CN114112659B - Method for determining dynamic deformation size effect of rock-fill material - Google Patents

Method for determining dynamic deformation size effect of rock-fill material Download PDF

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CN114112659B
CN114112659B CN202111313671.XA CN202111313671A CN114112659B CN 114112659 B CN114112659 B CN 114112659B CN 202111313671 A CN202111313671 A CN 202111313671A CN 114112659 B CN114112659 B CN 114112659B
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迟世春
闫世豪
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Dalian University of Technology
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    • G01N3/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N3/08—Investigating strength properties of solid materials by application of mechanical stress by applying steady tensile or compressive forces
    • G—PHYSICS
    • G01—MEASURING; TESTING
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    • G01N2203/0067—Fracture or rupture
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2203/00—Investigating strength properties of solid materials by application of mechanical stress
    • G01N2203/0058—Kind of property studied
    • G01N2203/0069—Fatigue, creep, strain-stress relations or elastic constants
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Abstract

The invention belongs to the field of finite element calculation of earth and rockfill dams, and relates to a method for determining dynamic deformation size effect of rockfill. According to the invention, by combining the dynamic strength characteristics of single particles, the stress and strain tensor relationship of the pile aggregate is deduced, the size effect rule of the corrected equivalent viscoelastic model is determined, the correction relationship of model parameters of indoor shrinkage scale and prototype full scale is provided, the size effect error of pile dynamic deformation finite element calculation is reduced, and references are provided for engineering design and safety evaluation of earth and rockfill dams.

Description

Method for determining dynamic deformation size effect of rock-fill material
Technical Field
The invention belongs to the field of finite element calculation of earth and rockfill dams, and relates to a method for determining dynamic deformation size effect of rockfill.
Background
The earth-rock dam has the advantages of local material availability, wide adaptability, convenient construction, low cost and the like, and is widely applied to water conservancy and hydropower engineering. The method is characterized in that the earth-rock dam is mainly filled with rock-fill materials, the crushing of particles is a main cause for the sedimentation of the dam body, in the deformation process of predicting the earth-rock dam through numerical calculation, the strength deformation parameters of the rock-fill materials need to be determined according to an indoor test, the indoor test is carried out under the condition of reduced scale, the easily-crushed rock-fill materials have the size effect characteristic that the strength is reduced along with the increase of the particle size, and the calculation result error is caused by directly using the constitutive parameters obtained through the reduced scale test, so that the safety analysis of the earth-rock dam deformation is not facilitated. In recent years, along with the increasing of the height of a construction dam, the rock-fill size effect has become an urgent problem to be solved in the safety evaluation of the high earth-rock dam.
In the pile material dynamic constitutive model, the Shen Zhujiang modified equivalent viscoelastic model based on the Hardin-Drnevich model not only follows the practical principle, but also considers the nonlinear property of the soil body, and can reasonably analyze the dynamic stress dynamic strain response under the action of earthquake. In the dynamic deformation calculation process, the average principal stress sigma calculated by static force is firstly calculated m Determining an initial maximum dynamic modulus E of a dam unit dmax The initial damping ratio is set to be 5%, then the whole seismic history is divided into a plurality of sections, and the dynamic modulus E of each section d Iterative solution according to equivalent dynamic strain epsilon of each unit d Check dynamic modulus ratio E d /E dmax And damping ratio lambda d Curve determination of New E d And lambda (lambda) d Therefore, the maximum dynamic modulus E is the focus of dynamic deformation calculation dmax Ratio of dynamic modulus E d /E dmax And damping ratio lambda d The dimensional effect of the curve.
The modulus damping bit property of the pile material is mainly tested by adopting an indoor dynamic triaxial apparatus, the maximum particle size of the indoor test is generally 60mm, the size of the pile material on site can reach 600-1000 mm, the existing engineering practice shows that the settlement deformation of the dam can not be accurately predicted by adopting a scale parameter, the on-site full-scale dynamic modulus parameter K is larger than a test value through inversion of an actual measurement result, and the n value is close to the test value. At present, the effect of dynamic stress strain size effect is still lack of clear understanding, the research of the rock-fill material size effect is carried out in two ways, one is to carry out triaxial test of samples with different sizes, overseas oversized triaxial apparatuses with the sample sizes of phi 1000 multiplied by 2000mm have been developed, the oversized triaxial apparatuses provide valuable data for researching the rock-fill material shrinkage effect, but the oversized triaxial apparatuses are high in manufacturing cost, extremely complex in test process and difficult to popularize and use, and under the condition that the diameter ratio is 5, the maximum particle size adopted by the oversized triaxial apparatuses is 200mm, which is far smaller than the maximum particle size of the rock-fill material on site. The second is to combine the single particle strength test with the conventional triaxial test, the particle crushing is a main cause of the deformation of the rock-fill material, and the size effect is introduced by carrying out the single particle strength test of the rock-fill material, so that the size effect is further expanded to the sample size to reflect the influence of the size effect on the deformation of the rock-fill material. Compared with the static size effect, the crushing strength of the particles is reduced along with the increase of the particle size, the strength of the particles under the dynamic condition is also influenced by the strain rate, the strength of the particles is integrally increased along with the increase of the strain rate, meanwhile, the size effect is reduced along with the increase of the strain rate, and how to determine the dynamic strength of the particles is one of the key problems for solving the problems.
In summary, when the model parameters obtained by the indoor test are adopted to perform dynamic deformation calculation, certain deviation exists between the model parameters and the actual measurement result, and the problem that the high dam calculation is not large and the low dam calculation is not small often occurs. The grain size of the stacking material in actual engineering is larger, the indoor triaxial test under the original grading can not be carried out under the existing test condition, the grading shrinkage of the site stacking material can be carried out, the cost of the ultra-large triaxial apparatus is high, the test process is complex, and the effect of the stacking material shrinkage effect is difficult to explain mechanically. Considering that particle crushing is a main source of rock-fill material deformation, the invention combines the characteristics of single particle crushing strength to determine the dynamic deformation size effect of the rock-fill material from a mesoscopic angle, and provides a size effect determination method of the dynamic constitutive modulus parameter of the rock-fill material.
Disclosure of Invention
The invention aims to provide a method for determining dynamic deformation size effect of a rock-fill material, which combines dynamic strength characteristics of single particles, deduces a stress and strain tensor relationship of a rock-fill aggregate, determines a size effect rule of a modified equivalent viscoelastic model, provides a modified relationship of model parameters of an indoor scale and a prototype full scale, reduces the size effect error calculated by finite element of the dynamic deformation of the rock-fill material, and provides references for engineering design and safety evaluation of earth-rock dams.
The technical scheme adopted by the invention is as follows:
a method for determining dynamic deformation size effect of a rock-fill material comprises the following steps:
the first step: carrying out single particle strength tests of different sizes and strain rates of the rock-fill particles to obtain a relation P of the rock-fill strength and the strain rate and a relation Q of the rock-fill strength and the size, which are shown in formulas (1) and (2), and then establishing a dynamic strength model of the single particles, which is shown in formula (3):
where DIF is the dynamic intensity growth factor,for strain rate, c, d, k are fitting coefficients, +.>In the form of a 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 grain 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 particle 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 +.>As determined by the single particle intensity test. The dynamic intensity model of the single particle is an improvement of a Weibull distribution static intensity size effect formula (4), and an increase relation P of the rate effect intensity and a weakening relation Q of the size effect are added.
In sigma s Is the static strength of the particles.
And a second step of: based on the dynamic intensity model of single particles proposed in the first step, stress and strain tensor relations of the heap and rock aggregate are established, see formulas (7 a) and (7 b).
The method for establishing the stress and strain tensor relationship of the particle aggregate 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.
Assuming that the original full-scale pr and the reduced-scale sc samples are similar in gradation, the corresponding feature size is d pr And d sc The two samples of the reduced scale and the full scale have the same contact state and pore distribution, namely the geometric state of the aggregate is the same, and when the crushing states of the reduced scale and the full scale sample are the same, the stress sigma of the full scale sample is calculated according to the dynamic strength formula of the particles pr And reduced sample stress sigma sc Force f of contact with full-length pr And a reduced contact force f sc Satisfy the following requirements
Wherein P is pr And P sc Representing the strain rate effects of full and reduced scales, respectivelyStress enhancement relationship, 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 load is obtained ij,sc And stress tensor sigma for full-scale test specimens ij,pr Strain tensor epsilon with a scaled sample ij,sc And strain tensor epsilon for full-scale test specimens ij,pr The following relationship is satisfied:
ε ij,pr ＝ε ij,sc (7b)
the establishment of the stress and strain tensor relationship of the particle aggregate shows that the stress tensors of samples with different sizes need to consider the influence of the dynamic size effect under the same crushing state, and the strain tensors are the same.
And a third step of: deriving maximum dynamic modulus E from stress and strain tensor relationships for samples of different sizes dmax Is a dimensional effect of (a). By the dynamic triaxial load application mode, the consolidation stress has only static size effect, and the dynamic size effect of the strain rate influence needs to be calculated by the dynamic stress.
The deriving the maximum dynamic modulus E dmax The dimensional effects of (a) are as follows:
dynamic stress and dynamic strain frameworks in Hardin-Drnevich model are in hyperbolic curve relationship, and the dynamic stress sigma is reduced d,sc Dynamic strain ε d,sc And full-scale dynamic stress sigma d,pr Dynamic strain ε d,pr The method comprises the following steps:
wherein a is sc 、b sc Is contracted intoRuler dynamic stress strain parameter, a pr 、b pr For the full-scale dynamic stress strain parameter, according to the scaling relation of (8 a) and (8 b), when the reduction scale and the breaking of the full-scale sample are consistent, the internal dynamic stress meets the following conditionStrain tensors are uniform, so there are:
it can be seen from (9) that if the equation is true at any dynamic strain, the dynamic stress strain parameters a and b satisfy:
E dmax =1/a, the maximum dynamic modulus relationship of the reduced scale and full scale samples is:
correction of equivalent viscoelastic model assumption E dmax And average principal stress sigma m Has the following relationship:
wherein K, n is the maximum dynamic modulus coefficient and index, respectively, pa is the atmospheric pressure, σ m ＝(2+K c )σ 3 /3，K c Is the consolidation stress ratio. Sigma (sigma) m The consolidation stress only needs to consider the static size effect, and the tensor sigma of the consolidation stress is reduced m,sc Tensor sigma of consolidation stress with full scale m,pr Satisfy the following requirementsAt this point, both P and Q are 1, then from (11) (12) it is possible to obtain:
wherein E is dmax,pr Maximum dynamic modulus, K, for full scale sc And K pr Maximum dynamic modulus coefficient, n, of the reduced and full scale respectively sc And n pr The maximum dynamic modulus indexes of the reduced scale and the full scale are respectively, and if the two formulas (13 a) and (13 b) are equal, the maximum dynamic modulus parameter relationship of the reduced scale and the full scale sample is:
n sc ＝n pr (14a)
the maximum dynamic modulus E dmax The maximum dynamic modulus coefficient K of the reduced scale and full scale samples satisfies the relationship of (14 b).
Fourth step: deriving dynamic modulus ratio E from equivalent stress and strain tensor relationships for differently sized samples d /E dmax And damping ratio lambda d Dimensional effect relationship of curves.
The derived dynamic modulus ratio E d /E dmax And damping ratio lambda d The method of the dimensional effect of the curve is as follows:
the expression of the dynamic modulus ratio in the equivalent viscoelastic model is:
wherein ε d,r For reference axial strain ε d,r ＝σ dmax /E dmax A/b, then full-scale reference axial strainAnd reduced scale reference axial strain->The method comprises the following steps:
ratio of dynamic modulus of reduced scale E d,sc /E dmax,sc And full-scale specimen dynamic modulus ratio E d,pr /E dmax,pr The relation of (2) is:
and due to lambda d /λ dmax ＝1-E d /E dmax ，λ dmax Is constant, thus the reduced-scale damping ratio lambda d,sc And full-scale damping ratio lambda d,pr The method meets the following conditions:
λ d,pr ＝λ d,sc (18)
the derivation determines the dynamic modulus ratio E d /E dmax And damping ratio lambda d The curves are not affected by the size effect.
The invention has the beneficial effects that:
1. the invention combines a single particle strength test and a dynamic triaxial test to deduce the size effect of dynamic deformation of the rock-fill material, a dynamic strength calculation model is provided by single particle strength tests with different sizes and strain rates, the dynamic strength size effect of single particle strength is introduced into the equivalent stress tensor and the strain tensor of the aggregate, and the maximum dynamic modulus E in the equivalent viscoelastic model is determined dmax Ratio of dynamic modulus E d /E dmax And damping ratio lambda d Size of curveAnd the effect rule gives the correction relation of the maximum dynamic modulus coefficient K of the indoor reduced scale and the prototype full scale.
2. Compared with the ultra-large triaxial test which is high in cost and time-consuming and labor-consuming, the method only needs to carry out the dynamic strength test and the conventional dynamic triaxial test of the single-particle strength, the single-particle strength mainly obtains the relation between the dynamic strength factor and the strain rate and the relation that the strength dimension effect decays along with the strain rate, and the dimension effect corrected dynamic constitutive model parameters can be obtained according to the conventional dynamic triaxial test result.
3. The invention has clear deducing logic for the dynamic deformation size effect of the rock-fill material, defines the stress and deformation rule caused by the shrinkage of the rock-fill material, adopts the parameters of the constitutive model corrected by the size effect to improve the accuracy of finite element calculation of the dynamic deformation of the rock-fill dam, and provides reference for engineering design and safety evaluation of the earth-rock dam.
Drawings
FIG. 1 is a plot of static strength versus particle size for example 1 of the present invention.
FIG. 2 is a fitted relationship of particle strength as strain rate increases for example 1 of the present invention.
FIG. 3 is a graph showing the reduction of the effect of the particle strength dimension in example 1 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 this embodiment, a certain pile of rock, which is a mother rock, is taken as an example to determine the size effect of dynamic deformation.
First, selecting particles with the size range of 20-200 mm to carry out a static strain rate strength test to determine a static size effect-n d FIG. 1 shows the fit of static strength to size of the rockfill particles. Particles in the size range of 40-60 mm are selected for particle crushing tests with different strain rates, the fitting relation of the strength of the rock-fill particles along with the increase of the strain rate is shown in fig. 2, the size effect weakening relation Q is shown in fig. 3, and a dynamic strength model of single particles is established.
Wherein the static strain rateIs 10 -5 s -1 Test according to different strain Rate FIG. 3 critical strain Rate can be obtained>Is 10 -1 s -1 。
Second, based on the dynamic strength model of single particle, building stress tensor sigma of particle aggregate reduced scale sample ij,sc And stress tensor sigma for full-scale test specimens ij,pr Strain tensor epsilon with a scaled sample ij,sc And strain tensor epsilon for full-scale test specimens ij,pr The following relationship is satisfied:
ε ij,pr ＝ε ij,sc
thirdly, deducing the maximum dynamic modulus index n of the reduced scale and the full scale based on the equivalent stress and strain tensor relation of the samples with different sizes in the second step sc And n pr Maximum dynamic modulus coefficient K of reduced scale and full scale sc And K pr The relation of (2) is:
n sc ＝n pr
the maximum dynamic modulus index n has no dimensional effect and does not need to be modified. When the maximum dynamic modulus coefficient K of the reduced scale and full scale samples is corrected,the average strain rate of the movable triaxial test in the removable chamber is about 10 -3 s -1 ，/>Based on the ratio of the in-situ seismic frequency to the dynamic triaxial frequency, e.g. if the in-situ frequency is 3Hz and the dynamic triaxial frequency is typically 0.3Hzd pr /d sc In order to obtain the ratio of the site rock-fill particle size to the test particle size, if the site rock-fill particle size is 600mm at maximum and the conventional dynamic triaxial maximum particle size is 60mm, d is as follows pr /d sc ＝10，K sc And n sc Is obtained by a conventional dynamic triaxial test, and finally the corrected ratio K of the field full-scale maximum dynamic modulus coefficient K can be obtained pr /K sc 。
Fourth step, deriving dynamic modulus ratio E based on equivalent stress and strain tensor relationship of the samples with different sizes in the second step d /E dmax And damping ratio lambda d The dimensional effect of the curve. In this embodiment, the dynamic modulus ratio E d /E dmax And damping ratio lambda d The curves have no size effect and do not need to be corrected.

Claims (1)

1. The method for determining the dynamic deformation size effect of the rockfill material is characterized by comprising the following steps of:
the first step: carrying out single particle strength tests of different sizes and strain rates of the rock-fill particles to obtain a relation P of the rock-fill strength and the strain rate and a relation Q of the rock-fill strength and the size, which are shown in formulas (1) and (2), and then establishing a dynamic strength model of the single particles, which is shown in formula (3):
where DIF is the dynamic intensity growth factor,for strain rate, c, f, k are 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 Is a geometric similarity parameter;
and a second step of: based on the single-particle dynamic strength model proposed in the first step, establishing a stress and strain tensor relationship of the heap and dump aggregate, wherein the stress and strain tensor relationship is as follows;
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 For the relative displacement of the centers of the two particles p and q constituting the edge e, d e The area compensation vector corresponding to the edge e is used;
assuming that the original full-scale pr and the reduced-scale sc samples are similar in gradation, the corresponding feature size is d pr And d sc The two samples of the reduced scale and the full scale have the same contact state and pore distribution, namely the geometric state of the aggregate is the same, and when the crushing states of the reduced scale and the full scale sample are the same, the stress sigma of the full scale sample is calculated according to the dynamic strength formula of the particles pr And reduced sample stress sigma sc Force f of contact with full-length pr And a reduced contact force f sc The method meets the following conditions:
wherein P is pr And P sc Respectively representing the stress improvement relation of full-scale strain rate effect and reduced-scale strain rate effect, 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 load is obtained ij,sc And stress tensor sigma for full-scale test specimens ij,pr Strain tensor epsilon with a scaled sample ij,sc And strain tensor epsilon for full-scale test specimens ij,pr The following relationship is satisfied:
ε ij,pr ＝ε ij,sc (6b)
and a third step of: deriving maximum dynamic modulus E from stress and strain tensor relationships for samples of different sizes dmax The size effect of (2); the specific method comprises the following steps:
dynamic stress sigma for reduced scale d,sc Dynamic strain ε d,sc And full-scale dynamic stress sigma d,pr Dynamic strain ε d,pr The method comprises the following steps:
wherein a is sc 、b sc A is a reduced dynamic stress strain parameter pr 、b pr For the full-scale dynamic stress strain parameter, according to the scaling relation of (7 a) and (7 b), when the reduction scale and the breaking of the full-scale sample are consistent, the internal dynamic stress meets the following conditionStrain tensors are uniform, so there are:
from equation (8), if the equation is true at any dynamic strain, the dynamic stress strain parameters a and b satisfy:
E dmax =1/a, the maximum dynamic modulus relationship of the reduced scale and full scale samples is:
correction of equivalent viscoelastic model assumption E dmax And average principal stress sigma m Has the following relationship:
wherein K, n is the maximum dynamic modulus coefficient and index, respectively, pa is the atmospheric pressure, σ m ＝(2+K c )σ 3 /3，K c Is the consolidation stress ratio; sigma (sigma) m The consolidation stress only needs to consider the static size effect, and the tensor sigma of the consolidation stress is reduced m,sc Tensor sigma of consolidation stress with full scale m,pr Satisfy the following requirementsAt this time, P and Q are both 1, and then, from (10) and (11):
wherein E is dmax,pr Maximum dynamic modulus, K, for full scale sc And K pr Maximum dynamic modulus coefficient, n, of the reduced and full scale respectively sc And n pr The maximum dynamic modulus indexes of the reduced scale and the full scale are respectively, and if the two formulas (12 a) and (12 b) are equal, the maximum dynamic modulus parameter relationship of the reduced scale and the full scale sample is:
n sc ＝n pr (13a)
fourth step: deriving dynamic modulus ratio E from equivalent stress and strain tensor relationships for differently sized samples d /E dmax And damping ratio lambda d The dimensional effect relationship of the curve is as follows:
the expression of the dynamic modulus ratio in the equivalent viscoelastic model is:
wherein ε d,r For reference axial strain ε d,r ＝σ dmax /E dmax A/b, then full-scale reference axial strainAnd reduced scale reference axial strain->The method comprises the following steps:
ratio of dynamic modulus of reduced scale E d,sc /E dmax,sc And full-scale specimen dynamic modulus ratio E d,pr /E dmax,pr The relation of (2) is:
and due to lambda d /λ dmax ＝1-E d /E dmax ，λ dmax Is constant, thus the reduced-scale damping ratio lambda d,sc And full-scale damping ratio lambda d,pr Satisfy the following requirements：
λ d,pr ＝λ d,sc (17)。
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