CN111159794A - Geometric damage rheological analysis method for mechanical properties of multi-fracture rock sample - Google Patents
Geometric damage rheological analysis method for mechanical properties of multi-fracture rock sample Download PDFInfo
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Abstract
The invention belongs to the field of civil engineering, and particularly relates to a geometric damage rheological analysis method for mechanical properties of a multi-fracture rock sample. The method comprises the following steps: (1) constructing a geometric model of a representative unit of the multi-fracture rock sample; (2) defining the damage tensor of the representative unit of the multi-fracture rock sample; (3) calculating the damage tensor of a single set of fractures in the multi-fracture rock sample; (4) calculating the damage tensor of a plurality of groups of fractures in the multi-fracture rock sample; (5) deducing an effective stress formula of the multi-fracture rock sample; (6) establishing a geometric damage rheological constitutive model of the multi-fracture rock sample; (7) programming a geometric damage rheological constitutive model of the multi-fracture rock sample; (8) and counting the geometric fracture parameters of the engineering rock mass, and carrying out numerical simulation on the damage rheological property of the engineering rock mass.
Description
Technical Field
The invention belongs to the field of civil engineering geotechnical engineering, and particularly relates to a geometric damage rheological analysis method for mechanical properties of a multi-fracture rock sample.
Background
The cracks are widely distributed in the rock mass and have important influence on the stability of the rock mass structure, and how to evaluate the damage influence of the multi-crack rock mass, particularly the long-term behavior of the rock mass, is an important problem. Understanding the mechanical properties of multi-fractured rock masses is important in rock engineering design, including foundations, slopes, or underground excavations in rock.
Previous studies on the mechanical behavior of fracture-containing specimens have focused primarily on crack propagation and polymerization. Some studies have investigated fracture polymerization between fractures using laboratory tests, and in addition, a number of numerical methods have been proposed to simulate crack initiation and polymerization. However, these studies have focused mainly on crack propagation and aggregation of rock specimens without analysis of the stability of the engineering project, as these results are difficult to use to predict the mechanical behavior of the primary jointed fractured rock mass.
Most rock masses contain multiple sets of fractures. If a rock mass comprises a number of cracks of relatively small dimensions compared to the structure, the rock mass can be idealized as a continuous body. However, when medium-sized discontinuities are present, this effect becomes important for the mechanical behaviour of the rock mass, since these discontinuities are very complex and their mechanical effect cannot be estimated in a simple manner. In this case, injury mechanics is an effective way to solve this problem.
Therefore, the invention provides a geometric damage rheological analysis method for the mechanical property of a multi-fracture rock mass sample. The method is used for comprehensively considering the influence of damage and rheology aiming at a rock sample containing a plurality of groups of cracks, and establishing a damage rheology model of the jointed rock mass, wherein the damage rheology model can predict viscoelastic strain corresponding to initial creep characteristics, viscoplastic strain corresponding to steady-state creep characteristics and damage strain reflecting the damage effect of the cracks on the rock mass. Deducing a viscoelastic-plastic damage constitutive model based on the mycoplasma model, and using finite difference software FLAC3DProgramming is performed.
The current research situation of the mechanical properties of the domestic related multi-fracture rock sample is as follows:
1. the preliminary research on equivalent damage rheological model of jointed rock mass assumes that the rock is isotropy damage of isotropy body, normal damage and tangential damage of a joint surface are different, and the evolution functions of rheological damage of the rock and the joint surface are respectively established. Assuming the situation that the material is not damaged, effective stress is adopted for calculating stress, a finite element calculation formula of an equivalent damage rheological model of the jointed rock mass is deduced, and a corresponding finite element program is compiled (see 'rock and soil mechanics' 2011, 12 th period, authors: yellow flare and the like);
2. the three-dimensional damage rheological analysis for deformation and fracture of surrounding rock of a silk screen primary hydropower station adopts a three-dimensional model and an analysis method of damage rheological coupling, combines an additional deformation analysis method generated by crack opening, analyzes the stability of a cavern group of an engineering underground powerhouse, and performs predictive analysis on long-term aging deformation of the cavern (see the report on rock mechanics and engineering in 2012, 5 th period, authors: Zhu Wei Shen, Zincianlian, and the like).
Disclosure of Invention
One of the more difficult places to study the mechanical behavior of multi-fracture rock-like samples is to correlate the time-dependent deformation with the effects of damage caused by the distribution of fractures in the rock mass. The invention provides a geometric damage rheological analysis method for mechanical properties of a multi-fracture rock sample by adopting a damage and rheological coupling method.
The geometric damage rheological analysis method of the mechanical property of the multi-fracture rock sample comprises the following steps:
(1) constructing a geometric model of a representative unit of the multi-fracture rock sample;
(2) defining the damage tensor of the representative unit of the multi-fracture rock sample according to the hypothesis of the distribution fracture in the sample;
(3) calculating the damage tensor of a single set of fractures in the multi-fracture rock sample;
(4) after determining the normal vector and the damage tensor of the unit, calculating the damage tensor of a plurality of groups of fractures in the multi-fracture rock sample by summing the unit;
(5) deducing an effective stress formula of the multi-fracture rock sample;
(6) comprehensively considering the influence of damage and rheology, and establishing a geometric damage rheology constitutive model of the multi-fracture rock sample;
(7) programming a geometric damage rheological constitutive model of the multi-fracture rock sample;
(8) and counting the geometric fracture parameters of the engineering rock mass, and carrying out numerical simulation on the damage rheological property of the engineering rock mass.
Compared with the prior art, the invention has the following beneficial effects:
1. the rheological phenomenon and the influence of the existence of cracks in the rock mass are comprehensively considered, and the mechanical property of the multi-crack rock mass can be better analyzed;
2. the damage rheological model can predict the viscoelasticity strain corresponding to the initial creep characteristic, the viscoelasticity strain corresponding to the steady-state creep characteristic and the damage strain reflecting the damage effect of the crack on the rock mass, and can predict the displacement and the damage zone of the rock mass around the underground cavern by utilizing the model;
3. the method can be applied to excavation of underground caverns, analyzes the stability of the underground caverns, has strong feasibility, and can be used for guiding actual engineering construction.
Drawings
FIG. 1 is a process flow diagram of a damage rheology model;
FIG. 2 is a schematic diagram of the effective area of a rock mass;
FIG. 3 is an observation schematic diagram of a rock mass surface fracture;
FIG. 4 is a schematic diagram of a unit normal vector of an arbitrary discontinuous surface;
FIG. 5 is a statistical representation of the number of fractures;
fig. 6 is a schematic diagram of a subterranean chamber in a multi-fractured rock mass.
Detailed Description
The geometric damage rheological analysis method of the mechanical property of the multi-fracture rock sample comprises the following specific steps:
1. the method comprises the following steps of (1) constructing a geometric model of a representative unit of the multi-fracture rock sample, wherein the specific method comprises the following steps:
the invention provides a second-order damage tensor to represent the damage state of a rock body with a plurality of plane fissures:
where Ω represents the areal density of a set of fractures, n is the unit vector perpendicular to the joint,
the tensor product is represented.
2. Defining the damage tensor of the representative unit of the multi-fracture rock sample by the following specific method:
the following assumptions were made about the fractures distributed in the rock mass:
1) the cracks are all planar;
2) rock mass consists of cells of intact rock, with fissures at the boundaries of the cells. The fracture will propagate along the surface and cannot penetrate into the cell, while the intact rock material yields;
3) the size of the rock mass is determined by the average fracture spacing;
4) only the influence of initial damage is considered, and the reduction of the effective area of the rock mass section is a main factor causing the deterioration of rock mass parameters.
If upsilon and V are the volumes of the cell body and the rock mass, respectively, the total effective area is defined by replacing the cell with an equivalent cube having the same volume:
wherein l is upsilon1/3。
Suppose there are N fractures in a rock mass, where the k-th fracture has an area akAnd unit normal nk. For this fracture, the areal density of the fracture is:
the damage tensor of the fracture can then be defined in the form:
summing all the N fractures after calculation through equation (4), and obtaining the damage tensor of the rock body V as follows:
3. calculating the damage tensor of a single set of fractures in the multi-fracture rock sample by the following specific method:
as shown in FIG. 4, if a set of cracks are respectively in the coordinate plane X1，X2，X3Has a theta1，θ2，θ3The angle of magnitude is such that the unit normal vector n of the set is equal to (n)1n2n3)：
n＝(n1n2n3)t＝(λcosθ1cosθ2λsinθ1sinθ2-λcosθ1sinθ2)t
λ＝(sin2θ1sin2θ2+cos2θ1sin2θ2+cos2θicos2θ2)-1/2(6)
Can also be expressed as:
n＝(n1n2n3)t＝(-λcosθ2sinθ3λcosθ2cosθ3λsinθ2sinθ3)t
λ＝(sin2θ2sin2θ3+cos2θ2sin2θ3+cos2θ2cos2θ3)-1/2(7)
or
n＝(n1n2n3)t＝(λsinθ3sinθ1-λcosθ3sinθ1λcosθ3cosθ1)t
λ＝(sin2θ3sin2θ1+cos2θ3sin2θ1+cos2θ3cos2θi)-1/2(8)
For each angle, the following relationship exists:
wherein (i, j, k) ═ 1, 2, 3), (2, 3, 1), (3, 1, 2).
If X of cubic unit1、X2、X3The surfaces respectively contain N1、N2And N3And (4) cutting into cracks. Assuming that one of the surfaces contains a minimum number of cracks, e.g. X3Then we rotate the cube cell so that the unit normal vector n of the set of fissures is with the new axis X'3Superposed on each other as shown in FIG. 5, i.e. the surface X'3Containing a minimum number of fractures. Along X'1The number of axial fissures was estimated as:
wherein N'1Is X'1Number of cracks in the face, L'2Is X'2Average length of cracks appearing on the face.
Likewise, along X'2Axis we can get:
the number of fissures in this cube can then be estimated as:
the average surface area of the fractures was:
by unit normal vector we can get:
it is known that:
L′1L′2＝L1L2(15)
the number of fissures in the cube is then:
substituting the formulas (13), (15) and (16) into the formula (5) to obtain a group of fracture damage tensors:
for the general case there are:
Ni＞Nj＞Nk(18)
then the single set of lesion tensors is deduced as:
4. after determining the normal vector and the damage tensor of the unit, calculating the damage tensors of the multiple groups of fractures by summing the unit, wherein the specific method comprises the following steps:
if there are N sets of rules and ΩiIf the set i is the damage tensor, the global damage tensor can be obtained as follows:
if the fractures are randomly distributed, the global damage tensor can be written as:
where I is the identity matrix.
If the unit normal vector of a fracture is parallel to the unit vector n ═ n (n)1，n2，n3) Then the damage tensor is expressed as:
5. the effective stress formula of the multi-fracture rock sample is deduced, and the specific process is as follows:
because the reduction in effective area is due to the distribution of the fissures, there are:
where σ is the Cauchy stress,
is the effective stress, the superscript "-1" indicates the inverse matrix. The conversion law of Cauchy stress to effective stress represents the mechanical effect of the damage. Equation (23) may be further expressed as:
equation (24) can be simplified and expressed as:
wherein:
the effective stress is given by:
the constitutive equation is expressed as:
where Φ is a function of the constitutive equation and ε is the strain tensor.
6. Comprehensively considering the influence of damage and rheology, establishing a multi-fracture rock sample geometric damage rheology constitutive model, and the specific method comprises the following steps:
and selecting a western original model to simulate the rheological property of the multi-fracture rock sample. The Western model may simulate a steady creep deformation phase at low stress levels, and an unsteady creep deformation phase at high stress levels.
The constitutive equation of the western primitive model is as follows:
when sigma is less than or equal to sigmasWhen the temperature of the water is higher than the set temperature,
when σ > σsWhen the temperature of the water is higher than the set temperature,
where σ and ε are the total stress and total strain, respectively. E0，E1，η1，η2Is the viscoelastic parameter of the model.
According to the strain equivalent principle, the damage effect is simulated by converting Cauchy stress into effective stress, so that a one-dimensional original viscoelastic-plastic damage flow constitutive equation can be obtained.
The rheological constitutive equation of the one-dimensional western original viscoelastic-plastic damage is expressed as follows:
when in use
When the temperature of the water is higher than the set temperature,
when in use
When the temperature of the water is higher than the set temperature,
7. programming a geometric damage rheological constitutive model of the multi-fracture rock sample.
8. According to the actual engineering, the geometric fracture parameters of the engineering rock mass, such as an inclination angle and a joint length, are counted, and the damage rheological property numerical simulation of the engineering rock mass is carried out by utilizing the damage rheological model and the numerical calculation software.
Claims (9)
1. The geometric damage rheological analysis method of the mechanical property of the multi-fracture rock sample comprises the following specific steps:
(1) constructing a geometric model of a representative unit of the multi-fracture rock sample;
(2) defining the damage tensor of the representative unit of the multi-fracture rock sample;
(3) calculating the damage tensor of a single set of fractures in the multi-fracture rock sample;
(4) calculating the damage tensor of a plurality of groups of fractures in the multi-fracture rock sample;
(5) deducing an effective stress formula of the multi-fracture rock sample;
(6) establishing a geometric damage rheological constitutive model of the multi-fracture rock sample;
(7) programming a geometric damage rheological constitutive model of the multi-fracture rock sample;
(8) and counting the fracture geometric parameters of the engineering rock mass, and carrying out numerical simulation on the damage rheological property of the engineering rock mass.
2. The geometric damage model analysis method based on the mechanical properties of the multi-fracture rock mass according to claim 1, characterized in that a geometric model of a representative unit of the multi-fracture rock sample is constructed by the following specific method: establishing a second-order damage tensor, namely:
in the formula: omega is the area density of a set of fractures, n is the unit normal vector of a fracture, and
the tensor product is represented.
3. The geometric damage model analysis method based on the mechanical properties of the multi-fracture rock sample as claimed in claim 1, wherein a damage tensor of a representative unit of the multi-fracture rock sample is defined by the following specific method: assuming that V and V are the volumes of the unit body and the rock body respectively and N cracks are arranged in V, the area of the kth crack is akIts unit normal vector is nkFor the kth fracture, the damage tensor can be defined in the form:
wherein l ═ v1/3。
Considering all the N fractures, the damage tensor of the representative unit of the multi-fracture rock sample can be obtained as follows:
4. the geometric damage model analysis method based on the mechanical properties of the multi-fracture rock sample as claimed in claim 1, wherein the damage tensor of a single set of fractures in the multi-fracture rock sample is calculated by the following specific method: for a multi-fracture rock sample with a single-group fracture, the geometric damage tensor is as follows:
in the formula, NiIs XiNumber of cracks on the surface, NjIs XjNumber of cracks on the surface, LiIs XiAverage length of fissures on the surface, LjIs XjAverage length of fissures on the face.
The unit normal vector n of any crack surface is equal to (n)1n2n3) Comprises the following steps:
n＝(n1n2n3)t＝(λcosθ1cosθ2λsinθ1sinθ2-λcosθ1sinθ2)t
λ＝(sin2θ1sin2θ2+cos2θ1sin2θ2+cos2θ1cos2θ2)-1/2
meanwhile, the unit normal vector can also be expressed as follows:
n＝(n1n2n3)t＝(-λcosθ2sinθ3λcosθ2cosθ3λsinθ2sinθ3)t
λ＝(sin2θ2sin2θ3+cos2θ2sin2θ3+cos2θ2cos2θ3)-1/2
or:
n＝(n1n2n3)t＝(λsinθ3sinθ1-λcosθ3sinθ1λcosθ3cosθ1)t
λ＝(sin2θ3sin2θ1+cos2θ3sin2θ1+cos2θ3cos2θ1)-1/2
wherein theta is1，θ2And theta3To sit onLabel surface X1，X2，X3The angle of the upper cleft.
5. The method for analyzing the geometric damage model based on the mechanical properties of the multi-fracture rock sample according to claim 1, wherein the damage tensor of a plurality of groups of fractures in the multi-fracture rock sample is calculated by the following specific method:
if there are N sets of fractures, Ωi(i 1, 2.. N) is the damage tensor for the ith set of fractures, giving a global damage tensor:
if the fractures are randomly distributed, the global damage tensor is written as:
where I is the identity matrix.
If the normal direction of the slit cell is parallel to the unit vector n ═ n (n)1n2n3) Then the damage tensor is expressed as:
6. the method for analyzing the geometric damage model based on the mechanical properties of the multi-fracture rock sample according to claim 1, wherein an effective stress formula of the multi-fracture rock sample is derived by the following specific method:
due to the distribution of the fractures, the effective area is reduced and the effective stress is expressed as:
wherein, σ is the Cauchy stress,
is the effective stress, I is the identity matrix, and the superscript "-1" indicates the inverse matrix.
The constitutive equation of the multi-fracture rock sample is expressed as follows:
the effective stress can be expressed in particular as:
7. the method for analyzing the geometric damage model based on the mechanical properties of the multi-fracture rock sample as claimed in claim 1, wherein the geometric damage rheological constitutive model of the multi-fracture rock sample is established by the following specific method:
the rheological constitutive equation of the one-dimensional Western primitive model is as follows:
when sigma is less than or equal to sigmasWhen there is
When σ > σsWhen there is
Replacing the Cauchy stress sigma in the above formula by
A rheological constitutive equation considering geometric damage is obtained.
8. The method for analyzing the geometric damage model based on the mechanical properties of the multi-fracture rock sample according to claim 1, wherein the geometric damage rheological constitutive model of the multi-fracture rock sample is programmed by the following specific method:
the geometric damage tensor is programmed in finite difference software or finite element software.
9. The geometric damage model analysis method based on the mechanical properties of the multi-fracture rock sample according to claim 1, is characterized in that the fracture geometric parameters of the engineering rock mass are counted, and the damage characteristic numerical simulation of the engineering rock mass is carried out, and the specific method is as follows:
and (3) carrying out statistics on the fracture geometric parameters of the engineering rock mass, such as an inclination angle and a fracture length, carrying out calculation analysis on the engineering rock mass deformation by using the established geometric damage model, and predicting the displacement of the engineering rock mass after excavation construction.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113361099A (en) * | 2021-06-04 | 2021-09-07 | 河北工业大学 | Fractured rock mass simulation method and system |
| CN114299239A (en) * | 2022-02-10 | 2022-04-08 | 煤炭科学研究总院有限公司 | Tensor determination method and equipment for rock natural fracture structure |
| CN114689448A (en) * | 2020-12-30 | 2022-07-01 | 中国石油大学(华东) | Damage fracture analysis method for opening fracture, compacting, closing and timely and effectively expanding |
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2018
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114689448A (en) * | 2020-12-30 | 2022-07-01 | 中国石油大学(华东) | Damage fracture analysis method for opening fracture, compacting, closing and timely and effectively expanding |
| CN113361099A (en) * | 2021-06-04 | 2021-09-07 | 河北工业大学 | Fractured rock mass simulation method and system |
| CN114299239A (en) * | 2022-02-10 | 2022-04-08 | 煤炭科学研究总院有限公司 | Tensor determination method and equipment for rock natural fracture structure |
| CN114299239B (en) * | 2022-02-10 | 2022-05-31 | 煤炭科学研究总院有限公司 | Tensor determination method and equipment for rock natural fracture structure |
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