CN101603960A - A kind of definite method of nonpenetrating jointed and fractured rock mass deformation parameter - Google Patents

Abstract

The invention discloses a kind of definite method of nonpenetrating jointed and fractured rock mass deformation parameter, this method is implemented according to following steps: step 1: image data, the fracture set analysis is carried out in crack to the non-perforation crack rock of sample rock, collect the some groups of fracture sets that account for main influence, and detect the numerical value of the thickness rate in the inclination angle obtain each fracture set, connection rate, spacing, each crack; Step 2: by indoor rock mechanics experiment, the deformation modulus of deformation modulus, Poisson ratio and the sillar of stuff, the numerical value of Poisson ratio in the non-perforation of each fracture set crack that acquisition step 1 is gathered; Step 3: set up non-perforation crack rock distorted pattern; Step 4: will obtain in the concrete numerical value model formation that substitution step 3 obtains respectively of each parameter in step 1 and step 3, obtain non-perforation crack rock deformation modulus and the Poisson ratio numerical value organized that contain in this sample rock more, this numerical error significantly reduces, and can satisfy engineering or designing requirement.

Description

A kind of definite method of nonpenetrating jointed and fractured rock mass deformation parameter

Technical field

The invention belongs to the geotechnical engineering investigation technical field, relate to a kind of definite method of nonpenetrating jointed and fractured rock mass deformation parameter.

Background technology

The science of non-perforation crack rock deformation parameter is determined, and is very important in the utilizations such as the design of rock mass engineerings such as cavern, rock side slope, rock matter roadbed under the rock quality, estimation of stability and formulation reinforcement measure.The non-perforation crack rock deformation parameter of tradition is to cut experiment greatly or lack representational laboratory experiment by costly scene to determine, though these two kinds of definite methods have obtained using widely on engineering, and summed up a large amount of application experiences, but these methods can't directly reflect key factors such as influencing the non-perforation of rock mass deformation character crack, determined non-perforation crack rock deformation parameter error is bigger, is difficult to satisfy the needs on the engineering.

Non-perforation crack rock deformation parameter is the concentrated reflection of deformation properties, this just requires must reflect when determining its deformation parameter influences rock mass deformation character principal element, as sillar deformation properties, fracture filling deformation properties, crack geometric parameter, crack deformation parameter etc., therefore set up a kind of definite method of nonpenetrating jointed and fractured rock mass deformation parameter, to help science, determine non-perforation crack rock deformation parameter exactly, make non-perforation crack rock deformation parameter error minimize, improve the science that engineering is used.

Summary of the invention

The definite method that the purpose of this invention is to provide a kind of nonpenetrating jointed and fractured rock mass deformation parameter, determined non-perforation crack rock deformation parameter error significantly reduces, and the science reflection influences the factor of rock mass deformation parameter, makes more science, reasonable and accurate of the method for determining.

The technical solution adopted in the present invention is, a kind of definite method of nonpenetrating jointed and fractured rock mass deformation parameter, and this method is implemented according to following steps:

Step 1: image data, the fracture set analysis is carried out in the crack of the non-perforation crack rock of sample rock, collect some groups fracture set, and detect the inclination alpha that obtains each fracture set _j, the connection rate Interval S _j, each crack the thickness rate

Numerical value;

Step 2: by indoor rock mechanics experiment, the deformation modulus of stuff in the non-perforation of each fracture set crack that acquisition step 1 is gathered

Poisson ratio

And the deformation modulus E of sillar _r, Poisson ratio μ _rNumerical value;

Step 3: set up non-perforation crack rock deformation parameter computation model

If contain m group crack in the rock mass, respectively organize inclination angle, non-perforation crack in the rock mass and be respectively α ₁, α ₂, α ₃..., α _m, the connection rate is respectively λ _F1, λ _F2, λ _F3..., λ _Fm, the thickness rate is respectively λ _H1, λ _H2, λ _H3..., λ _Hm, each is organized, and the stuff deformation modulus is respectively E in the crack _F1, E _F2, E _F3..., E _Fm, Poisson ratio is respectively μ _F1, μ _F2, μ _F3..., μ _Fm, each is organized fracture spacing and is respectively S ₁, S ₂, S ₃..., S _m,

For containing m group crack rock, every group contains the non-perforation of n bar crack, and the total deformation that can obtain rock mass is:

$d=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{d}_{{\mathrm{fr}}_{\mathrm{ij}}}+d_r---\left(1\right)$

In the formula:

$d_{\mathrm{fr}}=\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_{\mathrm{fr}}^2)}{\frac{E_f{E}_r(1-{\mathrm{\&mu;}}_{\mathrm{fr}}^2)}{{\mathrm{\&lambda;}}_f(1-{\mathrm{\&mu;}}_f^2)E_r+(1-{\mathrm{\&lambda;}}_f)(1-{\mathrm{\&mu;}}_r^2)E_{\mathrm{<figure-callout\; id="3"\; label="f\; hco\; s"\; filenames="A2009100231560015H2.png"\; state="\{\{state\}\}">f</figure-callout>}}}}\mathrm{hco}{s}^{}{}^3\mathrm{\&alpha;}+\frac{\mathrm{\&sigma;}}{\frac{E_f{E}_r}{2\{{\mathrm{\&lambda;}}_f{E}_r(1+{\mathrm{\&mu;}}_f)+(1-{\mathrm{\&lambda;}}_f)E_f(1+{\mathrm{\&mu;}}_r)\}}}d{\sin }^2\mathrm{\&alpha;}\cos \mathrm{\&alpha;}$

$d_r=\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_r^2)}{E_r}(L-h)$

Can get:

$d=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{\frac{E_{\mathrm{fij}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}(1-{\mathrm{\&mu;}}_{f_{\mathrm{ij}}}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})(1-{\mathrm{\&mu;}}_r^2)E_{f_{\mathrm{ij}}}}}{\mathrm{<figure-callout\; id="3"\; label="h\; ij\; cos"\; filenames="A2009100231560015H2.png"\; state="\{\{state\}\}">h</figure-callout>}}_{\mathrm{ij}}{\cos }^{}{}^3{\mathrm{\&alpha;}}_j+\frac{\mathrm{\&sigma;}}{\frac{E_{f_{\mathrm{ij}}}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}{E}_r(1+{\mathrm{\&mu;}}_{f_{\mathrm{ij}}})+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})E_{f_{\mathrm{ij}}}(1+{\mathrm{\&mu;}}_r)\}}}{h}_{\mathrm{ij}}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)$

$+\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_r^2)}{E_r}(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})---\left(2\right)$

Can get rock mass along the strain of external force σ direction is:

${\mathrm{\&epsiv;}}_a=\frac{d}{L}$

$=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{\frac{E_{\mathrm{fij}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}(1-{\mathrm{\&mu;}}_{f_{\mathrm{ij}}}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})(1-{\mathrm{\&mu;}}_r^2)E_{f_{\mathrm{ij}}}}}{h}_{\mathrm{ij}}{\cos }^2{\mathrm{\&alpha;}}_j+\frac{\mathrm{\&sigma;}}{\frac{E_{f_{\mathrm{ij}}}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}{E}_r(1+{\mathrm{\&mu;}}_{f_{\mathrm{ij}}})+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})E_{f_{\mathrm{ij}}}(1+{\mathrm{\&mu;}}_r)\}}}{h}_{\mathrm{ij}}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_r^2)}{E_r}(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})}{L}---\left(3\right)$

With formula (3) substitution E=σ (1-μ ²)/ε can contain the deformation modulus that m organizes the rock mass σ direction in non-perforation crack:

$E=\frac{(1-{\mathrm{\&mu;}}_a^2)}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{\frac{E_{\mathrm{fij}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}(1-{\mathrm{\&mu;}}_{f_{\mathrm{ij}}}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})(1-{\mathrm{\&mu;}}_r^2)E_{f_{\mathrm{ij}}}}}{\mathrm{\&lambda;}}_{h_{\mathrm{ij}}}{\cos }^2{\mathrm{\&alpha;}}_j+\frac{\mathrm{\&sigma;}}{\frac{E_{f_{\mathrm{ij}}}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}{E}_r(1+{\mathrm{\&mu;}}_{f_{\mathrm{ij}}})+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})E_{f_{\mathrm{ij}}}(1+{\mathrm{\&mu;}}_r)\}}}{\mathrm{\&lambda;}}_{h_{\mathrm{ij}}}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_r^2)}{E_r}(1-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_{h_{\mathrm{ij}}})}---\left(4\right)$

Non-perforation crack rock perpendicular to the strain on the compressive stress direction be:

${{\mathrm{\&epsiv;}}^x}_a=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}}\frac{1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2}{E_{{\mathrm{fr}}_{\mathrm{ij}}}}\mathrm{\&sigma;}{\mathrm{\&mu;}}_{\mathrm{fr}}+(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})\frac{1-{\mathrm{\&mu;}}_r^2}{E_r}\mathrm{\&sigma;}{\mathrm{\&mu;}}_r}{L}---\left(5\right)$

Substitution ${\mathrm{\&mu;}}_a={\mathrm{\&epsiv;}}_a^x/{\mathrm{\&epsiv;}}_a,$ The Poisson ratio that then can obtain containing m group crack rock is:

${\mathrm{\&mu;}}_a=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}}\frac{1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2}{E_{{\mathrm{fr}}_{\mathrm{ij}}}}{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}+(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})\frac{1-{\mathrm{\&mu;}}_r^2}{E_r}{\mathrm{\&mu;}}_r}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(\frac{(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{\frac{E_{\mathrm{fij}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}(1-{\mathrm{\&mu;}}_{f_{\mathrm{ij}}}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})(1-{\mathrm{\&mu;}}_r^2)E_{f_{\mathrm{ij}}}}}{\mathrm{<figure-callout\; id="3"\; label="h\; ij\; cos"\; filenames="A2009100231560015H2.png"\; state="\{\{state\}\}">h</figure-callout>}}_{\mathrm{ij}}{\cos }^{}{}^3{\mathrm{\&alpha;}}_j+\frac{1}{\frac{E_{f_{\mathrm{ij}}}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}{E}_r(1+{\mathrm{\&mu;}}_{f_{\mathrm{ij}}})+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})E_{f_{\mathrm{ij}}}(1+{\mathrm{\&mu;}}_r)\}}}{h}_{\mathrm{ij}}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{(1+{\mathrm{\&mu;}}_r^2)}{E_r}(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})}---\left(6\right)$

Introduce non-perforation fracture spacing S _jCan get:

$E=\frac{(1-{\mathrm{\&mu;}}_a^2)}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}(\frac{(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2)}{\frac{E_{\mathrm{fj}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2)}{{\mathrm{\&lambda;}}_{f_j}(1-{\mathrm{\&mu;}}_{f_j}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_j})(1-{\mathrm{\&mu;}}_r^2)E_{f_j}}}{\mathrm{\&lambda;}}_{{\mathrm{<figure-callout\; id="3"\; label="h\; j\; cos"\; filenames="A2009100231560015H2.png"\; state="\{\{state\}\}">h</figure-callout>}}_j}{\cos }^{}{}^3{\mathrm{\&alpha;}}_j+\frac{1}{\frac{E_{f_j}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_j}{E}_r(1+{\mathrm{\&mu;}}_{f_j})+(1-{\mathrm{\&lambda;}}_{f_j})E_{f_j}(1+{\mathrm{\&mu;}}_r)\}}}{\mathrm{\&lambda;}}_{h_j}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{(1-{\mathrm{\&mu;}}_r^2)}{E_r}(1-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{{\cos \mathrm{\&alpha;}}_j}{S_j}{\mathrm{\&lambda;}}_{h_j})}---\left(7\right)$

${\mathrm{\&mu;}}_a=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}{\mathrm{\&lambda;}}_{h_j}\frac{1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2}{E_{{\mathrm{fr}}_j}}{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}+(1-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}{\mathrm{\&lambda;}}_{h_j})\frac{1-{\mathrm{\&mu;}}_r^2}{E_r}{\mathrm{\&mu;}}_r}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}(\frac{(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2)}{\frac{E_{\mathrm{fj}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2)}{{\mathrm{\&lambda;}}_{f_j}(1-{\mathrm{\&mu;}}_{f_j}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_j})(1-{\mathrm{\&mu;}}_r^2)E_{f_j}}}{\mathrm{\&lambda;}}_{{\mathrm{<figure-callout\; id="3"\; label="h\; j\; cos"\; filenames="A2009100231560015H2.png"\; state="\{\{state\}\}">h</figure-callout>}}_j}{\cos }^{}{}^3{\mathrm{\&alpha;}}_j+\frac{1}{\frac{E_{f_j}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_j}{E}_r(1+{\mathrm{\&mu;}}_{f_j})+(1-{\mathrm{\&lambda;}}_{f_j})E_{f_j}(1+{\mathrm{\&mu;}}_r)\}}}{\mathrm{\&lambda;}}_{h_j}{\sin }^2{\mathrm{\&alpha;}}_j{\cos \mathrm{\&alpha;}}_j)+\frac{(1-{\mathrm{\&mu;}}_r^2)}{E_r}(1-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{{\cos \mathrm{\&alpha;}}_j}{S_j}{\mathrm{\&lambda;}}_{h_j})}---\left(8\right)$

In the formula,

E, μ _aBe respectively the deformation modulus and the Poisson ratio that contain the non-perforation of many groups crack;

Be respectively rock mass j and organize the deformation modulus and the Poisson ratio of stuff in the non-perforation crack;

E _r, μ _rBe respectively the deformation modulus and the Poisson ratio of sillar;

It is the thickness rate that j organizes non-perforation crack; α _jIt is the inclination angle that j organizes non-perforation crack;

It is the connection rate that j organizes non-perforation crack; S _jBe that j organizes non-perforation fracture spacing.

Step 4: will be in each parameter that step 1 and step 2 obtain concrete numerical value substitution formula (7) and formula (8) respectively, can obtain the containing deformation modulus of non-perforation crack rock and the values of Poisson ratio organized in this sample rock more.

Method of the present invention, carefully see deformation behaviour based on distortion equivalence principle, non-perforation crack rock architectural characteristic and non-perforation crack rock, realized obtaining fast and accurately the deformation parameter such as deformation modulus, Poisson ratio of non-perforation crack rock, determined non-perforation crack rock deformation parameter error significantly reduces, and has satisfied the requirement of various actual engineering design and construction.

Description of drawings

Fig. 1 a is the actual rock mass structure figure in the inventive method, and Fig. 1 b is the abstract rock mass structure synoptic diagram at Fig. 1 a;

Fig. 2 is the non-perforation crannied body geometric parameter synoptic diagram in the inventive method, and among the figure, h is that non-through structure thickness, 2a are single crack length (crack length), and 2c is crack end gap length (a rock bridge length), and α is crack and horizontal plane angle;

Fig. 3 is the stressed synoptic diagram of non-perforation crannied body in the inventive method, and among the figure, α is crack and horizontal plane angle, and σ is suffered normal stress, and τ is suffered shear stress;

Fig. 4 carefully sees distortion and macroscopic deformation figure for the non-perforation crannied body in the inventive method, among the figure, and d _fBe the distortion of joint stuff, d _rBe rock bridge distortion, d _FrBe non-through structure body macroscopic deformation, σ is suffered normal stress;

Fig. 5 is the non-perforation crack rock structural representations of organizing that contain in the inventive method more.

Embodiment

The present invention is described in detail below in conjunction with the drawings and specific embodiments.

Definite method of nonpenetrating jointed and fractured rock mass deformation parameter of the present invention, implement according to the following steps:

Step 1: image data, by engineering geological investigation, the fracture set analysis is carried out in the crack of the non-perforation crack rock of on-the-spot labyrinth, Fig. 1 a is the actual rock mass structure figure in the inventive method, Fig. 1 b is the abstract rock mass structure synoptic diagram at Fig. 1 a, analysis obtains some groups of fracture sets, sees Fig. 1 a, Fig. 1 b and Fig. 5, and detects the inclination alpha that obtains each fracture set _j, the connection rate

(determining), interval S according to the crack length a among Fig. 2, rock bridge length c value _jThe thickness rate in (seeing the vertical range between adjacent on the same group two cracks among Fig. 1 or Fig. 5), each crack

The numerical value of (seeing that crack rock bridge thickness among Fig. 4 accounts for the ratio of rock mass gross thickness).

Step 2: by indoor rock mechanics experiment, the deformation modulus of stuff in each non-perforation fracture set that acquisition step 1 is gathered

Poisson ratio

And the deformation modulus E of sillar _r, Poisson ratio μ _rNumerical value.

Step 3: set up non-perforation crack rock deformation parameter computation model

As Fig. 1, shown in Figure 5,, respectively organize inclination angle, non-perforation crack in the rock mass and be respectively α for the non-perforation crack rock that contains m group fracture set ₁, α ₂, α ₃..., α _m, the connection rate is respectively λ _F1, λ _F2, λ _F3..., λ _Fm, the thickness rate is respectively λ _H1, λ _H2, λ _H3..., λ _Hm, each is organized, and the stuff deformation modulus is respectively E in the crack _F1, E _F2, E _F3..., E _Fm, Poisson ratio is respectively μ _F1, μ _F2, μ _F3..., μ _Fm, each is organized fracture spacing and is respectively S ₁, S ₂, S ₃..., S _m

If contain m group crack in the rock mass, as Fig. 1, shown in Figure 5, for the total deformation that contains m group crack rock (every group contains the non-perforation of n bar crack), the total deformation that can obtain rock mass is:

$d=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{d}_{{\mathrm{fr}}_{\mathrm{ij}}}+d_r---\left(1\right)$

In the formula:

$d_{\mathrm{fr}}=\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_{\mathrm{fr}}^2)}{\frac{E_f{E}_r(1-{\mathrm{\&mu;}}_{\mathrm{fr}}^2)}{{\mathrm{\&lambda;}}_f(1-{\mathrm{\&mu;}}_f^2)E_r+(1-{\mathrm{\&lambda;}}_f)(1-{\mathrm{\&mu;}}_r^2)E_{\mathrm{<figure-callout\; id="3"\; label="f\; hco\; s"\; filenames="A2009100231560015H2.png"\; state="\{\{state\}\}">f</figure-callout>}}}}\mathrm{hco}{s}^{}{}^3\mathrm{\&alpha;}+\frac{\mathrm{\&sigma;}}{\frac{E_f{E}_r}{2\{{\mathrm{\&lambda;}}_f{E}_r(1+{\mathrm{\&mu;}}_f)+(1-{\mathrm{\&lambda;}}_f)E_f(1+{\mathrm{\&mu;}}_r)\}}}d{\sin }^2\mathrm{\&alpha;}\cos \mathrm{\&alpha;}$

$d_r=\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_r^2)}{E_r}(L-h)$

Can get:

$d=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{\frac{E_{\mathrm{fij}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}(1-{\mathrm{\&mu;}}_{f_{\mathrm{ij}}}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})(1-{\mathrm{\&mu;}}_r^2)E_{f_{\mathrm{ij}}}}}{\mathrm{<figure-callout\; id="3"\; label="h\; ij\; cos"\; filenames="A2009100231560015H2.png"\; state="\{\{state\}\}">h</figure-callout>}}_{\mathrm{ij}}{\cos }^{}{}^3{\mathrm{\&alpha;}}_j+\frac{\mathrm{\&sigma;}}{\frac{E_{f_{\mathrm{ij}}}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}{E}_r(1+{\mathrm{\&mu;}}_{f_{\mathrm{ij}}})+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})E_{f_{\mathrm{ij}}}(1+{\mathrm{\&mu;}}_r)\}}}{h}_{\mathrm{ij}}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)$

$+\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_r^2)}{E_r}(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})---\left(2\right)$

Can get rock mass along the strain of external force σ direction (as shown in Figure 3, Figure 4) is:

${\mathrm{\&epsiv;}}_a=\frac{d}{L}$

$=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{\frac{E_{\mathrm{fij}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}(1-{\mathrm{\&mu;}}_{f_{\mathrm{ij}}}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})(1-{\mathrm{\&mu;}}_r^2)E_{f_{\mathrm{ij}}}}}{h}_{\mathrm{ij}}{\cos }^2{\mathrm{\&alpha;}}_j+\frac{\mathrm{\&sigma;}}{\frac{E_{f_{\mathrm{ij}}}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}{E}_r(1+{\mathrm{\&mu;}}_{f_{\mathrm{ij}}})+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})E_{f_{\mathrm{ij}}}(1+{\mathrm{\&mu;}}_r)\}}}{h}_{\mathrm{ij}}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_r^2)}{E_r}(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})}{L}$

(3)

With formula (3) substitution E=σ (1-μ ²)/ε can contain the deformation modulus computing formula that m organizes the rock mass σ direction in non-perforation crack and is:

$E=\frac{(1-{\mathrm{\&mu;}}_a^2)}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{\frac{E_{\mathrm{fij}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}(1-{\mathrm{\&mu;}}_{f_{\mathrm{ij}}}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})(1-{\mathrm{\&mu;}}_r^2)E_{f_{\mathrm{ij}}}}}{\mathrm{\&lambda;}}_{h_{\mathrm{ij}}}{\cos }^2{\mathrm{\&alpha;}}_j+\frac{\mathrm{\&sigma;}}{\frac{E_{f_{\mathrm{ij}}}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}{E}_r(1+{\mathrm{\&mu;}}_{f_{\mathrm{ij}}})+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})E_{f_{\mathrm{ij}}}(1+{\mathrm{\&mu;}}_r)\}}}{\mathrm{\&lambda;}}_{h_{\mathrm{ij}}}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_r^2)}{E_r}(1-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_{h_{\mathrm{ij}}})}---\left(4\right)$

The non-perforation crack rock Poisson ratio of many groups

What contain m group (the non-perforation of n bar crack is contained in every group of crack) non-perforation crack rock perpendicular to the strain on the compressive stress direction is:

${{\mathrm{\&epsiv;}}^x}_a=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}}\frac{1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2}{E_{{\mathrm{fr}}_{\mathrm{ij}}}}\mathrm{\&sigma;}{\mathrm{\&mu;}}_{\mathrm{fr}}+(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})\frac{1-{\mathrm{\&mu;}}_r^2}{E_r}\mathrm{\&sigma;}{\mathrm{\&mu;}}_r}{L}---\left(5\right)$

Substitution ${\mathrm{\&mu;}}_a={\mathrm{\&epsiv;}}_a^x/{\mathrm{\&epsiv;}}_a,$ The Poisson ratio computing formula that then can obtain containing m group crack rock is:

${\mathrm{\&mu;}}_a=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}}\frac{1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2}{E_{{\mathrm{fr}}_{\mathrm{ij}}}}{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}+(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})\frac{1-{\mathrm{\&mu;}}_r^2}{E_r}{\mathrm{\&mu;}}_r}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(\frac{(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{\frac{E_{\mathrm{fij}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}(1-{\mathrm{\&mu;}}_{f_{\mathrm{ij}}}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})(1-{\mathrm{\&mu;}}_r^2)E_{f_{\mathrm{ij}}}}}{h}_{\mathrm{ij}}{\mathrm{<figure-callout\; id="3"\; label="cos"\; filenames="A2009100231560015H2.png"\; state="\{\{state\}\}">cos</figure-callout>}}^3{\mathrm{\&alpha;}}_j+\frac{1}{\frac{E_{f_{\mathrm{ij}}}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}{E}_r(1+{\mathrm{\&mu;}}_{f_{\mathrm{ij}}})+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})E_{f_{\mathrm{ij}}}(1+{\mathrm{\&mu;}}_r)\}}}{h}_{\mathrm{ij}}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{(1+{\mathrm{\&mu;}}_r^2)}{E_r}(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})}---\left(6\right)$

Drawn the computing formula that contains m group crack rock Poisson ratio by above derivation, convolution (4) can calculate deformation parameters such as the deformation modulus that contains any group of non-perforation crack rock of number and Poisson ratio.

Introduce non-perforation fracture spacing S at last _jCan get:

$E=\frac{(1-{\mathrm{\&mu;}}_a^2)}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}(\frac{(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2)}{\frac{E_{\mathrm{fj}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2)}{{\mathrm{\&lambda;}}_{f_j}(1-{\mathrm{\&mu;}}_{f_j}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_j})(1-{\mathrm{\&mu;}}_r^2)E_{f_j}}}{\mathrm{\&lambda;}}_{{\mathrm{<figure-callout\; id="3"\; label="h\; j\; cos"\; filenames="A2009100231560015H2.png"\; state="\{\{state\}\}">h</figure-callout>}}_j}{\cos }^{}{}^3{\mathrm{\&alpha;}}_j+\frac{1}{\frac{E_{f_j}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_j}{E}_r(1+{\mathrm{\&mu;}}_{f_j})+(1-{\mathrm{\&lambda;}}_{f_j})E_{f_j}(1+{\mathrm{\&mu;}}_r)\}}}{\mathrm{\&lambda;}}_{h_j}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{(1-{\mathrm{\&mu;}}_r^2)}{E_r}(1-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{{\cos \mathrm{\&alpha;}}_j}{S_j}{\mathrm{\&lambda;}}_{h_j})}---\left(7\right)$

${\mathrm{\&mu;}}_a=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}{\mathrm{\&lambda;}}_{h_j}\frac{1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2}{E_{{\mathrm{fr}}_j}}{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}+(1-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}{\mathrm{\&lambda;}}_{h_j})\frac{1-{\mathrm{\&mu;}}_r^2}{E_r}{\mathrm{\&mu;}}_r}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}(\frac{(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2)}{\frac{E_{\mathrm{fj}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2)}{{\mathrm{\&lambda;}}_{f_j}(1-{\mathrm{\&mu;}}_{f_j}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_j})(1-{\mathrm{\&mu;}}_r^2)E_{f_j}}}{\mathrm{\&lambda;}}_{{\mathrm{<figure-callout\; id="3"\; label="h\; j\; cos"\; filenames="A2009100231560015H2.png"\; state="\{\{state\}\}">h</figure-callout>}}_j}{\cos }^{}{}^3{\mathrm{\&alpha;}}_j+\frac{1}{\frac{E_{f_j}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_j}{E}_r(1+{\mathrm{\&mu;}}_{f_j})+(1-{\mathrm{\&lambda;}}_{f_j})E_{f_j}(1+{\mathrm{\&mu;}}_r)\}}}{\mathrm{\&lambda;}}_{h_j}{\sin }^2{\mathrm{\&alpha;}}_j{\cos \mathrm{\&alpha;}}_j)+\frac{(1-{\mathrm{\&mu;}}_r^2)}{E_r}(1-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{{\cos \mathrm{\&alpha;}}_j}{S_j}{\mathrm{\&lambda;}}_{h_j})}---\left(8\right)$

In the formula,

E, μ _aBe respectively the deformation modulus and the Poisson ratio that contain the non-perforation of many groups crack;

Be respectively rock mass j and organize the deformation modulus and the Poisson ratio of stuff in the non-perforation crack;

E _r, μ _rBe respectively the deformation modulus and the Poisson ratio of sillar;

It is the thickness rate that j organizes non-perforation crack; α _jIt is the inclination angle that j organizes non-perforation crack;

It is the connection rate that j organizes non-perforation crack; S _jBe that j organizes non-perforation fracture spacing.

Step 4: will obtain formula (7) and formula (8) respectively in the substitution step 3 at concrete numerical value that step 1 and step 2 obtain each parameter and can obtain result value that contain many non-perforation crack rock deformation modulus of group and Poisson ratio in this sample rock, this result value promptly can be applicable in engineering or the design.

Embodiment: certain engineering 1# diversion tunnel 0+150.0～0+170.0 hole section, show that through on-the-spot geologic report be distributed with 5 groups of fracture sets in this hole section country rock, fracture set distributes as shown in Figure 5, how much of each non-perforation fracture set, mechanics parameter see the following form 1:

Certain engineering 1# diversion tunnel 0+150.0 of table 1～0+170.0 hole section structure characteristics of rock mass parameter list

Group	Stuff deformation modulus/GPa	Sillar deformation modulus/GPa	Crack connection rate	Crack thickness rate	The stuff Poisson ratio	The sillar Poisson ratio	The fracture set inclination angle/°	Fracture spacing/m
									1	0.32	12	0.82	0.0020	0.45	0.2	5	0.5
2	0.32	12	0.80	0.0021	0.45	0.2	21	0.9
									3	0.32	12	0.81	0.0024	0.45	0.2	35	1.2
4	0.32	12	0.82	0.0020	0.45	0.2	62	0.4
									5	0.32	12	0.85	0.0022	0.45	0.2	80	0.9

With the parameter in 1# diversion tunnel 0+150.0～0+170.0 hole section structure characteristics of rock mass parameter list, substitution formula (7) and formula (8) can obtain, and this hole section surrouding rock deformation parameter comprises deformation modulus and Poisson ratio, as following table 2.In order to compare, listed the surrouding rock deformation parameter that obtains by 3 kinds of distinct methods respectively in the table 2, wherein, the 1st kind is the method that the present invention proposes, monitor achievement according to on-the-spot surrounding rock displacement for the 2nd kind and obtain by the back analysis method, at last a kind of is the achievement of geologic prospecting, prospecting.Referring to table 2, contrast 3 kinds of methods, obtain the surrouding rock deformation parameter according to the present invention, wherein, deformation modulus is that 11.1GPa, Poisson ratio are 0.21, with carry out the achievement basically identical that back analysis obtains according to the field measurement displacement, and with the achievement of the exploration of former geology, prospecting differ bigger, identity basis method of the present invention and inversion method the surrouding rock deformation parameter more reasonable.

The surrouding rock deformation parameter comparison table that table 20+150.0～three kinds of methods of 0+170.0 hole section are determined

Parameter	According to this method calculated value	The inverting income value	Former design adopted value
				Deformation modulus/GPa	11.1	11.3	6.0
Poisson ratio	0.21	0.22	0.25

Definite method of nonpenetrating jointed and fractured rock mass deformation parameter of the present invention, be to determine difficult problem at non-perforation crack rock deformation parameter in the rock mass engineering project, this method is input with the rock mass engineering project inspection of the scene of a crime and laboratory experiment result, based on the distortion equivalence principle, non-perforation crack rock architectural characteristic and non-perforation crack rock are carefully seen deformation behaviour, can directly obtain reflecting the sillar deformation properties, the fracture filling deformation properties, the geometric parameter in crack, distribution characteristicss etc. influence the key factor of rock mass deformation character, thereby reach the deformation modulus of the non-perforation crack rock of scientific forecasting, deformation parameters such as Poisson ratio.

Claims (1)

1, a kind of definite method of nonpenetrating jointed and fractured rock mass deformation parameter is characterized in that, this method is implemented according to following steps:

Step 1: image data, the fracture set analysis is carried out in the crack of the non-perforation crack rock of sample rock, collect some groups fracture set, and detect the inclination alpha that obtains each fracture set _j, the connection rate

Interval S _j, each crack the thickness rate

Numerical value;

Step 2: by indoor rock mechanics experiment, the deformation modulus of stuff in the non-perforation of each fracture set crack that acquisition step 1 is gathered

Poisson ratio And the deformation modulus E of sillar _r, Poisson ratio μ _rNumerical value;

Step 3: set up non-perforation crack rock deformation parameter computation model

If contain m group crack in the rock mass, respectively organize inclination angle, non-perforation crack in the rock mass and be respectively α ₁, α ₂, α ₃..., α _m, the connection rate is respectively λ _F1, λ _F2, λ _F3..., λ _Fm, the thickness rate is respectively λ _H1, λ _H2, λ _H3..., λ _Hm, each is organized, and the stuff deformation modulus is respectively E in the crack _F1, E _F2, E _F3..., E _Fm, Poisson ratio is respectively μ _F1, μ _F2, μ _F3..., μ _Fm, each is organized fracture spacing and is respectively S ₁, S ₂, S ₃..., S _m,

For containing m group crack rock, every group contains the non-perforation of n bar crack, and the total deformation that can obtain rock mass is:

$d=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{d}_{{\mathrm{fr}}_{\mathrm{ij}}}+d_r---\left(1\right)$

In the formula:

$d_{\mathrm{fr}}=\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_{\mathrm{fr}}^2)}{\frac{E_f{E}_r(1-{\mathrm{\&mu;}}_{\mathrm{fr}}^2)}{{\mathrm{\&lambda;}}_f(1-{\mathrm{\&mu;}}_f^2)E_r+(1-{\mathrm{\&lambda;}}_f)(1-{\mathrm{\&mu;}}_r^2)E_f}}h{\cos }^3\mathrm{\&alpha;}+\frac{\mathrm{\&sigma;}}{\frac{E_f{E}_r}{2\{{\mathrm{\&lambda;}}_f{E}_r(1+{\mathrm{\&mu;}}_f)+(1-{\mathrm{\&lambda;}}_f)E_f(1+{\mathrm{\&mu;}}_r)\}}}h{\sin }^2\mathrm{\&alpha;}\cos \mathrm{\&alpha;}$

$d_r=\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_r^2)}{E_r}(L-h)$

Can get:

$d=\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{\frac{E_{\mathrm{fij}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}(1-{\mathrm{\&mu;}}_{f_{\mathrm{ij}}}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})(1-{\mathrm{\&mu;}}_r^2)E_{f_{\mathrm{ij}}}}}{h}_{\mathrm{ij}}{\cos }^3{\mathrm{\&alpha;}}_j+\frac{\mathrm{\&sigma;}}{\frac{E_{f_{\mathrm{ij}}}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}{E}_r(1+{\mathrm{\&mu;}}_{f_{\mathrm{ij}}})+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})E_{f_{\mathrm{ij}}}(1+{\mathrm{\&mu;}}_r)\}}}{h}_{\mathrm{ij}}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)$

$+\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_r^2)}{E_r}(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})---\left(2\right)$

Can get rock mass along the strain of external force σ direction is:

${\mathrm{\&epsiv;}}_a=\frac{d}{L}$

$=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{\frac{E_{\mathrm{fij}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}(1-{\mathrm{\&mu;}}_{f_{\mathrm{ij}}}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})(1-{\mathrm{\&mu;}}_r^2)E_{f_{\mathrm{ij}}}}}{h}_{\mathrm{ij}}{\cos }^3{\mathrm{\&alpha;}}_j+\frac{\mathrm{\&sigma;}}{\frac{E_{f_{\mathrm{ij}}}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}{E}_r(1+{\mathrm{\&mu;}}_{f_{\mathrm{ij}}})+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})E_{f_{\mathrm{ij}}}(1+{\mathrm{\&mu;}}_r)\}}}{h}_{\mathrm{ij}}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_r^2)}{E_r}(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})}{L}---\left(3\right)$

With formula (3) substitution E=σ (1-μ ²)/ε can contain the deformation modulus that m organizes the rock mass σ direction in non-perforation crack:

$E=\frac{(1-{\mathrm{\&mu;}}_a^2)}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{\frac{E_{\mathrm{fij}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}(1-{\mathrm{\&mu;}}_{f_{\mathrm{ij}}}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})(1-{\mathrm{\&mu;}}_r^2)E_{f_{\mathrm{ij}}}}}{\mathrm{\&lambda;}}_{h_{\mathrm{ij}}}{\cos }^3{\mathrm{\&alpha;}}_j+\frac{\mathrm{\&sigma;}}{\frac{E_{f_{\mathrm{ij}}}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}{E}_r(1+{\mathrm{\&mu;}}_{f_{\mathrm{ij}}})+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})E_{f_{\mathrm{ij}}}(1+{\mathrm{\&mu;}}_r)\}}}{\mathrm{\&lambda;}}_{h_{\mathrm{ij}}}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{\mathrm{\&sigma;}(1-{\mathrm{\&mu;}}_r^2)}{E_r}(1-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_{h_{\mathrm{ij}}})}---\left(4\right)$

Non-perforation crack rock perpendicular to the strain on the compressive stress direction be:

${{\mathrm{\&epsiv;}}^x}_a=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}}\frac{1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2}{E_{{\mathrm{fr}}_{\mathrm{ij}}}}{\mathrm{\&sigma;\&mu;}}_{\mathrm{fr}}+(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})\frac{1-{\mathrm{\&mu;}}_r^2}{E_r}{\mathrm{\&sigma;\&mu;}}_r}{L}---\left(5\right)$

Substitution ${\mathrm{\&mu;}}_a={\mathrm{\&epsiv;}}_a^x/{\mathrm{\&epsiv;}}_a,$ The Poisson ratio that then can obtain containing m group crack rock is:

${\mathrm{\&mu;}}_a=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}}\frac{1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2}{E_{{\mathrm{fr}}_{\mathrm{ij}}}}{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}+(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})\frac{1-{\mathrm{\&mu;}}_r^2}{E_r}{\mathrm{\&mu;}}_r}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}(\frac{(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{\frac{E_{\mathrm{fij}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_{\mathrm{ij}}}^2)}{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}(1-{\mathrm{\&mu;}}_{f_{\mathrm{ij}}}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})(1-{\mathrm{\&mu;}}_r^2)E_{f_{\mathrm{ij}}}}}{h}_{\mathrm{ij}}{\cos }^3{\mathrm{\&alpha;}}_j+\frac{1}{\frac{E_{f_{\mathrm{ij}}}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}}{E}_r(1+{\mathrm{\&mu;}}_{f_{\mathrm{ij}}})+(1-{\mathrm{\&lambda;}}_{f_{\mathrm{ij}}})E_{f_{\mathrm{ij}}}(1+{\mathrm{\&mu;}}_r)\}}}{h}_{\mathrm{ij}}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{(1-{\mathrm{\&mu;}}_r^2)}{E_r}(L-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{h}_{\mathrm{ij}})}---\left(6\right)$

Introduce non-perforation fracture spacing S _jCan get:

$E=\frac{(1-{\mathrm{\&mu;}}_a^2)}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}(\frac{(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2)}{\frac{E_{\mathrm{fj}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2)}{{\mathrm{\&lambda;}}_{f_j}(1-{\mathrm{\&mu;}}_{f_j}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_j})(1-{\mathrm{\&mu;}}_r^2)E_{f_j}}}{\mathrm{\&lambda;}}_{h_j}{\cos }^3{\mathrm{\&alpha;}}_j+\frac{1}{\frac{E_{f_j}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_j}{E}_r(1+{\mathrm{\&mu;}}_{f_j})+(1-{\mathrm{\&lambda;}}_{f_j})E_{f_j}(1+{\mathrm{\&mu;}}_r)\}}}{\mathrm{\&lambda;}}_{h_j}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{(1-{\mathrm{\&mu;}}_r^2)}{E_r}(1-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}{\mathrm{\&lambda;}}_{h_j})}---\left(7\right)$

${\mathrm{\&mu;}}_a=\frac{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}{\mathrm{\&lambda;}}_{h_j}\frac{1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2}{E_{{\mathrm{fr}}_j}}{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}+(1-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}{\mathrm{\&lambda;}}_{h_j})\frac{1-{\mathrm{\&mu;}}_r^2}{E_r}{\mathrm{\&mu;}}_r}{\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}(\frac{(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2)}{\frac{E_{\mathrm{fj}}{E}_r(1-{\mathrm{\&mu;}}_{{\mathrm{fr}}_j}^2)}{{\mathrm{\&lambda;}}_{f_j}(1-{\mathrm{\&mu;}}_{f_j}^2)E_r+(1-{\mathrm{\&lambda;}}_{f_j})(1-{\mathrm{\&mu;}}_r^2)E_{f_j}}}{\mathrm{\&lambda;}}_{h_j}{\cos }^3{\mathrm{\&alpha;}}_j+\frac{1}{\frac{E_{f_j}{E}_r}{2\{{\mathrm{\&lambda;}}_{f_j}{E}_r(1+{\mathrm{\&mu;}}_{f_j})+(1-{\mathrm{\&lambda;}}_{f_j})E_{f_j}(1+{\mathrm{\&mu;}}_r)\}}}{\mathrm{\&lambda;}}_{h_j}{\sin }^2{\mathrm{\&alpha;}}_j\cos {\mathrm{\&alpha;}}_j)+\frac{(1-{\mathrm{\&mu;}}_r^2)}{E_r}(1-\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}\frac{\cos {\mathrm{\&alpha;}}_j}{S_j}{\mathrm{\&lambda;}}_{h_j})}---\left(8\right)$

In the formula,

E, μ _aBe respectively the deformation modulus and the Poisson ratio that contain the non-perforation of many groups crack;

Be respectively rock mass j and organize the deformation modulus and the Poisson ratio of stuff in the non-perforation crack;

E _r, μ _rBe respectively the deformation modulus and the Poisson ratio of sillar;

It is the thickness rate that j organizes non-perforation crack; α _jIt is the inclination angle that j organizes non-perforation crack;

It is the connection rate that j organizes non-perforation crack; S _jBe that j organizes non-perforation fracture spacing.

Step 4: will be in each parameter that step 1 and step 2 obtain concrete numerical value substitution formula (7) and formula (8) respectively, can obtain the containing deformation modulus of non-perforation crack rock and the values of Poisson ratio organized in this sample rock more.

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