CN117315179A - Construction method of macro-micro joint coupling model of jointed rock mass - Google Patents
Construction method of macro-micro joint coupling model of jointed rock mass Download PDFInfo
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Abstract
The invention discloses a construction method of a macro-micro joint coupling model of a jointed rock body, which is characterized in that in a rock mass numerical model, a macro joint surface model among rock mass units is used for reflecting relative sliding deformation among rock mass units at two sides, an expansion algorithm is used for describing expansion of a macro joint surface, meanwhile, a non-through joint rock mass model is adopted in the rock mass units for reflecting anisotropic deformation in the rock mass units, and finally, the macro joint surface model and the micro joint surface model are coupled in numerical calculation to form a macro-micro joint coupling model, so that a result is more approximate to a real situation.
Description
Technical Field
The invention relates to the technical field of jointed rock mass models, in particular to a method for constructing a macro-micro jointed coupling model of a jointed rock mass.
Background
The rock mass on the earth surface is subjected to earth crust movement and various geological actions in the long geological history, and discontinuous structural surfaces with different scales such as faults, joints, cracks and the like are gradually formed in the rock mass. The influence of the existence of the discontinuous structural surfaces in the surrounding rock of the tunnel on the deformation and stability of the tunnel is on the one hand reflected in that the anisotropy of the jointed rock mass can cause the uneven deformation of the tunnel and the change of the force distribution in the supporting structure, and the reduction of the strength and rigidity of the rock mass can cause the larger deformation of the tunnel, thereby affecting the stability of the tunnel; on the other hand, the discontinuous structural surface in the surrounding rock of the jointed rock body can generate stress concentration under the effect of tunnel excavation unloading, and the jointed cracks are expanded, converged and form new joints and cracks, so that the rock body is further weakened, and the tunnel is greatly deformed, and the support is damaged or even collapses. Numerous engineering practices have shown that destabilization failures of many mountain tunnel projects are related to their internal joint or crack expansion penetration. Therefore, for tunnel construction in an jointed rock, the physical mechanical properties of the jointed rock and its failure properties should be considered.
Discontinuous structural surfaces in jointed rock often have a plurality of scales with large difference, and the influence of structures with different scales on rock deformation is different. The large-scale structural surface represented by faults mainly causes relative movement such as shearing sliding among rock masses, and the small-scale structural surface represented by joint cracks mainly causes anisotropic deformation in the rock masses. The students analyze the relative motion of the rock mass near the structural surface through a Goodman joint surface unit or discrete element discontinuous medium numerical simulation method, and the anisotropic deformation of the joint rock mass in the rock mass is described by utilizing an equivalent continuous body model, but less students consider the influence of the two scale structures on the rock mass deformation at the same time.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for constructing a macro-micro joint coupling model of a jointed rock mass.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a construction method of a macro-micro joint coupling model of a jointed rock body comprises the following steps:
s1: establishing a rock mass model by adopting FLAC3D, dividing the rock mass model into a plurality of rock mass units, then generating an initial macroscopic joint surface between the rock mass units, and adopting a non-through joint rock mass model in the rock mass units;
s2: according to the initial stress and the boundary load, calculating the displacement and the strain increment of each rock mass unit by adopting a balance equation;
s3: according to the stress-strain relation of the non-through jointed rock mass model and the plastic correction thereof, calculating to obtain the stress tensor of each rock mass unit after the plastic correction;
s4: judging whether a new macro joint surface is generated at each joint expandable surface according to the stress tensor of each rock block unit and a macro joint expansion algorithm;
s5: and judging whether all the calculations are finished, and if not, repeating the steps S2-S4.
As a further preferable embodiment of the above-described aspect, the non-penetrating jointed rock mass model includes three aspects of deformation characteristics, failure modes, strength criteria, and post-peak strength.
As a further preferable technical aspect of the above technical aspect, the rock mass stress-strain relation expression of the non-penetrating jointed rock mass model in deformation characteristics is: dε=Cdσ, and the stress-strain increment is rewritten into a vector form:
wherein e.g. epsilon x 、γ xy Respectively representing positive x-direction strain and xy-direction shear strain, sigma x 、τ xy Respectively representing the positive stress in the x direction and the shear stress in the xy direction, { n } = (n) x ,n y ,n z ) Is a unit vector which is outwards perpendicular to the joint plane, namely a normal vector of the joint plane, n x 、n y 、n z The components of normal vector of joint surface in x, y and z directions, k n And k s The normal rigidity and the shear rigidity of the joint surfaces are respectively expressed, k is the joint connectivity rate, and d is the equivalent joint spacing, namely the joint spacing between two rows of joint surfaces.
As a further preferable technical scheme of the above technical scheme, the failure modes adopted by the non-penetrating jointed rock mass model are four, namely rock mass compression shear failure, rock mass tensile failure, joint surface compression shear failure and joint surface tensile failure, wherein:
1) The judgment criteria of rock compression shear damage and rock tensile damage are consistent with the composite molar coulomb strength criterion, and are respectively judged by adopting the molar coulomb strength criterion and the tensile strength criterion, namely:
in the method, in the process of the invention,c represents the friction angle and cohesion of the rock, respectively;
f t ＝σ 1 -σ t
in sigma t Is the tensile strength of the rock;
2) The joint surface compression shear fracture and the joint surface tensile fracture are respectively determined by adopting a non-through joint surface compression shear strength criterion and a non-through joint surface tensile strength criterion, and are determined by guidingThe joint communication rate k is used for describing the non-through joint surface, and the non-through joint surface is obtained through the compression shear strength criterionAnd tensile strength criterion>The expressions are respectively
In the above two formulas, σ j And τ j Respectively the normal stress and tangential stress on the non-through joint surface,c j and->The friction angle, cohesion and tensile strength of the non-penetrating joint surface are shown, respectively.
When (when)During the process, the joint surface is sheared and damaged; when->During this time, the joint surface is broken by stretching.
As a further preferable aspect of the above-mentioned technical solution, in the post-peak mechanical characteristics of the non-through jointed rock mass model rock mass compression shear or tensile failure, the post-peak curves of the rock mass compression shear failure and the rock mass tensile failure are described by a strain softening model and an ideal elastic brittleness model, respectively, and the sectional function expressions of the rock mass cohesion and tensile strength along with the shear or tensile plastic strain are as follows:
wherein ε p s And epsilon p Shear plastic strain and tensile plastic strain of rock mass, c and sigma respectively t The cohesive force and the tensile strength of the rock mass before plastic destruction are respectively shown;
similarly, in the peak-to-peak mechanical characteristics of the non-penetrating joint rock model joint surface compression shear or tensile failure, the influence of the friction angle of the joint surface is not considered, and the peak-to-peak curve of the joint surface compression shear failure and the joint surface tensile failure are also described by a strain softening model and an ideal elastic brittleness model respectively, and the piecewise function expressions of the joint surface cohesive force and the tensile strength along with the joint surface shear or tensile plastic strain are also as follows:
wherein ε jp s And epsilon jp t Respectively, joint surface shear plastic strain and joint surface tensile plastic strain, c j Sum sigma j t The joint surface cohesive force and the joint surface tensile strength before plastic fracture are respectively.
As a further preferable embodiment of the foregoing embodiment, the specific implementation steps of the step S4 are as follows:
s4.1, searching an expandable surface of all joints, and calculating the stress magnitude on the expandable surface according to the stress tensors of rock mass units at two sides of the expandable surface, namely normal stress sigma and tangential stress tau:
s4.2: if the stress of the joint expandable surface meets the expansion judging criterion, separating rock mass units at two sides of the surface and generating a new macroscopic joint surface, thereby realizing expansion of the joint surface;
s4.3: repeating the steps S4.1 to S4.2 until all the joint expandable surfaces are searched.
As a further preferable embodiment of the above-described embodiment, in the expansion determination criterion, the shearing fracture and the tensile fracture are respectively a molar coulomb criterion and a tensile strength criterion considering the influence of the expandable surface size, that is:
σ-λ s σ t ＝0
wherein, sigma and tau are normal stress and tangential stress at the expandable surface respectively, sigma is positive in tension, if so, the normal stress in the shear failure judgment criterion is 0; c.σt is the cohesion, friction angle and tensile strength of the rock, respectively; λs is a reduction coefficient considering the area influence of the joint expansion surface, and is generally 0.8 to 1.0.
In order to achieve the above object, the present invention further provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method for constructing a macro-micro joint coupling model of a jointed rock body when executing the program.
To achieve the above object, the present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program, characterized in that the computer program, when executed by a processor, implements the steps of the method for constructing a macro-micro joint coupling model of a jointed rock mass.
Compared with the prior art, the invention has the beneficial effects that:
according to the invention, in a rock mass numerical model, relative sliding deformation between rock mass units at two sides is reflected through a macroscopic joint surface model between the rock mass units, the extension of the macroscopic joint surface is described through an extension algorithm, meanwhile, anisotropic deformation in the rock mass units is reflected through a non-through joint rock mass model in the rock mass units, and finally, the macroscopic and the microscopic joint coupling model is formed by coupling the macroscopic and the microscopic joint coupling model in numerical calculation, so that the result is more similar to the real situation.
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For a clearer description of the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly introduced below, it being obvious that the drawings in the description below are only some embodiments of the present invention, and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art, wherein:
FIG. 1 is a flow chart of steps of a method of constructing a macro-micro joint coupling model of a jointed rock mass;
FIG. 2 is a schematic view of a model of a non-through jointed rock mass;
FIG. 3 is a typical stress strain graph of a non-through jointed rock mass model;
FIG. 4 is a graph of intensity criteria in a molar coulomb model;
FIG. 5 is a graph of joint face strength criteria in a non-through jointed rock mass model;
FIG. 6 is a graph of the change in the cohesion of a rock mass with shear plastic deformation;
FIG. 7 is a macrojoint expansion schematic;
FIG. 8 is a flow chart of a macrojoint expansion algorithm;
FIG. 9 is a numerical example diagram of a macro-micro joint coupling model;
FIG. 10 is a graph of rock mass tensile test example results;
FIG. 11 is a graph showing the results of uniaxial stretching test examples of rock mass.
Detailed Description
In the description of the present invention, it should be noted that, for the azimuth words such as the terms "center", "transverse (X)", "longitudinal (Y)", "vertical (Z)", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", etc., the azimuth and positional relationships are based on the azimuth or positional relationships shown in the drawings, only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the apparatus or element to be referred to must have a specific azimuth, be constructed and operated in a specific azimuth, and should not be construed as limiting the specific protection scope of the present invention.
Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features. Thus, the definition of "a first", "a second" feature may explicitly or implicitly include one or more of such feature, and in the description of the present invention, the meaning of "a number", "a number" is two or more, unless otherwise specifically defined.
A method for constructing a macro-micro joint coupling model of a jointed rock mass is shown in fig. 1, and comprises the following steps:
s1: establishing a rock mass model by adopting FLAC3D, dividing the rock mass model into a plurality of rock mass units, then generating an initial macroscopic joint surface between the rock mass units, and adopting a non-through joint rock mass model in the rock mass units;
s2: according to the initial stress and the boundary load, calculating the displacement and the strain increment of each rock mass unit by adopting a balance equation;
s3: according to the stress-strain relation of the non-through jointed rock mass model and the plastic correction thereof, calculating to obtain the stress tensor of each rock mass unit after the plastic correction;
s4: judging whether a new macro joint surface is generated at each joint expandable surface according to the stress tensor of each rock block unit and a macro joint expansion algorithm;
s5: and judging whether all the calculations are finished, and if not, repeating the steps S2-S4.
In the invention, step S2 can be directly calculated through FLAC 3D;
specifically, in FLAC3D, a rock-soil mass model is discretized into a plurality of rock mass units, and the nodes of the rock mass units are used as calculation objects, and forces and masses are both concentrated on the nodes, and then solved in the time domain by means of a motion equation.
The cell node equation of motion can be expressed as follows:
in the method, in the process of the invention,representing the speed of the l node in the i-direction, +.>Representing unbalanced force component of the l node in t moment and i direction, m l Representing the quality of the l node.
The left-hand offset is approximated by the center difference, and the displacement increment (i.e., the velocity at t+Δt/2) is obtained as:
wherein Δt represents a time increment; v i l (t-Deltat/2) represents the speed of the i-node in the i-direction at t-Deltat/2.
And then the unit strain increment of a certain time step is calculated according to the speed, namely:
wherein, delta epsilon ij Indicating the strain increment of the cell in ij direction (i=j is positive strain, i+.j is shear strain); v i,j Indicating a deviation of the velocity in the direction j of the unit i; v j,i Indicating a deviation of the velocity in the direction i of the cell j.
In the non-through jointed rock mass model, a model schematic diagram is shown in fig. 2, and a joint surface is assumed to be a common coin shape, namely a circular plane with a certain size and a circle center coincident with the center of the rock mass.
The non-penetrating joint surface of the model may be uniquely represented by a normal vector { n } and a joint connectivity k. Where the normal vector { n } is used to describe the direction of the joint plane and the connectivity rate k is used to describe the size of the joint plane within the rock mass.
Note that when k=0, there is no joint in the model, similar to the joint case in the molar coulomb model; and when k=1, intra-model joints are through, similar to the joints in a pervasive joint model.
A typical stress-strain curve of the non-through jointed rock mass model is shown in fig. 3. In the following, the relevant expressions of the non-penetrating jointed rock mass model will be presented from three aspects of deformation characteristics, failure modes, strength criteria, post-peak strength.
(1) Deformation characteristics:
the above formula is rock stress-strain relation expression dε=Cdσ in a non-through jointed rock mass model, wherein E is r And v represents the elastic modulus and poisson's ratio of the rock, respectively, the stress-strain increase being rewritten as a vector form:
wherein e.g. epsilon x 、γ xy Respectively representing positive x-direction strain and xy-direction shear strain, sigma x 、τ xy Respectively, positive x-direction stress and shear xy-direction stress, and the front d represents differentiation.
{n}＝(n x ,n y ,n z ) Is a unit vector perpendicular to the joint plane, i.e. normal vector of the joint plane, that is n x 、n y 、n z The components of the normal vector of the joint surface in the x, y and z directions are respectively.
k n And k s The normal stiffness and shear stiffness of the joint plane are indicated, respectively.
k is the joint connectivity; d is the equivalent joint spacing, i.e., the joint spacing between two rows of joint surfaces.
(2) Failure mode and anisotropic strength criterion:
the breaking modes adopted by the non-through jointed rock mass model are divided into 4 types, namely rock mass compression shear breaking, rock mass tensile breaking, joint surface compression shear breaking and joint surface tensile breaking.
1) The judgment criteria of rock compression shear damage and rock tensile damage are consistent with the composite molar coulomb strength criterion, and are respectively judged by adopting the molar coulomb strength criterion and the tensile strength criterion, namely:
assuming that the three principal stresses of the rock mass are sigma 1 、σ 2 Sum sigma 3 (negative in compressive stress) and there is the following relationship σ 1 ≥σ 2 ≥σ 3 Then at (sigma) 3 ,σ 1 ) The destabilizing envelope f (sigma) on the coordinate plane (as shown in fig. 4) 3 ,σ 1 ) =0 is defined as follows:
from point A to point B, the rock mass stress is at a compressive shear failure critical value, namely the molar coulomb strength criterion f is satisfied s ＝0。
In the method, in the process of the invention,c represents the friction angle and cohesion of the rock, respectively.
From point B to point C, the stress of the rock mass is at a tensile failure critical value, namely the tensile strength criterion f is met t =0, and
f t ＝σ 1 -σ t
in sigma t Is the tensile strength of the rock.
2) The joint surface compression shear fracture and the joint surface tensile fracture are respectively determined by adopting a non-through joint surface compression shear strength criterion and a non-through joint surface tensile strength criterion, and the non-through joint surface is described by introducing a joint communication rate k.
Non-through joint surface compression shear strengthDegree criterion f j s And tensile strength criterion f j t The expressions are respectively
In the above two formulas, σ j And τ j Respectively the normal stress and tangential stress on the non-through joint surface,c j and->The friction angle, cohesion and tensile strength of the non-penetrating joint surface are shown, respectively.
When f j s >When 0, the joint surface is sheared and damaged; when f j t >At 0, the joint surface is broken by stretching. As shown in FIG. 5, the joint surface instability envelope curve, the stress of the joint surface from the point A to the point B meets the joint surface compression shear strength criterion f j s =0, the joint plane stress from point B to point C satisfies the joint plane tensile strength criterion f j t ＝0。
(3) Post peak intensity characteristics:
in the peak-to-peak mechanical characteristics of the non-through jointed rock mass model rock mass compression shear or tensile failure, the peak-to-peak curves of the rock mass compression shear failure and the rock mass tensile failure are respectively described by a strain softening model and an ideal elastic brittleness model without considering the influence of a rock mass friction angle, and the sectional function expression of the rock mass cohesion and the tensile strength along with shear or tensile plastic strain is as follows:
in the middle of，ε p s And epsilon p t Shear plastic strain and tensile plastic strain of rock mass, c and sigma respectively t The cohesive force and the tensile strength of the rock mass before plastic destruction are respectively shown. Wherein, the piecewise function of the cohesive force of the rock mass is shown in figure 6, namely, when the shear plastic strain of the rock mass is increased to 0.9%, the cohesive force is reduced to 2/7 of the original cohesive force; when the shear plastic strain of the rock mass increases to 2.8%, the cohesion is reduced to 0.
Similarly, in the post-peak mechanical characteristics of the compressive shear or tensile fracture of the joint surface of the model, the influence of the friction angle of the joint surface is not considered, and the post-peak curve of the compressive shear fracture of the joint surface and the tensile fracture of the joint surface are respectively described by a strain softening model and an ideal elastic and brittle model, and the piecewise function expressions of the cohesive force and the tensile strength of the joint surface along with the shearing or tensile plastic strain of the joint surface are as follows:
wherein ε jp s And epsilon jp t Respectively, joint surface shear plastic strain and joint surface tensile plastic strain, c j Sum sigma j t The joint surface cohesive force and the joint surface tensile strength before plastic fracture are respectively.
The macro joint surface model is based on the Goodman joint surface model and is divided into two parts, namely joint surface shearing and joint surface stretching. Joint surface shear of the model passes through shear stiffness k s And shear strength sigma j s To describe, while joint plane stretching is through normal stiffness k n And tensile strength sigma j t To describe.
In engineering rock mass, the large-scale structural surface does not necessarily penetrate the entire rock mass, and expansion of the structural surface may occur. Even if large-scale structural surfaces which can slip are not present in the rock mass model, new macroscopic structural surfaces can be generated in the rock mass under the action of load. Therefore, it is necessary to propose a macrojoint expansion algorithm based on the inter-rock unit stresses to reflect the generation and expansion of large scale structural planes.
To achieve expansion of the macrojoint, it is assumed that the faces formed between all the rock mass units in the rock mass model, except the initial macrojoint face, are joint-expandable faces. In the numerical calculation, the stress tensor of the expandable surface center can be obtained according to the stress tensors of the rock mass units at two sides of the expandable surface, and then the normal stress sigma and the tangential stress tau of the expandable surface can be obtained. If the relevant decision criteria are met, the joint expansion is performed on the expandable surface, as shown in fig. 7.
The concrete implementation flow of the macro-node extension algorithm (as shown in fig. 8) can be divided into the following three steps:
(1) and searching the expandable surface of all joints, and calculating the stress magnitude, namely normal stress sigma and tangential stress tau, on the expandable surface according to the stress tensors of the rock mass units at two sides of the expandable surface.
(2) If the stress of the joint expandable surface meets the expansion judging criterion, separating rock mass units at two sides of the surface and generating a new macroscopic joint surface, thereby realizing expansion of the joint surface.
In the extended determination criterion, the shear failure and the tensile failure respectively adopt a molar coulomb criterion and a tensile strength criterion considering the influence of the expandable face size, namely:
σ-λ s σ t ＝0
wherein, sigma and tau are normal stress and tangential stress at the expandable surface respectively, sigma is positive in tension, if so, the normal stress in the shear failure judgment criterion is 0; c.σ t the cohesive force, the friction angle and the tensile strength of the rock are respectively; lambda (lambda) s In order to consider the area influence reduction factor of the joint expansion surface, 0.8 to 1.0 is generally used.
(3) Repeating the steps (1) and (2) until all the joint expandable surfaces are searched.
Specifically, the invention adopts the secondary development of the FISH language to realize the macro joint expansion algorithm, and adopts the software of FLAC3D6.0.
The invention is illustrated by the following calculation examples:
the rock mass with a single non-penetrating joint is used as a numerical experimental object, and a macro-micro joint coupling model is used for carrying out a tensile test and a uniaxial compression test. The dimensions of both numerical examples were 50mm (transverse) ×100mm (vertical) ×1mm (longitudinal), and the lengths of the included non-penetrating joint surfaces were 20mm, as shown in fig. 9.
In the tensile test calculation example, the inclination angle of the joint surface is 0 degrees, and a rock block unit adopts a regular hexahedral unit with the side length of 1 mm; in the uniaxial compression test example, the joint surface dip angle is 45 degrees, and a triangular prism unit with the side length of 1mm is adopted as the rock block unit. When the test is loaded, the rock mass is stretched or compressed by controlling the rock mass boundary to move vertically, so that the rock mass is allowed to deform transversely but not longitudinally. Thus, this numerical example can be seen as a two-dimensional plane strain problem.
In this numerical example, the relative slippage of the rock mass units on both sides of the non-penetrating joint surface of 20mm length has an important influence on the deformation of the rock mass, and therefore is regarded as a large-scale joint surface, and is simulated by using a macro joint surface model. In order to reflect the anisotropic deformation of the whole rock mass, which is influenced by the joint surface, a non-through joint rock mass model is adopted in a rock mass unit to simulate, and the inside of the unit is considered to be distributed with fine joints with the same inclination angle and the same communication rate. Thus, the establishment of the macro-micro joint coupling model is realized in the numerical example.
In the example of the macro-micro coupled model, the mechanical parameters of the rock and joint surface are shown in table 1. Parameters such as the joint inclination angle beta, the communication rate k, the equivalent joint spacing d and the like in the non-through joint rock mass model are valued according to joint distribution in corresponding calculation examples; for the tensile test examples, β=0 °, k=0.4, d=100 mm; for the uniaxial compression test example, β=45°, k=0.28, d=70.7 mm.
The non-through jointed rock mass model in the macro-micro coupling model is mainly used for reflecting the anisotropic deformation characteristic before the jointed expansion of the rock mass, and the deformation and load conditions of the rock mass after the jointed expansion are mainly reflected by the macro joint surface model and the expansion algorithm thereof, so that the softening after the peak is not needed to be considered in the non-through jointed rock mass model.
TABLE 1 mechanical parameters of materials in numerical examples
(1) Calculation result of rock mass stretching test calculation example
When the axial stress reaches sigma/sigma during the joint expansion of the rock mass tensile test (as shown in figure 10) cr When =0.015, the horizontal non-penetrating joint is broken by stretching in the direction of the joint surface at the tip, and then (σ/σ cr =0.018) joint plane starts to spread symmetrically at both sides tips; as the joint expands, tensile failure continues to occur at the joint face tip, and the joint expands further until the peak tensile stress (σ/σ cr =0.025), the rock mass peak tensile stress σ is about the rock tensile strength σ t 30% of the total weight of the rock mass, indicating that the joint does result in a substantial decrease in the tensile strength of the rock mass; along with the penetration of the joint surface, the tensile strength of the rock mass also rapidly decreases.
(2) Rock mass uniaxial compression test case calculation result
In the joint expansion process of the rock mass tensile test (as shown in fig. 11), the non-penetrating joint rock mass model is divided into four plastic damage forms, which are respectively represented by four different colors; the red lines represent the initial and extended joints between the rock mass units. When the axial stress reaches-sigma/sigma cr When =0.06, the rock mass unit undergoes tensile failure at the non-penetrating joint tip, then the rock mass unit tensile plastic region expands and the inter-unit joint cracks (- σ/σ) under tensile stress cr When =0.22), the included angle of the initiated wing crack to the initial joint is about 75 °. With the expansion of the tensile plastic region and the wing crack, the rock mass gradually reaches peak stress-sigma/sigma cr =0.33, the rock mass peak stress strength is also much lower than the uniaxial compressive strength of intact rock. Along with the continuous increase of the axial compressive strain, the wing crack gradually expands to the vertical direction and forms a through crack in the vertical direction, and meanwhile, the secondary inclined crack also developsAnd expands, and the rock strength gradually decreases. The numerical simulation uniaxial compression process has the cracking angle and the final crack expansion direction which are basically consistent with the uniaxial compression test and theoretical research results of the related non-penetrating jointed rock mass.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above examples, and all technical solutions belonging to the concept of the present invention belong to the protection scope of the present invention. It should be noted that modifications and adaptations to the present invention may occur to one skilled in the art without departing from the principles of the present invention and are intended to be within the scope of the present invention.
Claims (9)
1. The method for constructing the macro-micro joint coupling model of the jointed rock mass is characterized by comprising the following steps of:
s1: establishing a rock mass model by adopting FLAC3D, dividing the rock mass model into a plurality of rock mass units, then generating an initial macroscopic joint surface between the rock mass units, and adopting a non-through joint rock mass model in the rock mass units;
s2: according to the initial stress and the boundary load, calculating the displacement and the strain increment of each rock mass unit by adopting a balance equation;
s3: according to the stress-strain relation of the non-through jointed rock mass model and the plastic correction thereof, calculating to obtain the stress tensor of each rock mass unit after the plastic correction;
s4: judging whether a new macro joint surface is generated at each joint expandable surface according to the stress tensor of each rock block unit and a macro joint expansion algorithm;
s5: and judging whether all the calculations are finished, and if not, repeating the steps S2-S4.
2. The method for constructing the macro-micro joint coupling model of the jointed rock mass according to claim 1, wherein the method comprises the following steps: the non-penetrating jointed rock mass model comprises three aspects of deformation characteristics, a failure mode, strength criteria and post-peak strength.
3. The method for constructing a macro-micro joint coupling model of a jointed rock mass according to claim 2, wherein the rock mass stress-strain relation expression of the non-penetrating joint rock mass model in deformation characteristics is: dε=Cdσ, and the stress-strain increment is rewritten into a vector form:
wherein E is r And v represents the elastic modulus and Poisson's ratio, ε, of the rock, respectively x 、γ xy Respectively representing positive x-direction strain and xy-direction shear strain, sigma x 、τ xy Respectively representing the positive stress in the x direction and the shear stress in the xy direction, { n } = (n) x ,n y ,n z ) Is a unit vector which is outwards perpendicular to the joint plane, namely a normal vector of the joint plane, n x 、n y 、n z The components of normal vector of joint surface in x, y and z directions, k n And k s The normal rigidity and the shear rigidity of the joint surfaces are respectively expressed, k is the joint connectivity rate, and d is the equivalent joint spacing, namely the joint spacing between two rows of joint surfaces.
4. The method for constructing a macro-micro joint coupling model of a jointed rock mass according to claim 2, wherein the failure modes adopted by the non-penetrating jointed rock mass model are divided into four types, namely rock mass compression shear failure, rock mass tensile failure, joint surface compression shear failure and joint surface tensile failure, respectively, wherein:
1) The judgment criteria of rock compression shear damage and rock tensile damage are consistent with the composite molar coulomb strength criterion, and are respectively judged by adopting the molar coulomb strength criterion and the tensile strength criterion, namely:
in the method, in the process of the invention, c represents the friction angle and cohesion of the rock, respectively;
f t ＝σ 1 -σ t
in sigma t Is the tensile strength of the rock;
2) The joint surface compression shear fracture and the joint surface tensile fracture are respectively determined by adopting a non-through joint surface compression shear strength criterion and a non-through joint surface tensile strength criterion, and the non-through joint surface compression shear strength criterion f is obtained by describing the non-through joint surface by introducing the joint communication rate k j s And tensile strength criterion f j t The expressions are respectively
In the above two formulas, σ j And τ j Respectively the normal stress and tangential stress on the non-through joint surface,c j sum sigma j t The friction angle, cohesion and tensile strength of the non-penetrating joint surface are shown, respectively.
When f j s >When 0, the joint surface is sheared and damaged; when f j t >At 0, the joint surface is broken by stretching.
5. The method for constructing a macro-micro joint coupling model of a jointed rock mass according to claim 2, wherein, in the peak-to-peak mechanical characteristics of the non-penetrating joint rock mass model, the peak-to-peak curves of the rock mass compression shear failure and the rock mass tensile failure are described by a strain softening model and an ideal elastic brittleness model, respectively, without considering the influence of rock mass friction angles, the sectional function expressions of the rock mass cohesion and the tensile strength along with the shearing or tensile plastic strain are as follows:
wherein ε p s And epsilon p Shear plastic strain and tensile plastic strain of rock mass, c and sigma respectively t The cohesive force and the tensile strength of the rock mass before plastic destruction are respectively shown;
similarly, in the peak-to-peak mechanical characteristics of the non-penetrating joint rock model joint surface compression shear or tensile failure, the influence of the friction angle of the joint surface is not considered, and the peak-to-peak curve of the joint surface compression shear failure and the joint surface tensile failure are also described by a strain softening model and an ideal elastic brittleness model respectively, and the piecewise function expressions of the joint surface cohesive force and the tensile strength along with the joint surface shear or tensile plastic strain are also as follows:
wherein ε jp s And epsilon jp t Respectively, joint surface shear plastic strain and joint surface tensile plastic strain, c j Sum sigma j t The joint surface cohesive force and the joint surface tensile strength before plastic fracture are respectively.
6. The method for constructing a macro-micro joint coupling model of a jointed rock mass according to claim 1, wherein the specific implementation steps of step S4 are as follows:
s4.1, searching an expandable surface of all joints, and calculating the stress magnitude on the expandable surface according to the stress tensors of rock mass units at two sides of the expandable surface, namely normal stress sigma and tangential stress tau:
s4.2: if the stress of the joint expandable surface meets the expansion judging criterion, separating rock mass units at two sides of the surface and generating a new macroscopic joint surface, thereby realizing expansion of the joint surface;
s4.3: repeating the steps S4.1 to S4.2 until all the joint expandable surfaces are searched.
7. The method for constructing the macro-micro joint coupling model of the jointed rock mass according to claim 6, wherein the method comprises the following steps:
in the extended determination criterion, the shear failure and the tensile failure respectively adopt a molar coulomb criterion and a tensile strength criterion considering the influence of the expandable face size, namely:
σ-λ s σ t ＝0
wherein, sigma and tau are normal stress and tangential stress at the expandable surface respectively, sigma is positive in tension, if so, the normal stress in the shear failure judgment criterion is 0; c.σt is the cohesion, friction angle and tensile strength of the rock, respectively; λs is a reduction coefficient considering the area influence of the joint expansion surface, and is generally 0.8 to 1.0.
8. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of a method of constructing a macro-micro joint coupling model of a jointed rock mass according to any one of claims 1 to 7 when the program is executed.
9. A non-transitory computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of a method of constructing a macro-micro joint coupling model of a jointed rock mass according to any one of claims 1 to 7.
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