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

Abstract

The invention belongs to the field of finite element calculation of earth-rock dams and relates to a method for determining the size effect of dynamic deformation of rockfill materials. This invention combines the dynamic strength characteristics of single particles to deduce the stress and strain tensor relationship of the rockfill aggregate, determines the size effect law of the modified equivalent viscoelastic model, and proposes the correction relationship of indoor scale and prototype full-scale model parameters. Reduce the size effect error in finite element calculation of dynamic deformation of rockfill materials, and provide a reference for earth-rock dam engineering design and safety evaluation.

Description

A method for determining the size effect of dynamic deformation of rockfill materials

Technical field

The invention belongs to the field of finite element calculation of earth-rock dams and relates to a method for determining the size effect of dynamic deformation of rockfill materials.

Background technique

Earth-rock dams have the advantages of using local materials, wide adaptability, convenient construction, and low cost, and are widely used in water conservancy and hydropower projects. Earth-rock dams are mainly filled with rockfill materials. The crushing of particles is the main reason for the settlement of the dam body. In the process of predicting the deformation of earth-rockfill dams through numerical calculations, it is necessary to determine the strength and deformation parameters of rockfill materials based on indoor tests, and indoor tests are all Conducted under scale conditions, easily broken rockfill materials have size effect characteristics in which the strength decreases as the particle size increases. Direct use of the constitutive parameters obtained from the scale test will lead to errors in the calculation results, which is not conducive to the deformation of the earth-rock dam. Security analysis. In recent years, with the continuous increase in dam height, the size effect of rockfill materials has become an urgent problem to be solved in the safety evaluation of high earth-rock dams.

Among the dynamic constitutive models of rockfill materials, the modified equivalent viscoelastic model proposed by Shen Zhujiang based on the Hardin-Drnevich model not only follows practical principles, but also takes into account the nonlinear properties of the soil, and can reasonably analyze seismic effects. Dynamic stress and dynamic strain response. In the calculation process of dynamic deformation, the initial maximum dynamic modulus E _dmax of the dam unit should first be determined from the average principal stress σ _m calculated by static force, and the initial damping ratio is set to 5%. Then the entire earthquake history is divided into several segments. Iteratively solve the dynamic modulus E _d of each section. According to the equivalent dynamic strain ε _d of each unit, check the dynamic modulus ratio E _d /E _dmax and the damping ratio λ _d curve to determine the new E _d and λ _d . Therefore, the dynamic deformation calculation is What needs attention is the size effect of the maximum dynamic modulus E _dmax , dynamic modulus ratio E _d /E _dmax and damping ratio λ _d curve.

The modulus damping ratio characteristics of rockfill materials are mainly tested using an indoor dynamic triaxial instrument. The maximum particle size in indoor tests is generally 60mm, while the size of on-site rockfill materials can reach 600~1000mm. Actual projects have shown that scaling parameters cannot be accurately predicted. The settlement deformation of the dam was inverted from the actual measurement results. The on-site full-scale dynamic modulus parameter K was greater than the test value, and the n value was close to the test value. At present, there is still a lack of clear understanding of the role of dynamic stress and strain size effects. Research on the size effects of rockfill materials is carried out in two ways. One is to conduct triaxial tests on samples of different sizes. Samples have been developed at home and abroad. An ultra-large triaxial instrument with a size of φ1000×2000mm provides valuable data for studying the scaling effect of rockfill materials. However, the ultra-large triaxial instrument is not only expensive to build, but also has an extremely complicated test process, making it difficult to popularize and use it. Under the condition of a diameter ratio of 5, the maximum particle size used by the super-large triaxial instrument is 200mm, which is much smaller than the maximum particle size of on-site rockfill materials. The second method is to combine the single particle strength test with the conventional triaxial test. Particle crushing is the main reason for the deformation of the rockfill body. The size effect is introduced by conducting the single particle strength test of the rockfill material, and then expanded to the sample scale to reflect the size. Effect on the strength and deformation of rockfill materials. Compared with the static size effect, the particle crushing strength decreases as the particle size increases. The particle strength under dynamic conditions is also affected by the strain rate. The overall particle strength increases with the increase of the strain rate. At the same time, the size effect increases with the strain rate. Large and reduced, how to determine the dynamic strength of particles is one of the key issues to solve the problem.

To sum up, when using model parameters obtained from indoor tests to calculate dynamic deformation, there is a certain deviation from the actual measurement results, and the problem of "high dams are not considered large and low dams are not considered small" often occurs. In actual projects, the particle size of rockfill materials is relatively large. Under the existing test conditions, it is impossible to carry out indoor triaxial tests under the original gradation. The on-site rockfill materials can only be graded and scaled down. The cost of super-large triaxial instruments is high. The test process is complex, and it is difficult to explain the role of the scale effect of rockfill materials from a mechanistic perspective. Considering that particle crushing is the main source of rockfill material deformation, the present invention combines the characteristics of single particle crushing strength to determine the size effect of dynamic deformation of rockfill materials from a mesoscopic perspective, and proposes a method for determining the size effect of dynamic constitutive modulus parameters of rockfill materials.

Contents of the invention

The purpose of the present invention is to provide a method for determining the size effect of dynamic deformation of rockfill materials. This method combines the dynamic strength characteristics of single particles to deduce the stress and strain tensor relationship of the rockfill material aggregate and determine the size of the modified equivalent viscoelastic model. The law of effect is proposed, and the correction relationship between indoor scale and prototype full-scale model parameters is proposed to reduce the size effect error in finite element calculation of dynamic deformation of rockfill material, and provide reference for earth-rock dam engineering design and safety evaluation.

The technical solution adopted by the present invention is:

A method for determining the size effect of dynamic deformation of rockfill materials, including the following steps:

Step 1: Carry out single-grain strength tests of different sizes and strain rates of rockfill particles to obtain the relationship P between the strength of the rockfill material and the strain rate, and the relationship Q between the strength and size of the rockfill material. See formulas (1) and (2), and then Establish a single particle dynamic intensity model, see formula (3):

In the formula, DIF is the dynamic intensity growth factor, is the strain rate, c, d, k are fitting coefficients,/> is the static strain rate, is the critical strain rate for the disappearance of size effect, σ _d is the particle dynamic strength, σ ₀ is the base strength, d is the particle size, d ₀ is the base particle size, m is the Weibull distribution modulus, n _d is the geometric similarity parameter, n _d /m represents the strength of the size effect.

The single grain strength test refers to the flat plate load test. The P refers to the improvement relationship of strain rate effect intensity, which is obtained by fitting the relationship between strain rate and particle strength. The Q refers to the static strain rate determined by to critical strain rate/> The linear weakening relationship of the size effect, the critical strain rate at which the size effect disappears/> Determined by single grain strength test. The single particle dynamic strength model is an improvement of the Weibull distribution static strength size effect formula (4), adding the growth relationship P of the rate effect intensity and the weakening relationship Q of the size effect.

In the formula, σ _s is the static strength of the particles.

Step 2: Based on the single particle dynamic strength model proposed in the first step, establish the stress and strain tensor relationship of the rockfill aggregate, see formulas (7a) and (7b).

The method for establishing the stress and strain tensor relationship of particle aggregates is as follows:

The relationship between the stress σ _ij and the strain tensor ε _ij of the particle aggregate in the three-dimensional state is as follows:

Among them, V _σ is the total volume of the calculated stress area, f _(c/p) is the external force on the particle p at any contact point c in the area, and l _(c/p) is the branch vector of the contact point pointing to the center of the particle p. V _ε is the volume corresponding to the area where the strain is calculated, Δu ^e is the relative displacement of the centers of the two particles p and q that constitute the edge e, and d ^e is the area compensation vector corresponding to the edge e.

Assume that the prototype full-scale pr and scaled-scale sc specimens have similar gradations, and the corresponding characteristic dimensions are _dpr and _dsc . The two specimens, scaled-scale and full-scale, have the same contact state and pore distribution, that is, the geometric state of the aggregate is the same. , when the broken state of the scaled and full-scale specimens is the same, according to the particle dynamic strength formula, the stress of the full-scale specimen σ _pr and the stress of the scaled specimen σ _sc are related to the full-scale contact force f _pr and the scaled contact force f _sc satisfy

Among them, P _pr and P _sc represent the stress increase relationship of the full-scale and reduced-scale strain rate effects respectively, and Q _pr represents the weakening relationship of the full-scale size effect. At the same time, according to the size proportional relationship between the branch vector l _(c/p) , the volume V, the area compensation vector d ^e and the relative displacement Δu ^e , the stress tensor σ _ij,sc of the scaled specimen under dynamic load and the full-scale specimen are obtained. The stress tensor σ _ij,pr of the specimen, the strain tensor ε _ij,sc of the scaled specimen and the strain tensor ε _ij,pr of the full-scale specimen satisfy the following relationship:

εij _,pr =εij _,sc (7b)

The above-mentioned relationship between the stress and strain tensors of particle aggregates shows that in the same crushing state, the stress tensors of samples of different sizes need to consider the influence of dynamic size effects, while the strain tensors are the same.

Step 3: Derive the size effect of the maximum dynamic modulus E _dmax from the stress and strain tensor relationships of specimens of different sizes. Due to the dynamic triaxial load application method, the consolidation stress only has a static size effect, and the dynamic stress needs to calculate the dynamic size effect affected by the strain rate.

The method for deriving the size effect of the maximum dynamic modulus E _dmax is as follows:

The dynamic stress and dynamic strain skeleton in the Hardin-Drnevich model has a hyperbolic relationship. For scaled dynamic stress σ _d,sc and dynamic strain ε _d,sc, and full-scale dynamic stress σ _d,pr and dynamic strain ε _d,pr are:

Among them, a _sc and b _sc are the scaled dynamic stress and strain parameters, a _pr and b _pr are the full-scale dynamic stress and strain parameters. According to the scaling relationship of (8a) and (8b), the crushing of the scaled and full-scale samples is consistent. When , the internal dynamic stress satisfies The strain tensor is consistent, so we have:

It can be seen from (9) that if the equation holds under any dynamic strain, the dynamic stress and strain parameters a and b satisfy:

E _dmax =1/a, the relationship between the maximum dynamic modulus of scaled and full-scale specimens is:

The modified equivalent viscoelastic model assumes that E _dmax and the mean principal stress σ _m have the following relationship:

Among them, K and n are the maximum dynamic modulus coefficient and index respectively, pa is the atmospheric pressure, σ _m = (2+K _c )σ ₃ /3, and K _c is the consolidation stress ratio. The consolidation stress σ _m only needs to consider the static size effect, and the scaled-scale consolidation stress tensor σ _m,sc and the full-scale consolidation stress tensor σ _m,pr satisfy At this time, P and Q are both 1, and then from (11) (12) we can get:

Among them, E _dmax,pr is the maximum dynamic modulus of full scale, K _sc and K _pr are the maximum dynamic modulus coefficients of scale and full scale respectively, n _sc and n _pr are the maximum dynamic modulus of scale and full scale respectively. Quantitative index, if (13a) and (13b) are equal, the relationship between the maximum dynamic modulus parameters of scaled and full-scale specimens is:

n _sc = n _pr (14a)

The derivation of the size effect of the maximum dynamic modulus E _dmax determines that the maximum dynamic modulus index n has no size effect, and the maximum dynamic modulus coefficient K of scaled and full-scale specimens satisfies the relationship (14b).

Step 4: Derive the size effect relationship of the dynamic modulus ratio E _d /E _dmax and the damping ratio λ _d curve from the equivalent stress and strain tensor relationships of specimens of different sizes.

The method for deriving the size effect of the dynamic modulus ratio E _d /E _dmax and the damping ratio λ _d curve is as follows:

The expression of the dynamic modulus ratio in the equivalent viscoelastic model is:

Among them, ε _d,r is the reference axial strain, ε _d,r =σ _dmax /E _dmax =a/b, so the full-scale reference axial strain and scale reference axial strain/> have:

The relationship between the scaled dynamic modulus ratio E _d,sc /E _dmax,sc and the full-scale specimen dynamic modulus ratio E _d,pr /E _dmax,pr is:

Since λ _d /λ _dmax = 1-E _d /E _dmax and λ _dmax is a constant, the scaled damping ratio λ _d,sc and the full-scale damping ratio λ _d,pr satisfy:

λ _d,pr =λ _d,sc (18)

The derivation determines that neither the dynamic modulus ratio E _d /E _dmax nor the damping ratio λ _d curve is affected by size effects.

The beneficial effects of the present invention are:

1. The present invention combines single particle strength tests and dynamic triaxial tests to deduce the size effect of dynamic deformation of rockfill materials. Based on single particle strength tests of different sizes and strain rates, a dynamic strength calculation model is proposed. The equivalent stress tension of the aggregate is The dynamic strength size effect of single particle strength is introduced into the quantity and strain tensor, and the size effect rules of the maximum dynamic modulus E _dmax , dynamic modulus ratio E _d /E _dmax and damping ratio λ _d curve in the equivalent viscoelastic model are determined, giving The correction relationship between the maximum dynamic modulus coefficient K of the indoor scale and the full scale of the prototype is given.

2. Compared with the expensive and time-consuming ultra-large triaxial test, the present invention only needs to conduct the dynamic strength test and conventional dynamic triaxial test of single particle strength. The single particle strength mainly obtains the relationship between dynamic strength factor and strain rate and strength. The size effect attenuates with the strain rate, and then based on the conventional dynamic triaxial test results, the dynamic constitutive model parameters corrected for the size effect can be obtained.

3. The present invention has a clear derivation logic for the size effect of the dynamic deformation of the rockfill material, and clarifies the stress and deformation rules caused by the scale of the rockfill material. Using the constitutive model parameters modified by the size effect can improve the finite element calculation of the dynamic deformation of the rockfill dam. Accuracy, providing reference for earth-rock dam engineering design and safety evaluation.

Description of drawings

Figure 1 is a fitting relationship between the static strength and particle size of particles in Example 1 of the present invention.

Figure 2 is a fitting relationship between the particle strength and strain rate increase of Example 1 of the present invention.

Figure 3 shows the weakening relationship of particle strength size effect in Example 1 of the present invention.

Detailed ways

The specific embodiments of the present invention will be described in detail below with reference to the technical solutions and drawings.

In this embodiment, a certain rockfill material whose parent rock is red rock is used as an example to determine the size effect of dynamic deformation.

The first step is to select particles in the size range of 20 to 200mm and conduct static strain rate strength tests to determine the static size effect - n _d /m. Figure 1 shows the fitting relationship between the static strength and size of rockfill particles. Select particles in the size range of 40 to 60 mm and conduct particle crushing tests with different strain rates. Figure 2 shows the fitting relationship between the strength of rockfill material particles as the strain rate increases. Figure 3 shows the size effect weakening relationship Q, and establishes a single particle dynamic strength model. .

Among them, the static strain rate is 10 ^-5 s ^-1 . The critical strain rate can be obtained according to the test Figure 3 of different strain rates/> is 10 ^-1 s ^-1 .

In the second step, based on the single particle dynamic strength model proposed in the first step, the stress tensor σ _ij,sc of the particle aggregate scaled specimen and the stress tensor σ _ij,pr of the full-scale specimen are established, which are consistent with the scaled specimen. The strain tensor ε _ij,sc of the specimen and the strain tensor ε _ij,pr of the full-scale specimen satisfy the following relationship:

εij _,pr =εij _,sc

The third step is to derive the maximum dynamic modulus index n _sc and n _pr of scale and full scale, and the maximum dynamic modulus coefficient of scale and full scale based on the equivalent stress and strain tensor relationship of samples of different sizes in the second step. The relationship between K _sc and K _pr is:

_nsc = _npr

The maximum dynamic modulus index n has no size effect and does not require correction. When correcting the maximum dynamic modulus coefficient K of scaled and full-scale specimens, It is advisable that the average strain rate of indoor dynamic triaxial testing is about 10 ^-3 s ^-1 ,/> It is determined based on the ratio of the on-site seismic frequency and the dynamic triaxial frequency. For example, if the on-site frequency is 3Hz and the dynamic triaxial frequency is generally 0.3Hz, then d _pr /d _sc is the ratio of the on-site rockfill particle size to the test particle size. If the maximum on-site rockfill particle size is 600mm and the maximum particle size of the conventional dynamic triaxial axis is 60mm, then d _pr /d _sc = 10, K _sc and n _sc are obtained from conventional dynamic triaxial tests, and finally the corrected ratio K _pr /K _sc of the maximum dynamic modulus coefficient K at full scale on site can be obtained.

The fourth step is to derive the size effect of the dynamic modulus ratio E _d /E _dmax and the damping ratio λ _d curve based on the equivalent stress and strain tensor relationship of samples of different sizes in the second step. In this embodiment, the dynamic modulus ratio E _d /E _dmax and the damping ratio λ _d 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)。