CN114354430B - Size effect correction method for shear 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, deduces the macroscopic stress and strain tensor relation of different size rock-fill aggregate, analyzes the size effect rule of Moire-coulomb strength criterion under the action of static load, proposes the correction relation of cohesive force c, and further determines the size effect correction relation of dynamic shear strength and dynamic shear stress ratio under the strain damage standard. The invention can provide a reference for the stability analysis of the earth-rock 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
The earth-rock dam is widely applied to hydraulic and hydroelectric engineering due to good applicability and economy. The stability analysis of the earth and rockfill dam needs to be determined according to the intensity deformation parameters of the rockfill material determined by an indoor test, however, the indoor test is carried out under the condition of reduced scale, and the result of the past test and research shows that the brittle fracture of the rockfill material has obvious size effect, and the concrete is that the intensity of aggregate particles is reduced along with the increase of the particle size. The settlement deformation of the site can not be accurately predicted by directly using the strength deformation parameters obtained by the reduced scale indoor test, and the problems of small high dam calculation and small low dam calculation often occur, so that the safety evaluation of earth and rockfill dams is not facilitated. In particular, with the rapid development of the construction technology in China in recent years, more and more high earth and rockfill dam designs are proposed or under construction, and for the high earth and rockfill dam with larger gradient, the size effect of rockfill material has become a problem which needs to be solved urgently for high dam stability analysis.
The grain size of the site stacking material can reach 600-1000 mm, and the shearing strength of the site stacking material cannot be directly tested due to the limitation of the size of test equipment. After the grading shrinkage is tested in a room, the maximum grain diameter of the rock-fill material is generally 60mm, and the actual measurement and inversion results of the existing engineering show that the parameters of the shrinkage test have a certain difference from the parameters of the full scale. Some scholars are devoted to developing large-size test instruments to obtain parameters closer to a prototype, and the ultra-large triaxial apparatus provides precious data for researching the size effect of the heap material, but the ultra-large triaxial apparatus has high manufacturing cost, extremely complex test process and difficult popularization and application, and the maximum particle size adopted by the ultra-large triaxial apparatus is generally not more than 200mm and still smaller than the maximum particle size of the heap material on site.
To sum up, in order to evaluate the shear strength performance of the pile in the field, it is necessary to establish a relationship between the indoor scale test parameters and the full-scale parameters in the field. The particle crushing is a main reason for the deformation of the rock-fill material body, and the single-particle strength test and the triaxial test of the rock-fill material body can be combined, so that the size effect of the single-particle strength is introduced, and the size effect of the test sample is deduced according to the micromechanics of the aggregate body. In order to analyze the shear strength of the heap rock under static and dynamic load, single particle crushing tests with different sizes and strain rates should be performed, the particle strength is reduced with the increase of the particle size under static conditions, while the particle strength is not only increased with the strain rate under quasi-static conditions, the size effect of the particle strength is gradually reduced with the strain rate, and how to determine the dynamic strength of the particles is a problem of analyzing the relationship between the dynamic strength size and the rate effect.
At present, no better solution exists for the problem of the size effect of the shear strength of the pile material, and although the ultra-large triaxial test instrument can be developed to obtain parameters which are closer to the full scale of the prototype, the maximum particle size of the ultra-large triaxial test instrument is smaller than that of the prototype in situ, and the shrinkage effect of the pile material is difficult to explain mechanically.
Disclosure of Invention
The invention provides a method for correcting the size effect of the shear strength of a rockfill material from the perspective of micromechanics by combining the size and strain rate effect of the strength of single particles aiming at the shear strength of the rockfill material under the action of dynamic and static loads. The invention can provide a reference for the stability analysis of the earth-rock dam.
The technical scheme adopted by the invention is as follows:
a size effect correction method for the shear strength of a rock-fill material comprises the following steps:
the first step: carrying out single-particle strength tests of the rockfill materials with different sizes and strain rates to obtain a relation P of the rockfill material strength and the strain rate and a relation Q of the size effect of the rockfill material strength and the strain rate, wherein the relation P is shown in formulas (1) and (2), and then establishing a single-particle strength calculation model considering the sizes and the strain rates, wherein the single-particle strength calculation model is shown in formula (3).
Where DIF is the dynamic intensity growth factor,for strain rate, k 1 、k 2 、k 3 For fitting coefficients +.>Is static strain rate, +>For the size effect vanishing critical strain rate, σ d For particle dynamic strength, sigma 0 Taking the strength as a reference, d is the particle diameter of the particles, d 0 For the reference particle size, m is Weibull distribution modulus, n d N is a geometric similarity parameter d And/m is the strength of the size effect.
The single particle strength test refers to a plate load test. And P refers to an improvement relation of the strain rate effect strength, and is obtained by fitting the relation of the strain rate and the strength. The Q refers to the strain rate from static stateTo critical strain rate->The linear reduction of the dimensional effect of (2), critical strain rate for the disappearance of the dimensional effect +.>Is obtained from the single grain intensity data.
And a second step of: based on the single particle strength calculation model provided in the first step, macroscopic stress and strain tensor relations of aggregate aggregates with different sizes are established, and the macroscopic stress and strain tensor relations are shown in formulas (6 a) and (6 b).
The method for establishing macroscopic stress and strain tensor relationship of aggregate aggregates with different sizes comprises the following steps:
stress sigma of particle aggregate in three-dimensional state ij And strain tensor relationship ε ij The following are provided:
wherein V is σ To calculate the total volume of the stress region, f (c/p) For the external force, l, applied to the particle p at any contact point, c, in the region (c/p) Is the branch vector pointing to the center of the particle p at the contact point. V (V) ε To calculate the corresponding volume of the strained region, deltau e For the relative displacement of the centers of the two particles p and q constituting the edge e, d e The vector is compensated for the area corresponding to edge e.
If the characteristics of the indoor reduced scale sc and prototype full scale pr sample correspond to each otherA dimension d pr And d sc Assuming that the mineral components of the scaled sample pile material and the full-scale sample pile material are the same, the internal friction angle of the aggregate is irrelevant to the particle size of the particles, the breakage of the particles belongs to splitting, tensioning and breaking, the particle strength accords with Weibull distribution, and the contact state and the pore distribution of the sample aggregates with different sizes are the same, namely the geometric state is the same. When the broken state of the reduced scale and the full scale aggregate is the same, the particle stress sigma of the reduced scale sample is equal to that of the reduced scale sample sc And full-scale stress sigma pr Contact force f with reduced scale sample particles sc And full-scale contact force f pr The method meets the following conditions:
wherein P is sc And P pr Respectively represents the relationship between the reduced scale and the full scale stress improvement affected by the strain rate, Q pr Indicating the size effect reduction relationship of the full scale. At the same time according to the branch vector l (c/p) Volume V, area compensation vector d e And relative displacement Deltau e The dimension proportion relation of the scale sample under the action of dynamic and static load is obtained ij,sc And full-scale stress tensor sigma ij,pr Strain tensor epsilon with a scaled sample ij,sc And full-scale strain tensor epsilon ij,pr The following relationship is satisfied:
ε ij,pr ＝ε ij,sc (6b)
and a third step of: and deducing the size effect rule of the Moire-Coulomb strength rule under the action of static load from the macroscopic stress strain tensor relationship of the samples with different sizes.
The method for deducing the Moire-Coulomb intensity criterion size effect is as follows:
first, the particle strain rate of the reduced scale and full scale test sample under static load does not exceed the static strain rateThen P sc 、P pr 、Q pr All are 1, the stress tensor sigma of the reduced scale sample ij,sc And full-scale stress tensor sigma ij,pr The relationship of (2) is converted into:
normal stress sigma on triaxial specimen shear plane n And shear stress τ are:
in sigma 1 Sum sigma 3 For maximum principal stress and minimum principal stress,is the internal friction angle. According to the assumption and the tensor relationship of the static load stress in the second step, the normal stress sigma of the reduced-scale sample n,pr And full-scale normal stress sigma n,sc Shear stress τ with scaled sample pr And full-scale shear stress τ sc The following relationship is satisfied:
according to the Moire-coulomb intensity criterion, the relationship between the normal stress and the shearing stress of the reduced scale and the full scale sample is as follows:
wherein, c sc And c pr The cohesion of the scaled and full-scale samples, respectively. Substitution of formula (9) into formula (10) yields:
the cohesive force c of the on-site full scale in the deduction determination of the Moire-Coulomb intensity criterion pr For reducing the scale c sc A kind of electronic deviceMultiple times.
Fourth step: deriving shear strength τ from macroscopic stress-strain tensor relationships for samples of different sizes d And dynamic shear stress ratio τ d /σ 0 Is a rule of size effect.
The method for deducing the size effect of the dynamic strength and the dynamic shear stress ratio is as follows:
according to the macroscopic stress strain tensor relation of the aggregate, when the breaking rates of the reduced scale sample and the full scale sample are the same, the strain tensor of the reduced scale sample and the full scale sample is the same, and the axial dynamic strain epsilon of the reduced scale sample d,sc Relationship between vibration frequency N and full-scale axial dynamic strain epsilon d,pr The relationship with the vibration order N is the same:
ε d,sc ～N＝ε d,pr ～N (12)
further, vibration times N when the reduced scale and full scale sample reach 5% of the strain damage standard f The same is achieved by the relationship of the stress tensors and the average principal stress sigma of the reduced scale 0,sc And full-scale average principal stress sigma 0,pr And shrinkDynamic strength sigma of ruler d,sc And full-scale dynamic strength sigma d,pr The relation of (2) is:
full-scale dynamic shear strength tau d,pr And the dynamic shear strength tau of the reduced scale d,sc The dimensional effect relationship of (2) is:
final full-scale dynamic shear stress ratio tau d,sc /σ 0,sc And the dynamic shear stress ratio tau of the reduced scale d,pr /σ 0,pr The dimensional effect relationship of (2) is:
therefore, the on-site full-scale dynamic shear strength is the test reduced scaleThe dynamic shear stress ratio of the site full scale is +.>Multiple times.
The invention has the beneficial effects that:
1. the invention derives macroscopic stress and strain tensor relation of sample assemblies with different sizes from the angle of single particle breaking micro-mechanics according to the size and rate effect of single particle strength, determines that the cohesive force c in Moire-Coulomb strength criterion has size effect under the action of static load, and the cohesive force of the full-scale sample is that of the reduced-scale sampleMultiple times. Full-scale dynamic shear strength under dynamic load is +.>Double, full-scale dynamic shear stress ratio is a reduced scaleMultiple times.
2. Compared with the ultra-large triaxial test which is high in cost and time-consuming and labor-consuming, the invention can analyze the shear strength difference of the indoor scale and the on-site full scale according to the size and the strain rate effect of the single particle strength of the piled material by only carrying out the single particle crushing test and the conventional triaxial test with different sizes and strain rates.
3. The invention has clear deducing logic for the dynamic deformation size effect of the rock-fill material, considers the size effect to correct the shear strength of the rock-fill material, and provides reference for engineering design and safety and stability evaluation of earth-rock dams.
Drawings
FIG. 1 is a graph showing the fitted relationship of static strength of red rock particles according to the present invention with particle size.
FIG. 2 is a fitted relationship of the strength of the red rock particles of the present invention as a function of strain rate.
FIG. 3 is a graph showing the reduction of the effect of the strength and size of the red rock particles according to the present invention with strain rate.
FIG. 4 is a schematic representation of the Moire-Coulomb intensity criteria size effect of the present invention.
FIG. 5 is a graph showing the dynamic shear strength dimension effect of the present invention.
FIG. 6 is a graph showing the dynamic shear stress ratio size effect of the present invention.
Detailed Description
The following describes the embodiments of the present invention in detail with reference to the technical scheme and the accompanying drawings.
In the embodiment, the size effect of the shear strength of the rock-fill material is determined according to the crushing test result of the red rock particles.
First, single particle crushing test under different sizes and strain rates is carried outIn the experiment, FIG. 1 shows the variation of particle strength with size at static strain rate, fitted to the size effect-n d M; FIG. 2 is a graph showing the variation of the rock-fill particle strength with strain rate, fitted to obtain a dynamic strength improvement relationship P; FIG. 3 is a graph showing the dimensional effect of rock-fill particle strength as a function of strain rate, critical strain rateIn the range of 10 -1 s -1 A size effect reduction relationship Q and a single particle intensity calculation model were established.
Step two, based on the single particle strength calculation model proposed in the step one, establishing the stress tensor sigma of the reduced scale sample under the action of dynamic and static loads ij,sc And full-scale stress tensor sigma ij,pr Strain tensor epsilon with a scaled sample ij,sc And full-scale strain tensor epsilon ij,pr Is the relation of:
ε ij,pr ＝ε ij,sc
thirdly, deducing a size effect rule of a Moire-coulomb strength criterion under the action of static load based on a macroscopic stress-strain tensor relationship of the full scale and the reduced scale in the second step, wherein fig. 4 is a schematic diagram of the size effect of the Moire-coulomb strength criterion, and the relationship between the full scale cohesive force and the reduced scale cohesive force is as follows:
wherein d pr /d sc In order to obtain the ratio of the site particle size to the indoor test particle size, if the site rock-fill particle maximum particle size is 600mm and the conventional large triaxial maximum particle size is 60mm, d pr /d sc 10, the dimensional effect-n was obtained from the fit of FIG. 1 d And/m is-0.3, the full-scale cohesion is 0.501 times of the reduced-scale cohesion.
Fourth step: macroscopic stress strain tensor relation based on second step full scale and reduced scale to deduce pile material dynamic strength tau d And dynamic shear stress ratio τ d /σ 0 FIG. 5 is a schematic diagram showing the size effect of dynamic shear strength, full scale dynamic shear strength τ d,pr And the dynamic shear strength tau of the reduced scale d,sc The dimensional effect relationship of (2) is:
FIG. 6 is a schematic diagram of the dynamic shear stress ratio size effect, full scale dynamic shear stress ratio τ d,sc /σ 0,sc And the dynamic shear stress ratio tau of the reduced scale d,pr /σ 0,pr The dimensional effect relationship of (2) is:
wherein d pr /d sc Taken as 10, -n d Wherein m is-0.3,the average strain rate of the movable triaxial test in the removable chamber is about 10 -3 s -1 ，/>According to the ratio of the on-site seismic frequency to the dynamic triaxial frequency, for example if the on-site frequency is 3Hz and the dynamic triaxial frequency is typically 0.3Hz +.>The final full-scale dynamic shear strength is about 0.95 times the reduced-scale dynamic shear strength, and the full-scale dynamic shear stress ratio is about 1.90 times the reduced-scale dynamic shear stress ratio.
Claims (1)
1. The size effect correction method for the shear strength of the rockfill material is characterized by comprising the following steps of:
the first step: carrying out single-particle strength tests of the rock-fill material with different sizes and strain rates to obtain a relation P of the rock-fill material strength and the strain rate and a relation Q of the rock-fill material strength size effect and the strain rate, wherein the relation P is shown in formulas (1) and (2), and then establishing a single-particle strength calculation model considering the sizes and the strain rates, wherein the single-particle strength calculation model is shown in formula (3);
where DIF is the dynamic intensity growth factor,for strain rate, k 1 、k 2 、k 3 For fitting coefficients +.>Is static strain rate, +>For the size effect vanishing critical strain rate, σ d Is particle dynamic strength，σ 0 Taking the strength as a reference, d is the particle diameter of the particles, d 0 For the reference particle size, m is Weibull distribution modulus, n d N is a geometric similarity parameter d M is the intensity of the size effect;
the single particle strength test refers to a flat plate load test; the P refers to an improvement relation of the strain rate effect strength, and is obtained by fitting the relation of the strain rate and the strength; the Q refers to the strain rate from static stateTo critical strain rate->The linear reduction of the dimensional effect of (2), critical strain rate for the disappearance of the dimensional effect +.>The single grain intensity data is obtained integrally;
and a second step of: based on the single particle strength calculation model provided in the first step, establishing macroscopic stress and strain tensor relations of aggregate aggregates with different sizes, wherein the macroscopic stress and strain tensor relations are shown in formulas (6 a) and (6 b); the method comprises the following steps:
stress sigma of particle aggregate in three-dimensional state ij And a strain tensor ε ij The relationship is as follows:
wherein V is σ To calculate the total volume of the stress region, f (c/p) For the external force, l, applied to the particle p at any contact point, c, in the region (c/p) A branch vector pointing to the center of the particle p for the contact point; v (V) ε To calculate the corresponding volume of the strained region, deltau e To form edgese relative displacement of the centers of two particles p and q, d e The area compensation vector corresponding to the edge e is used;
if the feature size corresponding to the indoor reduced scale sc and the prototype full scale pr sample is d pr And d sc Assuming that the mineral components of the scaled sample pile stones are the same as those of the full-scale sample pile stones, the internal friction angle of the aggregate is irrelevant to the particle size of the particles, the crushing of the particles belongs to splitting, tensioning and breaking, the particle strength accords with Weibull distribution, and the contact state and pore distribution of the sample aggregates with different sizes are the same, namely the geometric state is the same; when the broken state of the reduced scale and the full scale aggregate is the same, the particle stress sigma of the reduced scale sample is equal to that of the reduced scale sample sc And full-scale stress sigma pr Contact force f with reduced scale sample particles sc And full-scale contact force f pr The method meets the following conditions:
wherein P is sc And P pr Respectively represents the relationship between the reduced scale and the full scale stress improvement affected by the strain rate, Q pr Representing the size effect weakening relation of the full scale; at the same time according to the branch vector l (c/p) Volume V, area compensation vector d e And relative displacement Deltau e The dimension proportion relation of the scale sample under the action of dynamic and static load is obtained ij,sc And full-scale stress tensor sigma ij,pr Strain tensor epsilon with a scaled sample ij,sc And full-scale strain tensor epsilon ij,pr The following relationship is satisfied:
ε ij,pr ＝ε ij,sc (6b)
and a third step of: deducing the size effect rule of the Moire-Coulomb strength rule under the action of static load according to the macroscopic stress strain tensor relationship of the samples with different sizes; the method comprises the following steps:
first, the particle strain rate of the reduced scale and full scale test sample under static load does not exceed the static strain rateThen P sc 、P pr 、Q pr All are 1, the stress tensor sigma of the reduced scale sample ij,sc And full-scale stress tensor sigma ij,pr The relationship of (2) is converted into:
normal stress sigma on triaxial specimen shear plane n And shear stress τ are:
in sigma 1 Sum sigma 3 For maximum principal stress and minimum principal stress,is an internal friction angle; according to the assumption and the tensor relationship of the static load stress in the second step, the normal stress sigma of the reduced-scale sample n,pr And full-scale normal stress sigma n,sc Shear stress τ with scaled sample pr And full-scale shear stress τ sc The following relationship is satisfied:
according to the Moire-coulomb intensity criterion, the relationship between the normal stress and the shearing stress of the reduced scale and the full scale sample is as follows:
wherein, c sc And c pr The cohesion of the reduced and full-scale samples; substitution of formula (9) into formula (10) yields:
the cohesive force c of the on-site full scale in the deduction determination of the Moire-Coulomb intensity criterion pr For reducing the scale c sc A kind of electronic deviceDoubling;
fourth step: deriving shear strength τ from macroscopic stress-strain tensor relationships for samples of different sizes d And dynamic shear stress ratio τ d /σ 0 Is a rule of size effect; the method comprises the following steps:
according to the macroscopic stress strain tensor relation of the aggregate, when the breaking rates of the reduced scale sample and the full scale sample are the same, the strain tensor of the reduced scale sample and the full scale sample is the same, and the axial dynamic strain epsilon of the reduced scale sample d,sc Relationship between vibration frequency N and full-scale axial dynamic strain epsilon d,pr The relationship with the vibration order N is the same:
ε d,sc ～N＝ε d,pr ～N (12)
further, vibration times N when the reduced scale and full scale sample reach 5% of the strain damage standard f The same is achieved by the relationship of the stress tensors and the average principal stress sigma of the reduced scale 0,sc And full-scale average principal stress sigma 0,pr And the dynamic strength sigma of the reduced scale d,sc And full-scale dynamic strength sigma d,pr The relation of (2) is:
full-scale dynamic shear strength tau d,pr And the dynamic shear strength tau of the reduced scale d,sc The dimensional effect relationship of (2) is:
final full-scale dynamic shear stress ratio tau d,sc /σ 0,sc And the dynamic shear stress ratio tau of the reduced scale d,pr /σ 0,pr The dimensional effect relationship of (2) is:
thus, the in-situ full-scale dynamic shear strength is the test reduced scaleThe dynamic shear stress ratio of the site full scale is +.>Multiple times.
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