CN112949065A - Double-scale method, device, storage medium and equipment for simulating mechanical behavior of layered rock mass - Google Patents

Double-scale method, device, storage medium and equipment for simulating mechanical behavior of layered rock mass Download PDF

Info

Publication number
CN112949065A
CN112949065A CN202110240440.4A CN202110240440A CN112949065A CN 112949065 A CN112949065 A CN 112949065A CN 202110240440 A CN202110240440 A CN 202110240440A CN 112949065 A CN112949065 A CN 112949065A
Authority
CN
China
Prior art keywords
simulating
layered
scale
mechanical behavior
model
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202110240440.4A
Other languages
Chinese (zh)
Other versions
CN112949065B (en
Inventor
卢波
邬爱清
徐栋栋
汪斌
胡伟
向前
刘小红
曾平
王复兴
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Changjiang River Scientific Research Institute Changjiang Water Resources Commission
Original Assignee
Changjiang River Scientific Research Institute Changjiang Water Resources Commission
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Changjiang River Scientific Research Institute Changjiang Water Resources Commission filed Critical Changjiang River Scientific Research Institute Changjiang Water Resources Commission
Priority to CN202110240440.4A priority Critical patent/CN112949065B/en
Publication of CN112949065A publication Critical patent/CN112949065A/en
Application granted granted Critical
Publication of CN112949065B publication Critical patent/CN112949065B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/14—Force analysis or force optimisation, e.g. static or dynamic forces

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)

Abstract

The invention provides a double-scale method, a device, a storage medium and equipment for simulating mechanical behavior of layered rock mass, and belongs to the technical field of rock-soil mechanics. The method comprises the following steps: acquiring a geometric model for simulating a rock engineering structure; in a geometric model for simulating a rock engineering structure, layers with the distance between layers being meter-scale are explicitly incorporated into a calculation model, and a block system in a discontinuous deformation analysis method is obtained; aiming at each individual in the discontinuous deformation analysis method, a COSSERAT layered model is adopted to carry out implicit simulation on the level of centimeter-level scales contained in the COSSERAT layered model in a macroscopic equivalent mode; and performing solving analysis under a discontinuous deformation analysis frame to obtain the mechanical behavior parameters of the simulated layered rock mass, wherein the mechanical behavior parameters of the simulated layered rock mass comprise displacement, strain and stress. The apparatus, storage medium, and device can be used to implement the method. Which enables a more accurate and efficient simulation of layered rock masses.

Description

Double-scale method, device, storage medium and equipment for simulating mechanical behavior of layered rock mass
Technical Field
The invention relates to the technical field of rock-soil mechanics, in particular to a double-scale method, a device, a storage medium and equipment for simulating mechanical behavior of layered rock mass.
Background
The sedimentary rock is widely distributed on the superficial part of the earth crust, and is characterized in that a group of parallel or nearly parallel layers with good extensibility, stable occurrence and unequal intervals develop, thereby forming a specific stratified rock mass structure. The bedding surface causes the deformation and strength characteristics of the stratified rock body to show remarkable anisotropy and is a control factor influencing the deformation and stability of the engineering structure. The laminated rock mass is divided into a thin layer (<10cm), a mutual layer (30-10 cm), a medium thick layer (50-30 cm), a thick layer (100-50 cm) and a huge thick layer (>100cm) according to the distance between layers, namely the layer thickness; exposed parts of the thin layer and interbedded rock mass are weak links which are mainly concerned by engineering. Numerical simulation is an indispensable important means for quantitatively evaluating the stability of an engineering structure, although in recent years, with the rapid improvement of the software and hardware level of a computer, a numerical method is rapidly developed and makes great progress; however, effective mechanical simulation of the extensively developed bedding surface with centimeter-level spacing in the stratified rock mass still cannot be well solved, and the mechanical behavior of the stratified rock mass is still a hotspot of research.
However, because the objective difference between the bedding surface spacing scale and the engineering structure characteristic dimension is limited by the calculation scale and the solving efficiency, it is difficult to truly simulate each bedding surface actually existing in the stratified rock mass no matter based on the continuous medium mechanics analysis method or the discrete medium mechanics analysis method.
Disclosure of Invention
In view of the above, the invention provides a double-scale method, device, storage medium and equipment for simulating the mechanical behavior of a layered rock mass, which are based on a discontinuous deformation analysis method and a cossera theory to establish a continuous-discontinuous coupling double-scale model, so that more accurate and efficient simulation of the layered rock mass can be realized, and the method is more practical.
In order to achieve the first object, the technical scheme of the double-scale method for simulating the mechanical behavior of the layered rock mass provided by the invention is as follows:
the double-scale method for simulating the mechanical behavior of the layered rock mass comprises the following steps of:
acquiring a geometric model for simulating a rock engineering structure;
in the geometric model of the simulated rock engineering structure, explicitly incorporating the layers with the distance of meter-scale dimension between the layers into a calculation model to obtain a block system in the discontinuous deformation analysis method, wherein the layers with the distance of meter-scale dimension between the layers incorporated into the computer model in the display form a contact boundary between blocks in the discontinuous deformation analysis method;
for each individual in the discontinuous deformation analysis method, a COSSERAT layered model is adopted to implicitly simulate the level of centimeter-level scales contained in the COSSERAT layered model in a macroscopic equivalent manner;
and performing solving analysis under a discontinuous deformation analysis frame to obtain simulation layered rock mechanical behavior parameters, wherein the simulation layered rock mechanical behavior parameters comprise displacement, strain and stress.
The double-scale method for simulating the mechanical behavior of the layered rock mass can be further realized by adopting the following technical measures.
Preferably, in the step of implicitly simulating a centimeter-scale layer included in each individual in the discontinuous deformation analysis method by using a coserat layered model in a macroscopic equivalent manner, the conditions that the layered rock mass needs to satisfy include:
the stratified rock mass is regarded as a composite structure body formed by periodically repeating the complete rock stratum and the bedding surface of the divided rock stratum;
the rock layer is homogeneous and isotropic;
the bedding plane is flat and parallel to develop, and has the same mechanical property;
the layer intervals are equal and only one group of layers is provided;
both the deformation and the curvature are infinitesimal;
for two-dimensional problems, the planar strain problem is considered.
Preferably, the step of implicitly simulating a centimeter-scale level contained in each individual of the discontinuous deformation analysis method by using a cossera layered model in a macroscopic equivalent manner specifically includes the following steps:
the x 'axis is consistent with the direction of the layer surface, the y' axis is vertical to the layer surface and upwards, and the translational displacement is respectively set as u, v and omegacFor rotational displacement, the strain and curvature κ in the global coordinate systemxIs composed of
Figure BDA0002961919740000031
Figure BDA0002961919740000032
Figure BDA0002961919740000033
Under normal conditions
Figure BDA0002961919740000034
From this, ε is knownxy≠εyx；
Considering the balance between the infinitesimal physical strength and the couple, the balance equation is as follows
Figure BDA0002961919740000041
Figure BDA0002961919740000042
Figure BDA0002961919740000043
In the above formula fx,fy,m,mxVolume force and volume force couple, respectively, where the material is considered here to be uniform in the direction of the layer plane, so myVanishing, balance of only mx(ii) present;
the boundary conditions may be expressed as:
σxnx+σyxny＝Px (3a)
σxynx+σyny＝Py (3b)
mxnx+myny＝M (3c)
in the above formula Px、PyM is the upper and lower force couple of the known boundary, nx、nyFor the outside boundary normal unit vector component, the constitutive equation is expressed as
σx＝A11ε′x+A12ε′y (4a)
σy＝A21ε′x+A22ε′y (4b)
σyx＝C11ε′yx+C12ε′xy (4c)
σxy＝C21ε′yx+C22ε′xy (4d)
mx＝Bκx′ (4e)
Of the above formula is epsilon'x、ε′y、ε′yx、ε′xy、κx' strain and curvature under local coordinate system, respectively;
the elastic matrix D in the global coordinate system (wherein the global coordinate system is equal to the geodetic coordinate system) can be selected from the elastic matrix D in the local coordinate system*To obtain
D＝CTD*C (5)
In the above formula
Figure BDA0002961919740000051
And C is a transformation matrix;
for the layered material, the elastic constants in the formula (6) are respectively
Figure BDA0002961919740000052
Figure BDA0002961919740000053
Figure BDA0002961919740000054
For the relation between the shearing stress and the shearing strain and between the even stress and the curvature of the laminated material is
Figure BDA0002961919740000055
Figure BDA0002961919740000056
C22＝C11+G (8c)
Figure BDA0002961919740000057
In the above formula, G is the formation shear modulus, knIs the normal stiffness of the bedding plane, ksShear stiffness of the bedding plane, B bedding plane spacing, and B bending stiffness.
Preferably, in the geometric model for simulating the rock engineering structure, the layer with the meter-scale distance between layers is explicitly incorporated into the calculation model to obtain the block system in the discontinuous deformation analysis method, wherein the step of explicitly incorporating the layer with the meter-scale distance between layers into the computer model to form the contact boundary between blocks in the discontinuous deformation analysis method further comprises the step of varying (u, v) of the blocks in the conventional discontinuous deformation analysis methodTPerforming an expansion to include a rotational displacement wcThe step (2).
Preferably, in the discontinuous deformation analysis method, in the coupling analysis model, the displacement (u, v, w) of any point (x, y) in the bulk is analyzed for discontinuous deformationc)TWherein the rotational displacement wcThe method does not participate in calculation, and the discontinuous deformation analysis method is the same as the traditional discontinuous deformation analysis method.
In order to achieve the second object, the technical scheme of the dual-scale device for simulating the mechanical behavior of the layered rock mass provided by the invention is as follows:
the invention provides a double-scale device for simulating the mechanical behavior of a layered rock mass,
the geometric model acquisition module is used for acquiring a geometric model for simulating a rock engineering structure;
the block system construction module in the discontinuous deformation analysis method is used for explicitly incorporating layers with the distance of meter-scale dimension between layers in the geometric model of the simulated rock engineering structure into a calculation model to obtain a block system in the discontinuous deformation analysis method, wherein the layers with the distance of meter-scale dimension between the layers which are explicitly incorporated into the computer model form a contact boundary between blocks in the discontinuous deformation analysis method;
the COSSERAT simulation module is used for carrying out implicit simulation on the level of centimeter-level scales contained in each individual in the discontinuous deformation analysis method by adopting a COSSERAT layered model in a macroscopic equivalent mode;
and the mechanical behavior parameter solving and analyzing module is used for solving and analyzing under a discontinuous deformation analysis frame to obtain the mechanical behavior parameters of the simulated layered rock mass, wherein the mechanical behavior parameters of the simulated layered rock mass comprise displacement, strain and stress.
In order to achieve the third object, the invention provides a computer-readable storage medium having the following technical solutions:
the present invention provides a computer-readable storage medium having stored thereon a control program for a dual-scale method for simulating a layered rock mechanical behavior, the control program for a dual-scale method for simulating a layered rock mechanical behavior implementing the steps of the dual-scale method for simulating a layered rock mechanical behavior as set forth in any one of claims 1 to 5 when executed by a processor.
In order to achieve the fourth object, the present invention provides an electronic device comprising:
the electronic device provided by the invention comprises a memory and a processor, wherein the memory is stored with a control program of a double-scale method for simulating the mechanical behavior of the layered rock, and the control program of the double-scale method for simulating the mechanical behavior of the layered rock realizes the steps of the double-scale method for simulating the mechanical behavior of the layered rock according to any one of claims 1 to 5 when being executed by the processor.
The invention takes a discontinuous deformation analysis method as a main program framework, fully exerts the advantages of the discontinuous large deformation contact mechanical behavior of the 'explicit' simulation layer, brings part of the layers into a calculation model in an 'explicit' mode, and the thickness formed by cutting rock mass by the 'explicit' layer brought into the calculation model is m-level; generating a Discontinuous Deformation Analysis (DDA) block by using the layer cutting calculation model with the m intervals to form a basic framework of the layered rock; for a DDA block with the thickness of m levels, on the layer surface containing a large number of cm-level intervals, performing macroscopic equivalent simulation by adopting a COSSERAT layered medium model; therefore, a continuous-discontinuous coupling double-scale model is established, and more accurate and efficient simulation of the layered structure rock mass can be realized. The method can fully reflect the influence of the layer surface on the deformation and the strength of the layered structure rock mass, thereby fully reflecting the control effect of the layer surface on the deformation and the stability of the engineering rock mass; meanwhile, all layers are effectively prevented from being brought into a calculation model, and calculation efficiency and solving precision are considered.
Drawings
Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings. In the drawings:
figure 1a shows a simplified schematic diagram of an idealized stratified rock mass in which the bedding spacing is in the order of centimetres;
FIG. 1b is a schematic view of a complete rock without bedding;
FIG. 1c is a schematic view of a discontinuous block model that can be used for DDA analysis;
FIG. 1d is a schematic diagram of a dual scale model based on continuous-discontinuous coupling;
FIG. 2 is a schematic diagram of a trace element model of a layered rock mass under a local coordinate system;
FIG. 3 is a schematic diagram of a relationship between a local coordinate system and a geodetic coordinate system;
fig. 4 is a schematic diagram of a hardware environment of a dual-scale electronic device for simulating a mechanical behavior of a layered rock mass according to an embodiment of the present invention;
FIG. 5 is a flow chart illustrating steps of a dual-scale method for simulating mechanical behavior of layered rock mass according to an embodiment of the present invention;
fig. 6 is a schematic diagram of a signal flow direction relationship between functional modules in a dual-scale device for simulating a layered rock mechanical behavior according to an embodiment of the present invention.
Detailed Description
In view of the above, the invention provides a double-scale method, device, storage medium and equipment for simulating the mechanical behavior of a layered rock mass, which are based on a discrete unit method, discontinuous deformation analysis and a cossera theory developed under a continuous medium mechanical framework, and establish a continuous-discontinuous coupling double-scale model, so that more accurate and efficient simulation of the layered rock mass can be realized, and the method is more practical.
To further illustrate the technical means and effects of the present invention adopted to achieve the predetermined objects, the following detailed description will be given of a dual-scale method, device, storage medium and apparatus for simulating the mechanical behavior of a layered rock mass according to the present invention, with reference to the accompanying drawings and preferred embodiments, and the detailed implementation, structure, features and effects thereof. In the following description, different "one embodiment" or "an embodiment" refers to not necessarily the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.
The term "and/or" herein is merely an association describing an associated object, meaning that three relationships may exist, e.g., a and/or B, with the specific understanding that: both a and B may be included, a may be present alone, or B may be present alone, and any of the three cases can be provided.
When mechanical analysis is carried out on a layered structure rock body, two processing modes of 'implicit' (implicit method) and 'explicit' (explicit method) are adopted for simulation of a layer surface. The 'implicit' processing mode, that is, the layer does not appear directly in the calculation model in the form of a geometric entity, and the mechanical effect is embodied by performing necessary modification on the constitutive model of the rock mass, so that the so-called macroscopic equivalent mechanical model is obtained. The pervasive joint model proposed and widely used by Zienkiewicz et al in 1977 belongs to this category. The essence of the distributed joint model is that when the unit is judged to generate plastic yield, the yield condition along a specific attitude layer is increased; namely, the influence of the bedding surface on the strength characteristic of the rock mass is considered, but the influence of the bedding surface on the deformation characteristic of the rock mass is not considered. The composite constitutive relation of the rock mass with the consideration of the unidirectional and bidirectional orthogonal joints and the oblique joints, which is established based on the homogenization method, does not consider the capability of the rock stratum to resist bending deformation (or damage), and particularly cannot truly reflect the bending deformation condition of the stratified rock mass when high stress gradient is generated.
The other effective way for establishing the stratified rock mass macroscopic equivalent mechanical model is to adopt the COSSERAT theory, the COSSERAT unit bodies have characteristic dimensions, and the influence of the stratified rock mass having macroscopic structure can be considered; therefore, the method has theoretical superiority on the mechanical simulation of the intrinsic structural characteristics of the stratified rock mass. Bogan mathematically demonstrates the feasibility of the cossera model. Adhikary et al examined buckling deformation of stratified slopes and deformation of stratified rock mass underground excavation and compared the joint unit simulation method. Mtihlhaus has developed more systematic research work in applying the COSSERAT theory to geotechnical engineering. R.D. application of COSSERAT theory to carry out research work on three-dimensional simulation of stratified rock mass under finite element architecture. The domestic Chenghhong and the like firstly use the constraint COSSERAT theory to investigate the influence of even stress on the stress of the jointed rock mass; the kudzu repairing and lubricating and the like adopt a constrained rotation COSSERAT medium theory to establish a double-group oblique crossing joint model; the theory and experimental research is carried out on the buckling and dumping damage of the anti-inclination rock stratum by the aid of the Shelving theory and the like; liujun et al studied the even stress theory and its application in stratified rock mass. In general, the cossera stratiform mechanics model has the advantages over the pervasive joint model in that the influence of the bedding plane on the deformation and strength properties of the rock mass can be considered at the same time, and has significant advantages in simulating the bending of the stratified rock mass.
When the layer surface is simulated in an explicit mode, the layer surface directly appears in a calculation model as a real geometric entity; the Goodman unit, the Desai thin layer unit, the Katona contact-friction interface unit and the like in the finite element method belong to special units introduced for simulating the mechanical discontinuities. However, due to the limitations of continuous medium mechanics, it is difficult to simulate a large number of mechanical discontinuities, and the discrete medium mechanics analysis methods represented by the Discrete Element Method (DEM) and the Discontinuous Deformation Analysis (DDA) have natural advantages. In the discrete unit method or DDA, the "explicitly" existing layers then appear as structural planes cut to form the rock mass block system and form the boundaries between the discrete blocks. However, the incorporation of a set of developmental, densely distributed layers in a computational model is also difficult to achieve in practical engineering calculations due to the inherent difficulties and large computational complexity of contact mechanics. Obviously, for many levels, with a centimeter pitch, an "explicit" simulation, whether in the FEM framework or in the DEM or DDA calculation framework, is not practical, but at least uneconomical.
It can be seen from the above research results that it is difficult to truly simulate each layer of the stratified rock mass that actually exists, no matter based on a continuous medium mechanical analysis method or a discrete medium mechanical analysis method, due to the objective difference between the layer spacing dimension and the engineering structure characteristic dimension, and limited by the calculation scale and the solving efficiency. Therefore, for mechanical calculation of engineering structures in layered rock masses, the adoption of a macroscopic equivalent mechanical model is an indispensable effective approach at present. The coserat layered model has significant advantages over the pervasive joint model. However, the current research work on simulating the stratified rock mass by the cossea is carried out under the framework of continuous medium mechanics; the method is limited by inherent limitations of continuous medium mechanics, and discontinuous large deformation characteristics such as opening, slippage and the like of a bedding plane cannot be truly simulated. Therefore, by utilizing the advantages of the DDA method and the COSSERAT theory, a layer cutting calculation model with m-level spacing is considered, and a basic framework of the stratified rock mass is formed; for the rock stratum with the thickness of m levels between the layers (the layer containing cm level), adopting a COSSERAT layered medium model to perform macroscopic equivalent simulation; therefore, a COSSERAT layered mechanical model is realized under the framework of discontinuous deformation analysis, and a continuous-discontinuous coupling double-scale model is established, so that more accurate and efficient simulation of a layered rock mass can be realized.
Simulating the mechanical behavior of layered rock massEmbodiments of the Dual Scale method
The double-scale method for simulating the mechanical behavior of the layered rock mass comprises the following steps of:
(1) firstly, directly establishing a geometric model for simulating a rock engineering structure under the condition of not considering a bedding plane;
(2) a Block Cutting method (Block Cutting) is adopted to 'explicitly' incorporate partial layers into the calculation model, and the distance between the partial layers is m-level scale; thus, a block system in a Discontinuous Deformation Analysis (DDA) method is formed preliminarily; the incorporated levels form the contact boundaries between the DDA blocks;
(3) for each DDA block generated as described above, a coserat layered model is used to perform "implicit" simulation in a macroscopic equivalent manner to simulate the level of cm scale contained inside.
When a macroscopic equivalent mechanical model of a stratified rock mass is established by adopting the COSSERAT theory, the stratified rock mass is generally considered to satisfy the following basic assumptions: firstly, the stratified rock mass is regarded as a composite structure body formed by periodically repeating the complete rock stratum and the bedding surface of the divided rock stratum; the rock layer is homogeneous and isotropic; the bedding surface is straight and develops in parallel and has the same mechanical property; fourthly, the distances among the layers are equal and only one group of layers is provided; the deformation and the curvature are all infinitely small (namely the problem of small deformation); for two-dimensional problems, the planar strain problem is considered.
Let the x 'axis be aligned with the plane direction and the y' axis be perpendicular to the plane direction, the cossert layered medium microelements are shown in fig. 2. For the infinitesimal body shown in FIG. 2, the translational displacements are set as u, v, and ω, respectivelycFor rotational displacement, the strain and curvature κ in the global coordinate systemxIs composed of
Figure BDA0002961919740000121
Figure BDA0002961919740000122
Figure BDA0002961919740000123
Under normal conditions
Figure BDA0002961919740000124
From this, ε is knownxy≠εyxI.e. the strain tensor is asymmetric.
Considering the balance between the infinitesimal physical strength and the couple, the balance equation is as follows
Figure BDA0002961919740000125
Figure BDA0002961919740000131
Figure BDA0002961919740000132
In the above formula fx,fy,m,mxRespectively, volume force and volume force couple. Since the material is considered here to be uniform in the direction of the layer plane, myDisappear, only m in balancexAre present.
The boundary conditions may be expressed as:
σxnx+σyxny＝Px (3a)
σxynx+σyny＝Py (3b)
mxnx+myny＝M (3c)
in the above formula Px、PyM is the upper and lower forces of the known boundary, respectivelyEven, nx、nyIs the outside boundary normal unit vector component. The constitutive equation can be expressed as
σx＝A11ε′x+A12ε′y (4a)
σy＝A21ε′x+A22ε′y (4b)
σyx＝C11ε′yx+C12ε′xy (4c)
σxy＝C21ε′yx+C22ε′xy (4d)
mx＝Bκx′ (4e)
Of the above formula is epsilon'x、ε′y、ε′yx、ε′xy、κx' strain and curvature in a local coordinate system, respectively.
The elastic matrix D in the global coordinate system (in the geodetic coordinate system) can be selected from the elastic matrix D in the local coordinate system*To obtain
D＝CTD*C (5)
In the above formula
Figure BDA0002961919740000141
And C is a transformation matrix, and the relation between the local coordinate system and the global coordinate system is shown in FIG. 3.
For layered materials, the elastic constants in formula (6) are the same as for the conventional continuous medium method, respectively
Figure BDA0002961919740000142
Figure BDA0002961919740000143
Figure BDA0002961919740000144
Adhikary considers that the relationship between shear stress and shear strain and even stress and curvature of the laminated material is
Figure BDA0002961919740000145
Figure BDA0002961919740000146
C22＝C11+G (8c)
Figure BDA0002961919740000147
In the above formula, G is the formation shear modulus, knIs the normal stiffness of the bedding plane, ksShear stiffness of the bedding plane, B bedding plane spacing, and B bending stiffness.
In order to realize the COSSERAT layer model in DDA, the variables (u, v) of DDA block are neededTPerforming an expansion to include a rotational displacement wc. For simplicity, the derivation is performed in the case where the displacement function of the mass is a first order perfect polynomial. The following description will take the planar strain problem as an example. Displacement (u, v, w) of any point (x, y) within a DDA massc)TThe expression of (a) is as follows:
Figure BDA0002961919740000151
the shift transformation matrix T is shown as follows
Figure BDA0002961919740000152
Generalized stress and generalized strain are respectively
[σ]＝[σ11 σ22 σ12 σ21 m1 m2]T (11a)
[ε]＝[ε11 ε22 ε12 ε21 κ1 κ2]T (12b)
The expression of the cell plane stress [ sigma ] is as follows
[σ]＝[E][ε] (13)
[E] The expression of the elastic matrix in a local coordinate system is as follows
Figure BDA0002961919740000153
Wherein the content of the first and second substances,
Figure BDA0002961919740000161
Figure BDA0002961919740000162
Figure BDA0002961919740000163
Figure BDA0002961919740000164
Figure BDA0002961919740000165
C22＝C11+G (16c)
Figure BDA0002961919740000166
in the above formula, G is the formation shear modulus, knIs the normal stiffness of the bedding plane, ksShear stiffness of the bedding plane, B bedding plane spacing, and B bending stiffness. B since it is generally assumed that the material is uniform along the layer direction1＝B，B2＝0。
Let β be the dip angle of the rock formation (measured in the X-axis positive counterclockwise direction of the global coordinate system, shown in fig. 3), c is cos β, and s is sin β, then the direction matrix for converting local coordinates into global coordinates is obtained as follows
Figure BDA0002961919740000171
The elastic matrix in the global coordinate system is obtained as follows
[E*]＝[C]T[E][C] (18)
Wherein E is*The non-zero element term of the upper triangular portion of (1) is as follows
Figure BDA0002961919740000172
Figure BDA0002961919740000173
Figure BDA0002961919740000174
Figure BDA0002961919740000175
Figure BDA0002961919740000176
Figure BDA0002961919740000177
Figure BDA0002961919740000178
Figure BDA0002961919740000179
Figure BDA00029619197400001710
Figure BDA00029619197400001711
Figure BDA00029619197400001712
Figure BDA00029619197400001713
The expression of the cell strain matrix is as follows
Figure BDA0002961919740000181
Note the book
[ε]＝[B][d] (21)
[σ]＝[E*][B][d] (22)
Wherein the content of the first and second substances,
Figure BDA0002961919740000182
elastic strain energy pi of block bodyeIs expressed as follows
Figure BDA0002961919740000191
The above equation is carried out in integral block units, t is the thickness. The elastic strain energy of the unit i is calculated as follows
Figure BDA0002961919740000192
Thus, by applying strain energy II to the celleThe rigidity matrix k of the triangular unit can be obtained by derivationiiAs follows
Figure BDA0002961919740000193
[Kii]Is a 9 x 9 matrix, and is represented byii]Superposition to the System Overall stiffness matrix [ K ]]Can reflect the contribution of the elastic strain energy of the block i to the potential energy functional of the system. [ K ]ii]The analytical expression of the middle integration part is derived as follows
Figure BDA0002961919740000194
The result matrix is [ K ]]，[K]The non-zero elements in the matrix are as follows
Figure BDA0002961919740000195
Figure BDA0002961919740000196
Figure BDA0002961919740000197
Figure BDA0002961919740000198
Figure BDA0002961919740000199
Figure BDA00029619197400001910
Figure BDA00029619197400001911
Figure BDA00029619197400001912
Figure BDA00029619197400001913
As can be seen,
Figure BDA00029619197400001914
can be given analytically.
For the matrices relating to the inertia matrix and the contact calculation, it can be seen that the rotational displacement w in the displacement variable is due tocDoes not participate in the calculation; therefore, the calculation and assembly processes of these core sub-matrices are the same as those in the conventional DDA, and are not described herein again.
(4) And (5) performing solution analysis under a DDA framework to obtain displacement, strain, stress and the like.
The invention takes a discontinuous deformation analysis method as a main program framework, fully exerts the advantages of the discontinuous large deformation contact mechanical behavior of the 'explicit' simulation layer, brings part of the layers into a calculation model in an 'explicit' mode, and the thickness formed by cutting rock mass by the 'explicit' layer brought into the calculation model is m-level; generating DDA blocks by the layer cutting calculation model with the m intervals to form a basic framework of the layered rock; for a DDA block body with the thickness of m levels (wherein the layer surface contains a large number of cm-level intervals), performing macroscopic equivalent simulation by adopting a COSSERAT layered medium model; therefore, a continuous-discontinuous coupling double-scale model is established, and more accurate and efficient simulation of the layered structure rock mass can be realized. The method can fully reflect the influence of the layer surface on the deformation and the strength of the layered structure rock mass, thereby fully reflecting the control effect of the layer surface on the deformation and the stability of the engineering rock mass; meanwhile, all layers are effectively prevented from being brought into a calculation model, and calculation efficiency and solving precision are considered.
Details not described in this specification are within the skill of the art that are well known to those skilled in the art.
Double-scale device embodiment for simulating mechanical behavior of layered rock mass
The invention provides a double-scale device for simulating the mechanical behavior of a layered rock mass,
the geometric model acquisition module is used for acquiring a geometric model for simulating a rock engineering structure;
the block system construction module in the discontinuous deformation analysis method is used for explicitly incorporating layers with the distance of meter-scale dimension between layers in the geometric model of the simulated rock engineering structure into a calculation model to obtain a block system in the discontinuous deformation analysis method, wherein the layers with the distance of meter-scale dimension between the layers which are explicitly incorporated into the computer model form a contact boundary between blocks in the discontinuous deformation analysis method;
the COSSERAT simulation module is used for carrying out implicit simulation on the level of centimeter-level scales contained in each individual in the discontinuous deformation analysis method by adopting a COSSERAT layered model in a macroscopic equivalent mode;
and the mechanical behavior parameter solving and analyzing module is used for solving and analyzing under a discontinuous deformation analysis frame to obtain the mechanical behavior parameters of the simulated layered rock mass, wherein the mechanical behavior parameters of the simulated layered rock mass comprise displacement, strain and stress.
Computer-readable storage medium embodiments
The computer readable storage medium provided by the invention stores a control program of the double-scale method for simulating the mechanical behavior of the layered rock, and the control program of the double-scale method for simulating the mechanical behavior of the layered rock realizes the steps of the double-scale method for simulating the mechanical behavior of the layered rock provided by the invention when being executed by a processor.
Electronic device embodiment
The electronic equipment provided by the invention comprises a memory and a processor, wherein the memory is stored with a control program of the double-scale method for simulating the mechanical behavior of the layered rock, and the control program of the double-scale method for simulating the mechanical behavior of the layered rock realizes the steps of the double-scale method for simulating the mechanical behavior of the layered rock provided by the invention when being executed by the processor.
Referring to fig. 4, fig. 4 is a schematic structural diagram of a dual-scale device for simulating a layered rock mechanical behavior in a hardware operating environment according to an embodiment of the present invention.
As shown in fig. 4, the dual-scale apparatus for simulating the mechanical behavior of layered rock may include: a processor 1001, such as a Central Processing Unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. Wherein a communication bus 1002 is used to enable connective communication between these components. The user interface 1003 may comprise a Display screen Display, an input unit such as a Keyboard, and the optional user interface 1003 may also comprise a standard wired interface, a wireless interface. The network interface 1004 may optionally include a standard wired interface, a WIreless interface such as a WI-FI interface, for example, a WIreless FIdelity (WI-FI) interface. The Memory 1005 may be a high-speed Random Access Memory, a RAM Memory, or a Non-Volatile Memory, a NVM, such as a disk Memory. The memory 1005 may alternatively be a storage device separate from the processor 1001.
Those skilled in the art will appreciate that the configuration shown in fig. 4 does not constitute a definition of a dual scale device for simulating the mechanical behavior of a layered rock mass, and may include more or fewer components than shown, or some components in combination, or a different arrangement of components.
As shown in fig. 4, the memory 1005, which is a storage medium, may include an operating system, a data storage module, a network communication module, a user interface module, and an operating program of a dual-scale method for simulating mechanical behavior of a layered rock mass.
In the dual-scale device for simulating the mechanical behavior of the layered rock mass shown in fig. 4, the network interface 1004 is mainly used for data communication with a network server; the user interface 1003 is mainly used for data interaction with a user; the processor 1001 and the memory 1005 of the dual-scale device for simulating the mechanical behavior of the layered rock body according to the present invention may be disposed in the dual-scale device for simulating the mechanical behavior of the layered rock body, and the dual-scale device for simulating the mechanical behavior of the layered rock body calls the running program of the dual-scale method for simulating the mechanical behavior of the layered rock body stored in the memory 1005 through the processor 1001, and executes the dual-scale method for simulating the mechanical behavior of the layered rock body according to the embodiment of the present invention.
In the present application, the units of the physical quantities are international units, and the symbols of the other physical quantities are international symbols except for special descriptions.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (8)

1. A double-scale method for simulating mechanical behavior of a layered rock mass is characterized by comprising the following steps:
acquiring a geometric model for simulating a rock engineering structure;
in the geometric model of the simulated rock engineering structure, explicitly incorporating the layers with the distance of meter-scale dimension between the layers into a calculation model to obtain a block system in the discontinuous deformation analysis method, wherein the layers with the distance of meter-scale dimension between the layers incorporated into the computer model in the display form a contact boundary between blocks in the discontinuous deformation analysis method;
for each individual in the discontinuous deformation analysis method, a COSSERAT layered model is adopted to implicitly simulate the level of centimeter-level scales contained in the COSSERAT layered model in a macroscopic equivalent manner;
and performing solving analysis under a discontinuous deformation analysis frame to obtain simulation layered rock mechanical behavior parameters, wherein the simulation layered rock mechanical behavior parameters comprise displacement, strain and stress.
2. The dual-scale method for simulating mechanical behavior of layered rock according to claim 1, wherein, in the step of performing implicit simulation of the centimeter-scale layer contained in the layered rock by using a cossera layered model in a macroscopic equivalent manner for each individual in the discontinuous deformation analysis method, the conditions that the layered rock needs to satisfy include:
the stratified rock mass is regarded as a composite structure body formed by periodically repeating the complete rock stratum and the bedding surface of the divided rock stratum;
the rock layer is homogeneous and isotropic;
the bedding plane is flat and parallel to develop, and has the same mechanical property;
the layer intervals are equal and only one group of layers is provided;
both the deformation and the curvature are infinitesimal;
for two-dimensional problems, the planar strain problem is considered.
3. The dual-scale method for simulating mechanical behavior of layered rock according to claim 1, wherein the step of implicitly simulating centimeter-scale layers contained therein in a macroscopic equivalent manner by using a cossera layered model for each individual in the discontinuous deformation analysis method specifically comprises the following steps:
the x 'axis is consistent with the direction of the layer surface, the y' axis is vertical to the layer surface and upwards, and the translational displacement is respectively set as u, v and omegacFor rotational displacement, the strain and curvature κ in the global coordinate systemxIs composed of
Figure FDA0002961919730000021
Figure FDA0002961919730000022
Figure FDA0002961919730000023
Under normal conditions
Figure FDA0002961919730000024
From this, ε is knownxy≠εyx；
Considering the balance between the infinitesimal physical strength and the couple, the balance equation is as follows
Figure FDA0002961919730000025
Figure FDA0002961919730000026
Figure FDA0002961919730000027
In the above formula fx,fy,m,mxVolume force and volume force couple, respectively, where the material is considered here to be uniform in the direction of the layer plane, so myVanishing, balance of only mx(ii) present;
the boundary conditions may be expressed as:
σxnx+σyxny＝Px (3a)
σxynx+σyny＝Py (3b)
mxnx+myny＝M (3c)
in the above formula Px、PyM is the upper and lower force couple of the known boundary, nx、nyFor the outside boundary normal unit vector component, the constitutive equation is expressed as
σx＝A11εx′+A12εy′ (4a)
σy＝A21εx′+A22εy′ (4b)
σyx＝C11εy′x+C12εx′y (4c)
σxy＝C21εy′x+C22εx′y (4d)
mx＝Bκx′ (4e)
In the above formulax′、εy′、εy′x、εx′y、κx' strain and curvature under local coordinate system, respectively;
integral bodyThe elastic matrix D in the coordinate system can be selected from the elastic matrix D in the local coordinate system*To obtain
D＝CTD*C (5)
In the above formula
Figure FDA0002961919730000031
And C is a transformation matrix;
for the layered material, the elastic constants in the formula (6) are respectively
Figure FDA0002961919730000032
Figure FDA0002961919730000033
Figure FDA0002961919730000041
For the relation between the shearing stress and the shearing strain and between the even stress and the curvature of the laminated material is
Figure FDA0002961919730000042
Figure FDA0002961919730000043
C22＝C11+G (8c)
Figure FDA0002961919730000044
In the above formula, G is the formation shear modulus, knIs the normal stiffness of the bedding plane, ksShear stiffness of the bedding plane, B bedding plane spacing, B bending stiffness, and E elastic modulus.
4. The dual-scale method for simulating mechanical behavior of layered rock mass according to claim 1, wherein the step of explicitly incorporating the layers with the meter-scale distance between the layers into the computational model in the geometric model for simulating the rock engineering structure to obtain the block system in the discontinuous deformation analysis method, wherein the step of explicitly incorporating the layers with the meter-scale distance between the layers into the computational model to form the contact boundary between the blocks in the discontinuous deformation analysis method further comprises the step of applying the variable (u, v) of the block in the conventional discontinuous deformation analysis methodTPerforming an expansion to include a rotational displacement wcThe step (2).
5. A dual scale method of simulating mechanical behaviour of layered rock mass according to claim 4, wherein in said discontinuous deformation analysis method, in a coupled analysis model, discontinuous deformation is used to analyze the displacement (u, v, w) of any point (x, y) in the massc)TWherein the rotational displacement wcThe method does not participate in calculation, and the discontinuous deformation analysis method is the same as the traditional discontinuous deformation analysis method.
6. A double-scale device for simulating the mechanical behavior of a layered rock mass is characterized by comprising,
the geometric model acquisition module is used for acquiring a geometric model for simulating a rock engineering structure;
the block system construction module in the discontinuous deformation analysis method is used for explicitly incorporating layers with the distance of meter-scale dimension between layers in the geometric model of the simulated rock engineering structure into a calculation model to obtain a block system in the discontinuous deformation analysis method, wherein the layers with the distance of meter-scale dimension between the layers which are explicitly incorporated into the computer model form a contact boundary between blocks in the discontinuous deformation analysis method;
the COSSERAT simulation module is used for carrying out implicit simulation on the level of centimeter-level scales contained in each individual in the discontinuous deformation analysis method by adopting a COSSERAT layered model in a macroscopic equivalent mode;
and the mechanical behavior parameter solving and analyzing module is used for solving and analyzing under a discontinuous deformation analysis frame to obtain the mechanical behavior parameters of the simulated layered rock mass, wherein the mechanical behavior parameters of the simulated layered rock mass comprise displacement, strain and stress.
7. A computer-readable storage medium, characterized in that the computer-readable storage medium has stored thereon a control program of a dual-scale method for simulating a layered rock mechanical behavior, which, when executed by a processor, implements the steps of the dual-scale method for simulating a layered rock mechanical behavior according to any one of claims 1 to 5.
8. An electronic device comprising a memory and a processor, the memory having stored thereon a control program for a dual-scale method of simulating a layered rock mechanical behavior, the control program for a dual-scale method of simulating a layered rock mechanical behavior when executed by the processor implementing the steps of the dual-scale method of simulating a layered rock mechanical behavior of any of claims 1-5.
CN202110240440.4A 2021-03-04 2021-03-04 Double-scale method, device, storage medium and equipment for simulating mechanical behavior of layered rock mass Active CN112949065B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110240440.4A CN112949065B (en) 2021-03-04 2021-03-04 Double-scale method, device, storage medium and equipment for simulating mechanical behavior of layered rock mass

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110240440.4A CN112949065B (en) 2021-03-04 2021-03-04 Double-scale method, device, storage medium and equipment for simulating mechanical behavior of layered rock mass

Publications (2)

Publication Number Publication Date
CN112949065A true CN112949065A (en) 2021-06-11
CN112949065B CN112949065B (en) 2022-05-27

Family

ID=76247624

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110240440.4A Active CN112949065B (en) 2021-03-04 2021-03-04 Double-scale method, device, storage medium and equipment for simulating mechanical behavior of layered rock mass

Country Status (1)

Country Link
CN (1) CN112949065B (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113553751A (en) * 2021-07-23 2021-10-26 长江水利委员会长江科学院 Coarse particle material three-dimensional block system generation method and device, storage medium and equipment
CN113781441A (en) * 2021-09-13 2021-12-10 中铁一局集团第二工程有限公司 Grouting range optimization method applied to jointed rock mass tunnel excavation process
CN114608476A (en) * 2022-03-09 2022-06-10 东北大学 Intelligent analysis and extraction method for three-dimensional point cloud structural surface of complex rock mass

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20060184346A1 (en) * 2005-02-07 2006-08-17 Panga Mohan K Modeling, simulation and comparison of models for wormhole formation during matrix stimulation of carbonates
CN110598273A (en) * 2019-08-23 2019-12-20 成都理工大学 Stability analysis method for non-saturated soil slope hydraulic mechanics coupling
CN110852004A (en) * 2019-08-23 2020-02-28 成都理工大学 Mechanical seepage coupling unsaturated soil numerical simulation method and system
US20200132869A1 (en) * 2016-07-15 2020-04-30 Hohai University Seismic rock physics inversion method based on large area tight reservoir
CN112131802A (en) * 2020-08-14 2020-12-25 山东大学 Near-field dynamics-based fractured rock mass seepage simulation method and system

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20060184346A1 (en) * 2005-02-07 2006-08-17 Panga Mohan K Modeling, simulation and comparison of models for wormhole formation during matrix stimulation of carbonates
US20200132869A1 (en) * 2016-07-15 2020-04-30 Hohai University Seismic rock physics inversion method based on large area tight reservoir
CN110598273A (en) * 2019-08-23 2019-12-20 成都理工大学 Stability analysis method for non-saturated soil slope hydraulic mechanics coupling
CN110852004A (en) * 2019-08-23 2020-02-28 成都理工大学 Mechanical seepage coupling unsaturated soil numerical simulation method and system
CN112131802A (en) * 2020-08-14 2020-12-25 山东大学 Near-field dynamics-based fractured rock mass seepage simulation method and system

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
李银平等: "层状盐岩体的三维Cosserat介质扩展本构模型", 《岩土力学》 *

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113553751A (en) * 2021-07-23 2021-10-26 长江水利委员会长江科学院 Coarse particle material three-dimensional block system generation method and device, storage medium and equipment
CN113553751B (en) * 2021-07-23 2022-05-17 长江水利委员会长江科学院 Coarse particle material three-dimensional block system generation method and device, storage medium and equipment
CN113781441A (en) * 2021-09-13 2021-12-10 中铁一局集团第二工程有限公司 Grouting range optimization method applied to jointed rock mass tunnel excavation process
CN113781441B (en) * 2021-09-13 2024-02-27 中铁一局集团第二工程有限公司 Grouting range optimization method applied to jointed rock mass tunnel excavation process
CN114608476A (en) * 2022-03-09 2022-06-10 东北大学 Intelligent analysis and extraction method for three-dimensional point cloud structural surface of complex rock mass

Also Published As

Publication number Publication date
CN112949065B (en) 2022-05-27

Similar Documents

Publication Publication Date Title
CN112949065B (en) Double-scale method, device, storage medium and equipment for simulating mechanical behavior of layered rock mass
Jing A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering
Bui et al. Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic–plastic soil constitutive model
Yu et al. Generalized Timoshenko theory of the variational asymptotic beam sectional analysis
He et al. Development of 3D numerical manifold method
JP5911077B2 (en) Coupling calculation apparatus, coupling calculation method, and coupling calculation program for air, water and soil skeleton
CN113360992B (en) Phase field material point method for analyzing large deformation fracture of rock-soil structure
Viré et al. Modelling of fluid–solid interactions using an adaptive mesh fluid model coupled with a combined finite–discrete element model
Nikravesh et al. Improved state-based peridynamic lattice model including elasticity, plasticity and damage
Shen et al. Construction of peridynamic beam and shell models on the basis of the micro-beam bond obtained via interpolation method
Sun et al. Particle manifold method (PMM): A new continuum‐discontinuum numerical model for geomechanics
Zhang et al. Multi-spring edge-to-edge contact model for discontinuous deformation analysis and its application to the tensile failure behavior of rock joints
He et al. Numerical estimation and prediction of stress-dependent permeability tensor for fractured rock masses
Khan Investigation of discontinuous deformation analysis for application in jointed rock masses
Ibrahimbegovic et al. Nonlinear dynamics of structures under extreme transient loads
Antonya et al. Design evaluation and modification of mechanical systems in virtual environments
Cerrolaza et al. A Cosserat non-linear finite element analysis software for blocky structures
Long et al. Stochastic fracture analysis of cracked structures with random field property using the scaled boundary finite element method
Baudet et al. Integrating tensile parameters in mass-spring system for deformable object simulation
Salehian et al. Continuum modeling of an innovative space-based radar antenna truss
Khademalrasoul NURBS-based isogeometric analysis method application to mixed-mode computational fracture mechanics
Qingyun et al. Numerical simulation of impact and entrainment behaviors of debris flow by using SPH–DEM–FEM coupling method
MA Hashash et al. Visual framework for development and use of constitutive models
Dasgupta Locking-free compressible quadrilateral finite elements: Poisson’s ratio-dependent vector interpolants
Özdemir Dynamic analysis of thick plates resting on Winkler foundation using a new finite element

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant