CN117408012A - Rock triaxial strength criterion construction method and device based on ultimate strength - Google Patents
Rock triaxial strength criterion construction method and device based on ultimate strength Download PDFInfo
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Abstract
The invention discloses a method and a device for constructing a triaxial strength criterion of rock based on ultimate strength, wherein the method comprises the following steps: based on the deflection stress (sigma) at rock failure 1 ‑σ 3 ) And confining pressure sigma 3 Nonlinear relation between them, find sigma 1 ‑σ 3 Ultimate strength p and sigma of curve 1 ‑σ 3 The difference of the curve with confining pressure sigma 3 Instead of a linear decrease, a difference curve is defined taking into account the difference having two end points, defining the boundary of q; for different types of rock, the descending trend of q is different, and q is sigma to ensure the consistency of dimension 3 Sum sigma ci Is a nonlinear function of (2); let q be sigma 3 Sum sigma ci Is substituted into the difference relation to construct sigma 1 、p、σ ci Sigma (sigma) 3 I.e. the first rock triaxial strength criterion. Based on the comprehensive database, the inventionEmbodiments establish a simplified criterion for rock strength estimation without triaxial test data, namely a second rock triaxial strength criterion.
Description
Technical Field
The invention relates to the technical field of rock strength estimation, in particular to a method and a device for constructing a triaxial rock strength criterion based on ultimate strength.
Background
Rock engineering applications (e.g., tunnel, mining operations, oil and gas extraction, geothermal energy extraction) often face stability problems such as subsidence, collapse, etc. These problems are all related to the destruction of rock under complex stress conditions. The strength of rock under complex stress can be considered as a function of the stress state, which is often referred to as the strength criterion. The strength criteria may be used not only to determine the strength of the rock at a given stress field, but also to determine the extent of the plastic zone at which failure occurs. Thus, establishing appropriate strength criteria is of great importance for rock engineering design and corresponding geophysical research.
Since the establishment of the International Society of Rock Mechanics (ISRM), the rock strength criterion has been one of the most challenging research topics in the fields of rock mechanics and rock engineering. To date, numerous theoretical and empirical standards have been proposed by scientists and engineers worldwide. The Mohr-coulomb (MC) criterion is one of the earliest and most reliable theoretical guidelines for soil and rock. This theoretical criterion was originally proposed by Coulomb and later developed by Mohr to describe the linear relationship between maximum principal stress and minimum principal stress. Hoekand Brown is inspired by brittle fracture theory, and a plurality of distorted parabolic envelopes are summarized through repeated experiments, so that a well-known Hoek-Brown (HB) criterion is provided, and the mechanics principle is applied to analysis and design of rock engineering structures.
While the above-described theoretical guidelines provide the necessary basis for determining rock strength using an ergonomic model, the predicted outcome of some theoretical guidelines often does not coincide with the outcome of an experiment. Based on triaxial test results of 132 groups of rocks, a correction term is added on the basis of MC criterion, and a corrected nonlinear Mohr-Coulomb criterion (MM-C criterion) is proposed. The results lay a solid analysis foundation for understanding the strength criterion, and provide accurate strength prediction for rock damage under specific conditions. However, there is currently no failure criterion with significant advantages in terms of mechanical mechanisms or mathematical forms due to the discreteness of rock materials. Therefore, there is a need to establish a new failure criterion that provides an improved, convenient method for failure calculation of rock material during engineering design.
Disclosure of Invention
In order to overcome the defects of the prior art, the embodiment of the invention aims to provide a method and a device for constructing a triaxial strength criterion of rock based on ultimate strength, which can estimate the rock strength without triaxial test data.
In order to solve the above problems, a first aspect of the embodiments of the present invention discloses a method for constructing a triaxial strength criterion of rock based on ultimate strength, which includes the following steps:
Based on the deflection stress (sigma) at rock failure 1 -σ 3 ) And confining pressure sigma 3 Nonlinear relation between them, find sigma 1 -σ 3 Ultimate strength p and sigma of curve 1 -σ 3 The difference of the curve with confining pressure sigma 3 Not a linear decrease, taking into account that the difference curve formed by the differences has two endpoints, thenThe following boundaries exist:
wherein q is sigma 1 -σ 3 Ultimate strength p and bias stress (sigma) 1 -σ 3 ) The difference in the curves, obviously q=p- (σ) 1 -σ 3 ) I.e. q=p- σ 1 +σ 3 ，σ 1 Maximum principal stress at different surrounding pressures, sigma ci Is the uniaxial compressive strength of the rock; sigma (sigma) crt Is critical confining pressure;
for different types of rock, the descending trend of q is different, and q is sigma to ensure the consistency of dimension 3 Sum sigma ci Is a nonlinear function of (a):
wherein A is an empirical parameter;
since q=p- σ 1 +σ 3 Then, in conjunction with equation (2), there is:
converting equation (3) to:
the formula (4) is a constructed first rock triaxial strength criterion, and the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock are obtained ci Confining pressure sigma 3 When the maximum principal stress sigma under different surrounding pressures is predicted by the formula (4) 1 Uniaxial compressive strength sigma of said rock ci Confining pressure sigma 3 Can be obtained through a rock triaxial test.
As a preferred embodiment, in the first aspect of the embodiment of the present invention, the method further includes:
By a correlation coefficient R 2 And average absolute relative error percentage AAREP to evaluate the predictive performance of the first rock triaxial strength criteria:
wherein sigma 1i，mea Sum sigma 1i，pre Respectively obtaining an i-th measured value of the maximum principal stress under different surrounding pressures and an i-th predicted value of the maximum principal stress under different surrounding pressures, which is predicted by a first rock triaxial strength criterion; n is the number of data to be processed,is the measured average of the maximum principal stresses, and:
when the correlation coefficient R2 is greater than a first preset threshold value, or/and when the average absolute relative error percentage AAREP is smaller than a second preset threshold value, the prediction precision of the first rock triaxial strength criterion meets the requirement.
As a preferred embodiment, in the first aspect of the embodiment of the present invention, when the triaxial test of the rock cannot be performed, the method further includes:
determining empirical parameters and uniaxial compressive strength sigma of rock based on historical data ci A first relation between the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock ci A second relationship between;
and constructing a second rock triaxial strength criterion based on the first and second relationships and the first rock triaxial strength criterion.
In a first aspect of the present embodiment, the empirical parameter and the uniaxial compressive strength σ of the rock are determined based on historical data ci A first relation between the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock ci A second relationship between, comprising:
by collecting the conventional triaxial experiment results, a comprehensive database covering the magma rock, metamorphic rock and sedimentary rock is compiled; the comprehensive database includes 1642 triaxial test results from 207 rocks around the world; based on the data in the comprehensive database, A/sigma is established by a data fitting mode ci And sigma (sigma) ci A functional relation of (a), namely a first relation:
σ ci ＝2.55(A/σ ci ) -0.778 (6)
also, by means of data fittingAnd sigma (sigma) ci A second relationship:
constructing a second rock triaxial strength criterion based on the first and second relationships and the first rock triaxial strength criterion, including:
a second rock triaxial strength criterion is constructed in combination with equations 6, 7 and the first rock triaxial strength criterion, equation (4):
the formula (8) is a constructed second rock triaxial strength criterion, and the uniaxial compressive strength sigma of the rock is obtained ci When the method is used, the maximum principal stress sigma under different surrounding pressures can be predicted by the formula (8) 1 。
As a preferred embodiment, in the first aspect of the embodiment of the present invention, the method further includes:
by a correlation coefficient R 2 And average absolute relative error percentage AAREP to evaluate the secondPrediction performance of rock triaxial strength criteria:
wherein sigma 1i，mea Sum sigma 1i，pre Respectively obtaining an i-th measured value of the maximum principal stress under different surrounding pressures and an i-th predicted value of the maximum principal stress under different surrounding pressures, which is predicted by a second rock triaxial strength criterion; n is the number of data to be processed,is the measured average of the maximum principal stresses, and:
when the correlation coefficient R2 is greater than a first preset threshold value, or/and when the average absolute relative error percentage AAREP is smaller than a second preset threshold value, the prediction precision of the second rock triaxial strength criterion meets the requirement.
The second aspect of the embodiment of the invention discloses a rock triaxial strength criterion construction device based on ultimate strength, which comprises:
a boundary determination unit for determining a boundary value based on the rock failure time bias stress (sigma 1 -σ 3 ) And confining pressure sigma 3 Nonlinear relation between them, find sigma 1 -σ 3 Ultimate strength p and sigma of curve 1 -σ 3 The difference of the curve with confining pressure sigma 3 Considering that the difference curve formed by the differences has two endpoints, there are the following boundaries:
wherein q is sigma 1 -σ 3 Ultimate strength p and bias stress (sigma) 1 -σ 3 ) The difference in the curves, obviously q=p- (σ) 1 -σ 3 ) I.e. q=p- σ 1 +σ 3 ，σ 1 Maximum principal stress at different surrounding pressures, sigma ci Is the uniaxial compressive strength of the rock; sigma (sigma) crt Is critical confining pressure;
a dimension consistent unit for ensuring the consistency of the dimension by setting q as sigma 3 Sum sigma ci Is a nonlinear function of (a):
wherein A is an empirical parameter;
since q=p- σ 1 +σ 3 Then, in conjunction with equation (10), there is:
a conversion unit for converting the formula (11) into:
the formula (12) is a constructed first rock triaxial strength criterion, and the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock are obtained ci Confining pressure sigma 3 When the maximum principal stress sigma under different surrounding pressures is predicted by the formula (12) 1 Uniaxial compressive strength sigma of said rock ci Confining pressure sigma 3 Can be obtained through a rock triaxial test.
As a preferred implementation manner, in the second aspect of the embodiment of the present invention, the apparatus further includes a first prediction performance evaluation unit, configured to:
by a correlation coefficient R 2 And average absolute relative error percentage AAREP to evaluate the predictive performance of the first rock triaxial strength criteria:
wherein sigma 1i，mea Sum sigma 1i，pre Respectively obtaining an i-th measured value of the maximum principal stress under different surrounding pressures and an i-th predicted value of the maximum principal stress under different surrounding pressures, which is predicted by a first rock triaxial strength criterion; n is the number of data to be processed, Is the measured average of the maximum principal stresses, and:
when the correlation coefficient R2 is greater than a first preset threshold value, or/and when the average absolute relative error percentage AAREP is smaller than a second preset threshold value, the prediction precision of the first rock triaxial strength criterion meets the requirement.
In a second aspect of the embodiment of the present invention, when the triaxial test of the rock is impossible, the apparatus further includes a simplifying unit for:
determining empirical parameters and uniaxial compressive strength sigma of rock based on historical data ci A first relation between the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock ci A second relationship between;
and constructing a second rock triaxial strength criterion based on the first and second relationships and the first rock triaxial strength criterion.
As a preferred embodiment, in the second aspect of the embodiment of the present invention, the simplifying unit includes:
the first relation fitting subunit is used for compiling a comprehensive database covering the magma rock, metamorphic rock and sedimentary rock by collecting the conventional triaxial experiment results; the comprehensive database includes 1642 triaxial test results from 207 rocks around the world; the first relation fitting subunit is used for calculating the pass number based on the data in the comprehensive database Building A/sigma according to fitting mode ci And sigma (sigma) ci A functional relation of (a), namely a first relation:
σ ci ＝2.55(A/σ ci ) -0.778 (14)
a second relation fitting subunit for establishing p+ by means of data fitting based on the data in the comprehensive databaseAnd sigma (sigma) ci A second relationship:
a construction subunit for constructing a second rock triaxial strength criterion in combination with equations 6, 7 and the first rock triaxial strength criterion, equation (12):
the formula (16) is a constructed second rock triaxial strength criterion, and the uniaxial compressive strength sigma of the rock is obtained ci When the method is used, the maximum principal stress sigma under different surrounding pressures can be predicted by the formula (16) 1 。
As a preferred implementation manner, in the second aspect of the embodiment of the present invention, the apparatus further includes a second prediction performance evaluation unit, configured to:
by a correlation coefficient R 2 And average absolute relative error percentage AAREP to evaluate the predictive performance of the second rock triaxial strength criteria:
wherein sigma 1i，mea Sum sigma 1i，pre Respectively, the i maximum principal stress measured value under different surrounding pressures and the i maximum principal stress predicted by the second rock triaxial strength criterionMaximum principal stress predicted values at different confining pressures; n is the number of data to be processed,is the measured average of the maximum principal stresses, and:
When the correlation coefficient R2 is greater than a first preset threshold value, or/and when the average absolute relative error percentage AAREP is smaller than a second preset threshold value, the prediction precision of the second rock triaxial strength criterion meets the requirement.
A third aspect of an embodiment of the present invention discloses an electronic device, including: a memory storing executable program code; a processor coupled to the memory; the processor invokes the executable program code stored in the memory to perform a method for constructing a triaxial strength criterion of rock based on ultimate strength according to the first aspect of the embodiment of the present invention.
A fourth aspect of the embodiments of the present invention discloses a computer-readable storage medium storing a computer program, wherein the computer program causes a computer to execute a method for constructing a rock triaxial strength criterion based on ultimate strength disclosed in the first aspect of the embodiments of the present invention.
A fifth aspect of the embodiments of the present invention discloses a computer program product which, when run on a computer, causes the computer to perform a method of constructing a rock triaxial strength criterion based on ultimate strength according to the first aspect of the embodiments of the present invention.
A sixth aspect of the embodiment of the present invention discloses an application publishing platform, which is configured to publish a computer program product, where when the computer program product runs on a computer, the computer is caused to execute a method for constructing a triaxial strength criterion of rock based on ultimate strength disclosed in the first aspect of the embodiment of the present invention.
Compared with the prior art, the beneficial effects of the method are as follows:
the present embodiment simplifies the existing rock strength estimation criteria and in order to verify the proposed criteria, a database is compiled including more than triaxial tests on different rocks worldwide. The predicted performance of the established criteria is then compared with other classical strength criteria and finally a simplified criterion is established for rock strength estimation without triaxial test data.
Drawings
FIG. 1 is a schematic flow chart of a method for constructing triaxial strength criteria of rock based on ultimate strength according to an embodiment of the present invention;
FIG. 2 is a typical bias-confining pressure curve under conventional triaxial compression conditions as disclosed in an embodiment of the present invention;
FIG. 3 is a graph I of laboratory measured values versus a first rock triaxial strength criteria disclosed in an embodiment of the present invention;
FIG. 4 is a graph II comparing laboratory measured values disclosed in the example of the present invention with a first rock triaxial strength criterion;
FIG. 5 is a comparison of different types of rock failure envelopes for 5 criteria disclosed in an embodiment of the present invention;
FIG. 6 (a) is a graph of predicted performance (AAREP based) for different criteria under different lithology as disclosed in an embodiment of the invention;
FIG. 6 (b) is a graph of predicted performance (R-based) for different lithology for different criteria disclosed in an embodiment of the invention 2 )；
FIG. 7 is a diagram illustrating a sigma of an embodiment of the present invention ci And A/sigma ci Is a relationship of (2);
FIG. 8 is a diagram illustrating a sigma of an embodiment of the present invention ci And p/sigma 2 ci Is a relationship of (2);
FIG. 9 is a graph I of laboratory measured values versus a second rock triaxial strength criteria disclosed in an embodiment of the present invention;
FIG. 10 is a graph II of laboratory measured values versus a second rock triaxial strength criterion according to an embodiment of the present invention;
FIG. 11 is a schematic structural diagram of a device for constructing triaxial strength criteria of rock based on ultimate strength according to an embodiment of the present invention;
fig. 12 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
The present embodiment is only for explanation of the present invention and is not to be construed as limiting the present invention, and those skilled in the art can make modifications to the present embodiment without creative contribution as required after reading the present specification, but are protected by patent laws within the scope of claims of the present invention.
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, apparatus, article, or device that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed or inherent to such process, method, article, or device.
In embodiments of the invention, words such as "exemplary" or "such as" are used to mean serving as an example, instance, or illustration. Any embodiment or design described herein as "exemplary" or "for example" is not necessarily to be construed as preferred or advantageous over other embodiments or designs. Rather, the use of words such as "exemplary" or "such as" is intended to present related concepts in a concrete fashion.
The following detailed description refers to the accompanying drawings.
Example 1
Referring to fig. 1, a method for constructing a triaxial strength criterion of rock based on ultimate strength includes the following steps:
s110, based on the rock failure time bias stress (sigma 1 -σ 3 ) And confining pressure sigma 3 Nonlinear relation between them, find sigma 1 -σ 3 Ultimate strength p and sigma of curve 1 -σ 3 The difference of the curve with confining pressure sigma 3 And not linearly decreasing.
The research result of the conventional triaxial compression test shows that the deflection stress (sigma) 1 -σ 3 ) And confining pressure sigma 3 And exhibit a nonlinear relationship therebetween as shown in figure 2. In the figure, p is the critical state bias stress (also called ultimate strength), σ ci Is the uniaxial compressive strength of the rock. At (sigma) 1 -σ 3 )-σ 3 In the plane, the intensity curve exhibits convexity. When the confining pressure is low, the nonlinearity is weak, which can be approximated as linearity, which is why the linearity MC criterion is more accurate at low confining pressures. As the confining pressure increases, the nonlinear characteristics are evident. When the confining pressure increases to a critical value, the bias stress upon rock failure will reach a maximum value. If the confining pressure continues to increase, this value remains unchanged.
By observing σ in FIG. 2 1 –σ 3 And confining pressure sigma 3 Nonlinear relation between them, find sigma 1 –σ 3 Ultimate strength p and sigma of curve 1 –σ 3 The difference q of the curve is sigma dependent 3 Is decreased by an increase in (c). Considering the two endpoints of the curve, there are two endpoints of the difference curve that the following boundary conditions consider the difference, the following boundaries exist:
wherein q is sigma 1 -σ 3 Ultimate strength p and sigma of curve 1 -σ 3 Difference in curve, q=p- σ 1 +σ 3 ，σ 1 Maximum principal stress at different surrounding pressures, sigma ci Is the uniaxial compressive strength of the rock; sigma (sigma) crt Is critical confining pressure.
S120, for different types of rocks, the descending trend of q is different, and q is sigma to ensure the consistency of dimension 3 Sum sigma ci Is a nonlinear function of (a):
wherein A is an empirical parameter.
Since q=p- σ 1 +σ 3 Then, in conjunction with equation (2), there is:
s130, converting the formula (3) into:
the formula (4) builds a new criterion for the invention, which is recorded as a first rock triaxial strength criterion, and acquires the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock ci Confining pressure sigma 3 When the maximum principal stress sigma under different surrounding pressures is predicted by the formula (4) 1 Uniaxial compressive strength sigma of said rock ci Confining pressure sigma 3 Can be obtained through a rock triaxial test.
The reliability of the strength criterion depends on its application in large rock mechanics experiments. To verify the proposed first rock triaxial strength criteria, we have collected a number of valuable conventional triaxial experimental results and compiled a comprehensive database covering the magma, metamorphic and sedimentary rocks. The database includes 1642 triaxial test results from 207 rocks around the world.
In addition, the invention also uses two widely adopted statistical indexes, namely the correlation coefficient R 2 And Average Absolute Relative Error Percent (AAREP) to evaluate predictability of the established criteriaCan be used. These two statistical indicators are represented by the following formula:
wherein sigma 1i，mea Sum sigma 1i，pre Respectively obtaining an i-th measured value of the maximum principal stress under different surrounding pressures and an i-th predicted value of the maximum principal stress under different surrounding pressures, which is predicted by a first rock triaxial strength criterion; n is the number of data to be processed,is the measured average of the maximum principal stresses, and:
when R is 2 When the AAREP tends to be 1, the criterion has higher precision when the AAREP tends to be 0. Fig. 3 shows the predicted outcome of the inventive criteria. If the measurement point is lower than the prediction curve, the criterion is used for overestimating the rock strength; conversely, if the measurement point is higher than the predicted curve, the proposed criterion underestimates the rock strength. As can be seen from the figure, the predicted curve has the same trend as the actual point. R of each sample 2 All above 0.989, AAREP is less than 3.5%, indicating that the proposed intensity criteria have higher accuracy. Among the comparisons of different lithologies, the criteria for the various sandstones (sandstone) and the England (Darite) are the best and the criteria for Gneiss (Gneiss) the worst.
The above results demonstrate that the established intensity criteria perform well in selected samples, and that the general applicability of the criteria remains to be further verified and analyzed. The results of 1642 sets of experiments in the database were analyzed. The results are shown in FIG. 4. The abscissa and ordinate in the figure represent the measured value and predicted value of the criterion, respectively. The closer the slope of the regression line is to 1, the higher the accuracy of the criterion. As can be seen from fig. 4, the slope of the regression curve reaches 0.9976, and by calculation, the AARPE for all data is 2.84%, indicating that the criterion is still well-behaved in a wide range of samples. In addition, the slope of the criterion regression line is smaller than 1, and the criterion is stated to underestimate the rock mass strength as a whole, so that a safe redundant space can be reserved for engineering design, and the engineering safety is guaranteed.
Some well-known strength criteria, such as MC criteria, HB criteria, MMC criteria, and MHB criteria, have been applied for decades. It is valuable to compare the predictive performance of the proposed criteria with these classical criteria. Fig. 5 shows a comparison of the proposed intensity criteria with the classical intensity criteria destruction envelope for different lithologies. It can be seen that this criterion is closer to the triaxial test data of the rock than the other four criteria. The curvature of the proposed criterion envelope is very suitable and exhibits a high degree of nonlinearity. It is clear from fig. 5 that at lower confining pressures, the triaxial strengths of the rock predicted by the MC and HB criteria are very close to the test points. However, as the confining pressure increases, the predicted curves of both criteria are progressively higher than the measured point, and the deviation increases as the confining pressure increases. It follows that MC criteria and HB criteria overestimate rock strength at high confining pressures, resulting in potential safety hazards for deep underground engineering (e.g., deep mine, deep tunnel engineering) designs.
Fig. 6 illustrates the predictive performance of different intensity criteria. It is apparent from FIGS. 6 (a), 6 (b) that HB, MMC and the strength criteria proposed by the present invention exhibit lower AAREP @ for most samples<5%) and high R 2 (>0.975). R of the first intensity criterion proposed by the invention 2 0.997, R in all intensity criteria discussed 2 Highest. The AAREP for this intensity criterion is only 1.28%, much lower than for other intensity criteria. In other words, the accuracy of the intensity criteria presented by the present invention is higher than other intensity criteria.
The accuracy of the established criteria is fully demonstrated in the discussion above. Nevertheless, these studies were all based on existing triaxial data. Obtaining the rock strength criterion parameters by fitting a large amount of data is a key step in predicting triaxial strength. Because of the high triaxial test requirements, many rocks (e.g., strong weathered rock and weak cemented rock) are difficult to develop. It is certain that the criterion parameters are related to the mechanical properties of the rock-although in many cases the exact physical meaning of these parameters is not clear. The aim of this program is to establish a relationship between the criterion parameters and the uniaxial compressive strength of the rock, thereby eliminating the independence of the criterion parameters and constructing a strength criterion comprising only the uniaxial compressive strength of the rock. This will help to expand the applicability of the strength criterion, given that uniaxial compressive strength in an in situ environment is readily available.
A/sigma built based on database samples ci And sigma (sigma) ci The relationship of (2) is shown in FIG. 7. It can be found that there is a clear power function relationship, sigma ci With A/sigma ci Is rapidly decreased by the increase in (c). Thus A/sigma ci And sigma (sigma) ci The relationship of (2) can be written as:
σ ci ＝2.55(A/σ ci ) -0.778 (6)
for ultimate strength p, FIG. 8 shows p/σ 2 ci And sigma (sigma) ci Is a relationship of (3). As can be seen from the figure, both have a clear power function relationship:
combining equations 6 and 7 and the proposed triaxial strength criteria (equation 4), a corrected triaxial strength criteria may be obtained, denoted as a second rock triaxial strength criteria:
for the above-mentioned simplified rule, it is unnecessary to use triaxial test data, and only the uniaxial compressive strength sigma of different lithologies are input ci The triaxial strength of the rock, namely the maximum principal stress sigma under different surrounding pressures, can be predicted 1 . Fig. 9 shows the predictive performance of such a reduced intensity criterion. As can be seen from the figure, most of the comparison points are distributed around the contour (quality), indicating that this criterion is acceptable for the predicted performance of most samples. Meanwhile, the slope of the regression line is 0.85, illustrating underestimation of the criterionMost of the samples are available, which is advantageous in that it leaves more safety redundancy in the engineering. It should be noted that the accuracy of the reduced intensity criterion is much lower than the original criterion (equation 4), with AARPE reaching 22.3%. The reason is that in order to eliminate the parameters, a fitting method is adopted to obtain the relation between the parameters and the uniaxial compressive strength. This fitting process introduces new errors, resulting in larger errors in the predicted results.
To further analyze the feasibility of predicting triaxial strength of rock using uniaxial compressive strength, four lithologies, coconno sandstone (Coconino sandstone), dunham dolomite (Dunham dolomite), gneiss (Gneiss) and Tawny sandstone (Tawny pandstone), were selected as prediction sets, respectively, and other rock test results in the database were used as training sets. And establishing a simplification criterion through the training set data, and predicting the triaxial compressive strength of the rock in the prediction set.
Fig. 10 shows the prediction performance of the reduction criterion in the prediction set. The results show that the criteria underestimates the rock triaxial strength of all samples and that the difference between the predicted value and the test curve gradually increases as the confining pressure increases. In comparison of the different samples, the simplification criteria gave the best predicted performance for Tawny sandstone, AAREP was only 1.03%, and the predicted performance for Gneiss (Gneiss) was the worst, AAREP was 14.87%.
Example two
Referring to fig. 11, fig. 11 is a schematic structural diagram of a triaxial strength criterion construction device for rock based on ultimate strength according to an embodiment of the present invention. As shown in fig. 11, the device for constructing the triaxial strength criterion of rock based on the ultimate strength may include:
A boundary determination unit 210 for determining a boundary value based on the rock breaking bias stress (sigma 1 -σ 3 ) And confining pressure sigma 3 Nonlinear relation between them, find sigma 1 -σ 3 Ultimate strength p and sigma of curve 1 -σ 3 The difference of the curve with confining pressure sigma 3 Considering that the difference curve formed by the differences has two endpoints, there are the following boundaries:
wherein q is sigma 1 -σ 3 Ultimate strength p and bias stress (sigma) 1 -σ 3 ) The difference in the curves, obviously q=p- (σ) 1 -σ 3 ) I.e. q=p- σ 1 +σ 3 ，σ 1 Maximum principal stress at different surrounding pressures, sigma ci Is the uniaxial compressive strength of the rock; sigma (sigma) crt Is critical confining pressure;
a dimension matching unit 220 for setting q as sigma to ensure dimension matching, wherein the decreasing trend of q is different for different types of rocks 3 Sum sigma ci Is a nonlinear function of (a):
wherein A is an empirical parameter;
since q=p- σ 1 +σ 3 Then, in conjunction with equation (10), there is:
a conversion unit 230 for converting the formula (11) into:
the formula (12) is a constructed first rock triaxial strength criterion, and the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock are obtained ci Confining pressure sigma 3 When the stress is applied, the maximum principal stress value sigma under different surrounding pressures is predicted by a formula (12) 1 Uniaxial compressive strength sigma of said rock ci Confining pressure sigma 3 Can be obtained through a rock triaxial test.
Preferably, the apparatus further comprises a first prediction performance evaluation unit 240, configured to:
by a correlation coefficient R 2 And average absolute relative error percentage AAREP to evaluate the predictive performance of the first rock triaxial strength criteria:
wherein sigma 1i，mea Sum sigma 1i，pre Respectively obtaining an i-th measured value of the maximum principal stress under different surrounding pressures and an i-th predicted value of the maximum principal stress under different surrounding pressures, which is predicted by a first rock triaxial strength criterion; n is the number of data to be processed,is the measured average of the maximum principal stresses, and:
when the correlation coefficient R2 is greater than a first preset threshold value, or/and when the average absolute relative error percentage AAREP is smaller than a second preset threshold value, the prediction precision of the first rock triaxial strength criterion meets the requirement.
Preferably, when the rock triaxial test cannot be performed, the apparatus further comprises a simplification unit 250 for:
determining empirical parameters and uniaxial compressive strength sigma of rock based on historical data ci A first relation between the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock ci A second relationship between;
and constructing a second rock triaxial strength criterion based on the first and second relationships and the first rock triaxial strength criterion.
Preferably, the simplification unit comprises:
a first relationship fits to the sub-unit,
by collecting the conventional triaxial experiment results, a comprehensive database covering the magma rock, metamorphic rock and sedimentary rock is compiled; the comprehensive database package1642 triaxial test results from 207 rocks around the world are included; the first relation fitting subunit is configured to establish a/sigma by means of data fitting based on data in the comprehensive database ci And sigma (sigma) ci A functional relation of (a), namely a first relation:
σ ci ＝2.55(A/σ ci ) -0.778 (14)
a second relation fitting subunit for establishing p+ by means of data fitting based on the data in the comprehensive databaseAnd sigma (sigma) ci A second relationship:
a construction subunit for constructing a second rock triaxial strength criterion in combination with equations 6, 7 and the first rock triaxial strength criterion, equation (12):
the formula (16) is a constructed second rock triaxial strength criterion, and the uniaxial compressive strength sigma of the rock is obtained ci When the method is used, the maximum principal stress sigma under different surrounding pressures can be predicted by the formula (16) 1 。
Preferably, the apparatus further comprises a second prediction performance evaluation unit 260 for:
by a correlation coefficient R 2 And average absolute relative error percentage AAREP to evaluate the predictive performance of the second rock triaxial strength criteria:
Wherein sigma 1i，mea Sum sigma 1i，pre Respectively the i-th different circumferenceA maximum principal stress actual measurement value under pressure and an i-th maximum principal stress predicted value under different surrounding pressures predicted by a second rock triaxial strength criterion; n is the number of data to be processed,is the measured average of the maximum principal stresses, and:
when the correlation coefficient R2 is greater than a first preset threshold value, or/and when the average absolute relative error percentage AAREP is smaller than a second preset threshold value, the prediction precision of the second rock triaxial strength criterion meets the requirement.
Example III
Referring to fig. 12, fig. 12 is a schematic diagram of an electronic device that may be used to implement an embodiment of the present invention. Electronic devices are intended to represent various forms of digital computers, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. Electronic equipment may also represent various forms of mobile devices, such as personal digital processing, cellular telephones, smartphones, wearable devices (e.g., helmets, glasses, watches, etc.), and other similar computing devices. The components shown in this disclosure, their connections and relationships, and their functions, are meant to be exemplary only, and are not meant to limit implementations of the embodiments of the invention described and/or claimed in this disclosure.
As shown in fig. 12, the electronic device includes at least one processor 410, and a memory, such as a ROM (read only memory) 420, a RAM (random access memory) 430, etc., communicatively connected to the at least one processor 410, wherein the memory stores a computer program executable by the at least one processor, and the processor 410 can perform various suitable actions and processes according to the computer program stored in the ROM 420 or the computer program loaded from the storage unit 480 into the random access memory RAM 430. In the RAM 430, various programs and data required for the operation of the electronic device may also be stored. The processor 410, ROM 420, and RAM 430 are connected to each other by a bus 440. An I/O (input/output) interface 450 is also connected to bus 440.
A number of components in the electronic device are connected to the I/O interface 450, including: an input unit 460 such as a keyboard, a mouse, etc.; an output unit 470 such as various types of displays, speakers, and the like; a storage unit 480 such as a magnetic disk, an optical disk, or the like; and a communication unit 490, such as a network card, modem, wireless communication transceiver, etc. The communication unit 490 allows the electronic device to exchange information/data with other devices via a computer network, such as the internet, or/and various telecommunications networks.
Processor 410 can be a variety of general-purpose or/and special-purpose processing components having processing and computing capabilities. Some examples of processor 410 include, but are not limited to, a Central Processing Unit (CPU), a Graphics Processing Unit (GPU), various specialized Artificial Intelligence (AI) computing chips, various processors running machine learning model algorithms, digital Signal Processors (DSPs), and any suitable processor, controller, microcontroller, etc. The processor 410 performs one or more steps of a method of constructing a triaxial strength criterion for rock based on ultimate strength as described in any of the above embodiments.
In some embodiments, a method of rock triaxial strength criteria construction based on ultimate strength may be implemented as a computer program tangibly embodied on a computer readable storage medium, such as the storage unit 480. In some embodiments, part or all of the computer program may be loaded onto and/or installed onto the electronic device via ROM 420 or/and communication unit 490. When loaded into RAM 430 and executed by processor 410, one or more steps of a method of constructing a triaxial strength criterion for rock based on ultimate strength as described in embodiment one above may be performed. Alternatively, in other embodiments, the processor 410 may be configured to perform a method of rock triaxial strength criterion construction based on ultimate strength in any other suitable manner (e.g., by means of firmware).
Various implementations of the apparatus and techniques described above in this invention may be implemented in digital electronic circuit devices, integrated circuit devices, field Programmable Gate Arrays (FPGAs), application Specific Integrated Circuits (ASICs), application Specific Standard Products (ASSPs), on-chip device (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, or/and combinations thereof. These various embodiments may include: implemented in one or more computer programs, the one or more computer programs may be executed or/and interpreted on programmable devices including at least one programmable processor, which may be a special purpose or general-purpose programmable processor, operable to receive data and instructions from, and to transmit data and instructions to, a storage device, at least one input device, and at least one output device.
A computer program for implementing the methods of embodiments of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus, such that the computer programs, when executed by the processor, cause the functions/acts specified in the flowchart and/or block diagram block or blocks to be implemented. The computer program may execute entirely on the machine, partly on the machine, as a stand-alone software package, partly on the machine and partly on a remote machine or entirely on the remote machine or server.
In the context of embodiments of the present invention, a computer-readable storage medium may be a tangible medium that can contain, or store a computer program for use by or in connection with an instruction execution apparatus, device, or apparatus. The computer readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor apparatus, device, or apparatus, or any suitable combination of the foregoing. Alternatively, the computer readable storage medium may be a machine readable signal medium. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
To provide for interaction with a user, the apparatus and techniques described here may be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to a user; and a keyboard and a pointing device (e.g., a mouse or a trackball) through which a user can provide input to the electronic device. Other kinds of devices may also be used to provide for interaction with a user; for example, feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form, including acoustic input, speech input, or tactile input.
The apparatus and techniques described here may be implemented in a computing device that includes a background component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front-end component (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with an implementation of the apparatus and techniques described here), or any combination of such background, middleware, or front-end components. The components of the apparatus may be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: local Area Networks (LANs), wide Area Networks (WANs), blockchain networks, and the internet.
The computing devices may include clients and servers. The client and server are typically remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. The server can be a cloud server, also called a cloud computing server or a cloud host, and is a host product in a cloud computing service system, so that the defects of high management difficulty and weak service expansibility in the traditional physical hosts and VPS service are overcome.
The invention discloses a method and a device for constructing a triaxial strength criterion of rock based on ultimate strength, which are described in detail above, wherein specific examples are applied to the invention to explain the principle and the implementation mode of the invention, and the description of the examples is only used for helping to understand the method and the core idea of the invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Claims (10)
1. The method for constructing the triaxial strength criterion of the rock based on the ultimate strength is characterized by comprising the following steps of:
based on the deflection stress (sigma) at rock failure 1 -σ 3 ) And confining pressure sigma 3 Nonlinear relation between them, find sigma 1 -σ 3 Ultimate strength p and sigma of curve 1 -σ 3 The difference of the curve with confining pressure sigma 3 Considering that the difference curve formed by the differences has two endpoints, there are the following boundaries:
wherein q is sigma 1 -σ 3 Ultimate strength p and bias stress (sigma) 1 -σ 3 ) The difference in the curves, obviously q=p- (σ) 1 -σ 3 ) I.e. q=p- σ 1 +σ 3 ，σ 1 Maximum principal stress at different surrounding pressures, sigma ci Is the uniaxial compressive strength of the rock; sigma (sigma) crt Is critical confining pressure;
for different types of rock, the q tends to decreaseThe potentials are different, q is sigma to ensure the consistency of dimension 3 Sum sigma ci Is a nonlinear function of (a):
wherein A is an empirical parameter;
since q=p- σ 1 +σ 3 Then, in conjunction with equation (2), there is:
converting equation (3) to:
the formula (4) is a constructed first rock triaxial strength criterion, and the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock are obtained ci Confining pressure sigma 3 When the maximum principal stress sigma under different surrounding pressures is predicted by the formula (4) 1 Uniaxial compressive strength sigma of said rock ci Confining pressure sigma 3 Can be obtained through a rock triaxial test.
2. The method for constructing the triaxial strength criterion of rock based on the ultimate strength according to claim 1, further comprising:
by a correlation coefficient R 2 And average absolute relative error percentage AAREP to evaluate the predictive performance of the first rock triaxial strength criteria:
wherein sigma 1i，mea Sum sigma 1i，pre Respectively the ithThe method comprises the steps of measuring the maximum principal stress actual measurement value under different surrounding pressures and the ith maximum principal stress predicted value under different surrounding pressures predicted by a first rock triaxial strength criterion; n is the number of data to be processed,is the measured average of the maximum principal stresses, and:
When the correlation coefficient R 2 And when the average absolute relative error percentage AAREP is smaller than a second preset threshold value, the prediction accuracy of the first rock triaxial strength criterion meets the requirement.
3. The method for constructing the triaxial strength criterion of rock based on the ultimate strength according to claim 1, wherein when the triaxial test of rock is impossible, the method further comprises:
determining empirical parameters and uniaxial compressive strength sigma of rock based on historical data ci A first relation between the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock ci A second relationship between;
and constructing a second rock triaxial strength criterion based on the first and second relationships and the first rock triaxial strength criterion.
4. The method for constructing a triaxial strength criterion for rock based on ultimate strength according to claim 3, wherein the empirical parameter and uniaxial compressive strength σ of rock are determined based on historical data ci A first relation between the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock ci A second relationship between, comprising:
by collecting the conventional triaxial experiment results, a comprehensive database covering the magma rock, metamorphic rock and sedimentary rock is compiled; the integrated database includes 164 from 207 rocks worldwide 2 triaxial test results; based on the data in the comprehensive database, A/sigma is established by a data fitting mode ci And sigma (sigma) ci A functional relation of (a), namely a first relation:
σ ci ＝2.55(A/σ ci ) -0.778 (6)
also, by means of data fittingAnd sigma (sigma) ci A second relationship:
constructing a second rock triaxial strength criterion based on the first and second relationships and the first rock triaxial strength criterion, including:
a second rock triaxial strength criterion is constructed in combination with equations 6, 7 and the first rock triaxial strength criterion, equation (4):
the formula (8) is a constructed second rock triaxial strength criterion, and the uniaxial compressive strength sigma of the rock is obtained ci When the method is used, the maximum principal stress sigma under different surrounding pressures can be predicted by the formula (8) 1 。
5. The method for constructing the triaxial strength criterion of rock based on the ultimate strength according to claim 4, further comprising:
by a correlation coefficient R 2 And average absolute relative error percentage AAREP to evaluate the predictive performance of the second rock triaxial strength criteria:
wherein sigma 1i，mea Sum sigma 1i，pre Respectively obtaining an i-th measured value of the maximum principal stress under different surrounding pressures and an i-th predicted value of the maximum principal stress under different surrounding pressures, which is predicted by a second rock triaxial strength criterion; n is the number of data to be processed, Is the measured average of the maximum principal stresses, and:
when the correlation coefficient R 2 And when the average absolute relative error percentage AAREP is smaller than a second preset threshold value, the prediction accuracy of the second rock triaxial strength criterion meets the requirement.
6. A rock triaxial strength criterion construction device based on ultimate strength, characterized in that it comprises:
a boundary determination unit for determining a boundary value based on the rock failure time bias stress (sigma 1 -σ 3 ) And confining pressure sigma 3 Nonlinear relation between them, find sigma 1 -σ 3 Ultimate strength p and sigma of curve 1 -σ 3 The difference of the curve with confining pressure sigma 3 Considering that the difference curve formed by the differences has two endpoints, there are the following boundaries:
wherein q is sigma 1 -σ 3 Ultimate strength p and bias stress (sigma) 1 -σ 3 ) The difference in the curves, obviously q=p- (σ) 1 -σ 3 ) I.e. q=p- σ 1 +σ 3 ，σ 1 Is the largest main under different surrounding pressuresStress, sigma ci Is the uniaxial compressive strength of the rock; sigma (sigma) crt Is critical confining pressure;
a dimension consistent unit for ensuring the consistency of the dimension by setting q as sigma 3 Sum sigma ci Is a nonlinear function of (a):
wherein A is an empirical parameter;
since q=p- σ 1 +σ 3 Then, in conjunction with equation (10), there is:
A conversion unit for converting the formula (11) into:
the formula (12) is a constructed first rock triaxial strength criterion, and the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock are obtained ci Confining pressure sigma 3 When the maximum principal stress sigma under different surrounding pressures is predicted by the formula (12) 1 Uniaxial compressive strength sigma of said rock ci Confining pressure sigma 3 Can be obtained through a rock triaxial test.
7. The apparatus for constructing the triaxial strength criterion of rock based on the ultimate strength according to claim 6, further comprising a first predictive performance evaluation unit for:
by a correlation coefficient R 2 And average absolute relative error percentage AAREP to evaluate the predictive performance of the first rock triaxial strength criteria:
wherein sigma 1i，mea Sum sigma 1i，pre Respectively obtaining an i-th measured value of the maximum principal stress under different surrounding pressures and an i-th predicted value of the maximum principal stress under different surrounding pressures, which is predicted by a first rock triaxial strength criterion; n is the number of data to be processed,is the measured average of the maximum principal stresses, and:
when the correlation coefficient R 2 And when the average absolute relative error percentage AAREP is larger than a first preset threshold value or smaller than a second preset threshold value, the prediction precision of the first rock triaxial strength criterion meets the requirement.
8. The ultimate strength based rock triaxial strength criterion construction apparatus according to claim 6, further comprising a simplification unit for, when a rock triaxial test cannot be performed:
determining empirical parameters and uniaxial compressive strength sigma of rock based on historical data ci A first relation between the ultimate strength p of the rock and the uniaxial compressive strength sigma of the rock ci A second relationship between;
and constructing a second rock triaxial strength criterion based on the first and second relationships and the first rock triaxial strength criterion.
9. The ultimate strength based rock triaxial strength criteria construction apparatus according to claim 8, wherein the simplifying unit includes:
a first relation fitting subunit, which is used for compiling a rule by collecting the conventional triaxial experiment resultComprehensive databases covering magma, metamorphic and sedimentary rocks; the comprehensive database includes 1642 triaxial test results from 207 rocks around the world; the first relation fitting subunit is configured to establish a/sigma by means of data fitting based on data in the comprehensive database ci And sigma (sigma) ci A functional relation of (a), namely a first relation:
σ ci ＝2.55(A/σ ci ) -0.778 (14)
a second relation fitting subunit for establishing a data fitting mode based on the data in the comprehensive database And sigma (sigma) ci A second relationship:
a construction subunit for constructing a second rock triaxial strength criterion in combination with equations 6, 7 and the first rock triaxial strength criterion, equation (12):
the formula (16) is a constructed second rock triaxial strength criterion, and the uniaxial compressive strength sigma of the rock is obtained ci When the method is used, the maximum principal stress sigma under different surrounding pressures can be predicted by the formula (16) 1 。
10. The ultimate strength based rock triaxial strength criterion construction apparatus according to claim 9, further including a second predictive performance evaluation unit for:
by a correlation coefficient R 2 And average absolute relative error percentage AAREP to evaluate the predictive performance of the second rock triaxial strength criteria:
wherein sigma 1i，mea Sum sigma 1i，pre Respectively obtaining an i-th measured value of the maximum principal stress under different surrounding pressures and an i-th predicted value of the maximum principal stress under different surrounding pressures, which is predicted by a second rock triaxial strength criterion; n is the number of data to be processed,is the measured average of the maximum principal stresses, and:
when the correlation coefficient R 2 And when the average absolute relative error percentage AAREP is larger than a first preset threshold value or smaller than a second preset threshold value, the prediction precision of the second rock triaxial strength criterion meets the requirement.
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