CN114354430A - Size effect correction method for shearing strength of rockfill material - Google Patents
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Abstract
The invention belongs to the field of stability analysis of earth and rockfill dams, and relates to a size effect correction method for shear strength of rockfill materials. The method combines the size effect characteristics of single particle strength to deduce the relationship of macroscopic stress and strain tensor of rockfill aggregates with different sizes, analyzes the size effect rule of the Moire-Coulomb strength criterion under the action of static load, provides the correction relationship of cohesive force c, and further determines the size effect correction relationship of dynamic shear strength and dynamic shear stress ratio under the strain failure standard. The method can provide reference for stability analysis of the earth and rockfill dam.
Description
Technical Field
The invention belongs to the field of stability analysis of earth and rockfill dams, and relates to a size effect correction method for shear strength of rockfill materials.
Background
Due to good applicability and economy, the earth-rock dam is widely applied to water conservancy and hydropower engineering. The rockfill material is used as a main filling material, the stability analysis of the earth-rock dam needs rockfill material strength deformation parameters determined according to indoor tests, however, the indoor tests are carried out under a scale reducing condition, and the previous test research results show that the rockfill material which is damaged by brittleness has an obvious size effect, and the concrete effect is that the strength of aggregate particles is reduced along with the increase of particle size. The settlement deformation on site can not be accurately predicted by directly using the strength deformation parameters obtained by the scale indoor test, so that the problems of small high dam calculation and small low dam calculation are frequently caused, and the safety evaluation of the earth-rock dam is not facilitated. Particularly, with the rapid development of Chinese construction technology in recent years, more and more high earth-rock dam designs are proposed or built, and for a high earth-rock dam with a larger gradient, the size effect of rockfill materials becomes a problem which needs to be solved urgently in the analysis of the stability of the high dam.
The particle size of the on-site rockfill material can reach 600-1000 mm, and the shear strength of the on-site rockfill material cannot be directly tested due to the limitation of the size of test equipment. After the indoor test grading scale is matched, the maximum grain size of the rockfill material is generally 60mm, and the existing engineering actual measurement and inversion results show that the parameters of the scale test are different from the full-scale parameters to a certain extent. Some researchers are dedicated to developing large-size test instruments to obtain parameters closer to a prototype, and the ultra-large triaxial apparatus provides valuable data for researching the size effect of the rockfill material, but the ultra-large triaxial apparatus has high manufacturing cost, is extremely complex in test process and difficult to popularize and apply, and the maximum particle size adopted by the ultra-large triaxial apparatus is generally not more than 200mm and is still smaller than the maximum particle size of the on-site rockfill material.
In summary, in order to evaluate the shear strength performance of the on-site rockfill material, a relation between the indoor scale-down test parameters and the on-site full-scale parameters needs to be established. Particle breakage is the main reason of deformation of the rockfill, and can combine a single-grain strength test and a triaxial test of the rockfill, introduce the size effect of the single-grain strength and further deduce the size effect of a test sample according to mesomechanics of aggregate aggregates. In order to analyze the shear strength of the rockfill material under static and dynamic loads, single-particle crushing tests with different sizes and strain rates are carried out, the particle strength under a static condition is reduced along with the increase of the particle size, the particle strength under a quasi-static condition is not only increased along with the strain rate, but also the size effect of the particle strength is gradually reduced along with the strain rate, and how to determine the dynamic strength of the particles is the problem of analyzing the relation between the size of the dynamic strength and the rate effect.
At present, no better solution exists for the size effect problem of the shearing strength of the rockfill material, although a super-large triaxial test instrument can be developed to obtain parameters closer to a prototype full scale, the maximum particle size of super-large triaxial is smaller than that of a field prototype, and the rockfill material scale-down effect is difficult to explain mechanically.
Disclosure of Invention
The invention provides a size effect correction method of the shear strength of the rockfill material from a mesomechanics angle by aiming at the shear strength of the rockfill material under the action of dynamic and static loads and combining the size and the strain rate effect of single-particle strength. The method can provide reference for stability analysis of the earth and rockfill dam.
The technical scheme adopted by the invention is as follows:
a size effect correction method for the shear strength of rockfill comprises the following steps:
the first step is as follows: carrying out rockfill single-particle strength tests with different sizes and strain rates to obtain a relational expression P of rockfill strength and strain rate and a relational expression Q of rockfill strength size effect and strain rate, see formulas (1) and (2), and then establishing a single-particle strength calculation model considering the sizes and the strain rates, see formula (3).
Where DIF is the dynamic intensity increase factor,
is strain rate, k1、k2、k3In order to be a coefficient of fit,
in order to be a static strain rate,
critical strain rate, σ, for dimensional effect to disappeardIs the dynamic intensity of the particles, σ0As the reference strength, d is the particle size of the particles, d0Is the reference particle diameter, m is the Weibull distribution modulus, ndAs a geometric similarity parameter, ndAnd/m represents the strength of the size effect.
The single particle strength test is referred to as a flat plate load test. And P refers to the improvement relation of strain rate effect strength and is obtained by fitting the relation of strain rate and strength. The Q is the static strain rate
To critical strain rate
Linear reduction of the size effect of (1), critical strain rate at which the size effect disappears
And obtaining the single particle intensity data in a whole.
The second step is that: and (3) establishing a macroscopic stress and strain tensor relation of aggregate aggregates with different sizes based on the single particle strength calculation model provided in the first step, and obtaining the formulas (6a) and (6 b).
The method for establishing the macroscopic stress and strain tensor relation of aggregate aggregates with different sizes comprises the following steps:
stress σ of particle aggregate in three-dimensional stateijAnd strain tensor relation epsilonijThe following were used:
wherein, VσTo calculate the total volume of the stressed region, f(c/p)Is the external force applied to the particle p at any contact point c in the region, l(c/p)Is the support vector of the contact point pointing to the center of the particle p. VεTo calculate the volume corresponding to the region of strain, Δ ueFor the relative displacement of the centers of the two particles p and q constituting the edge e, deThe area compensation vector corresponding to the edge e.
If the characteristic dimension corresponding to the indoor sc and the prototype pr is dprAnd dscAssuming that the mineral components of the aggregate of the reduced-scale and full-scale test samples are the same, the internal friction angle of the aggregate is irrelevant to the particle size of the particles, the crushing of the particles belongs to splitting tension damage, the particle strength conforms to Weibull distribution, and the contact state and the pore distribution of the aggregate of the test samples with different sizes are the same, namely the geometric state is the same. When the crushing state of the reduced scale and the full scale aggregate is the same, the particle stress sigma of the reduced scale samplescHarmonic foot stress sigmaprContact force f with particles of reduced-scale samplescContact force f with foot rulerprSatisfies the following conditions:
in the formula, PscAnd PprRespectively showing the relationship between the stress increase of the reduced scale and the full scale affected by the strain rate, QprShowing the relationship of decreasing dimensional effect of full size. Simultaneously according to the vector l(c/p)Volume V, area compensation vector deAnd relative displacement Deltau ueThe stress tensor sigma of the reduced scale sample under the action of dynamic and static loads is obtainedij,scAnd full-scale stress tensor σij,prStrain tensor epsilon with scaled sampleij,scAnd full-scale strain tensor epsilonij,prThe following relationship is satisfied:
εij,pr＝εij,sc (6b)
the third step: and deducing a size effect rule of a Moire-Coulomb strength rule under the action of static load according to the macroscopic stress strain tensor relation of the samples with different sizes.
The method for deducing the size effect of the Moire-Coulomb intensity criterion is as follows:
firstly, the particle strain rate of the reduced and full-scale test pieces under the static load does not exceed the static strain rate
Then P issc、Ppr、QprAll 1, stress tensor σ of reduced-scale sampleij,scAnd full-scale stress tensor σij,prThe relationship of (c) translates into:
normal stress sigma on shear plane of triaxial samplenAnd the shear stress τ is:
in the formula, σ1And σ3For the maximum principal stress and the minimum principal stress,
is the internal friction angle. According to the hypothesis and the static load stress tensor relation in the second step, the normal stress sigma of the reduced-scale samplen,prAnd full scale normal stress sigman,scShear stress tau with scaled test specimensprAnd full scale shear stress τscThe following relationship is satisfied:
according to the Mohr-Coulomb strength criterion, the relationship between the normal stress and the shear stress of the reduced-scale and full-scale test samples is as follows:
in the formula, cscAnd cprRespectively, the cohesive force of the reduced-scale and full-scale test samples. The formula (9) may be substituted for the formula (10):
the derivation determines the cohesive force c of the on-site foot rule in the Moire-Coulomb strength criterionprIs a reduced scale cscIs/are as follows
And (4) doubling.
The fourth step: deriving the dynamic shear strength tau from the macroscopic stress-strain tensor relationship of differently sized samplesdAnd dynamic shear stress ratio taud/σ0The size effect rule of (1).
The method for deriving the size effect of the dynamic strength and the dynamic shear stress ratio comprises the following steps:
according to the macroscopic stress-strain tensor relation of the aggregate, when the fracture rates of the reduced-scale and full-scale samples are the same, the strain tensors of the reduced-scale and full-scale samplesSame, axial dynamic strain epsilon of reduced-scale sampled,scRelation of sum vibration times N and axial dynamic strain epsilon of foot ruled,prSame relationship with the vibration number N:
εd,sc～N＝εd,pr～N (12)
further, the number of oscillations N at which the reduced and full scale samples reached the strain failure criterion of 5%fSame, reduced mean principal stress sigma0,scAnd full-scale mean principal stress σ0,prDynamic strength sigma of scale reductiond,scHarmonic foot motion intensity sigmad,prThe relationship of (1) is:
intensity of shear τ of full footd,prDynamic shear strength tau of harmonic scaled,scThe dimensional effect relationship of (A) is as follows:
final full scale dynamic shear stress ratio taud,sc/σ0,scAnd dynamic shear stress ratio tau of reduced scaled,pr/σ0,prThe dimensional effect relationship of (A) is as follows:
thus, the on-site full-scale dynamic shear strength is the test scale
The ratio of dynamic shear stress of full-scale on site is the test scale
And (4) doubling.
The invention has the beneficial effects that:
1. according to the method, from the perspective of single-particle crushing mesomechanics, the macroscopic stress and strain tensor relation of sample aggregates with different sizes is deduced according to the size and rate effect of single-particle strength, the fact that the cohesive force c has the size effect in the Moire-Coulomb strength criterion under the action of static load is determined, and the cohesive force of a full-scale sample is the cohesive force of a reduced-scale sample
And (4) doubling. The dynamic shear strength of the full scale under the action of dynamic load being reduced
The dynamic shear stress ratio of full scale is reduced scale
And (4) doubling.
2. Compared with an ultra-large triaxial test which is high in manufacturing cost and time-consuming and labor-consuming, the shear strength difference of the indoor scale and the field full scale can be analyzed according to the size and the strain rate effect of the single particle strength of the rockfill material only by carrying out single particle crushing tests and conventional triaxial tests with different sizes and strain rates.
3. The invention has clear logic for deducing the dynamic deformation size effect of the rockfill material, corrects the shear strength of the rockfill material by considering the size effect, and provides reference for engineering design and safety and stability evaluation of the earth-rock dam.
Drawings
FIG. 1 is a fitting relation of static strength of the rubble particles according to the invention with particle size.
FIG. 2 is a fitting relationship of the strength of the rubble particles according to the invention with the increase of strain rate.
FIG. 3 is a graph showing the reduction of the effect of the strength size of the rubble particles according to the invention as a function of strain rate.
FIG. 4 is a diagram illustrating the size effect of the Moire-Coulomb intensity criterion of the present invention.
FIG. 5 is a graph showing the effect of the dynamic shear strength dimension of the present invention.
FIG. 6 is a schematic diagram of the dynamic shear stress ratio size effect of the present invention.
Detailed Description
The following detailed description of the invention refers to the accompanying drawings.
This example determines the size effect of the shear strength of the rockfill material from the results of the rubble particle crushing test.
The first step, single particle crushing tests under different sizes and strain rates are carried out, FIG. 1 shows that the particle strength changes with the size under the static strain rate, and the size effect-n is obtained by fittingd(ii)/m; FIG. 2 is a graph showing the dynamic strength improvement relationship P obtained by fitting the variation of the rockfill particle strength with the strain rate; FIG. 3 is a graph showing the variation of the size effect of the rockfill particle strength with strain rate, critical strain rate
In the range of 10-1s-1And establishing a size effect weakening relation Q and a single particle intensity calculation model.
Secondly, establishing a stress tensor sigma of the reduced-scale test sample under the action of dynamic and static loads based on the single-particle strength calculation model provided in the first stepij,scAnd full-scale stress tensor σij,prStrain tensor epsilon with scaled sampleij,scAnd full-scale strain tensor epsilonij,prThe relationship of (1):
εij,pr＝εij,sc
thirdly, deducing a size effect rule of a Moire-Coulomb strength criterion under the action of static load based on the macroscopic stress strain tensor relation of the second step of the foot size and the reduced size, wherein a size effect schematic diagram of the Moire-Coulomb strength criterion is shown in FIG. 4, and the relation between the cohesive force of the foot size and the cohesive force of the reduced size is as follows:
in the formula (d)pr/dscIn terms of the ratio of the on-site particle size to the laboratory test particle size, if the maximum particle size of the on-site rockfill particles is 600mm and the maximum particle size of the conventional triaxial macroreticular particle is 60mm, then dpr/dscAt 10, the size effect-n is obtained from the fit of FIG. 1dAnd/m is-0.3, the full-scale cohesive force is 0.501 time of the reduced-scale cohesive force.
The fourth step: deducing dynamic strength tau of rockfill material based on macroscopic stress strain tensor relation of second step full scale and reduced scaledAnd dynamic shear stress ratio taud/σ0FIG. 5 is a schematic diagram of the size effect of dynamic shear strength, full scale dynamic shear strength τd,prAnd scale dynamic shear strength taud,scThe dimensional effect relationship of (A) is as follows:
FIG. 6 is a graph showing the effect of the dynamic shear stress ratio size, full scale dynamic shear stress ratio τd,sc/σ0,scAnd dynamic shear stress ratio tau of reduced scaled,pr/σ0,prThe dimensional effect relationship of (A) is as follows:
in the formula (d)pr/dscIs taken to be 10, -ndThe value of/m is-0.3,
the average strain rate of the movable indoor triaxial test is about 10-3s-1，
Determined by the ratio of the on-site seismic frequency to the dynamic triaxial frequency, e.g. if the on-site frequency is 3Hz and the dynamic triaxial frequency is typically 0.3Hz
Finally, the dynamic shear strength of the full scale is about 0.95 time of that of the reduced scale, and the dynamic shear stress ratio of the full scale is about 1.90 times of that of the reduced scale.
Claims (1)
1. A size effect correction method for the shear strength of rockfill is characterized by comprising the following steps:
the first step is as follows: carrying out rockfill single-particle strength tests with different sizes and strain rates to obtain a relational expression P of rockfill strength and strain rate and a relational expression Q of rockfill strength size effect and strain rate, see formulas (1) and (2), and then establishing a single-particle strength calculation model considering the sizes and the strain rates, see formula (3);
where DIF is the dynamic intensity increase factor,
in order to be the strain rate of the steel,k1、k2、k3in order to be a coefficient of fit,
in order to be a static strain rate,
critical strain rate, σ, for dimensional effect to disappeardIs the dynamic intensity of the particles, σ0As the reference strength, d is the particle size of the particles, d0Is the reference particle diameter, m is the Weibull distribution modulus, ndAs a geometric similarity parameter, ndThe value of/m represents the strength of the size effect;
the single particle strength test is a flat plate load test; the P refers to the improvement relation of strain rate effect strength and is obtained by fitting the relation of strain rate and strength; the Q is the static strain rate
To critical strain rate
Linear reduction of the size effect of (1), critical strain rate at which the size effect disappears
Obtaining the single particle intensity data integrally;
the second step is that: establishing a macroscopic stress and strain tensor relation of aggregate aggregates with different sizes based on the single particle strength calculation model provided in the first step, and obtaining formulas (6a) and (6 b); the method comprises the following specific steps:
stress σ of particle aggregate in three-dimensional stateijAnd strain tensor relation epsilonijThe following were used:
wherein, VσTo calculate the total volume of the stressed region, f(c/p)Is the external force applied to the particle p at any contact point c in the region, l(c/p)A component vector pointing to the center of the particle p for the contact point; vεTo calculate the volume corresponding to the region of strain, Δ ueFor the relative displacement of the centers of the two particles p and q constituting the edge e, deThe area compensation vector corresponding to the edge e;
if the characteristic dimension corresponding to the indoor sc and the prototype pr is dprAnd dscAssuming that the mineral components of the aggregate of the reduced-scale and full-scale test samples are the same, the internal friction angle of an aggregate is irrelevant to the particle size of particles, the crushing of the particles belongs to splitting tension damage, the particle strength accords with Weibull distribution, and the contact state and the pore distribution of the aggregate of the test samples with different sizes are the same, namely the geometric state is the same; when the crushing state of the reduced scale and the full scale aggregate is the same, the particle stress sigma of the reduced scale samplescHarmonic foot stress sigmaprContact force f with particles of reduced-scale samplescContact force f with foot rulerprSatisfies the following conditions:
in the formula, PscAnd PprRespectively showing the relationship between the stress increase of the reduced scale and the full scale affected by the strain rate, QprShowing the relation of size effect reduction of the full scale; simultaneously according to the vector l(c/p)Volume V, area compensation vector deAnd relative displacement Deltau ueThe stress tensor sigma of the reduced scale sample under the action of dynamic and static loads is obtainedij,scAnd full-scale stress tensor σij,prStrain tensor epsilon with scaled sampleij,scAnd full-scale strain tensor epsilonij,prThe following relationship is satisfied:
εij,pr＝εij,sc (6b)
the third step: deducing a size effect rule of a Moire-Coulomb strength criterion under the action of static load according to the macroscopic stress strain tensor relation of the samples with different sizes; the method comprises the following specific steps:
firstly, the particle strain rate of the reduced and full-scale test pieces under the static load does not exceed the static strain rate
Then P issc、Ppr、QprAll 1, stress tensor σ of reduced-scale sampleij,scAnd full-scale stress tensor σij,prThe relationship of (c) translates into:
normal stress sigma on shear plane of triaxial samplenAnd the shear stress τ is:
in the formula, σ1And σ3For the maximum principal stress and the minimum principal stress,
is an internal friction angle; according to the hypothesis and silence in the second stepTensor relationship of load stress, normal stress sigma of scaled samplen,prAnd full scale normal stress sigman,scShear stress tau with scaled test specimensprAnd full scale shear stress τscThe following relationship is satisfied:
according to the Mohr-Coulomb strength criterion, the relationship between the normal stress and the shear stress of the reduced-scale and full-scale test samples is as follows:
in the formula, cscAnd cprRespectively the cohesive force of the reduced-scale and full-scale test samples; the formula (9) may be substituted for the formula (10):
the derivation determines the cohesive force c of the on-site foot rule in the Moire-Coulomb strength criterionprIs a reduced scale cscIs/are as follows
Doubling;
the fourth step: deriving the dynamic shear strength tau from the macroscopic stress-strain tensor relationship of differently sized samplesdAnd dynamic shear stress ratio taud/σ0The size effect rule of (1); in particular asThe following:
according to the macroscopic stress-strain tensor relation of the aggregate, when the fracture rates of the reduced scale and the full scale test sample are the same, the strain tensors of the reduced scale and the full scale test sample are the same, and the axial dynamic strain epsilon of the reduced scale test sampled,scRelation of sum vibration times N and axial dynamic strain epsilon of foot ruled,prSame relationship with the vibration number N:
εd,sc～N＝εd,pr～N (12)
further, the number of oscillations N at which the reduced and full scale samples reached the strain failure criterion of 5%fSame, reduced mean principal stress sigma0,scAnd full-scale mean principal stress σ0,prDynamic strength sigma of scale reductiond,scHarmonic foot motion intensity sigmad,prThe relationship of (1) is:
full scale shear strength τd,prAnd scale dynamic shear strength taud,scThe dimensional effect relationship of (A) is as follows:
final full scale dynamic shear stress ratio taud,sc/σ0,scAnd dynamic shear stress ratio tau of reduced scaled,pr/σ0,prThe dimensional effect relationship of (A) is as follows:
thus, the on-site full-scale shear strength is the test scale
The ratio of dynamic shear stress of full-scale on site is the test scale
And (4) doubling.
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