CN114166628B - Method for determining relative crushing rate of calcareous sand under different stress paths - Google Patents
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- 239000004576 sand Substances 0.000 title claims abstract description 140
- 238000000034 method Methods 0.000 title claims abstract description 44
- 238000012360 testing method Methods 0.000 claims abstract description 133
- 238000012669 compression test Methods 0.000 claims abstract description 91
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- 238000004364 calculation method Methods 0.000 claims description 24
- 230000008859 change Effects 0.000 claims description 23
- 238000010008 shearing Methods 0.000 claims description 15
- 239000002689 soil Substances 0.000 claims description 13
- 230000008569 process Effects 0.000 claims description 10
- 238000012216 screening Methods 0.000 claims description 10
- 229920006395 saturated elastomer Polymers 0.000 claims description 8
- 238000009738 saturating Methods 0.000 claims description 7
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- 239000012153 distilled water Substances 0.000 description 2
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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Abstract
The invention relates to a method for determining the relative breaking rate of calcareous sand under different stress paths, which comprises the steps of taking a calcareous sand sample; carrying out isotropic compression tests on the calcareous sand sample at different confining pressures to obtain an isotropic compression test experimental parameter and a crushing parameter when the average effective principal stress value under the isotropic compression test is 1; taking a calcareous sand sample with the same grading and initial pore ratio, and carrying out an equal average effective main stress test to obtain an equal average effective main stress test parameter and a crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1; and drawing a surface with relative breaking rate such as calcareous sand. The invention can reliably obtain each parameter in the indoor test, the result is accurate, and the parameters have universality; the experimental difficulty and the measurement time are greatly reduced, the application conditions and the application scene are widened, the universality is realized, and the practical situation of the calcareous sand is more matched; the influence of the stress path on the particle crushing is solved, and the influence of the stress path on the particle crushing is more consistent with the actual influence factor of the particle crushing.
Description
Technical Field
The invention relates to the technical field of determination of the relative crushing rate of granular soil, in particular to a method for determining the relative crushing rate of calcareous sand under different stress paths.
Background
Calcareous sand is a granular soil with a high void ratio, low particle strength, irregular particle shape and rich internal voids. The rock-soil material is easy to generate particle crushing phenomenon under the load action, and the particle crushing has important influence on the strength, compressibility and critical state of the calcareous sand. With the rapid development of ocean economy, the development capability of ocean resources is continuously improved, the protection consciousness of the ocean ecological environment is improved, the number and the scale of ocean engineering built on island reefs taking calcareous sand as main sediment are increased, and the phenomenon of crushing calcareous sand particles gradually attracts attention of scientific researchers. In addition, the marine environment and the loading environment are bad, the loading condition of a stress path of the calcareous sand serving as a foundation of the marine structure is complex, and the stress path has an important influence on the particle breakage of the calcareous sand. It is therefore necessary to study the degree of particle breakage of calcareous sand under the action of different stress paths.
There are many general expressions of the relation between particle breakage and stress in the prior art, such as a stress related model established by Hardin under a constant stress ratio path:
wherein: n is n b Sum sigma r Is a constant associated with the granular soil material; sigma (sigma) b Is the crushing stress; p is the average effective principal stress; q is the bias force.
In addition, there are studies on considering the influence of shear strain on particle breakage, and relational expressions of stress, strain and relative breakage rate are proposed, but these findings are often obtained based on the results of conventional triaxial test.
The defects of the prior art are that:
1. the stress path also affects the particle crushing property of the calcareous sand, but the current research results of the relationship between the influence of shear strain on particle crushing and the influence of the stress path on the particle crushing property of the calcareous sand are very limited, so that a functional relational expression capable of reflecting the relationship among stress, strain, stress path and particle crushing cannot be established;
2. because the determination of the relative crushing rate of the calcareous sand in the prior art depends on a specific and specific obtaining method, in ocean engineering, the calcareous sand is often in a complex ocean environment and a severe loading condition, and the adoption of a plurality of obtaining paths greatly improves the experiment difficulty and the determination time of the relative crushing rate, thereby limiting the application conditions and the application scenes and having no universality;
3. because the parameter acquisition of the calcareous sand in the prior art depends on a specific acquisition method, the acquired parameter has no universality and cannot provide reference value for re-application;
4. because the prior art also relies on site sampling and personnel operation experience to measure various parameters of the calcareous sand, the parameters cannot be standardized, and thus the accuracy of the finally obtained parameters is not high.
Disclosure of Invention
Aiming at the problems, the invention provides a method for determining the relative crushing rate of calcareous sand under different stress paths, which aims to solve the influence of the stress paths on particle crushing, and further enables the influence of the stress paths on particle crushing and the actual influence factors of particle crushing to be more consistent, so as to more meet the requirements of engineering design; the final result is accurate, and the acquired parameters have universality; the application conditions and the application scenes are widened, the universality is realized, and the actual conditions of the calcareous sand are matched.
In order to solve the problems, the technical scheme provided by the invention is as follows:
the method for determining the relative crushing rate of the calcareous sand under different stress paths comprises the following steps:
s100, taking a calcareous sand sample with the same grading of not less than 3 parts and the same initial pore ratio; then carrying out the isotropic compression test on each calcareous sand sample one by using different confining pressures preset manually to obtain an isotropic compression test experimental parameter and a crushing parameter when the average effective principal stress value under the isotropic compression test is 1;
s200, taking at least 3 parts, carrying out an equal average effective main stress test on a calcareous sand sample with the same grade as that in S100 and the same initial pore ratio, and obtaining an equal average effective main stress test parameter and a crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1;
s300, drawing a relative crushing rate surface of calcareous sand and the like according to the isotropic compression test experimental parameter, the crushing parameter when the average effective main stress value under the isotropic compression test is 1, the equal average effective main stress test parameter and the crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1; the crushing rate surface of the calcareous sand and the like is the final result of the invention.
Preferably, the step S100 specifically includes the following steps:
s110, directly preparing at least 3 parts of calcareous sand samples with the same grading and the same initial pore ratio on an instrument base;
s120, saturating each part of calcareous sand sample prepared in S110;
s130, carrying out the isotropic compression test on each saturated calcareous sand sample to obtain the volume variation and average effective principal stress value of each calcareous sand sample in the isotropic compression test;
s140, screening each part of the calcareous sand sample subjected to the isotropic compression test to obtain a particle size distribution curve of each part of the calcareous sand sample subjected to the isotropic compression test;
s150, calculating and obtaining the relative crushing rate under the isotropic compression test according to the particle size distribution curve;
s160, drawing an average effective main stress-volume change relation curve of an isotropic compression test, and then directly reading the average effective main stress under different surrounding pressures in the average effective main stress-volume change relation curve of the isotropic compression test;
s170, calculating to obtain the experimental parameters of the isotropic compression test and the crushing parameters when the average effective main stress value under the isotropic compression test is 1.
Preferably, the step S170 specifically includes the following steps:
the Sa171 is used for constructing a rectangular coordinate system by taking the average effective main stress under the isotropic compression test as an abscissa and taking the relative crushing rate under the isotropic compression test as an ordinate;
sa172 drawing data scattered points in a rectangular coordinate system constructed by Sa 171;
sa173 performing fitting calculation on the data scattered points drawn in Sa172 to obtain the parameters of the isotropic compression test and the crushing parameters when the average effective principal stress value under the isotropic compression test is 1; fitting calculation is expressed as:
B r,p ＝p a /(p a +b)
wherein: b (B) r,p The relative crushing rate under the isotropic compression test is given; p is the average effective principal stress at different confining pressures; a is the experimental parameter of the isotropic compression test; b is the crushing parameter at an average effective principal stress value of 1 in the isotropic compression test.
Preferably, the step S170 specifically includes the following steps:
sc171 adopting a calculation formula of particle breakage under the test condition of Hardin equal stress ratio, calculating to obtain the experimental parameters of the isotropic compression test, wherein the calculation process is expressed as follows:
wherein: a is the experimental parameter of the isotropic compression test; h is a s The method is characterized in that the method is manually preset by taking the granular soil with the same grading as a constant for the strength related parameters of the granular soil; n is n s Is a particle shape factor, and is pre-prepared by manpower according to the shape of the particlesSetting the sharp angle-shaped particles to be 25, the half angle-shaped particles to be 20, the oval-shaped particles to be 17 and the round-shaped particles to be 15; e, e 0 The initial pore ratio for sample preparation is manually preset;
sc172 the crushing parameters when the average effective principal stress value under the isotropic compression test is 1 are calculated by adopting a calculation formula of particle crushing under the test condition of Hardin equal stress ratio, wherein the calculation process is expressed as follows:
wherein: b is a crushing parameter when the average effective principal stress value under the isotropic compression test is 1; ζ is a material coefficient, and is preset manually for granular soil with the same grading as a constant; pa is standard atmospheric pressure, is constant, and is preset manually.
Preferably, the step S200 specifically includes the following steps:
s210, directly preparing a calcareous sand sample with the grading of not less than 3 parts, which is the same as that of the calcareous sand sample in S110, on an instrument base, wherein the initial pore ratio is the same as that of the calcareous sand sample in S110;
s220, saturating each part of calcareous sand sample prepared in the S210;
s230, carrying out the equal average effective principal stress test on each saturated calcareous sand sample to obtain the values of the offset stress, the body deformation and the axial strain of each calcareous sand sample in the equal average effective principal stress test;
s240, screening each sample of the calcareous sand sample subjected to the equal-average effective principal stress test to obtain a particle size distribution curve of each sample of the calcareous sand subjected to the equal-average effective principal stress test;
s250, calculating and obtaining the relative crushing rate under an equal average effective main stress test according to the particle size distribution curve;
s260, subtracting the relative crushing rate under the equidirectional compression test under the corresponding confining pressure obtained in the S150 from the relative crushing rate under the equidirectional effective main stress test under different confining pressures one by one to obtain the relative crushing rate in the shearing stage;
s270, drawing a bias stress-body change-axial strain relation curve under an equal average effective main stress test according to the bias stress, body change and axial strain values obtained in S230, and then directly reading the maximum bias stress under different surrounding pressures of the equal average effective main stress test in the bias stress-body change-axial strain relation curve under the equal average effective main stress test; directly reading the axial strain at the end of the equal average effective main stress test and the body strain at the end of the equal average effective main stress test from the offset stress-body strain-axial strain relation curve under the equal average effective main stress test, and calculating to obtain the shear strain at the end of the equal average effective main stress test; the shear strain at the end of the equal average effective principal stress test is the difference of the value of the axial strain at the end of the equal average effective principal stress test minus one third of the value of the body strain at the end of the equal average effective principal stress test;
s280, calculating to obtain an equal average effective main stress test strain influence parameter according to the offset stress-body change-axial strain relation curve under the equal average effective main stress test; the strain influence parameter of the equal average effective main stress test is expressed as follows:
v＝4.6/ε cs
wherein: v is the strain influence parameter of the equal average effective main stress test; epsilon cs Critical shear strain for calcareous sand samples; the critical shear strain of the calcareous sand sample is the difference of the value of the critical axial strain minus one third of the value of the critical physical strain; the critical axial strain value is an axial strain value when both the bias stress and the volume change are kept unchanged in a bias stress-volume change-axial strain relation curve under the equal average effective main stress test; the critical body change value is the body change value corresponding to the critical axial strain value in the offset stress-body change-axial strain relation curve under the equal average effective main stress test;
s290, calculating to obtain the equal average effective main stress test parameter and the crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1.
Preferably, S290 includes the following steps:
s291, constructing a rectangular coordinate system by taking the maximum bias stress under different surrounding pressures as an abscissa and taking the functional relation between the relative crushing rate of the shearing stage and the shearing strain at the end of the equal average effective main stress test as an ordinate;
the relative crushing rate of the shear stage as a function of shear strain at the end of the equi-average effective principal stress test is expressed as:
B r,q /[1-exp(-νε s )]
wherein: b (B) r,q Is the relative rate of fracture of the shear stage; epsilon s Shear strain at the end of the equal average effective principal stress test;
s292, drawing data scattered points in a rectangular coordinate system constructed in the S291;
s293, performing fitting calculation on the data scattered points drawn in the S292 to obtain the equal average effective main stress test parameter and the crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1; fitting calculation is expressed as:
wherein: q max Maximum bias stress under different surrounding pressures is tested for the equal average effective principal stress; m is the equal average effective principal stress test parameter; n is the breaking parameter when the maximum bias stress value under the equal average effective main stress test is 1.
Preferably, the relative crushing rate surface of the calcareous sand in S300 is expressed as follows:
wherein: b (B) r Is the relative crushing rate of the calcareous sand under the different stress paths.
Compared with the prior art, the invention has the following advantages:
1. according to the method, the acquisition operation of the calcareous sand parameters is simplified, and the parameter acquisition process is standardized, so that each parameter can be reliably acquired in an indoor test through a related test, the final result is accurate, the acquired parameter has universality, and a reference value can be provided for re-application;
2. the invention not only can calculate the relative crushing rate of the calcareous sand under the conventional triaxial test condition, but also can determine the relative crushing rate of the calcareous sand under other stress path conditions, and can also determine the relative crushing rate of the calcareous sand under any appointed shearing strain condition in the shearing process, thereby greatly reducing the experimental difficulty and the measurement time of the relative crushing rate, widening the application conditions and application scenes, having universality and being more suitable for the actual conditions that the calcareous sand is often in a complex ocean environment and a severe loading condition in ocean engineering;
3. according to the invention, particles under different stress path conditions are crushed, and the two parts of particle crushing caused by isotropic compression deformation and particle crushing caused by shear deformation are respectively calculated, so that the influence of the stress path on the particle crushing is solved, and the influence of the stress path on the particle crushing and the actual influence factor of the particle crushing are more consistent, and the requirements of engineering design are more met.
Drawings
FIG. 1 is a schematic flow chart of a method according to an embodiment of the invention;
FIG. 2 is a graph showing the average effective principal stress-body change relationship in an isotropic compression test according to an embodiment of the present invention;
FIG. 3 is a graph showing the relationship between the average effective principal stress under the conditions of the isotropic compression test and the relative crushing rate under the isotropic compression test in the embodiment of the present invention;
FIG. 4 is a graph showing the axial strain-bias stress relationship in a bias stress-bulk strain-axial strain relationship curve under an equal average effective principal stress test in an embodiment of the present invention;
FIG. 5 is a graph showing axial strain-strain relationship in a bias stress-strain-axial strain relationship curve under an equal average effective principal stress test in an embodiment of the present invention;
FIG. 6 is a graph showing the relationship between maximum bias stress at different peripheral pressures and the relative crushing rate at the shearing stage and the shearing strain at the end of the equal average effective principal stress test under the equal average effective principal stress test condition in an embodiment of the present invention;
fig. 7 is a schematic diagram of a surface view of a crushing rate of calcareous sand and the like in an embodiment of the present invention.
Detailed Description
The present invention is further illustrated below in conjunction with specific embodiments, it being understood that these embodiments are meant to be illustrative of the invention only and not limiting the scope of the invention, and that modifications of the invention, which are equivalent to those skilled in the art to which the invention pertains, will fall within the scope of the invention as defined in the claims appended hereto.
The method for determining the relative crushing rate of the calcareous sand under different stress paths comprises the following steps:
s100, taking a calcareous sand sample with the same grading of not less than 3 parts and the same initial pore ratio as shown in FIG. 1; and then carrying out isotropic compression test on each calcareous sand sample one by using different confining pressures preset manually to obtain the experimental parameters of the isotropic compression test and the crushing parameters when the average effective principal stress value under the isotropic compression test is 1.
In this embodiment, the confining pressure values are preset to 0.3MPa, 0.6MPa, 1.2MPa, 2.4MPa and 4.8MPa.
S100 specifically comprises the following steps:
s110, directly preparing at least 3 parts of calcareous sand samples with the same grading and the same initial pore ratio on an instrument base;
in this embodiment, the calcareous sand sample has a gradation of 1mm to 0.5mm and an initial void ratio of 0.9.
In this embodiment, the preparation method of the calcareous sand sample specifically comprises the following steps:
directly sleeving a rubber film with the thickness of 1mm on the instrument base and fastening the rubber film by using a rubber ring; and then, air-drying the calcareous sand, and adopting a sand rain method to prepare a calcareous sand sample, so as to keep the height and the quality of the calcareous sand sample to be the same.
S120, each calcareous sand sample prepared in S110 is saturated.
In this embodiment, the method for saturating the calcareous sand sample is specifically as follows:
and (3) adding airless distilled water into the calcareous sand sample prepared in the step (S110) for standing for 24 hours, and then saturating the calcareous sand sample by adopting a back pressure saturation method.
S130, performing an isotropic compression test on each saturated calcareous sand sample, and obtaining the volume variation and average effective principal stress value of each calcareous sand sample in the isotropic compression test.
In this particular example, after saturation, an isotropic compression test was performed. In the isotropic compression test process, when the volume change rate of the calcareous sand sample is less than 5mm 3 And (3) at the time of/min, the volume change size of the calcareous sand sample is considered to be stable, the consolidation of the calcareous sand sample is completed, and the test is stopped. And then, the volume change and average effective principal stress values of each calcareous sand sample at the end of the isotropic compression test under different confining pressures are recorded one by one.
S140, screening each part of the calcareous sand sample subjected to the isotropic compression test to obtain a particle size distribution curve of each part of the calcareous sand sample subjected to the isotropic compression test.
In this embodiment, the sample screening operation is as follows:
after the isotropic compression test under each confining pressure is finished, carefully taking out the calcareous sand sample and placing the calcareous sand sample in a ceramic disc; then placing the ceramic disc into an electric oven with the temperature set at 105 ℃ and drying until the calcareous sand sample is constant weight; then, obtaining the particle size and grading condition of the calcareous sand sample by adopting a screening method, and drawing a particle size distribution curve of each calcareous sand sample subjected to the isotropic compression test;
s150, calculating and obtaining the relative crushing rate B under the isotropic compression test according to the particle size distribution curve r,p 。
It should be noted that S150 is obtained by quantifying the particle breakage using the relative breakage rate proposed by Hardin.
S160, as shown in fig. 2, drawing an average effective principal stress-volume change relation curve of the isotropic compression test, and then directly reading the values of the average effective principal stresses p under different surrounding pressures in the average effective principal stress-volume change relation curve of the isotropic compression test.
S170, calculating to obtain an isotropic compression test experimental parameter and a crushing parameter when the average effective main stress value under the isotropic compression test is 1.
For the step of completing S170, there are two implementations, the following steps numbers of two different implementations are calibrated with Sa and Sc, respectively:
it should be noted that either of these two methods can achieve the purpose of S170, and is equally positioned, and one may be selected in actual operation.
The first mode specifically comprises the following steps:
sa171 the rectangular coordinate system is constructed by taking the average effective principal stress under the isotropic compression test as the abscissa and the relative crushing rate under the isotropic compression test as the ordinate.
Sa172 drawing data scattered points in a rectangular coordinate system constructed by Sa171.
Sa173 performing fitting calculation on the data scattered points drawn in Sa172 to obtain an isotropic compression test experimental parameter and a crushing parameter when the average effective principal stress value under the isotropic compression test is 1; fitting calculation is expressed as formula (1):
B r,p ＝p a /(p a +b) (1)
wherein: b (B) r,p Relative crushing rate under the isotropic compression test; p is the average effective principal stress at different confining pressures; a is an isotropic compression test experimental parameter; b is the crushing parameter at an average effective principal stress value of 1 in the isotropic compression test.
In this embodiment, the fitting result may be obtained as follows:
thus, as shown in fig. 3, using the first method, it can be expressed as:
B r,p ＝p 0.44 /(p 0.44 +93.8)
it should be noted that, R in fig. 3 is a fitting degree parameter, which is used to represent the fitting degree of the points and the lines in fig. 3, and the value of R is actually calculated by simulation software.
The second mode specifically comprises the following steps:
sc171 adopting a calculation formula of particle breakage under the test condition of Hardin equal stress ratio, calculating to obtain the experimental parameters of the isotropic compression test, wherein the calculation process is expressed according to the formula (2):
wherein: a is an isotropic compression test experimental parameter; h is a s The method is characterized in that the method is manually preset by taking the granular soil with the same grading as a constant for the strength related parameters of the granular soil; n is n s The particle shape factor is preset by manpower according to the shape of the particle, and specifically, the value of the sharp angle-shaped particle is 25, the value of the half-square angle-shaped particle is 20, the value of the oval particle is 17, and the value of the round particle is 15; e0 is the initial void ratio of the sample preparation, which is manually preset.
In this embodiment, the particle shape is sharp, and then the parameters are set as follows:
h s ＝2.6；e 0 ＝0.9；n s ＝25
then, it is possible to obtain:
a＝2.6 2 /[(1+0.9)×25]+0.3
sc172 the crushing parameters when the average effective principal stress value under the isotropic compression test is 1 are calculated by adopting a calculation formula of particle crushing under the test condition of Hardin equal stress ratio, and the calculation process is expressed according to the formula (3):
wherein: b is a crushing parameter when the average effective principal stress value under the isotropic compression test is 1; ζ is a material coefficient, and is preset manually for granular soil with the same grading as a constant; pa is standard atmospheric pressure, is constant, and is preset manually.
In this embodiment, the following parameters are set:
ξ＝1.54；pa＝101.25
then, it is possible to obtain:
s200, taking not less than 3 parts, carrying out an equal average effective main stress test on a calcareous sand sample with the same grade as that in S100 and the same initial pore ratio, and obtaining an equal average effective main stress test parameter and a crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1.
In this embodiment, the values of the confining pressure are the same as those in S100, and are preset to 0.3MPa, 0.6MPa, 1.2MPa, 2.4MPa and 4.8MPa.
S200 specifically comprises the following steps:
s210, preparing a calcareous sand sample with the grading of not less than 3 parts, which is the same as that of the calcareous sand sample in S110, and the initial pore ratio of which is the same as that of the calcareous sand sample in S110, directly on an instrument base.
In this embodiment, the calcareous sand sample has a gradation of 1mm to 0.5mm and an initial void ratio of 0.9.
In this embodiment, the method for preparing the calcareous sand sample is the same as that in S100, and specifically includes the following steps:
directly sleeving a rubber film with the thickness of 1mm on the instrument base and fastening the rubber film by using a rubber ring; and then, air-drying the calcareous sand, and adopting a sand rain method to prepare a calcareous sand sample, so as to keep the height and the quality of the calcareous sand sample to be the same.
S220, each calcareous sand sample prepared in S210 is saturated.
In this embodiment, the saturation method is the same as that in S100, and specifically includes:
and (2) adding airless distilled water into the calcareous sand sample prepared in the step (S210) for standing for 24 hours, and then saturating the calcareous sand sample by adopting a back pressure saturation method.
S230, carrying out an equal average effective principal stress test on each saturated calcareous sand sample, and obtaining the values of the offset stress, the body deformation and the axial strain of each calcareous sand sample in the equal average effective principal stress test.
In this particular example, after saturation, an isotropic compression test was performed. In the isotropic compression test process, when the volume change rate of the calcareous sand sample is less than 5mm 3 And (3) at the time of/min, the volume change size of the calcareous sand sample is considered to be stable, the consolidation of the calcareous sand sample is completed, and the test is stopped. The shear test is then started. The shearing adopts stress control, and the shearing rate is the change rate delta sigma of confining pressure 3 -2.5kPa/min and the test is terminated when the axial strain reaches 20%; and finally, recording and obtaining the values of the partial stress, the body deformation and the axial strain of each calcareous sand sample in an equal average effective main stress test.
S240, screening each sample of the calcareous sand sample subjected to the equal-average effective principal stress test to obtain a particle size distribution curve of each sample of the calcareous sand subjected to the equal-average effective principal stress test.
In this embodiment, the sample screening operation is as follows:
carefully taking out the calcareous sand sample and placing the calcareous sand sample in a ceramic disc after the equal average effective main stress test under each confining pressure is finished; then placing the ceramic disc into an electric oven with the temperature set at 105 ℃ and drying until the calcareous sand sample is constant weight; and then, obtaining the particle size and grading condition of the calcareous sand sample by adopting a screening method, and drawing the particle size distribution curve of each calcareous sand sample subjected to the equal average effective principal stress test.
S250, calculating and obtaining the relative crushing rate under an equal average effective main stress test according to the particle size distribution curve;
it should be noted that S250 is obtained by quantifying the particle breakage using the relative breakage rate proposed by Hardin.
S260, equal average effectiveness under different confining pressures one by oneThe relative crushing rate under the main stress test minus the relative crushing rate B under the isotropic compression test under the corresponding confining pressure obtained in S150 r,p Obtaining the relative breaking rate B of the shearing stage r,q 。
S270, as shown in fig. 4 and 5, drawing a bias stress-body change-axial strain relation curve under an equal average effective principal stress test according to the bias stress, body change and axial strain values obtained in S230, and then directly reading the maximum bias stress q under different surrounding pressures of the equal average effective principal stress test in the bias stress-body change-axial strain relation curve under the equal average effective principal stress test max The method comprises the steps of carrying out a first treatment on the surface of the Directly reading the axial strain at the end of the equal average effective main stress test and the body strain at the end of the equal average effective main stress test in a bias stress-body strain-axial strain relation curve under the equal average effective main stress test, and calculating to obtain the shear strain at the end of the equal average effective main stress test; the shear strain at the end of the equi-average effective principal stress test is the difference of the value of the axial strain at the end of the equi-average effective principal stress test minus one third of the value of the body strain at the end of the equi-average effective principal stress test.
S280, calculating to obtain strain influence parameters of the equal average effective main stress test according to a bias stress-body deformation-axial strain relation curve under the equal average effective main stress test; the strain-influencing parameter for the equi-average effective principal stress test is expressed in terms of formula (4):
v＝4.6/ε cs (4)
wherein: v is an equal average effective principal stress test strain influencing parameter; epsilon cs Critical shear strain for calcareous sand samples; the critical shear strain of the calcareous sand sample is the difference of the value of the critical axial strain minus one third of the value of the critical physical strain; the critical axial strain value is the axial strain value when the bias stress and the volume change are kept unchanged in a bias stress-volume change-axial strain relation curve under an equal average effective main stress test; the critical strain value is the strain value corresponding to the critical axial strain value in the offset stress-strain-axial strain relation curve under the equal average effective principal stress test.
It should be further noted that, for the calcareous sand sampleCritical shear strain, may also take the value epsilon cs ＝0.5。
S290, calculating to obtain an equal average effective main stress test parameter and a crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1; s290 includes the following steps:
s291, constructing a rectangular coordinate system by taking maximum bias stress under different surrounding pressures as an abscissa and taking a functional relation between the relative breaking rate of a shearing stage and the shearing strain at the end of an equal average effective main stress test as an ordinate.
The relative crushing rate at the shear stage as a function of shear strain at the end of the equi-average effective principal stress test is expressed as in equation (5):
B r,q /[1-exp(-νε s )] (5)
wherein: b (B) r,q Epsilon for relative crushing rate in shear stage s Is the shear strain at the end of the equal average effective principal stress test.
S292, drawing data scattered points in a rectangular coordinate system constructed in S291.
S293, as shown in FIG. 6, fitting calculation is carried out on the data scattered points drawn in S292, so as to obtain an equal average effective main stress test parameter and a crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1; fitting calculation is expressed as formula (6):
wherein: q max Maximum bias stress under different surrounding pressures is tested for the equal average effective main stress; m is an equal average effective principal stress test parameter; n is a crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1.
In this embodiment, the values of the parameters are as follows:
v＝0.92；m＝1.18；n＝47.5
thus, as shown in fig. 6, it is possible to obtain:
it should be noted that, R in fig. 6 is a fitting degree parameter, which is used to represent the fitting degree of the points and the lines in fig. 6, and the value of R is actually calculated by simulation software.
S300, drawing a relative crushing rate surface of calcareous sand and the like according to an isotropic compression test experimental parameter, a crushing parameter when an average effective main stress value is 1 in an isotropic compression test, an equal average effective main stress test parameter and a crushing parameter when a maximum bias stress value is 1 in an equal average effective main stress test; the relative crushing rate surface of the calcareous sand and the like is the final result of the invention; the surface of the crushing rate of the calcareous sand and the like in S300 is expressed as a formula (7):
wherein: b (B) r Is the relative breaking rate of the calcareous sand under different stress paths.
According to the above parameter settings, it is possible to:
as shown in fig. 7, the surface of the calcareous sand and other relative crushing rate is the final result of the invention.
In the foregoing detailed description, various features are grouped together in a single embodiment for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments of the subject matter require more features than are expressly recited in each claim. Rather, as the following claims reflect, invention lies in less than all features of a single disclosed embodiment. Thus the following claims are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate preferred embodiment of this invention.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. As will be apparent to those skilled in the art; various modifications to these embodiments will be readily apparent, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the disclosure. Thus, the present disclosure is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
The foregoing description includes examples of one or more embodiments. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the aforementioned embodiments, but one of ordinary skill in the art may recognize that many further combinations and permutations of various embodiments are possible. Accordingly, the embodiments described herein are intended to embrace all such alterations, modifications and variations that fall within the scope of the appended claims. Furthermore, as used in the specification or claims, the term "comprising" is intended to be inclusive in a manner similar to the term "comprising," as interpreted when employed as a transitional word in a claim. Furthermore, any use of the term "or" in the specification of the claims is intended to mean "non-exclusive or".
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the scope of the invention, but to limit the invention to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (2)
1. A method for determining the relative crushing rate of calcareous sand under different stress paths is characterized by comprising the following steps: comprises the following steps:
s100, taking a calcareous sand sample with the same grading of not less than 3 parts and the same initial pore ratio; then carrying out isotropic compression test on each calcareous sand sample one by using different confining pressures preset manually to obtain an isotropic compression test experimental parameter and a crushing parameter when the average effective principal stress value under the isotropic compression test is 1;
s200, taking at least 3 parts, carrying out an equal average effective main stress test on a calcareous sand sample with the same grade as that in S100 and the same initial pore ratio, and obtaining an equal average effective main stress test parameter and a crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1;
s300, drawing a relative crushing rate surface of calcareous sand and the like according to the isotropic compression test experimental parameter, the crushing parameter when the average effective main stress value under the isotropic compression test is 1, the equal average effective main stress test parameter and the crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1; the crushing rate surface of the calcareous sand and the like is the final result of the method;
s100 specifically comprises the following steps:
s110, directly preparing at least 3 parts of calcareous sand samples with the same grading and the same initial pore ratio on an instrument base;
s120, saturating each part of calcareous sand sample prepared in S110;
s130, carrying out the isotropic compression test on each saturated calcareous sand sample to obtain the volume variation and average effective principal stress value of each calcareous sand sample in the isotropic compression test;
s140, screening each part of the calcareous sand sample subjected to the isotropic compression test to obtain a particle size distribution curve of each part of the calcareous sand sample subjected to the isotropic compression test;
s150, calculating and obtaining the relative crushing rate under the isotropic compression test according to the particle size distribution curve;
s160, drawing an average effective main stress-volume change relation curve of an isotropic compression test, and then directly reading the average effective main stress under different surrounding pressures in the average effective main stress-volume change relation curve of the isotropic compression test;
s170, calculating and obtaining the experimental parameters of the isotropic compression test and the crushing parameters when the average effective main stress value under the isotropic compression test is 1;
s170 specifically comprises the following steps:
the Sa171 is used for constructing a rectangular coordinate system by taking the average effective main stress under the isotropic compression test as an abscissa and taking the relative crushing rate under the isotropic compression test as an ordinate;
sa172 drawing data scattered points in a rectangular coordinate system constructed by Sa 171;
sa173 performing fitting calculation on the data scattered points drawn in Sa172 to obtain the parameters of the isotropic compression test and the crushing parameters when the average effective principal stress value under the isotropic compression test is 1; fitting calculation is expressed as:
B r,p ＝p a /(p a +b)
wherein: b (B) r,p The relative crushing rate under the isotropic compression test is given; p is the average effective principal stress at different confining pressures; a is the experimental parameter of the isotropic compression test; b is a crushing parameter when the average effective principal stress value under the isotropic compression test is 1;
s170 specifically comprises the following steps:
sc171 adopting a calculation formula of particle breakage under the test condition of Hardin equal stress ratio, calculating to obtain the experimental parameters of the isotropic compression test, wherein the calculation process is expressed as follows:
wherein: a is the experimental parameter of the isotropic compression test; h is a s The method is characterized in that the method is manually preset by taking the granular soil with the same grading as a constant for the strength related parameters of the granular soil; n is n s The particle shape factor is preset by manpower according to the shape of the particle, and specifically, the value of the sharp angle-shaped particle is 25, the value of the half-square angle-shaped particle is 20, the value of the oval particle is 17, and the value of the round particle is 15; e, e 0 The initial pore ratio for sample preparation is manually preset;
sc172 the crushing parameters when the average effective principal stress value under the isotropic compression test is 1 are calculated by adopting a calculation formula of particle crushing under the test condition of Hardin equal stress ratio, wherein the calculation process is expressed as follows:
wherein: b is a crushing parameter when the average effective principal stress value under the isotropic compression test is 1; ζ is a material coefficient, and is preset manually for granular soil with the same grading as a constant; pa is standard atmospheric pressure, is constant and is preset manually;
s200 specifically comprises the following steps:
s210, directly preparing a calcareous sand sample with the grading of not less than 3 parts, which is the same as that of the calcareous sand sample in S110, on an instrument base, wherein the initial pore ratio is the same as that of the calcareous sand sample in S110;
s220, saturating each part of calcareous sand sample prepared in the S210;
s230, carrying out the equal average effective principal stress test on each saturated calcareous sand sample to obtain the values of the offset stress, the body deformation and the axial strain of each calcareous sand sample in the equal average effective principal stress test;
s240, screening each sample of the calcareous sand sample subjected to the equal-average effective principal stress test to obtain a particle size distribution curve of each sample of the calcareous sand subjected to the equal-average effective principal stress test;
s250, calculating and obtaining the relative crushing rate under an equal average effective main stress test according to the particle size distribution curve;
s260, subtracting the relative crushing rate under the equidirectional compression test under the corresponding confining pressure obtained in the S150 from the relative crushing rate under the equidirectional effective main stress test under different confining pressures one by one to obtain the relative crushing rate in the shearing stage;
s270, drawing a bias stress-body change-axial strain relation curve under an equal average effective main stress test according to the bias stress, body change and axial strain values obtained in S230, and then directly reading the maximum bias stress under different surrounding pressures of the equal average effective main stress test in the bias stress-body change-axial strain relation curve under the equal average effective main stress test; directly reading the axial strain at the end of the equal average effective main stress test and the body strain at the end of the equal average effective main stress test from the offset stress-body strain-axial strain relation curve under the equal average effective main stress test, and calculating to obtain the shear strain at the end of the equal average effective main stress test; the shear strain at the end of the equal average effective principal stress test is the difference of the value of the axial strain at the end of the equal average effective principal stress test minus one third of the value of the body strain at the end of the equal average effective principal stress test;
s280, calculating to obtain an equal average effective main stress test strain influence parameter according to the offset stress-body change-axial strain relation curve under the equal average effective main stress test; the strain influence parameter of the equal average effective main stress test is expressed as follows:
v＝4.6/ε cs
wherein: v is the strain influence parameter of the equal average effective main stress test; epsilon cs Critical shear strain for calcareous sand samples; the critical shear strain of the calcareous sand sample is the difference of the value of the critical axial strain minus one third of the value of the critical physical strain; the critical axial strain value is an axial strain value when both the bias stress and the volume change are kept unchanged in a bias stress-volume change-axial strain relation curve under the equal average effective main stress test; the critical body change value is the body change value corresponding to the critical axial strain value in the offset stress-body change-axial strain relation curve under the equal average effective main stress test;
s290, calculating to obtain the equal average effective main stress test parameter and the crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1;
s290 includes the following steps:
s291, constructing a rectangular coordinate system by taking the maximum bias stress under different surrounding pressures as an abscissa and taking the functional relation between the relative crushing rate of the shearing stage and the shearing strain at the end of the equal average effective main stress test as an ordinate;
the relative crushing rate of the shear stage as a function of shear strain at the end of the equi-average effective principal stress test is expressed as:
B r,q /[1-exp(-νε s )]
wherein: b (B) r,q Is the relative rate of fracture of the shear stage; epsilon s Shear strain at the end of the equal average effective principal stress test;
s292, drawing data scattered points in a rectangular coordinate system constructed in the S291;
s293, performing fitting calculation on the data scattered points drawn in the S292 to obtain the equal average effective main stress test parameter and the crushing parameter when the maximum bias stress value under the equal average effective main stress test is 1; fitting calculation is expressed as:
wherein: q max Maximum bias stress under different surrounding pressures is tested for the equal average effective principal stress; m is the equal average effective principal stress test parameter; n is the breaking parameter when the maximum bias stress value under the equal average effective main stress test is 1.
2. The method for determining the relative crushing rate of calcareous sand under different stress paths according to claim 1, wherein: the relative crushing rate surface of the calcareous sand and the like in the S300 is expressed as follows:
wherein: b (B) r Is the relative crushing rate of the calcareous sand under the different stress paths.
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