CN101614537A - A kind of quantitative calculation method of crack extending depth of clay structure - Google Patents

Abstract

The present invention relates to a kind of quantitative calculation method of crack extending depth of clay structure, this method comprises: S1. contains fracture intensive, parallel crack with one and brings the macroscopic fracture of describing clay structure; S2. utilize the stretching experiment of clay material, find the solution the energy to failure and the tensile strength of clay structure zone of fracture resisting crack extending capability; S3. utilize the energy to failure index of being found the solution, find the solution clay structure zone of fracture size; S4. according to described zone of fracture size, division unit grid; S5. utilize finite element method, each unit grid of being divided is calculated stress deformation, obtain the crack extending depth under certain seam face acting force.The computing method of crack extending depth of clay structure of the present invention have advantages such as quantification, practicality, precision height, future in engineering applications be wide.

Description

A kind of quantitative calculation method of crack extending depth of clay structure

Technical field

The present invention relates to the quantitative calculation method of crack extending depth in the works that a kind of tailing dam, soil-slope, dyke etc. are built by clay class bing.

Background technology

Large-scale Geotechnical Engineerings such as tailing dam, soil-slope, dyke, mostly build formation with clay class bing, these clay structure generation dam breaks, disaster such as come down and inrush are mostly based on the transverse and longitudinal through crack, fully realizing the clay structure crack produces and propagation law, quantitative Analysis is also predicted crack extending depth in the clay structure, for the generation of prevention industrial accident, guarantee that these clay structure periphery life property safety of people are significant.

For a long time, Chinese scholars mostly lays particular emphasis on the mensuration of soil body tensile strength at the research of clay structure crack problem, still the quantitative calculation method that does not have crack extending depth of clay structure, still there are not index and the method for weighing the clay structure resisting crack extending capability, mainly qualitatively judge and illustrate according to engineering experience, clay structure pressurized degree, these prior aries existence are subjected to the subjectivity factor affecting more, shortcomings such as operability is poor, shortage scientific basis.

Summary of the invention

Purpose of the present invention just is to provide a kind of quantitative calculation method of crack extending depth of clay structure, to solve above-mentioned defective of the prior art.

For achieving the above object, technical scheme of the present invention is to adopt a kind of quantitative calculation method of crack extending depth of clay structure, and this method comprises:

S1, contain fracture intensive, parallel crack with one and bring the macroscopic fracture of describing clay structure;

S2, utilize the stretching experiment of clay material, find the solution the energy to failure and the tensile strength of clay structure zone of fracture resisting crack extending capability;

The energy to failure index that S3, utilization are found the solution is found the solution clay structure zone of fracture size;

S4, according to described zone of fracture size, division unit grid;

S5, utilize finite element method, each unit grid of being divided is calculated stress deformation, obtain the crack extending depth under certain seam face acting force.

Wherein, described step S5 comprises:

S5-1, according to the cracking criterion, judge whether each unit grid ftractures;

S5-2, if cracking not, then utilize isotropy nonlinear elastic model under the global coordinate system to represent the nonlinear relationship of ess-strain;

If ftracture, then utilize the nonlinear relationship behind the cracking of this unit of the blunt zone of fracture model description of anisotropy under the local coordinate system;

S5-3, by global coordinate system and local coordinate system transition matrix, the nonlinear relationship of unit grid behind the cracking is converted into the relation of global coordinate system, obtain the crack extending depth under certain seam face acting force.

Wherein, the cracking criterion of described step S5-1 is for when the least principal stress of unit grid reaches tensile strength, and fail in tension can take place clay material, and in the direction perpendicular to least principal stress the crack takes place.

Wherein, the isotropy nonlinear elastic model among the described step S5-2 is:

$\left\{\begin{array}{c}{\mathrm{\Δ\σ}}_x\\ {\mathrm{\Δ\σ}}_y\\ {\mathrm{\Δ\τ}}_{\mathrm{xy}}\end{array}\right\}=\left[\begin{array}{ccc}\frac{E_t(1-v)}{(1+v)(1-2v)}& \frac{E_{t}v}{(1+v)(1-2v)}& 0\\ \frac{E_{t}v}{(1+v)(1-2v)}& \frac{E_t(1-v)}{(1+v)(1-2v)}& 0\\ 0& 0& G\end{array}\right]\left\{\begin{array}{c}{\mathrm{\Δ\ϵ}}_x\\ {\mathrm{\Δ\ϵ}}_y\\ {\mathrm{\Δ\γ}}_{\mathrm{xy}}\end{array}\right\}$

Wherein: Δ σ _x, Δ σ _y, Δ τ _XyBe respectively horizontal stress increment, perpendicular stress increment, the shear stress increment of plane strain lower unit grid; Δ ε _x, Δ ε _y, Δ γ _XyBe respectively horizontal strain increment, vertical strain increment, the shearing strain increment of plane strain lower unit grid; V is a Poisson ratio; G is a modulus of shearing; E _tBe tangent modulus of elasticity, computing formula is:

$E_t=E-E{A}_1{\left(\frac{\mathrm{\ϵ}}{{\mathrm{\ϵ}}_f}\right)}^{B_1}-E{A}_1{B}_1{\left(\frac{\mathrm{\ϵ}}{{\mathrm{\ϵ}}_f}\right)}^{B_1}.$

Wherein, the blunt zone of fracture model of the anisotropy among the described step S5-2 is:

$\left\{\mathrm{\σ}\right\}=\left[D^{\′}\right]\left\{\mathrm{\ϵ}\right\}=\left[\begin{array}{ccc}{D}_{11}^{\′}& D_{12}^{\′}& 0\\ D_{21}^{\′}& D_{22}^{\′}& 0\\ 0& 0& D_{33}^{\′}\end{array}\right]\left\{\mathrm{\ϵ}\right\}$

Wherein: [D '] is the stress-strain relation matrix of soil body unit in local coordinate system; β is the modulus of shearing reduction coefficient; μ is the elastic modulus reduction coefficient, and other CALCULATION OF PARAMETERS method is:

$D_{11}^{\′}=\frac{\mathrm{\μ}(1-v)E}{1-v-2\mathrm{\μ}{v}^2}$

$D_{22}^{\′}=\frac{E(1-\mathrm{\μ}{v}^2)}{(1+v)(1-v-2\mathrm{\μ}{v}^2)}$

D′ ₃₃＝βG

$D_{12}^{\′}=D_{21}^{\′}=\frac{\mathrm{\μvE}}{1-v-2\mathrm{\μ}{v}^2}.$

Wherein, the transition matrix among the described step S5-3 is:

$\left[R\right]=\left[\begin{array}{ccc}{\cos }^2{\mathrm{\β}}_j& {\sin }^2{\mathrm{\β}}_j& \cos {\mathrm{\β}}_j\sin {\mathrm{\β}}_j\\ {\sin }^2{\mathrm{\β}}_j& {\cos }^2{\mathrm{\β}}_j& -\cos {\mathrm{\β}}_j\sin {\mathrm{\β}}_j\\ -2\cos {\mathrm{\β}}_j\sin {\mathrm{\β}}_j& 2\cos {\mathrm{\β}}_j\sin {\mathrm{\β}}_j& {\cos }^2{\mathrm{\β}}_j-{\sin }^2{\mathrm{\β}}_j\end{array}\right]$

Wherein, β _jAngle for local coordinate system and global coordinate system.

Wherein, the calculation formula of fracture energy of described step S2 is:

G _f＝∫σdW

Wherein: G _fBe energy to failure, σ is the tension of zone of fracture, and W is the additional deformation of zone of fracture.

The quantitative calculation method of crack extending depth of clay structure of the present invention is not only practical, precision is high, future in engineering applications is wide, and has a quantification, advantages such as authentication method advanced person, calculating is accurate, future in engineering applications is wide, can provide important evidence for the industrial accident early-warning and predicting of large-scale Geotechnical Engineering clay structures such as tailing dam, soil-slope, dyke, be of great practical significance for the safety management of large-scale Geotechnical Engineering.

Description of drawings

Fig. 1 is the precedence diagram of crack extending depth of clay structure quantitative calculation method involved in the present invention;

Fig. 2 is a clay structure zone of fracture synoptic diagram;

Fig. 3 is the ELEMENT MESH GRAPH of clay structure test specimen;

Fig. 4 is a clay structure energy to failure index synoptic diagram;

Fig. 5 is the preceding isotropy nonlinear elastic model of cracking;

Fig. 6 is the blunt zone of fracture model of cracking back anisotropy;

Fig. 7 is the figure of the expression clay structure test specimen cracking degree of depth.

Embodiment

Following examples are used to illustrate the present invention, but are not used for limiting the scope of the invention.

As shown in Figure 1, the quantitative calculation method of crack extending depth of clay structure of the present invention may further comprise the steps:

S1, contain fracture intensive, parallel crack with one and bring the macroscopic fracture of describing clay structure, clay structure crack propagation behavior shows as the constantly softening and failure procedure of zone of fracture intensity.

As shown in Figure 2, according to a large amount of clay material tension tests, the present invention with the crack propagation process of clay material be divided into fine fisssure (as Fig. 2 a), subcritical expansion (as Fig. 2 b) and unstable propagation (as Fig. 2 c) three phases.The lower situation of corresponding tensile stress level of fine fisssure stage, expansion and connection take place in the microporosity in the clay structure at this moment, and the macroscopic deformation modulus reduces not obvious.Subcritical extension phase is near the stage the clay structure ultimate tensile strength (UTS) both sides, and this stage, porosity communication took place, crackle merges and intersection, shows as the slow increase of load-bearing capacity or slowly reduction on macroscopic view.When hole continues to be communicated with, can progressively form the crack that macroscopic view is communicated with, this moment, the resistance to tension of clay structure can take place to reduce apace until completely losing, and this stage is called the unstable propagation stage.In each extension phase, the crack produces and expansion process all shows as constantly softening and failure procedure of the interior intensity in zone of fracture among Fig. 2 (Lc) zone.

S2, utilize the stretching experiment of clay material, find the solution the energy to failure and the tensile strength of clay structure zone of fracture resisting crack extending capability.

The energy to failure index that S3, utilization are found the solution is found the solution clay structure zone of fracture size.

S4, according to described zone of fracture size, division unit grid.

As shown in Figure 3, get the long and high square test specimen that is 30m, two fixed ends up and down, there is the weakness band of a long 3m next-door neighbour test specimen center, upstream, in the process of retaining (approximate simulation clay core wall and reservoir filling process), hydraulic pressure can at first infiltrate in the initial seam before test specimen, and the effect of water pressure can produce hydraulic pressure " wedge cleaving effect ", the crack is expanded, calculated and initially sew on the degree of depth that expansion is continued in crack, stressed back.

Fig. 4 is a clay structure energy to failure index synoptic diagram, and among the figure, the σ among Fig. 4 a is that tension, ε are stretching strain; W among Fig. 4 b is additional deformation, the W of zone of fracture _LThe additional deformation of zone of fracture when rupturing fully for clay structure.The relation of tensile stress sigma and zone of fracture additional deformation W can obtain by the clay material uniaxial tensile test.

Energy to failure G _fBe the area that surrounds under tensile stress sigma and the zone of fracture additional deformation W half interval contour, computing formula is:

G _f＝∫σdW

S5, utilize finite element method, each unit grid of being divided is calculated stress deformation, obtain the crack extending depth under certain seam face acting force.

S5-1, judge clay structure cracking state according to the cracking criterion.

The present invention obtains according to a large amount of uniaxial tensile tests, and when the least principal stress of clay material reached tensile strength, fail in tension can take place clay material, and in the direction perpendicular to least principal stress the crack takes place.So the present invention adopts following cracking criterion:

σ ₃＜σ _t

Wherein, σ ₃Be minor principal stress; σ _tBe tensile strength.

Derivation also calculates the preceding isotropy nonlinear elastic model of clay structure cracking, the cracking back blunt zone of fracture model of anisotropy.

S5-2, if cracking not, then utilize isotropy nonlinear elastic model under the global coordinate system to represent the nonlinear relationship of ess-strain; If ftracture, then utilize the nonlinear relationship behind the cracking of this unit of the blunt zone of fracture model description of anisotropy under the local coordinate system.

Fig. 5 is the preceding isotropy nonlinear elastic model of clay structure cracking, among the figure, and σ _tBe tensile strength; E represents stretching initial elasticity modulus; μ ₀Be initial elasticity modulus reduction coefficient; ε _fBe peak strain.

Stress-strain relation was expressed as before the present invention will ftracture:

$\mathrm{\&sigma;}=\mathrm{E\&epsiv;}({\mathrm{\&mu;}}_0-A_1{\left(\frac{\mathrm{\&epsiv;}}{{\mathrm{\&epsiv;}}_f}\right)}^{B_1}),(0<\mathrm{\&epsiv;}<{\mathrm{\&epsiv;}}_f)$

Wherein, A ₁And B ₁Be material constant, computing formula is:

$A_1={\mathrm{\&mu;}}_0-\frac{{\mathrm{\&sigma;}}_t}{E{\mathrm{\&epsiv;}}_f}$

$B_1=\frac{{\mathrm{\&sigma;}}_t}{{\mathrm{\&mu;}}_{0}E{\mathrm{\&epsiv;}}_f-{\mathrm{\&sigma;}}_t}$

In the formula, μ ₀, σ _t, E, ε _fObtain by uniaxial tensile test.

Under plane strain condition, ess-strain nonlinear elasticity matrix is:

$\left\{\begin{array}{c}{\mathrm{\&Delta;\&sigma;}}_x\\ {\mathrm{\&Delta;\&sigma;}}_y\\ {\mathrm{\&Delta;\&tau;}}_{\mathrm{xy}}\end{array}\right\}=\left[\begin{array}{ccc}\frac{E_t(1-v)}{(1+v)(1-2v)}& \frac{E_{t}v}{(1+v)(1-2v)}& 0\\ \frac{E_{t}v}{(1+v)(1-2v)}& \frac{E_t(1-v)}{(1+v)(1-2v)}& 0\\ 0& 0& G\end{array}\right]\left\{\begin{array}{c}{\mathrm{\&Delta;\&epsiv;}}_x\\ {\mathrm{\&Delta;\&epsiv;}}_y\\ {\mathrm{\&Delta;\&gamma;}}_{\mathrm{xy}}\end{array}\right\}$

Wherein, Δ σ _x, Δ σ _y, Δ τ _XyBe respectively horizontal stress increment under the plane strain, perpendicular stress increment, shear stress increment; Δ ε _x, Δ ε _y, Δ γ _XyBe respectively horizontal strain increment under the plane strain, vertical strain increment, shearing strain increment; V is a Poisson ratio; G is a modulus of shearing; E _tBe tangent modulus of elasticity, computing formula is:

$E_t=E-E{A}_1{\left(\frac{\mathrm{\&epsiv;}}{{\mathrm{\&epsiv;}}_f}\right)}^{B_1}-E{A}_1{B}_1{\left(\frac{\mathrm{\&epsiv;}}{{\mathrm{\&epsiv;}}_f}\right)}^{B_1}$

Fig. 6 is the blunt zone of fracture model of clay structure cracking back anisotropy, and among the figure, x/y is a global coordinate system; X '/y ' is the crack local coordinate system; β _jAngle for local coordinate system and global coordinate system; σ _{X '}, σ _{Y '}Be respectively horizontal stress and perpendicular stress under the local coordinate system; σ ₁, σ ₃Be respectively big principle stress and minor principal stress.

After the least principal stress of clay material reached the ultimate tensile strength (UTS) of the soil body, the soil body produced the crack in the direction perpendicular to least principal stress.The crack produces the back clay material and promptly loses extensional rigidity in the normal direction in crack, but other direction still can bearing load effect, so the soil body behind the generation crack can be processed into anisotropic body, to simulate the soil body in the forfeiture of crack normal direction extensional rigidity and the load-bearing capacity of vertical direction.

For this reason, vertically to set up the local coordinate system of unit with the direction that is parallel to fracture plane.In this local coordinate system, can be with the blunt stress-strain relation matrix representation of splitting band in clay material cracking back:

$\left\{\mathrm{\&sigma;}\right\}=\left[D^{\&prime;}\right]\left\{\mathrm{\&epsiv;}\right\}=\left[\begin{array}{ccc}{D}_{11}^{\&prime;}& D_{12}^{\&prime;}& 0\\ D_{21}^{\&prime;}& D_{22}^{\&prime;}& 0\\ 0& 0& D_{33}^{\&prime;}\end{array}\right]\left\{\mathrm{\&epsiv;}\right\}$

Wherein, [D '] is the stress-strain relation matrix of soil body unit in local coordinate system; β is the modulus of shearing reduction coefficient; μ is the elastic modulus reduction coefficient.In addition, other CALCULATION OF PARAMETERS method is:

$D_{11}^{\&prime;}=\frac{\mathrm{\&mu;}(1-v)E}{1-v-2\mathrm{\&mu;}{v}^2}$

$D_{22}^{\&prime;}=\frac{E(1-\mathrm{\&mu;}{v}^2)}{(1+v)(1-v-2\mathrm{\&mu;}{v}^2)}$

D′ ₃₃＝βG

$D_{12}^{\&prime;}=D_{21}^{\&prime;}=\frac{\mathrm{\&mu;vE}}{1-v-2\mathrm{\&mu;}{v}^2}$

S5-3, by global coordinate system and local coordinate system transition matrix, the nonlinear relationship of unit grid behind the cracking is converted into the relation of global coordinate system, obtain the crack extending depth under certain seam face acting force.

[D] and [D '] is respectively the stiffness matrix under global coordinate system and the local coordinate system, and the pass of two stiffness matrix is:

[D]＝[R] ^T[D′][R]

Wherein, [R] is global coordinate system and crack local coordinate system transition matrix.

The computing method of transition matrix are:

$\left[R\right]=\left[\begin{array}{ccc}{\cos }^2{\mathrm{\&beta;}}_j& {\sin }^2{\mathrm{\&beta;}}_j& \cos {\mathrm{\&beta;}}_j\sin {\mathrm{\&beta;}}_j\\ {\sin }^2{\mathrm{\&beta;}}_j& {\cos }^2{\mathrm{\&beta;}}_j& -\cos {\mathrm{\&beta;}}_j\sin {\mathrm{\&beta;}}_j\\ -2\cos {\mathrm{\&beta;}}_j\sin {\mathrm{\&beta;}}_j& 2\cos {\mathrm{\&beta;}}_j\sin {\mathrm{\&beta;}}_j& {\cos }^2{\mathrm{\&beta;}}_j-{\sin }^2{\mathrm{\&beta;}}_j\end{array}\right]$

Wherein, β _jAngle for local coordinate system and global coordinate system.

As shown in Figure 7, calculate, when this unit does not reach tensile strength, represent the nonlinear relationship (this relation is under the global coordinate system) of ess-strain with the isotropy nonlinear elastic model the then calculating in each unit, unit; When certain unit reaches tensile strength, with the behavior behind the cracking of this unit of the blunt zone of fracture model description of anisotropy (behavior is under the local coordinate system), by global coordinate system and crack local coordinate system transition matrix, the nonlinear relationship of the unit behind the cracking is converted into the relation of global coordinate system then.After the unit has calculated one by one, just can obtain the crack extending depth under this seam face acting force, finally obtain the expansion depth of 8m as shown in Figure 7:

Authentication method advanced person of the present invention, calculate accurately, future in engineering applications is wide, can provide important evidence for the industrial accident early-warning and predicting of large-scale Geotechnical Engineering clay structures such as tailing dam, soil-slope, dyke, be of great practical significance for the safety management of large-scale Geotechnical Engineering.

The above; only for the preferable embodiment of the present invention, but protection scope of the present invention is not limited thereto, and anyly is familiar with those skilled in the art in the technical scope that the present invention discloses; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.

Claims (7)

1, a kind of quantitative calculation method of crack extending depth of clay structure is characterized in that, this method comprises:

S1, contain fracture intensive, parallel crack with one and bring the macroscopic fracture of describing clay structure;

S2, utilize the stretching experiment of clay material, find the solution the energy to failure and the tensile strength of clay structure zone of fracture resisting crack extending capability;

The energy to failure index that S3, utilization are found the solution is found the solution clay structure zone of fracture size;

S4, according to described zone of fracture size, division unit grid;

S5, utilize finite element method, each unit grid of being divided is calculated stress deformation, obtain the crack extending depth under certain seam face acting force.

2, the quantitative calculation method of crack extending depth of clay structure as claimed in claim 1 is characterized in that, described step S5 comprises:

S5-1, according to the cracking criterion, judge whether each unit grid ftractures;

S5-2, if cracking not, then utilize isotropy nonlinear elastic model under the global coordinate system to represent the nonlinear relationship of ess-strain;

If ftracture, then utilize the nonlinear relationship behind the cracking of this unit of the blunt zone of fracture model description of anisotropy under the local coordinate system;

S5-3, by global coordinate system and local coordinate system transition matrix, the nonlinear relationship of unit grid behind the cracking is converted into the relation of global coordinate system, obtain the crack extending depth under certain seam face acting force.

3, the quantitative calculation method of crack extending depth of clay structure as claimed in claim 2, it is characterized in that, the cracking criterion of described step S5-1 is for when the least principal stress of unit grid reaches tensile strength, fail in tension can take place in clay material, and in the direction perpendicular to least principal stress the crack takes place.

4, the quantitative calculation method of crack extending depth of clay structure as claimed in claim 2 is characterized in that, the isotropy nonlinear elastic model among the described step S5-2 is:

$\left\{\begin{array}{c}\mathrm{\&Delta;}{\mathrm{\&sigma;}}_x\\ \mathrm{\&Delta;}{\mathrm{\&sigma;}}_y\\ \mathrm{\&Delta;}{\mathrm{\&tau;}}_{\mathrm{xy}}\end{array}\right\}=\left[\begin{array}{ccc}\frac{E_t(1-v)}{(1+v)(1-2v)}& \frac{E_{t}v}{(1+v)(1-2v)}& 0\\ \frac{E_{t}v}{(1+v)(1-2v)}& \frac{E_t(1-v)}{(1+v)(1-2v)}& 0\\ 0& 0& G\end{array}\right]\left\{\begin{array}{c}\mathrm{\&Delta;}{\mathrm{\&epsiv;}}_x\\ \mathrm{\&Delta;}{\mathrm{\&epsiv;}}_y\\ \mathrm{\&Delta;}{\mathrm{\&gamma;}}_{\mathrm{xy}}\end{array}\right\}$

Wherein: Δ δ _x, Δ δ _y, Δ τ _XyBe respectively horizontal stress increment, perpendicular stress increment, the shear stress increment of plane strain lower unit grid; Δ ε _x, Δ ε _y, Δ γ _XyBe respectively horizontal strain increment, vertical strain increment, the shearing strain increment of plane strain lower unit grid; V is a Poisson ratio; G is a modulus of shearing; E _tBe tangent modulus of elasticity, computing formula is:

$E_t=E-{\mathrm{EA}}_1{\left(\frac{\mathrm{\&epsiv;}}{{\mathrm{\&epsiv;}}_f}\right)}^{B_1}-{\mathrm{EA}}_1{B}_1{\left(\frac{\mathrm{\&epsiv;}}{{\mathrm{\&epsiv;}}_f}\right)}^{B_1}.$

5, the quantitative calculation method of crack extending depth of clay structure as claimed in claim 2 is characterized in that, the blunt zone of fracture model of the anisotropy among the described step S5-2 is:

$\left\{\mathrm{\&sigma;}\right\}=\left[D^{\&prime;}\right]\left\{\mathrm{\&epsiv;}\right\}=\left[\begin{array}{ccc}{D}_{11}^{\&prime;}& D_{12}^{\&prime;}& 0\\ D_{21}^{\&prime;}& D_{22}^{\&prime;}& 0\\ 0& 0& D_{33}^{\&prime;}\end{array}\right]\left\{\mathrm{\&epsiv;}\right\}$

Wherein: [D '] is the stress-strain relation matrix of soil body unit in local coordinate system; β is the modulus of shearing reduction coefficient; μ is the elastic modulus reduction coefficient, and other CALCULATION OF PARAMETERS method is:

$D_{11}^{\&prime;}=\frac{\mathrm{\&mu;}(1-v)E}{1-v-2\mathrm{\&mu;}{v}^2}$

$D_{22}^{\&prime;}=\frac{E(1-\mathrm{\&mu;}{v}^2)}{(1+v)(1-v-2\mathrm{\&mu;}{v}^2)}$

D′ ₃₃＝βG

$D_{12}^{\&prime;}=D_{21}^{\&prime;}=\frac{\mathrm{\&mu;vE}}{1-v-2\mathrm{\&mu;}{v}^2}.$

6, the quantitative calculation method of crack extending depth of clay structure as claimed in claim 2 is characterized in that, the transition matrix among the described step S5-3 is:

$\left[R\right]=\left[\begin{array}{ccc}{\cos }^2{\mathrm{\&beta;}}_j& {\sin }^2{\mathrm{\&beta;}}_j& \cos {\mathrm{\&beta;}}_j\sin {\mathrm{\&beta;}}_j\\ {\sin }^2{\mathrm{\&beta;}}_j& {\cos }^2{\mathrm{\&beta;}}_j& -\cos {\mathrm{\&beta;}}_j\sin {\mathrm{\&beta;}}_j\\ -2\cos {\mathrm{\&beta;}}_j\sin {\mathrm{\&beta;}}_j& 2\cos {\mathrm{\&beta;}}_j\sin {\mathrm{\&beta;}}_j& {\cos }^2{\mathrm{\&beta;}}_j-{\sin }^2{\mathrm{\&beta;}}_j\end{array}\right]$

Wherein, β _jAngle for local coordinate system and global coordinate system.

7, the quantitative calculation method of crack extending depth of clay structure as claimed in claim 1 is characterized in that, the calculation formula of fracture energy of described step S2 is:

G _f＝∫σdW

Wherein: G _fBe energy to failure, σ is the tension of zone of fracture, and W is the additional deformation of zone of fracture.

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