.
According to the triaxial test data, the number of the molar stress circles can be drawn in a plane coordinate system, and the number of the molar stress circles is the same as the number n of the groups of the triaxial test data. Next, an example of n =2 is explained with reference to fig. 4.
Constraint one: the sum of vector distances from the tangent point of each molar stress circle to the line of the to-be-solved breaking strength or the parallel line of the to-be-solved breaking strength to the line of the to-be-solved breaking strength is 0. The vector distance is a distance having positive and negative values according to the direction, and the distance from the tangent point on one side of the line of the failure strength to be obtained to the line of the failure strength to be obtained is defined as negative, and the distance from the tangent point on the other side of the line of the failure strength to be obtained to the line of the failure strength to be obtained is defined as positive, or vice versa. For example, referring to a slant line in the 4,x axis and the first quadrant of the y axis as the to-be-determined failure strength line, 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 as follows:
wherein: the sigma i3 and the sigma i1 are stress values measured by the triaxial test of the ith group of samples in unit of kPa;
is the internal friction angle, in degrees; c is cohesion in kPa.
Constraint two: the sum of the distances from the tangent point of each molar stress circle to the line of the to-be-solved breaking strength or the parallel line of the to-be-solved breaking strength is the minimum. The distance in constraint two is a scalar. For example, constraint two is calculated as:
the value of (a) is minimal. The sign meaning in the formula of constraint two is the same as before.
The constraint condition one and the constraint condition two respectively contain two unknowns to be solved, namely the internal friction angle
And cohesive force c, so that constraint one and constraint two form a system of equations of a binary system. By solving, the unique shear strength parameter cohesive force c and the internal friction angle can be obtained
The shear strength parameter calculation method can be implemented through computer programming and has the characteristic of convenient solution.
Considering that the shear strength parameter has a certain reasonable range, the cohesive force c and the internal friction angle are directly calculated according to the constraint condition I and the constraint condition II
Possibly exceeding the reasonable range, and in order to avoid obtaining unreasonable result values, the invention also directly calculates the cohesive force c and the internal friction angle according to the constraint condition I and the constraint condition II
The following modifications were made: if the cohesive force c is less than 0, taking the cohesive force c =0, and obtaining an internal friction angle according to a constraint condition I
If internal friction angle
Taking the internal friction angle
And acquiring the cohesive force c according to the constraint condition II.
The second subject of the present invention is a method for evaluating a method for calculating a shear strength parameter, which comprises determining the cohesion c and the internal friction angle according to the method for calculating a shear strength parameter
The cohesive force c and the internal friction angle can be directly calculated according to the constraint condition I and the constraint condition II
The cohesive force c and the internal friction angle after correction in the above-described manner may be used
Then, the quality evaluation is carried out through a maximum distance ratio delta, and the calculation formula of the maximum distance ratio delta is
The maximum distance ratio delta is used as a basis for quantitatively evaluating the reliability of the result value of the shear strength parameter, and the magnitude of the maximum distance ratio delta and the quality of the test result are in a negative correlation relationship. For a number of experiments only, the applicant provides a piecewise recommendation as to the maximum distance ratio δ: when delta is less than or equal to 0.05, the test result quality is excellent; when delta is more than 0.05 and less than or equal to 0.15, the quality of the test result is general; when delta is greater than 0.15, the quality of the test result is poor, and technicians need to apply the shear strength parameter result value carefully.
The correctness of the invention is verified by three groups of triaxial test data.
The data of the three-axis tests are shown in Table 1, and the number of the three-axis testsAccording to the three groups of triaxial test data corresponding to the sample 1, the sample 2 and the sample 3 respectively, firstly drawing a molar stress circle, and then determining a common tangent line of the molar stress circle to obtain a shear strength parameter: cohesion c =0.21kPa, internal friction angle
As shown in fig. 5.
Table 1 three sets of triaxial test data.
| Sample number | σ13(kPa) | σ11(kPa) |
| Sample No. 1 | 0.2748 | 1.5662 |
| Sample No. 2 | 0.6116 | 2.5884 |
| Sample No. 3 | 0.9205 | 3.5536 |
The three sets of triaxial test data shown in Table 1 are used to calculate the cohesive force c and the internal friction angle according to the shear strength parameter calculation method of the present invention
By the calculation of constraint one, the following can be obtainedCohesive force c and internal friction angle meeting constraint condition one
The corresponding values of (a) are shown in table 2.
Table 2 calculated shear strength parameters that meet constraint one.
Calculating all cohesive force c and internal friction angle meeting the first constraint condition through a calculation formula of the second constraint condition
The sum of the distance branches corresponding to the values of (a) is shown in table 3.
Table 3 calculation table of calculation formula of constraint two.
As can be seen from the calculation of Table 3, the minimum cohesive force c corresponding to the sum of the distances of the second constraint conditions is 0.2175kPa, and the internal friction angle is set to be equal to
Is 30 deg.. In order to further improve the calculation accuracy, the internal friction angle is calculated based on the calculation
And performing the calculation again according to the calculation formula of the constraint condition I and the calculation formula of the constraint condition II in the range of 29.1-30.9 degrees, and finally determining the calculation value as follows: internal friction angle
Cohesion c =0.21kPa.
The shear strength parameter obtained by the drawing method is consistent with the shear strength parameter directly calculated by the method, and the correctness of the method for calculating the shear strength parameter is proved. According to the evaluation method of the shear strength parameter calculation method of the present invention, the maximum distance ratio δ was 0.00016 for the above directly calculated shear strength. As can be seen from the foregoing, the maximum distance ratio δ should be 0 since the three sets of triaxial test data are complete tangent circles, but the calculation results are slightly different due to the error in reading the coordinates by the computer (the values of σ 13 and σ 11 are 4 decimal places in the current reading), but the evaluation of the quality of the test results is not affected by the evaluation criteria, and the test result quality is excellent.
The invention is described below with reference to engineering examples.
As shown in the table 4, three triaxial test achievements in a certain hydropower engineering semi-diagenesis chamber are selected for analysis, wherein the test 1 and the test 2 are undisturbed samples, the three test positions are remolded samples, the remolded samples are more uniform in character, and the achievements are generally better in quality. For comparison and verification, two experienced workers who invite this time respectively provide relevant test results by adopting a mapping method and combining the work experience of the two experienced workers, and the relevant test results are compared with the result value calculated according to the invention.
Table 4 comparison of the results of the three triaxial tests.
As can be seen from Table 4, the process of the invention has the advantages: the test result is unique; the result has clear and reasonable mathematical meaning; the quality of the test can also be evaluated quantitatively.
Claims (7)
1. The shear strength parameter calculation method is characterized by comprising the following steps: directly calculating cohesive force c and internal friction angle according to the constraint condition I and the constraint condition II through n groups of triaxial test data
n is not less than 2 and is an integer; constraint one: parallel lines of the to-be-determined breaking strength or the lines of the to-be-determined breaking strength and the respective molesThe sum of the vector distances from the tangent point of the stress circle to the line of the failure strength to be solved is 0; and the constraint condition two is as follows: the sum of the distances from the tangent point of the parallel line of the line or lines of the strength of damage to be solved and each molar stress circle to the line or lines of the strength of damage to be solved is the smallest.
2. The shear strength parameter calculation method according to claim 1, wherein: the calculation formula of the constraint condition one is
Wherein: the sigma i3 and the sigma i1 are stress values measured by the triaxial test of the ith group of samples, and the unit is kPa;
internal friction angle, in degrees; c is cohesion in kPa.
3. The shear strength parameter calculation method according to claim 1, wherein: the second constraint is calculated as
Has the smallest value, wherein: the sigma i3 and the sigma i1 are stress values measured by the triaxial test of the ith group of samples, and the unit is kPa;
is the internal friction angle, in degrees; c is cohesion in kPa.
4. The shear strength parameter calculation method according to claim 1, wherein: n is 3, 4 or 5.
5. The shear strength parameter calculation method according to any one of claims 1 to 4, wherein: for cohesive force c and internal friction angle directly calculated according to constraint condition one and constraint condition two
The following modifications were made: if the cohesive force c is less than 0, taking the cohesive force c =0, and obtaining an internal friction angle according to a constraint condition I
If internal angle of friction
Taking the internal friction angle
And acquiring the cohesive force c according to the second constraint condition.
6. The evaluation method of the shear strength parameter calculation method is characterized by comprising the following steps: determining the cohesive force c and the internal friction angle by the method for calculating the shear strength parameter according to any one of the claims 1 to 5
And then, carrying out quality evaluation through a maximum distance ratio delta, wherein the magnitude of the maximum distance ratio delta and the quality of the test result are in a negative correlation relationship, and the calculation formula of the maximum distance ratio delta is
7. The method for evaluating a shear strength parameter calculation method according to claim 6, wherein: when delta is less than or equal to 0.05, the test result quality is excellent; when delta is more than 0.05 and less than or equal to 0.15, the quality of the test result is general; when delta is greater than 0.15, the quality of the test results is poor.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116593320A (en) * | 2023-01-06 | 2023-08-15 | 广东有色工程勘察设计院 | Experimental system for acquiring shear strength parameters of rock and soil mass and application method thereof |
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116593320A (en) * | 2023-01-06 | 2023-08-15 | 广东有色工程勘察设计院 | Experimental system for acquiring shear strength parameters of rock and soil mass and application method thereof |
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