CN113283054B - Calculation method of anchor rod reinforcement effect and related equipment - Google Patents

Calculation method of anchor rod reinforcement effect and related equipment Download PDF

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CN113283054B
CN113283054B CN202110423975.5A CN202110423975A CN113283054B CN 113283054 B CN113283054 B CN 113283054B CN 202110423975 A CN202110423975 A CN 202110423975A CN 113283054 B CN113283054 B CN 113283054B
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rock mass
strength
anchored rock
anchored
parameters
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CN113283054A (en
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徐鼎平
李邵军
江权
黄翔
瞿定军
刘建
陈涛
闫生存
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HUBEI SHANSHUYA MINING CO Ltd
HUBEI YIHUA GROUP MINING CO Ltd
Wuhan Institute of Rock and Soil Mechanics of CAS
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HUBEI SHANSHUYA MINING CO Ltd
HUBEI YIHUA GROUP MINING CO Ltd
Wuhan Institute of Rock and Soil Mechanics of CAS
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Abstract

The embodiment of the invention provides a calculation method of an anchor rod reinforcing effect and related equipment, which can accurately predict the macroscopic mechanical response of a fully-bonded anchor rod reinforcing surrounding rock. The method comprises the following steps: constructing a composite material structure model; determining an anisotropic elastoplasticity mechanical model corresponding to the composite material structure model; embedding the anisotropic elastoplasticity mechanical model into a target analysis program; determining basic input parameters corresponding to the anisotropic elastoplasticity mechanical model after the target analysis program is embedded; and determining a surrounding rock deformation value and a plastic zone value according to the basic input parameters and the anisotropic elastoplasticity mechanical model embedded into the target program, wherein the surrounding rock deformation value and the plastic zone value are used for expressing the reinforcing effect of the fully-bonded anchor bolt support on the anchored rock mass in the aspects of strength and rigidity, and the fully-bonded anchor bolt support and the anchored rock mass correspond to the composite material structure model.

Description

Calculation method of anchor rod reinforcement effect and related equipment
Technical Field
The invention relates to the technical field of geotechnical engineering, in particular to a calculation method for an anchor rod reinforcement effect and related equipment.
Background
The fully-bonded anchor rod is a common support component in the excavation process of underground engineering, and the mechanical components of the fully-bonded anchor rod comprise a rock-grouting interface, grouting, a grouting-anchor rod interface and an anchor rod. The complex interaction mechanism between the anchor rod and the rock body makes it one of the basic geomechanical problems which are of great concern in the fields of rock mechanics and engineering. In general, physical model tests and large-scale in-situ tests are always common methods for researching the interaction mechanism of the anchor rod and the rock mass. However, with the advent and perfection of advanced continuous medium modeling methods, numerical simulation methods have gradually evolved into an important means of analyzing the interaction between the bolt and the rock mass and the influence of the bolt on the mechanical properties of the anchored rock mass. In the existing continuous medium modeling method, the interaction between the fully-bonded anchor rod and the rock is mainly simulated by adopting the following two methods: (1) a microscopic method; (2) macro-process, i.e. homogenization process.
In the microscopic method, a rock bolt unit method (RB-E method) or a solid bolt unit method (SB-E method) is mainly adopted to simulate the interaction between the bolt and the rock body on the microscopic scale. The RB-E method adopts shearing and normal coupling springs to simplify and simulate the interaction between grout, a bolt and a rock body, and the SB-E method adopts rock body-grouting and grouting-bolt interfaces to simulate the interaction between the grout, the bolt and the rock body. However, the RB-E method and the SB-E method both have the problem that the estimation of the anchor rod reinforcing effect in the full-bonding anchor rod supporting scheme is inaccurate.
In the homogenization method, the macroscopic mechanical response of the anchored rock mass is generally reflected by regarding both the anchor and the rock mass as equivalent homogeneous media and then assigning the rock mass in the anchoring zone to an anisotropic model with the same physical mechanical parameters. However, unreliable analysis results are often obtained when the existing homogenization methods are applied to large and complex underground engineering practices with high stress and large differences in bolt direction, length and spacing.
Disclosure of Invention
The embodiment of the invention provides a calculation method of an anchor rod reinforcing effect and related equipment, which can accurately predict the macroscopic mechanical response of a fully-bonded anchor rod reinforcing surrounding rock.
The first aspect of the embodiment of the invention provides a method for calculating the reinforcing effect of an anchor rod, which comprises the following steps:
constructing a composite material structure model, wherein the side length of the composite material structure model is the transverse distance or the longitudinal distance between two adjacent anchor rods, the height of the composite material structure model is the length of the anchor rods, and the composite material structure model is a polygonal right prism with the anchor rods positioned at the geometric center;
determining an anisotropic elastoplasticity mechanical model corresponding to the composite material structure model;
embedding the anisotropic elastoplasticity mechanical model into a target analysis program;
determining basic input parameters corresponding to the anisotropic elastoplasticity mechanical model after the target analysis program is embedded;
and determining a surrounding rock deformation value and a plastic zone value according to the basic input parameters and the anisotropic elastoplasticity mechanical model embedded into the target program, wherein the surrounding rock deformation value and the plastic zone value are used for expressing the reinforcing effect of the fully-bonded anchor bolt support on the anchored rock mass in the aspects of strength and rigidity, and the fully-bonded anchor bolt support and the anchored rock mass correspond to the composite material structure model.
A second aspect of an embodiment of the present invention provides an anchor rod reinforcement effect calculation device, including:
the building unit is used for building a composite material structure model, wherein the side length of the composite material structure model is the transverse distance or the longitudinal distance between two adjacent anchor rods, the height of the composite material structure model is the length of the anchor rods, and the composite material structure model is a polygonal right prism with the anchor rods positioned at the geometric center;
the first determining unit is used for determining an anisotropic elastoplasticity mechanical model corresponding to the composite material structure model;
an embedding unit configured to embed the anisotropic elastoplasticity mechanical model into a target analysis program;
the second determining unit is used for determining the basic input parameters corresponding to the anisotropic elastoplasticity mechanical model after the target analysis program is embedded;
and a third determining unit, configured to determine a surrounding rock deformation value and a plastic region value according to the basic input parameters and the anisotropic elastoplasticity mechanical model after the target program is embedded, where the surrounding rock deformation value and the plastic region value are used to represent a reinforcing effect of a fully-cemented rock bolt support on an anchored rock mass in terms of strength and rigidity, and the fully-cemented rock bolt support and the anchored rock mass correspond to the composite material structural model.
Optionally, the first determining unit is specifically configured to:
determining the relation between the stress increment and the elastic strain increment in a local coordinate system, wherein the local coordinate system is the coordinate system of an isotropic plane corresponding to the anchored rock body;
determining a strength reduction coefficient, a shear yield function and a tensile yield function corresponding to the anchored rock mass;
determining the corresponding shear strength parameter of the anchored rock mass;
determining a plastic potential function corresponding to the anchored rock mass, wherein the plastic potential function is used for representing shear plastic flow and tensile plastic flow of the anchored rock mass in the longitudinal direction;
and constructing the anisotropic elastoplasticity mechanical model according to the relation between the stress increment and the elastic strain increment, the strength reduction coefficient, the shear yield function, the tensile yield function, the shear strength parameter and the plastic potential function.
Optionally, the first determining unit is further specifically configured to:
determining the relationship between the stress delta and the elastic strain delta by the following formula:
[Δσ]＝[Q][K′][Q] T [Δε e ]；
wherein, [ Delta sigma ]]Is the increment of stress in the global coordinate system, [ Delta ε ] e ]For the elastic strain increment in the global coordinate system, [ Q ]]Is a coordinate transformation matrix of direction sine and direction cosine in the global coordinate system, [ K']Is a local stiffness matrix.
Optionally, the first determining unit is further specifically configured to:
the intensity reduction factor is obtained by the following formula:
Figure GDA0003698312670000031
wherein λ is the strength reduction coefficient, θ is the angle between the direction of the maximum principal stress and the same face tendency, k and n are parameters determined by fitting uniaxial or triaxial compressive strengths of different values of θ, σ 1 (theta) rock mass strength at an angle theta, sigma 3 Is the minimum principal stress;
the shear yield function is obtained by the following formula:
Figure GDA0003698312670000032
wherein f is c s For the purpose of the shear yield function,
Figure GDA0003698312670000033
for the longitudinal cohesion of the anchored rock mass,
Figure GDA0003698312670000034
the longitudinal friction angle of the anchored rock mass;
the tensile yield function is obtained by the following formula:
Figure GDA0003698312670000035
wherein the content of the first and second substances,
Figure GDA0003698312670000036
for the said tensile yield function,
Figure GDA0003698312670000037
is the tensile strength of the anchored rock mass, and
Figure GDA0003698312670000038
gamma is the angle between the minimum principal stress direction and the normal direction of the same-polarity surface,
Figure GDA0003698312670000039
for the longitudinal tensile strength of the anchored rock mass,
Figure GDA00036983126700000310
the transverse tensile strength of the anchored rock mass.
Optionally, the first determining unit is further specifically configured to:
calculating the shear strength parameter by the following formula:
Figure GDA0003698312670000041
Figure GDA0003698312670000042
wherein the content of the first and second substances,
Figure GDA0003698312670000043
as the parameter of the shear strength is,
Figure GDA0003698312670000044
in order to be equivalent to the shear plastic strain,
Figure GDA0003698312670000045
is composed of
Figure GDA0003698312670000046
Is set to the initial value of (a),
Figure GDA0003698312670000047
is composed of
Figure GDA0003698312670000048
The value of the remaining of (a) is,
Figure GDA0003698312670000049
is composed of
Figure GDA00036983126700000410
Is set to the initial value of (a),
Figure GDA00036983126700000411
is composed of
Figure GDA00036983126700000412
The remaining value of (a) is,
Figure GDA00036983126700000413
is the ultimate equivalent plasticity reduction strain corresponding to the longitudinal residual cohesive force of the anchored rock mass,
Figure GDA00036983126700000414
and the ultimate equivalent plasticity reduction strain is corresponding to the friction angle of the anchored rock mass.
Optionally, the first determining unit is further specifically configured to:
calculating the plasticity potential function by the following formula:
Figure GDA00036983126700000415
Figure GDA00036983126700000416
wherein the content of the first and second substances,
Figure GDA00036983126700000417
and
Figure GDA00036983126700000418
for the purpose of the plastic potential function,
Figure GDA00036983126700000419
the longitudinal shear expansion angle of the anchored rock mass is defined as lambda, and the lambda is the strength reduction coefficient.
Optionally, the basic input parameters include an elasticity parameter, an anchored rock mass strength parameter, a isotropic plane geometric parameter, and a fitting parameter, and the second determining unit is specifically configured to:
determining the elasticity parameter by the following formula:
Figure GDA00036983126700000420
Figure GDA00036983126700000421
Figure GDA0003698312670000051
Figure GDA0003698312670000052
Figure GDA0003698312670000053
wherein the content of the first and second substances,
Figure GDA0003698312670000054
and
Figure GDA0003698312670000055
are all the said elastic parameters, V b Is the volume percentage of the anchor rod in the anchored rock body, and V b ＝πd 2 /4s 1 s 2 ，E r Is the Young's modulus of the anchored rock mass, E f Is the Young's modulus, mu, of the fully bonded anchor r Is the Poisson's ratio, mu, of the anchored rock mass b Is the Poisson's ratio, G, of the fully-bonded anchor rod r Is the shear modulus, G, of the anchored rock mass b Is the shear modulus of the fully bonded anchor rod, and G r ＝E r /2(1+μ r )，G b ＝E b /2(1+μ b )；
In shear failure mode, the strength parameter is calculated by the following formula:
Figure GDA0003698312670000061
Figure GDA0003698312670000062
Figure GDA0003698312670000063
Figure GDA0003698312670000064
wherein the content of the first and second substances,
Figure GDA0003698312670000065
and
Figure GDA0003698312670000066
are all the parameters of the intensity, and are,
Figure GDA0003698312670000067
in order to achieve the tensile strength of the anchor rod,
Figure GDA0003698312670000068
is the tensile strength of the anchored rock mass, C r For the residual cohesion of the anchored rock mass,
Figure GDA0003698312670000069
is the friction angle, tau, of the anchored rock mass b Is the shear strength of the anchor rod, and
Figure GDA00036983126700000610
in the cleavage damage mode, the strength parameter is calculated by the following formula:
Figure GDA00036983126700000611
Figure GDA00036983126700000612
Figure GDA00036983126700000613
Figure GDA00036983126700000614
wherein the content of the first and second substances,
Figure GDA00036983126700000615
and
Figure GDA00036983126700000616
are all said intensity parameters, σ b For the anchor rod at
Figure GDA0003698312670000071
The tensile strength of the steel sheet is high,
Figure GDA0003698312670000072
is the tensile strength of the anchored rock mass, and
Figure GDA0003698312670000073
Figure GDA0003698312670000074
Figure GDA0003698312670000075
is the uniaxial compressive strength of the anchored rock mass, an
Figure GDA0003698312670000076
Figure GDA0003698312670000077
For ultimate tensile strain of the anchored rock mass,
Figure GDA0003698312670000078
Figure GDA0003698312670000079
zeta is the Young's modulus in tension for the tensile strength of the anchored rock mass
Figure GDA00036983126700000710
And compressive Young's modulus E r The ratio of (A) to (B);
the geometrical parameters of the isotropic plane comprise an inclination angle and an inclination angle, and the inclination angle are obtained through the following formulas:
α＝180-90sgn(x′ 2 -x′ 1 )-atan((y′ 2 -y′ 1 )/(x′ 2 -x′ 1 ))；
Figure GDA00036983126700000711
wherein alpha is the inclination angle, beta is the inclination angle, (x' 1 ,y′ 1 ,z′ 1 ) As the starting point coordinates of the fully-bonded anchor rod，(x′ 2 ,y′ 2 ,z′ 2 ) The sgn is a sign function which is the terminal point coordinate of the fully-bonded anchor rod;
performing curve fitting by the following formula to obtain the fitting parameters:
Figure GDA00036983126700000712
k and n are the fitting parameters.
A third aspect of an embodiment of the present invention provides an electronic device, including a memory and a processor, where the processor is configured to implement the steps of the method for calculating the anchor rod reinforcing effect according to the first aspect when executing a computer management program stored in the memory.
A fourth aspect of embodiments of the present invention provides a computer-readable storage medium, on which a computer management-like program is stored, which, when executed by a processor, implements the steps of the method of calculating a bolt-strengthening effect as described in the first aspect above.
In summary, in the embodiment provided by the invention, based on elastoplasticity mechanics and composite material mechanics theories, a composite material structure model of the anchored rock mass is provided, the problem that the influence of the direction, the distance and the diameter of the anchor rod on the physical and mechanical parameters of the anchored rock mass cannot be considered in the existing model is solved, the macroscopic mechanical response of the fully-bonded anchor rod reinforced surrounding rock can be accurately predicted, and the engineering practice is better guided.
Drawings
FIG. 1 is a schematic diagram of a fully bonded bolt reinforcement effect simulation provided by an embodiment of the present invention;
FIG. 2 is a schematic diagram of a composite structure generalized model of an anchored rock mass characteristic unit provided by the embodiment of the invention;
fig. 3 is a schematic flow chart of a method for calculating a reinforcing effect of an anchor rod according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of calculation of a mechanical isotropic plane in a composite material structural model of an anchored rock mass characteristic unit provided by the embodiment of the invention;
FIG. 5 is a schematic diagram illustrating the determination of fitting parameters provided by an embodiment of the present invention;
fig. 6 is a schematic virtual structure diagram of a computing device for anchor rod reinforcement effect according to an embodiment of the present invention;
fig. 7 is a hardware structure diagram of a computing device with anchor rod reinforcement effect according to an embodiment of the present invention;
fig. 8 is a schematic diagram of an embodiment of an electronic device according to an embodiment of the present invention;
fig. 9 is a schematic diagram of an embodiment of a computer-readable storage medium according to an embodiment of the present invention.
Detailed Description
The terms "first," "second," "third," "fourth," and the like in the description and in the claims, as well as in the drawings, if any, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It will be appreciated that the data so used may be interchanged under appropriate circumstances such that the embodiments described herein may be implemented in other sequences than those illustrated or described herein. Moreover, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus. The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.
Referring to fig. 1, fig. 1 is an application schematic diagram of a calculation method of a rock bolt reinforcement effect, which includes a cavern and a plurality of anchored rock mass characteristic unit bodies, where the anchored rock mass characteristic unit bodies are a composite material structural model constructed according to an embodiment of the present invention. As shown in FIG. 2, the composite material structural model is a 4-sided prism with 4 sides being squaresThe material structure model comprises anchor rods, the anchor rods are all bonded anchor rods, the side length of the composite material structure model is the transverse distance or the longitudinal distance between the two anchor rods, as shown in figure 2, the transverse distance s between the two anchor rods is 201 on one side length in the composite material structure model 1 The other side length 202 of the composite material structural model is the longitudinal spacing s between the two anchor rods 2 That is, the side length of the composite material structural model may be s 1 May also be s 2 Alternatively, as shown in FIG. 2, the side length of one side is s 1 The side length of one side is s 2 And is not particularly limited.
In addition, the height of the composite material structural model is the anchor length, as shown in fig. 2, the side length 203 of the composite material structural model is the anchor length l, the composite material structural model is a polygonal right prism with the anchor at the geometric center, and 204 is a local coordinate system. .
The following describes a method for calculating the anchor reinforcement effect from the perspective of an anchor reinforcement effect calculation device, which may be a server or a service unit in the server.
Referring to fig. 3, fig. 3 is a schematic view of an embodiment of a method for calculating a reinforcing effect of an anchor rod according to an embodiment of the present invention, where the method includes:
301. and constructing a composite material structure model.
In this embodiment, the device for calculating the anchor rod reinforcing effect may first construct a composite material structural model, where the composite material structural model is a composite material structural model of an anchored rock mass constructed based on elastoplasticity mechanics and composite material mechanics theory, and the composite material structural model is composed of a fully-bonded anchor rod and a rock mass in an anchoring region thereof. The length of a side of the composite material structure model is a transverse distance or a longitudinal distance between two adjacent anchor rods, the height of the composite material structure model is the length of the anchor rods, the composite material structure model is a polygonal right prism of which the anchor rods are positioned at the geometric center, the polygonal right prism is a 4-sided right prism, and other polygonal right prisms such as a 5-sided polygon or a 6-sided polygon can be adopted, and the limitation is not specifically made.
302. And determining an anisotropic elastoplasticity mechanical model corresponding to the composite material structure model.
In this embodiment, after obtaining the composite material structural model, the apparatus for calculating the anchor rod reinforcing effect may establish an anisotropic elastoplasty model of the composite material structural model including an anisotropic strength criterion and a plastic potential function based on an anisotropic elastoplasty theory, and is described with reference to fig. 4, as shown in the drawing, where 401 is a coordinate of a starting point a of the anchor rod, 402 is a coordinate of an end point B of the anchor rod, 403 is a global coordinate system, 404 is a local coordinate system, and 405 is a same-polarity surface in the composite material structural model, where the composite material structural model includes a plurality of same-polarity surfaces. Specifically, the anisotropic elastoplasticity mechanical model corresponding to the composite material structure model can be determined through the following steps:
step 1, determining the relation between the stress increment and the elastic strain increment in a local coordinate system, wherein the local coordinate system is a coordinate system of an isotropic plane corresponding to an anchored rock body.
In this embodiment, the relationship between the stress increment and the elastic strain increment of the composite material structural model in the local coordinate system of the mechanically isotropic plane (the coordinate system corresponding to the isotropic plane trend-dip-normal direction, such as the coordinate system shown as 404 in fig. 4) can be described by the following formula:
[Δσ′]＝[K′][Δε′ e ]；
wherein, [ delta sigma']Represents the stress increment of the same plane in a local coordinate system, [ Delta epsilon' e ]Representing the elastic strain increment of the same plane in a local coordinate system, [ K']Denotes a local rigidity matrix, wherein [ K']This can be represented by the following matrix:
Figure GDA0003698312670000101
in the above-mentioned matrix, the matrix is,
Figure GDA0003698312670000102
Figure GDA0003698312670000103
Figure GDA0003698312670000104
Figure GDA0003698312670000105
wherein the content of the first and second substances,
Figure GDA0003698312670000106
in order to obtain the transverse Young's modulus of the anchored rock body,
Figure GDA0003698312670000107
in order to obtain the longitudinal young's modulus of the anchored rock body,
Figure GDA0003698312670000108
in order to obtain the longitudinal shear modulus of the anchored rock body,
Figure GDA0003698312670000109
in order to obtain the transverse poisson ratio of the anchored rock,
Figure GDA00036983126700001010
is the longitudinal poisson's ratio of the anchored rock mass.
Further, the composite material structure model, the relationship between the stress increment and the elastic strain increment in the global coordinate system can be determined by the following formula:
[Δσ]＝[Q][K′][Q] T [Δε e ]；
wherein [ Delta sigma ]]Is the increment of stress in the global coordinate system, [ Delta ε ] e ]For elastic strain increment in global coordinate system, [ Q ]]Is a coordinate transformation matrix of direction sine and direction cosine in a global coordinate system, [ K']Is a local stiffness matrix, [ Q ]]Specifically, the method comprises the following stepsMatrix shows:
Figure GDA0003698312670000111
wherein l 1 ＝cosαcosβ，l 2 ＝sinα，l 3 ＝-cosαcosβ，m 1 ＝-sinαcosβ，m 2 ＝cosα，m 3 ＝-sinαsinβ，n 1 ＝-sinβ，n 2 ＝0，n 3 ＝cosβ。
And 3, determining the strength reduction coefficient, the shear yield function and the tensile yield function corresponding to the anchored rock mass.
In this embodiment, the yield criterion of the anisotropic elastoplasticity mechanical model is a sum judgment criterion including a mol-coulomb criterion and an interlaminar rock shear strength criterion, and the longitudinal shear strength is specified as a reference shear strength of the anchored rock mass
Figure GDA0003698312670000112
And describing the longitudinal strength of the anchored rock mass by adopting a maximum tensile criterion, and obtaining a strength reduction coefficient by the following formula:
Figure GDA0003698312670000113
wherein λ is the strength reduction coefficient, θ is the angle between the direction of the maximum principal stress and the tendency of the same plane, k and n are parameters determined by fitting uniaxial or triaxial compressive strengths of different values of θ, σ 1(θ) Rock mass strength at an angle theta 3 Is the minimum principal stress;
the shear yield function is obtained by the following formula:
Figure GDA0003698312670000114
wherein, f c s In order to be a function of the shear yield,
Figure GDA0003698312670000121
in order to anchor the longitudinal cohesive force of the rock mass,
Figure GDA0003698312670000122
the longitudinal friction angle of the anchored rock mass;
the tensile yield function is obtained by the following formula:
Figure GDA0003698312670000123
wherein the content of the first and second substances,
Figure GDA0003698312670000124
in order to be a function of the tensile yield,
Figure GDA0003698312670000125
in order to increase the tensile strength of the anchored rock mass,
Figure GDA0003698312670000126
the angle gamma decreases linearly with the maximum principal stress and the normal to the bedding plane. And is
Figure GDA0003698312670000127
Figure GDA0003698312670000128
In order to achieve the longitudinal tensile strength of the anchored rock body,
Figure GDA0003698312670000129
the transverse tensile strength of the anchored rock body is shown.
And 4, determining the shear strength parameter corresponding to the anchored rock mass.
In this embodiment, for the composite material structural model, the behavior of the anchored rock mass after being damaged is considered by the following method: all shear strength parameters
Figure GDA00036983126700001210
And
Figure GDA00036983126700001211
plastic strain with equivalent shear
Figure GDA00036983126700001212
From an initial value of (
Figure GDA00036983126700001213
And
Figure GDA00036983126700001214
) Linear movement to the rest value (
Figure GDA00036983126700001215
And
Figure GDA00036983126700001216
) Specifically, the shear strength parameter corresponding to the anchored rock mass can be obtained through the following formula:
Figure GDA00036983126700001217
Figure GDA00036983126700001218
wherein the content of the first and second substances,
Figure GDA00036983126700001219
as a parameter of the shear strength,
Figure GDA00036983126700001220
in order to be equivalent to the shear plastic strain,
Figure GDA00036983126700001221
is composed of
Figure GDA00036983126700001222
Is set to the initial value of (a),
Figure GDA00036983126700001223
is composed of
Figure GDA00036983126700001224
The value of the remaining of (a) is,
Figure GDA00036983126700001225
is composed of
Figure GDA00036983126700001226
Is set to the initial value of (a),
Figure GDA00036983126700001227
is composed of
Figure GDA00036983126700001228
The value of the remaining of (a) is,
Figure GDA00036983126700001229
is the ultimate equivalent plasticity reduction strain corresponding to the longitudinal residual cohesive force of the anchored rock mass,
Figure GDA00036983126700001230
the ultimate equivalent plasticity reduction strain corresponding to the friction angle of the anchored rock body.
And 5, determining a plastic potential function corresponding to the anchored rock mass.
In this embodiment, the plastic potential functions of the composite material structure model are respectively
Figure GDA00036983126700001231
And
Figure GDA00036983126700001232
the method comprises the following steps of forming two functions, respectively defining shear plastic flow and tensile plastic flow of an anchored rock body in the longitudinal direction, and specifically obtaining a plastic potential function corresponding to the anchored rock body through the following formula:
Figure GDA0003698312670000131
Figure GDA0003698312670000132
wherein the content of the first and second substances,
Figure GDA0003698312670000133
and
Figure GDA0003698312670000134
and lambda is the intensity reduction factor as a function of plastic potential.
And 6, constructing an anisotropic elastoplasticity mechanical model according to the relation between the stress increment and the elastic strain increment, the strength reduction coefficient, the shear yield function, the tensile yield function, the shear strength parameter and the plastic potential function.
In this embodiment, after obtaining the relationship between the stress increment and the elastic strain increment, the strength reduction coefficient, the shear yield function, the tensile yield function, the shear strength parameter, and the plastic potential function, an anisotropic elastoplasticity mechanical model including an anisotropic strength criterion and a plastic potential function may be established based on the relationship between the stress increment and the elastic strain increment, the strength reduction coefficient, the shear yield function, the tensile yield function, the shear strength parameter, and the plastic potential function.
303. The anisotropic elasto-plastic mechanical model is embedded into the target analysis program.
In this embodiment, after determining the anisotropic elastoplasticity mechanical model corresponding to the composite material structure model, the established anisotropic elastoplasticity mechanical model may be compiled based on C + +, and the three-dimensional continuous fast lagrangian analysis program (FLAC3D) is entered, where the three-dimensional continuous fast lagrangian analysis program (FLAC3D) is a target analysis program, and a manner of importing the three-dimensional continuous fast lagrangian analysis program (FLAC3D) is not specifically limited herein.
It should be noted that, for a large-scale three-dimensional grid model, a cylinder with an anchor rod as a central shaft can be used as an alternative to the prism characteristic unit in the composite material structural model; in this case, the length of the cylindrical feature unit is equal to the bolt length, and the radius R thereof can be calculated based on the area equivalent according to the following formula:
Figure GDA0003698312670000135
s 1 is the transverse spacing between the anchor rods, s 2 Is the longitudinal spacing between the anchor rods.
304. And determining the basic input parameters corresponding to the anisotropic elastoplasticity mechanical model after the target analysis program is embedded.
In this embodiment, the basic input parameters include 5 elastic parameters: (
Figure GDA0003698312670000136
Figure GDA0003698312670000141
And
Figure GDA0003698312670000142
) 4 parameters of the strength of the rock mass added with anchor (a)
Figure GDA0003698312670000143
And
Figure GDA0003698312670000144
) Two same-plane geometric parameters (alpha and beta) and fitting parameters (k and n), and particularly can collect the geometric and mechanical parameters of the anchor rod, including the diameter d and the distance(s) of the anchor rod 1 And s 2 ) Anchor point coordinates, anchor modulus of elasticity (E) b ) Poisson's ratio (mu) b ) And tensile strength
Figure GDA0003698312670000145
And then calculated by the following formulas, respectively.
Further, 5 elastic parameters (modulus of elasticity in the direction of isotropy parallel)
Figure GDA0003698312670000146
Is perpendicular toModulus of elasticity in the same plane direction
Figure GDA0003698312670000147
Shear modulus in the direction perpendicular to the plane of identity
Figure GDA0003698312670000148
Poisson's ratio in the direction parallel to the same plane
Figure GDA0003698312670000149
And Poisson's ratio in the direction perpendicular to the same plane
Figure GDA00036983126700001410
) It can be obtained by the following formula:
Figure GDA00036983126700001411
Figure GDA00036983126700001412
Figure GDA00036983126700001413
Figure GDA0003698312670000151
Figure GDA0003698312670000152
wherein the content of the first and second substances,
Figure GDA0003698312670000153
and
Figure GDA0003698312670000154
are all elastic parameters, V b In rock anchoring for anchoringVolume percent in the body, and V b ＝πd 2 /4s 1 s 2 ，E r Young's modulus of anchored rock mass, E f Young's modulus, mu, for fully bonded anchors r Is the Poisson's ratio, mu, of the anchored rock mass b Poisson ratio, G, for fully-bonded anchors r Shear modulus of anchored rock mass, G b Shear modulus of fully-bonded anchor, and G r ＝E r /2(1+μ r )，G b ＝E b /2(1+μ b )；
4 strength parameters of the anchored rock mass: (
Figure GDA0003698312670000155
And
Figure GDA0003698312670000156
) Calculating according to two different damage modes of shearing and splitting respectively as follows:
1. anchoring rock strength parameter under shear failure model
Figure GDA0003698312670000157
And
Figure GDA0003698312670000158
the calculation is made by the following formula:
Figure GDA0003698312670000159
Figure GDA00036983126700001510
Figure GDA0003698312670000161
Figure GDA0003698312670000162
wherein the content of the first and second substances,
Figure GDA0003698312670000163
and
Figure GDA0003698312670000164
are all the parameters of the intensity, and the intensity,
Figure GDA0003698312670000165
in order to achieve the tensile strength of the anchor rod,
Figure GDA0003698312670000166
for tensile strength of the anchored rock mass, C r In order to add the residual cohesive force of the anchored rock body,
Figure GDA0003698312670000167
for the friction angle, tau, of the anchored rock mass b Is the shear strength of the anchor rod, and
Figure GDA0003698312670000168
2. the strength parameter of the rock mass added with the anchor under the fracture damage model (
Figure GDA0003698312670000169
And
Figure GDA00036983126700001610
) The calculation is performed by the following formula:
Figure GDA00036983126700001611
Figure GDA00036983126700001612
Figure GDA00036983126700001613
Figure GDA00036983126700001614
wherein the content of the first and second substances,
Figure GDA00036983126700001615
for tensile strength, sigma, of anchored rock masses b Is a fully-bonded anchor rod
Figure GDA00036983126700001616
Tensile strength of time, and
Figure GDA00036983126700001617
Figure GDA00036983126700001618
Figure GDA00036983126700001619
for uniaxial compressive strength of the anchored rock mass, and
Figure GDA0003698312670000171
Figure GDA0003698312670000172
in order to anchor the ultimate tensile strain of the rock mass,
Figure GDA0003698312670000173
zeta is tensile Young's modulus
Figure GDA0003698312670000174
And compressive Young's modulus E r The ratio of (a) to (b).
Further, 2 fitting parameters k and n can be obtained by curve fitting according to the following formula based on anchor rod uniaxial compression test data in different anchor rod arrangement directions under a general condition:
Figure GDA0003698312670000177
when bolt uniaxial compression test data for different bolt deployment directions are not available, the estimation can be performed based on fig. 4 by the following steps:
the k value when θ is 0 is calculated by the following formula:
Figure GDA0003698312670000175
the initial value of n is set between 1.0 and 3.0 and plotted as a λ ═ θ curve through points 1(0, k) and 2(90,1) at points 501 and 502 in fig. 5, with the value of n being continually adjusted until point 3 at point 503
Figure GDA0003698312670000176
The corresponding n value is based on the fitting n value required for the minimum uniaxial compressive strength of the anchored rock mass to be equal to the minimum uniaxial compressive strength of the rock mass.
305. And determining a deformation value and a plastic zone value of the surrounding rock according to the basic input parameters and the anisotropic elastoplasticity mechanical model after the target program is embedded.
In this embodiment, after the basic input parameters are obtained, the deformation values and the plastic region values of the surrounding rock may be determined according to the basic input parameters and the anisotropic plastic mechanical model after the target program is embedded. Namely, three-dimensional continuous medium numerical simulation of high-stress underground cavern excavation is carried out based on the obtained basic input parameters, a three-dimensional continuous rapid Lagrange analysis program (FLAC3D) platform and an anisotropic elastoplasticity mechanical model, and the reinforcing effect of the fully-bonded anchor bolt support on the anchored rock mass in the aspects of strength and rigidity is obtained by comparing the deformation of the surrounding rock and the size of a plastic zone under the condition of no anchor bolt support.
It should be noted that, when the elastic-plastic numerical value is calculated, certain requirements are provided for the grid size of the anchored rock, the maximum unit size perpendicular to the axis of the anchor rod should be smaller than 2R, otherwise, analysis errors are easy to generate, and in addition, when the deformation value and the plastic region value of the surrounding rock are determined, the grid of the anchored rock can be encrypted based on the local grid encryption technology of FLAC3D, so that the unit size requirements of a local homogenization method are met.
In summary, in the embodiment provided by the invention, based on elastoplasticity mechanics and composite material mechanics theories, a composite material structure model of the anchored rock mass is provided, the problem that the influence of the direction, the distance and the diameter of the anchor rod on the physical and mechanical parameters of the anchored rock mass cannot be considered in the existing model is solved, the macroscopic mechanical response of the surrounding rock reinforced by the fully-bonded anchor rod of the surrounding rock can be accurately predicted, and the engineering practice can be better guided.
The embodiment of the present invention is described above with reference to the calculation method of the anchor rod reinforcement effect, and the embodiment of the present invention is described below with reference to the calculation device of the anchor rod reinforcement effect.
Referring to fig. 6, a schematic view of a virtual structure of a computing device for anchor rod reinforcement effect according to an embodiment of the present invention, the computing device 600 for anchor rod reinforcement effect includes:
the building unit 601 is configured to build a composite material structure model, where a side length of the composite material structure model is a transverse distance or a longitudinal distance between two adjacent anchor rods, a height of the composite material structure model is an anchor rod length, and the composite material structure model is a polygonal rectangular prism with anchor rods located at a geometric center;
a first determining unit 602, configured to determine an anisotropic elastoplasticity mechanical model corresponding to the composite material structure model;
an embedding unit 603 configured to embed the anisotropic elasto-plastic mechanical model into a target analysis program;
a second determining unit 604, configured to determine a basic input parameter corresponding to the anisotropic elastoplasticity mechanical model after the target analysis program is embedded;
a third determining unit 605, configured to determine a surrounding rock deformation value and a plastic region value according to the basic input parameters and the anisotropic elastoplasticity mechanical model after the target program is embedded, where the surrounding rock deformation value and the plastic region value are used to represent a reinforcing effect of a fully-cemented rock bolt support on an anchored rock mass in terms of strength and rigidity, and the fully-cemented rock bolt support and the anchored rock mass correspond to the composite material structural model.
Optionally, the first determining unit 602 is specifically configured to:
determining the relation between the stress increment and the elastic strain increment in a local coordinate system, wherein the local coordinate system is the coordinate system of an isotropic plane corresponding to the anchored rock body;
determining a strength reduction coefficient, a shear yield function and a tensile yield function corresponding to the anchored rock mass;
determining the corresponding shear strength parameter of the anchored rock mass;
determining a plastic potential function corresponding to the anchored rock mass, wherein the plastic potential function is used for representing shear plastic flow and tensile plastic flow of the anchored rock mass in the longitudinal direction;
and constructing the anisotropic elastoplasticity mechanical model according to the relation between the stress increment and the elastic strain increment, the strength reduction coefficient, the shear yield function, the tensile yield function, the shear strength parameter and the plastic potential function.
Optionally, the first determining unit 602 is further specifically configured to:
determining the relationship between the stress increment and the elastic strain increment by the following formula:
[Δσ]＝[Q][K′][Q] T [Δε e ]；
wherein [ Delta sigma ]]Is the increment of stress in the global coordinate system, [ Delta ε ] e ]For the elastic strain increment in the global coordinate system, [ Q ]]Is a coordinate transformation matrix of direction sine and direction cosine in the global coordinate system, [ K']Is a local stiffness matrix.
Optionally, the first determining unit is further specifically configured to:
the intensity reduction factor is obtained by the following formula:
Figure GDA0003698312670000191
wherein, lambda is the strength reduction coefficient, theta is the included angle between the direction of the maximum principal stress and the same polarity inclination,k and n are parameters determined by fitting uniaxial or triaxial compressive strengths of different values of theta, sigma 1 (theta) rock mass strength at an angle theta, sigma 3 Is the minimum principal stress;
the shear yield function is obtained by the following formula:
Figure GDA0003698312670000192
wherein f is c s For the purpose of the shear yield function,
Figure GDA0003698312670000193
for the longitudinal cohesion of the anchored rock mass,
Figure GDA0003698312670000194
the longitudinal friction angle of the anchored rock mass;
the tensile yield function is obtained by the following formula:
Figure GDA0003698312670000195
wherein the content of the first and second substances,
Figure GDA0003698312670000196
for the said tensile yield function,
Figure GDA0003698312670000197
is the tensile strength of the anchored rock mass, and
Figure GDA0003698312670000198
gamma is the angle between the minimum principal stress direction and the normal direction of the same-polarity surface,
Figure GDA0003698312670000199
for the longitudinal tensile strength of the anchored rock mass,
Figure GDA00036983126700001910
the transverse tensile strength of the anchored rock mass.
Optionally, the first determining unit 602 is further specifically configured to:
calculating the shear strength parameter by the following formula:
Figure GDA0003698312670000201
Figure GDA0003698312670000202
wherein the content of the first and second substances,
Figure GDA0003698312670000203
as the parameter of the shear strength is,
Figure GDA0003698312670000204
in order to achieve an equivalent shear plastic strain,
Figure GDA0003698312670000205
is composed of
Figure GDA0003698312670000206
Is set to the initial value of (a),
Figure GDA0003698312670000207
is composed of
Figure GDA0003698312670000208
The remaining value of (a) is,
Figure GDA0003698312670000209
is composed of
Figure GDA00036983126700002010
Is set to the initial value of (a),
Figure GDA00036983126700002011
is composed of
Figure GDA00036983126700002012
The value of the remaining of (a) is,
Figure GDA00036983126700002013
is the ultimate equivalent plasticity reduction strain corresponding to the longitudinal residual cohesive force of the anchored rock mass,
Figure GDA00036983126700002014
and the ultimate equivalent plasticity reduction strain is corresponding to the friction angle of the anchored rock mass.
Optionally, the first determining unit 602 is further specifically configured to:
calculating the plasticity potential function by the following formula:
Figure GDA00036983126700002015
Figure GDA00036983126700002016
wherein the content of the first and second substances,
Figure GDA00036983126700002017
and
Figure GDA00036983126700002018
for the purpose of the plastic potential function,
Figure GDA00036983126700002019
the longitudinal shear expansion angle of the anchored rock mass is defined as lambda, and the lambda is the strength reduction coefficient.
Optionally, the basic input parameters include an elasticity parameter, an anchored rock strength parameter, an isotropic plane geometric parameter, and a fitting parameter, and the second determining unit 604 is specifically configured to:
determining the elasticity parameter by the following formula:
Figure GDA00036983126700002020
Figure GDA00036983126700002021
Figure GDA0003698312670000211
Figure GDA0003698312670000212
Figure GDA0003698312670000213
wherein the content of the first and second substances,
Figure GDA0003698312670000214
and
Figure GDA0003698312670000215
are all the said elastic parameters, V b Is the volume percentage of the anchor rod in the anchored rock body, and V b ＝πd 2 /4s 1 s 2 ，E r Is the Young's modulus of the anchored rock mass, E f Is the Young's modulus, mu, of the fully bonded anchor r Is the Poisson's ratio, mu, of the anchored rock mass b Is the Poisson's ratio, G, of the fully-bonded anchor rod r Is the shear modulus, G, of the anchored rock mass b Is the shear modulus of the fully bonded anchor rod, and G r ＝E r /2(1+μ r )，G b ＝E b /2(1+μ b )；
In shear failure mode, the strength parameter is calculated by the following formula:
Figure GDA0003698312670000221
Figure GDA0003698312670000222
Figure GDA0003698312670000223
Figure GDA0003698312670000224
wherein the content of the first and second substances,
Figure GDA0003698312670000225
and
Figure GDA0003698312670000226
are all the parameters of the intensity, and are,
Figure GDA0003698312670000227
in order to achieve the tensile strength of the anchor rod,
Figure GDA0003698312670000228
is the tensile strength of the anchored rock mass, C r For the residual cohesion of the anchored rock mass,
Figure GDA0003698312670000229
is the friction angle, tau, of the anchored rock mass b Is the shear strength of the anchor rod, and
Figure GDA00036983126700002210
in the cleavage damage mode, the strength parameter is calculated by the following formula:
Figure GDA00036983126700002211
Figure GDA00036983126700002212
Figure GDA00036983126700002213
Figure GDA00036983126700002214
wherein the content of the first and second substances,
Figure GDA00036983126700002215
and
Figure GDA00036983126700002216
are all said intensity parameters, σ b For the anchor rod at
Figure GDA0003698312670000231
The tensile strength of the steel sheet is high,
Figure GDA0003698312670000232
is the tensile strength of the anchored rock mass, and
Figure GDA0003698312670000233
Figure GDA0003698312670000234
Figure GDA0003698312670000235
is the uniaxial compressive strength of the anchored rock mass, an
Figure GDA0003698312670000236
Figure GDA0003698312670000237
For ultimate tensile strain of the anchored rock mass,
Figure GDA0003698312670000238
Figure GDA0003698312670000239
zeta is the Young's modulus in tension for the tensile strength of the anchored rock mass
Figure GDA00036983126700002310
And compressive Young's modulus E r The ratio of (A) to (B);
the geometrical parameters of the isotropic plane comprise an inclination angle and an inclination angle, and the inclination angle are obtained through the following formulas:
α＝180-90sgn(x′ 2 -x′ 1 )-atan((y′ 2 -y′ 1 )/(x′ 2 -x′ 1 ))；
Figure GDA00036983126700002311
wherein alpha is the inclination angle, beta is the inclination angle, (x' 1 ,y′ 1 ,z′ 1 ) Is the origin coordinate of the fully bonded bolt, (x' 2 ,y′ 2 ,z′ 2 ) The sgn is a sign function which is the terminal point coordinate of the fully-bonded anchor rod;
performing curve fitting by the following formula to obtain the fitting parameters:
Figure GDA00036983126700002312
k and n are the fitting parameters.
Fig. 6 above describes the computing device for anchor rod reinforcement effect in the embodiment of the present invention from the perspective of the modular functional entity, and the computing device for anchor rod reinforcement effect in the embodiment of the present invention is described in detail below from the perspective of hardware processing, and referring to fig. 7, an embodiment of the computing device 700 for anchor rod reinforcement effect in the embodiment of the present invention is schematically illustrated, and the computing device 700 for anchor rod reinforcement effect in the embodiment of the present invention includes:
an input device 701, an output device 702, a processor 703 and a memory 704 (wherein the number of the processor 703 may be one or more, and one processor 703 is taken as an example in fig. 7). In some embodiments of the present invention, the input device 701, the output device 702, the processor 703 and the memory 704 may be connected by a communication bus or other means, wherein the communication bus connection is taken as an example in fig. 7.
Wherein, by calling the operation instruction stored in the memory 704, the processor 703 is configured to execute the following steps:
constructing a composite material structure model, wherein the side length of the composite material structure model is the transverse distance or the longitudinal distance between two adjacent anchor rods, the height of the composite material structure model is the length of the anchor rods, and the composite material structure model is a polygonal right prism with the anchor rods positioned at the geometric center;
determining an anisotropic elastoplasticity mechanical model corresponding to the composite material structure model;
embedding the anisotropic elastoplasticity mechanical model into a target analysis program;
determining basic input parameters corresponding to the anisotropic elastoplasticity mechanical model after the target analysis program is embedded;
and determining a surrounding rock deformation value and a plastic zone value according to the basic input parameters and the anisotropic elastoplasticity mechanical model embedded into the target program, wherein the surrounding rock deformation value and the plastic zone value are used for expressing the reinforcing effect of the fully-bonded anchor bolt support on the anchored rock mass in the aspects of strength and rigidity, and the fully-bonded anchor bolt support and the anchored rock mass correspond to the composite material structure model.
The processor 703 is also configured to perform any of the methods of the corresponding embodiments of fig. 3 by invoking operational instructions stored by the memory 704.
Referring to fig. 8, fig. 8 is a schematic view illustrating an embodiment of an electronic device according to an embodiment of the invention.
As shown in fig. 8, an embodiment of the present invention provides an electronic device, which includes a memory 810, a processor 820, and a computer program 811 stored in the memory 820 and operable on the processor 820, wherein the processor 820 implements the following steps when executing the computer program 811:
constructing a composite material structure model, wherein the side length of the composite material structure model is the transverse distance or the longitudinal distance between two adjacent anchor rods, the height of the composite material structure model is the length of the anchor rods, and the composite material structure model is a polygonal right prism with the anchor rods positioned at the geometric center;
determining an anisotropic elastoplasticity mechanical model corresponding to the composite material structure model;
embedding the anisotropic elastoplasticity mechanical model into a target analysis program;
determining basic input parameters corresponding to the anisotropic elastoplasticity mechanical model after the target analysis program is embedded;
and determining a surrounding rock deformation value and a plastic zone value according to the basic input parameters and the anisotropic elastoplasticity mechanical model embedded into the target program, wherein the surrounding rock deformation value and the plastic zone value are used for expressing the reinforcing effect of the fully-bonded anchor rod support on the anchored rock mass in the aspects of strength and rigidity, and the fully-bonded anchor rod support and the anchored rock mass correspond to the composite material structure model.
In particular, when the processor 820 executes the computer program 811, any of the embodiments corresponding to fig. 3 may be implemented.
Since the electronic device described in this embodiment is a device used for implementing a computing apparatus for an anchor rod reinforcing effect in the embodiment of the present invention, based on the method described in this embodiment of the present invention, a person skilled in the art can understand a specific implementation manner of the electronic device of this embodiment and various variations thereof, so that how to implement the method in the embodiment of the present invention by the electronic device will not be described in detail herein, and as long as the person skilled in the art implements the device used for implementing the method in the embodiment of the present invention, the device used for implementing the method in the embodiment of the present invention belongs to the protection scope of the present invention.
Referring to fig. 9, fig. 9 is a schematic diagram of an embodiment of a computer-readable storage medium according to the present invention.
As shown in fig. 9, an embodiment of the present invention further provides a computer-readable storage medium 900, on which a computer program 911 is stored, where the computer program 911 when executed by a processor implements the following steps:
constructing a composite material structure model, wherein the side length of the composite material structure model is the transverse distance or the longitudinal distance between two adjacent anchor rods, the height of the composite material structure model is the length of the anchor rods, and the composite material structure model is a polygonal right prism with the anchor rods positioned at the geometric center;
determining an anisotropic elastoplasticity mechanical model corresponding to the composite material structure model;
embedding the anisotropic elastoplasticity mechanical model into a target analysis program;
determining basic input parameters corresponding to the anisotropic elastoplasticity mechanical model after the target analysis program is embedded;
and determining a surrounding rock deformation value and a plastic zone value according to the basic input parameters and the anisotropic elastoplasticity mechanical model embedded into the target program, wherein the surrounding rock deformation value and the plastic zone value are used for expressing the reinforcing effect of the fully-bonded anchor bolt support on the anchored rock mass in the aspects of strength and rigidity, and the fully-bonded anchor bolt support and the anchored rock mass correspond to the composite material structure model.
In specific implementation, the computer program 911 is executed by a processor to implement any one of the embodiments corresponding to fig. 3.
It should be noted that, in the foregoing embodiments, the descriptions of the respective embodiments have respective emphasis, and reference may be made to relevant descriptions of other embodiments for parts that are not described in detail in a certain embodiment.
As will be appreciated by one skilled in the art, embodiments of the present invention may be provided as a method, system, or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present invention is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Embodiments of the present invention further provide a computer program product, where the computer program product includes computer software instructions, and when the computer software instructions are run on a processing device, the processing device executes a flow in the calculation method for a rock bolt reinforcement effect in the embodiment corresponding to fig. 1.
The computer program product includes one or more computer instructions. When loaded and executed on a computer, cause the processes or functions described in accordance with the embodiments of the invention to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored on a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, from one website, computer, server, or data center to another website, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that a computer can store or a data storage device, such as a server, a data center, etc., that is integrated with one or more available media. The usable medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In the embodiments provided in the present invention, it should be understood that the disclosed system, apparatus and method may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is merely a logical division, and the actual implementation may be in other divisions, for example, multiple units or components may be combined or integrated into another system, or some features may be omitted, or not implemented. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The integrated unit, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
The above-mentioned embodiments are only used for illustrating the technical solutions of the present invention, and not for limiting the same; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (9)

1. A method for calculating the reinforcing effect of an anchor rod is characterized by comprising the following steps:
constructing a composite material structure model, wherein the side length of the composite material structure model is the transverse distance or the longitudinal distance between two adjacent anchor rods, the height of the composite material structure model is the length of the anchor rods, and the composite material structure model is a polygonal right prism with the anchor rods positioned at the geometric center;
determining an anisotropic elastoplasticity mechanical model corresponding to the composite material structure model;
embedding the anisotropic elastoplasticity mechanical model into a target analysis program;
determining basic input parameters corresponding to the anisotropic elastoplasticity mechanical model after the target analysis program is embedded;
determining a surrounding rock deformation value and a plastic zone value according to the basic input parameters and the anisotropic elastoplasticity mechanical model after the target analysis program is embedded, wherein the surrounding rock deformation value and the plastic zone value are used for expressing the reinforcing effect of a fully-bonded anchor bolt support on the anchored rock mass in the aspects of strength and rigidity, and the fully-bonded anchor bolt support and the anchored rock mass correspond to the composite material structure model;
the basic input parameters comprise elastic parameters, anchored rock mass strength parameters, isotropic plane geometric parameters and fitting parameters, and the determination of the basic input parameters corresponding to the anisotropic elastoplasticity mechanical model embedded in the target analysis program comprises the following steps:
determining the elasticity parameter by the following formula:
Figure FDA0003660385850000011
Figure FDA0003660385850000012
Figure FDA0003660385850000013
Figure FDA0003660385850000021
Figure FDA0003660385850000022
wherein the content of the first and second substances,
Figure FDA0003660385850000023
and
Figure FDA0003660385850000024
are all the said elastic parameters, V b Is the volume percentage of the anchor rod in the anchored rock body, and V b ＝πd 2 /4s 1 s 2 ，E r Is the Young's modulus of the anchored rock mass, E f Is the Young's modulus, mu, of the fully bonded anchor r Is the Poisson's ratio, mu, of the anchored rock mass b Is the Poisson's ratio, G, of the fully-bonded anchor rod r Is the shear modulus, G, of the anchored rock mass b Is the shear modulus of the fully bonded anchor rod, and G r ＝E r /2(1+μ r )，G b ＝E b /2(1+μ b )，E b The elastic modulus of the fully bonded anchor rod;
in shear failure mode, the strength parameter is calculated by the following formula:
Figure FDA0003660385850000025
Figure FDA0003660385850000026
Figure FDA0003660385850000031
Figure FDA0003660385850000032
wherein the content of the first and second substances,
Figure FDA0003660385850000033
and
Figure FDA0003660385850000034
are all the parameters of the intensity, and are,
Figure FDA0003660385850000035
in order to achieve the tensile strength of the anchor rod,
Figure FDA0003660385850000036
is the tensile strength of the anchored rock mass, C r For the residual cohesion of the anchored rock mass,
Figure FDA0003660385850000037
is the friction angle, tau, of the anchored rock mass b Is the shear strength of the anchor rod, and
Figure FDA0003660385850000038
in the cleavage damage mode, the strength parameter is calculated by the following formula:
Figure FDA0003660385850000039
Figure FDA00036603858500000310
Figure FDA00036603858500000311
Figure FDA00036603858500000312
wherein the content of the first and second substances,
Figure FDA00036603858500000313
and
Figure FDA00036603858500000314
are the strength parameters, sigma b is that the anchor rod is in
Figure FDA00036603858500000315
The tensile strength of the steel sheet is high,
Figure FDA00036603858500000316
is the tensile strength of the anchored rock mass, and
Figure FDA00036603858500000317
Figure FDA00036603858500000318
Figure FDA00036603858500000319
is the uniaxial compressive strength of the anchored rock mass, an
Figure FDA0003660385850000041
Figure FDA0003660385850000042
For ultimate tensile strain of the anchored rock mass,
Figure FDA0003660385850000043
Figure FDA0003660385850000044
zeta is the Young's modulus in tension for the tensile strength of the anchored rock mass
Figure FDA0003660385850000045
And compressive Young's modulus E r The ratio of (A) to (B);
the geometrical parameters of the isotropic plane comprise an inclination angle and an inclination angle, and the inclination angle are obtained through the following formulas:
α＝180-90sgn(x′ 2 -x′ 1 )-atan((y′ 2 -y′ 1 )/(x′ 2 -x′ 1 ))；
Figure FDA0003660385850000046
wherein alpha is the inclination angle, beta is the inclination angle, (x' 1 ,y′ 1 ,z′ 1 ) Is the origin coordinate of the fully bonded bolt, (x' 2 ,y′ 2 ,z′ 2 ) The sgn is a sign function which is the terminal point coordinate of the fully-bonded anchor rod;
performing curve fitting by the following formula to obtain the fitting parameters:
Figure FDA0003660385850000047
k and n are the fitting parameters, lambda is the intensity reduction coefficient, theta is the included angle between the direction of the maximum principal stress and the same plane tendency, and sigma is 1(θ) Rock mass strength at an angle theta 3 Is the minimum principal stress.
2. The method of claim 1, wherein determining the anisotropic elasto-plastic mechanical model to which the composite structural model corresponds comprises:
determining the relation between the stress increment and the elastic strain increment in a local coordinate system, wherein the local coordinate system is the coordinate system of an isotropic plane corresponding to the anchored rock body;
determining a strength reduction coefficient, a shear yield function and a tensile yield function corresponding to the anchored rock mass;
determining the shear strength parameter corresponding to the anchorage rock mass;
determining a plastic potential function corresponding to the anchored rock mass, wherein the plastic potential function is used for representing shear plastic flow and tensile plastic flow of the anchored rock mass in the longitudinal direction;
and constructing the anisotropic elastoplasticity mechanical model according to the relation between the stress increment and the elastic strain increment, the strength reduction coefficient, the shear yield function, the tensile yield function, the shear strength parameter and the plastic potential function.
3. The method of claim 2, wherein determining the relationship between the stress delta and the elastic strain delta in the local coordinate system comprises:
determining the relationship between the stress delta and the elastic strain delta by the following formula:
[Δσ]＝[Q][K′][Q] T [Δε e ]；
wherein [ Delta sigma ]]For the stress increment in the global coordinate system, [ Delta ε ] e ]For the elastic strain increment in the global coordinate system, [ Q ]]Is a coordinate transformation matrix of direction sine and direction cosine in the global coordinate system, [ K']Is a local stiffness matrix.
4. The method of claim 2, wherein determining the strength reduction factor, the shear yield function, and the tensile yield function for the anchored rock mass comprises:
the intensity reduction factor is obtained by the following formula:
Figure FDA0003660385850000051
wherein λ is the strength reduction coefficient, θ is the angle between the direction of the maximum principal stress and the same face tendency, k and n are parameters determined by fitting uniaxial or triaxial compressive strengths of different values of θ, σ 1(θ) Rock mass strength at an angle theta 3 Is the minimum principal stress;
the shear yield function is obtained by the following formula:
Figure FDA0003660385850000052
wherein the content of the first and second substances,
Figure FDA0003660385850000053
for the purpose of the shear yield function,
Figure FDA0003660385850000054
for the longitudinal cohesion of the anchored rock mass,
Figure FDA0003660385850000055
the longitudinal friction angle of the anchored rock mass;
the tensile yield function is obtained by the following formula:
Figure FDA0003660385850000056
wherein the content of the first and second substances,
Figure FDA0003660385850000057
as a function of the tensile yield, is,
Figure FDA0003660385850000058
is the tensile strength of the anchored rock mass, and
Figure FDA0003660385850000059
gamma is the angle between the minimum principal stress direction and the normal direction of the same-polarity surface,
Figure FDA00036603858500000510
for the longitudinal tensile strength of the anchored rock mass,
Figure FDA00036603858500000511
the transverse tensile strength of the anchored rock mass.
5. The method of claim 4, wherein the determining the shear strength parameter corresponding to the anchored rock mass comprises:
calculating the shear strength parameter by the following formula:
Figure FDA0003660385850000061
wherein the content of the first and second substances,
Figure FDA0003660385850000062
as the parameter of the shear strength is,
Figure FDA0003660385850000063
in order to be equivalent to the shear plastic strain,
Figure FDA0003660385850000064
is composed of
Figure FDA0003660385850000065
Is set to the initial value of (a),
Figure FDA0003660385850000066
is composed of
Figure FDA0003660385850000067
The value of the remaining of (a) is,
Figure FDA0003660385850000068
is composed of
Figure FDA0003660385850000069
Is set to the initial value of (a),
Figure FDA00036603858500000610
is composed of
Figure FDA00036603858500000611
The remaining value of (a) is,
Figure FDA00036603858500000612
is the ultimate equivalent plasticity reduction strain corresponding to the longitudinal residual cohesive force of the anchored rock mass,
Figure FDA00036603858500000613
and the equivalent plastic strain is reduced for the limit corresponding to the friction angle of the anchored rock body.
6. The method of claim 4, wherein the determining the plastic potential function for the anchored rock mass comprises:
calculating the plasticity potential function by the following formula:
Figure FDA00036603858500000614
Figure FDA00036603858500000615
wherein the content of the first and second substances,
Figure FDA00036603858500000616
and
Figure FDA00036603858500000617
and lambda is the intensity reduction coefficient for the plasticity potential function.
7. An anchor rod reinforcement effect calculation device, comprising:
the building unit is used for building a composite material structure model, wherein the side length of the composite material structure model is the transverse distance or the longitudinal distance between two adjacent anchor rods, the height of the composite material structure model is the length of the anchor rods, and the composite material structure model is a polygonal right prism with the anchor rods positioned at the geometric center;
the first determining unit is used for determining an anisotropic elastoplasticity mechanical model corresponding to the composite material structure model;
an embedding unit for embedding the anisotropic elastoplasticity mechanical model into a target analysis program;
the second determining unit is used for determining the basic input parameters corresponding to the anisotropic elastoplasticity mechanical model after the target analysis program is embedded;
a third determining unit, configured to determine a surrounding rock deformation value and a plastic region value according to the basic input parameters and the anisotropic elastoplasticity mechanical model after the target analysis program is embedded, where the surrounding rock deformation value and the plastic region value are used to represent a reinforcing effect of a fully-bonded anchor bolt support on an anchored rock mass in terms of strength and rigidity, and the fully-bonded anchor bolt support and the anchored rock mass correspond to the composite material structural model;
the basic input parameters comprise elastic parameters, anchored rock mass strength parameters, isotropic plane geometric parameters and fitting parameters, and the second determining unit is specifically used for:
determining the elasticity parameter by the following formula:
Figure FDA0003660385850000071
Figure FDA0003660385850000072
Figure FDA0003660385850000073
Figure FDA0003660385850000074
Figure FDA0003660385850000075
wherein the content of the first and second substances,
Figure FDA0003660385850000076
and
Figure FDA0003660385850000077
are all the said elastic parameters, V b Is the volume percentage of the anchor rod in the anchored rock body, and V b ＝πd 2 /4s 1 s 2 ，E r Is the Young's modulus of the anchored rock mass, E f Is the Young's modulus, mu, of the fully bonded anchor r Is the Poisson's ratio, mu, of the anchored rock mass b Is the Poisson's ratio, G, of the fully-bonded anchor rod r Is the shear modulus, G, of the anchored rock mass b Is the shear modulus of the fully bonded anchor rod, and G r ＝E r /2(1+μ r )，G b ＝E b /2(1+μ b )，E b The elastic modulus of the fully bonded anchor rod;
in shear failure mode, the strength parameter is calculated by the following formula:
Figure FDA0003660385850000081
Figure FDA0003660385850000082
Figure FDA0003660385850000083
Figure FDA0003660385850000084
wherein the content of the first and second substances,
Figure FDA0003660385850000085
and
Figure FDA0003660385850000086
are all the parameters of the intensity, and are,
Figure FDA0003660385850000087
in order to achieve the tensile strength of the anchor rod,
Figure FDA0003660385850000088
is the tensile strength of the anchored rock mass, C r For the residual cohesion of the anchored rock mass,
Figure FDA0003660385850000089
is the friction angle, tau, of the anchored rock mass b Is the shear strength of the anchor rod, and
Figure FDA00036603858500000810
in the cleavage damage mode, the strength parameter is calculated by the following formula:
Figure FDA00036603858500000811
Figure FDA0003660385850000091
Figure FDA0003660385850000092
Figure FDA0003660385850000093
wherein the content of the first and second substances,
Figure FDA0003660385850000094
and
Figure FDA0003660385850000095
are all said intensity parameters, σ b For the anchor rod at
Figure FDA0003660385850000096
The tensile strength of the steel sheet is high,
Figure FDA0003660385850000097
is the tensile strength of the anchored rock mass, and
Figure FDA0003660385850000098
Figure FDA0003660385850000099
Figure FDA00036603858500000910
is the uniaxial compressive strength of the anchored rock mass, an
Figure FDA00036603858500000911
Figure FDA00036603858500000912
For ultimate tensile strain of the anchored rock mass,
Figure FDA00036603858500000913
Figure FDA00036603858500000914
zeta is the Young's modulus in tension for the tensile strength of the anchored rock mass
Figure FDA00036603858500000915
And compressive Young's modulus E r The ratio of (A) to (B);
the geometrical parameters of the isotropic plane comprise an inclination angle and an inclination angle, and the inclination angle are obtained through the following formulas:
α＝180-90sgn(x′ 2 -x′ 1 )-atan((y′ 2 -y′ 1 )/(x′ 2 -x′ 1 ))；
Figure FDA00036603858500000916
wherein alpha is the inclination angle, beta is the inclination angle, (x' 1 ,y′ 1 ,z′ 1 ) Is the origin coordinate of the fully bonded bolt, (x' 2 ,y′ 2 ,z′ 2 ) The sgn is a sign function which is the terminal point coordinate of the fully-bonded anchor rod;
performing curve fitting by the following formula to obtain the fitting parameters:
Figure FDA0003660385850000101
k and n are the fitting parameters, lambda is the intensity reduction coefficient, theta is the included angle between the direction of the maximum principal stress and the same plane tendency, and sigma is 1(θ) Rock mass strength at an angle theta 3 Is the minimum principal stress.
8. An electronic device, comprising:
a memory, a processor for implementing a method of calculating a bolt-strengthening effect as claimed in any one of claims 1 to 6 when executing a computer management-like program stored in the memory.
9. A computer-readable storage medium having stored thereon a computer management-like program, characterized in that: the computer management program when executed by a processor implements a method of calculating a bolt strengthening effect as claimed in any one of claims 1 to 6.
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Publication number Priority date Publication date Assignee Title
CN109209455A (en) * 2018-09-26 2019-01-15 浙江普泰克金属制品有限公司 A kind of expansion shell type prestressing force hollow grouting anchor with plasma resistance plug

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