CN102279421A - Slope rock mass stability evaluation method - Google Patents

Abstract

As for a composite underground and surface exploitation mode, according to a spatial corresponding relation of a mining area, one part of two mining influence domains is mutually overlapped, which cause interaction and mutual superposition of a mining effect so that a composite dynamic system can be formed. Therefore, a slope rock mass deformation mechanism is more complex. The underground exploitation has three effects on the overlying rock mass in the influence domain. The effects comprises: a stratum change of an overlying rock stratum; integral intensity reduction; an influence of a stress field change in the domain. The third effect is generated because underground excavation changes the stress distribution of the original rock. In the influence domain, a stress value and a property in different space positions are different. Damages to the overlying rock mass caused by the underground excavation are divisional. The stress change divisional property can generate different change processes along with the subsequent excavation. The change processes can directly influence a stable state of the slope rock mass which means the stable state of the slope rock mass can be restricted or changed by an occurrence condition of the stress. Therefore, the above main influence factor should be taken into consideration during analyzing the stability of the slope rock mass. However, when processing such problems in the past, an analysis method under the influence of single open mining is approximately applied so that there are certain differences existing between a result and a reality. In the invention, a slope rock mass stability evaluation method is deduced based on the theoretical analysis so as to provide a scientific basis for a subsequent mining design of this kind of mines and safety productions.

Description

A kind of slope rock mass method for estimating stability

This method not only is suitable for the evaluation of the slope stability under the underground and open-air compound mining conditions, equally also is applicable to the evaluation of underground mining to slope, mountain area, hills body, railway bed stability; Can before exploitation, carry out necessary checking computations like this, to avoid or to reduce the economic loss that causes thus.

Background technology

Under underground and open-air compound mining influence, owing to the part in two kinds of mining influence territories comprises mutually, cause between them disturbance mutually, mutual superposition between the change of stress field process and homeostasis process, the essence variation has taken place in the initial stress of slope rock mass on the diverse location of space, and the variation of the slope rock mass stress field result of this two kinds of mining influence combined factors stack just, if ignore a certain influence factor, net result will there is some difference with actual conditions; Thereby have influence on the authenticity of theoretical evaluation.Thereby, need carry out the perfect of necessity to the relevant calculation method to the problems such as safety evaluatio under this type of mining condition, thereby for determining that reasonably the stability of slope situation provides scientific basis.

Summary of the invention

As shown in Figure 1, under underground and open-air compound mining influence, slope rock mass is except that the influence that change produced of STRESS VARIATION that produced by oprn-work and various environmental engineering conditions; Because slope rock mass is positioned within the underground mining influence territory, so the mechanics condition in the slope rock mass also will be subjected to underground influence of adopting effect.Generally speaking, the effect that underground mining produces three aspects to the last overlying strata body in the domain of influence, the i.e. variation in the reduction of the variation of superincumbent stratum layer position, bulk strength and the domain of influence planted agent field of force.Wherein the latter is because underground excavation has changed the stress distribution of protolith.In its domain of influence, stress value on different spatial size all is different with condition, so underground excavation has subregion to the destruction of last overlying strata body, and this STRESS VARIATION subregion will produce different change procedures with follow-up excavation.This change procedure will directly influence the steady state (SS) of slope rock mass, and the tax of this stress is just deposited the situation restriction or changed the stable condition of side slope body.Therefore, in the stability analysis of slope rock mass, this major influence factors should be taken into account.In Fig. 1, get a block abcd, and appoint therein and get a cell cube (Fig. 2); Because in underground mining influence territory, the cell cube both sides produce unbalanced move horizontally and cell cube produces unbalanced sedimentation up and down, make to produce horizontal strain and vertically strain (Fig. 2) in the cell cube; Wherein undergroundly adopt caused horizontal stress and be:

$\mathrm{\ϵ}=\frac{1}{E}(\mathrm{\σ}-{\mathrm{\μ\σ}}_j)---\left(1\right)$

$\mathrm{\σ}=E\·\mathrm{\ϵ}=E\·b\frac{d^{2}W\left(\mathrm{\ρ}\right)}{d{\mathrm{\ρ}}^2}---\left(2\right)$

In the formula, b is a displacement factor, and E is the rock mass elastic modulus, and W (ρ) is the sinking value in cell cube left side, and opposite side sinking value is W (ρ+Δ ρ).

The sedimentation of cell cube top and bottom is inconsistent and vertical stress that produce is:

${\mathrm{\ϵ}}_j=\frac{1}{E}({\mathrm{\σ}}_j-\mathrm{\μ\σ})---\left(3\right)$

${\mathrm{\σ}}_j=E\·\mathrm{\ϵ}=E\frac{\mathrm{dW}\left(z\right)}{\mathrm{dz}}---\left(4\right)$

In the formula, E is the rock mass elastic modulus, and W (z), W (z-Δ z) are the sinking value of cell cube top and bottom.

Generally under underground mining influence, the sinking value of arbitrfary point is on the different depth of ground:

$w(x,y)=\frac{W_{\max }}{R_z}{\∫\∫}_e-\mathrm{\π}(x^2+y^2)\mathrm{dxdy}{Z}_i---\left(5\right)$

In the formula, W _MaxFor being Z in the degree of depth _iMaximum sinking value on the plane, R _zFor being Z in the degree of depth _iMaximum effect radius on the plane, A are productive area.

As shown in Figure 2, the skid resistance of bar block:

The sliding force of bar block:

$T_{\mathrm{Ii}}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Δz}}_{\mathrm{ij}}{\mathrm{\Δ\ρ}}_i\·r\sin {\mathrm{\α}}_i+{\mathrm{\Δ\ρ}}_i\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\σ}}_{\mathrm{ij}}\sin {\mathrm{\α}}_i+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Δz}}_{\mathrm{ij}}{\mathrm{\σ}}_i\cos {\mathrm{\α}}_i---\left(7\right)$

As shown in Figure 1, the skid resistance of potential gliding mass and sliding force are respectively:

$T_I=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{T}_i$ $T_i^{,}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{T}_i^{,}---\left(8\right)$

The stability factor of potential gliding mass is:

In the formula, r is a rock mass unit weight, α _iBe the angle between cell cube base mid point normal and the gravity vertical, ε _iBe the horizontal strain value of arbitrfary point in the cell cube, ε _IjBe the vertical strain value of arbitrfary point in the cell cube, C,

E is respectively rock mass cohesiveness, angle of internal friction and elastic modulus.

Because:

Then (9) formula is:

(10) formula is the theoretical formula that slope stability is calculated under underground and the Subaerial comprehensive mining effect.Wherein

With

Can obtain according to following method.

Can derive following parameters by (5) formula:

(1) along the horizontal strain of any direction

(2) the sinking distribution coefficient of on the strike principal section and tendency principal section:

$c_x=\left\{\right[\mathrm{erf}\left(\stackrel{\‾}{\mathrm{\π}}\frac{x}{R_z}\right)+1]-[\mathrm{erf}(\stackrel{\‾}{\mathrm{\π}}(x-L_x)/R_z)+1\left]\right\}/2---\left(12\right)$

$c_{\text{y}}=\left\{\right[\mathrm{erf}\left(\stackrel{\‾}{\mathrm{\π}}\frac{y}{R_z}\right)+1]-[\mathrm{erf}(\stackrel{\‾}{\mathrm{\π}}(y-L_y)/R_z)+1\left]\right\}/2---\left(13\right)$

(3) inclination and distortion

$i_x=\frac{w_{\max }}{R_z}[e^{-\mathrm{\π}\frac{x^2}{R_z^2}}-e^{-\mathrm{\π}\frac{{(x-L_x)}^2}{R_z^2}}],i_y=\frac{w_{\max }}{R_z}\left[e^{-\mathrm{\π}\frac{y^2}{R_z^2}}{-e}^{-\mathrm{\π}\frac{{(y-L_y)}^2}{R_z^2}}\right]---\left(14\right)$

(4) move horizontally

$u_x={\mathrm{bw}}_{\max }[e^{-\mathrm{\π}\frac{x^2}{R_z^2}}-e^{-\mathrm{\π}\frac{{(x-L_x)}^2}{R_z^2}}]$ $u_y={\mathrm{bw}}_{\max }[e^{-\mathrm{\π}\frac{y^2}{R_z^2}}-e^{-\mathrm{\π}\frac{{(y-L_y)}^2}{R_z^2}}]---\left(15\right)$

(5) curvature distortion

$k_x=-2\mathrm{\π}\frac{w_{\max }}{R_z}[\frac{x}{R_z}{e}^{-\mathrm{\π}\frac{x^2}{R_z^2}}-\frac{x-L_x}{R_z}{e}^{-\mathrm{\π}\frac{{(x-L_x)}^2}{R_z^2}}]$ (16)

$k_y=-2\mathrm{\π}\frac{w_{\max }}{R_z}[\frac{y}{R_z}{e}^{-\mathrm{\π}\frac{y^2}{R_z^2}}-\frac{y-L_y}{R_z}{e}^{-\mathrm{\π}\frac{{(y-L_y)}^2}{R_z^2}}]$

In the formula, L _x, L _yBe respectively the horizontal projection value of the exploitation length of on the strike and across strike, all the other symbols are identical with the front.

Horizontal strain along the derivative of any direction is:

$\frac{\mathrm{d\ϵ}}{\mathrm{d\ρ}}=\frac{1}{E}(\frac{\mathrm{d\σ}}{\mathrm{d\ρ}}-u\frac{{\mathrm{d\σ}}_j}{\mathrm{d\ρ}})=\frac{1}{E}(\frac{\mathrm{d\σ}}{\mathrm{d\ρ}}-u\frac{{\mathrm{d\σ}}_j}{\mathrm{dz}}\frac{\mathrm{dz}}{\mathrm{d\ρ}})=\frac{1}{E}(\frac{\mathrm{d\σ}}{\mathrm{d\ρ}}-\mathrm{utg\β}\frac{{\mathrm{d\σ}}_j}{\mathrm{d\ρ}})---\left(17\right)$

Vertically strain to the derivative of the degree of depth is:

$\frac{{\mathrm{d\ϵ}}_j}{\mathrm{dz}}=\frac{1}{E}(\frac{{\mathrm{d\σ}}_j}{\mathrm{dz}}-u\frac{\mathrm{d\σ}}{\mathrm{dz}})=\frac{1}{E}(\frac{{\mathrm{d\σ}}_j}{\mathrm{dz}}-u\frac{\mathrm{d\σ}}{\mathrm{d\ρ}}\frac{\mathrm{d\ρ}}{\mathrm{dz}})=\frac{1}{E}(\frac{{\mathrm{d\σ}}_j}{\mathrm{dz}}-\frac{u}{\mathrm{tg\β}}\frac{\mathrm{d\σ}}{\mathrm{d\ρ}})---\left(19\right)$

In the formula, β is the rock stratum angle of critical deformation.

Can calculate the stability factor of potential gliding mass on the arbitrary section according to (1)～(20) formula.

Derive as can be seen by above-mentioned theory, the degree of stability of slope rock mass is directly related with the relative tertiary location between the underground exploiting field, the stability factor that is to say side slope be sink, move horizontally, the function of horizontal distortion, inclination and curvature; And be positioned on the different spatial of overlying strata body on the underground exploiting field, above-mentioned distortion parameter size is consistent anything but; Meanwhile, these value of consult volume sizes also depend on the acting in conjunction of multiple factors such as coal winning method, roof control method, architectonic distribution situation, lithology power; This shows, if ignore or do not consider underground influence of adopting, obviously be imperfection or irrational.Other computing method of Slope Stability Evaluation equally also can add underground mining influence factor, and its derivation therewith roughly the same.

Description of drawings

Fig. 1 concerns synoptic diagram for the present invention is underground with the Subaerial comprehensive exploitation;

Fig. 2 is a stress schematic diagram of the present invention;

Embodiment

In underground mining influence territory, the cell cube both sides produce unbalanced move horizontally and cell cube produces unbalanced sedimentation up and down, make to produce horizontal strain and vertically strain in the cell cube; Wherein undergroundly adopt caused horizontal stress and be:

$\mathrm{\ϵ}=\frac{1}{E}(\mathrm{\σ}-{\mathrm{\μ\σ}}_j)---\left(1\right)$

$\mathrm{\σ}=E\·\mathrm{\ϵ}=E\·b\frac{d^{2}W\left(\mathrm{\ρ}\right)}{{\mathrm{d\ρ}}^2}---\left(2\right)$

In the formula, b is a displacement factor, and E is the rock mass elastic modulus, and W (ρ) is the sinking value in cell cube left side, and opposite side sinking value is W (ρ+Δ ρ).

The sedimentation of cell cube top and bottom is inconsistent and vertical stress that produce is:

${\mathrm{\ϵ}}_j=\frac{1}{E}({\mathrm{\σ}}_j-\mathrm{\μ\σ})---\left(3\right)$

${\mathrm{\σ}}_j=E\·\mathrm{\ϵ}=E\frac{\mathrm{dW}\left(z\right)}{\mathrm{dz}}---\left(4\right)$

In the formula, E is the rock mass elastic modulus, and W (z), W (z-Δ z) are the sinking value of cell cube top and bottom.

Generally under underground mining influence, the sinking value of arbitrfary point is on the different depth of ground:

$w(x,y)=\frac{W_{\max }}{R_z}{\∫\∫}_e-\mathrm{\π}(x^2+y^2)\mathrm{dxdy}{Z}_i---\left(5\right)$

In the formula, W _MaxFor being Z in the degree of depth _iMaximum sinking value on the plane, R _zFor being Z in the degree of depth _iMaximum effect radius on the plane, A are productive area.

The skid resistance of bar block:

The sliding force of bar block:

$T_{\mathrm{Ii}}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Δz}}_{\mathrm{ij}}{\mathrm{\Δ\ρ}}_i\·r\sin {\mathrm{\α}}_i+{\mathrm{\Δ\ρ}}_i\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\σ}}_{\mathrm{ij}}\sin {\mathrm{\α}}_i+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Δz}}_{\mathrm{ij}}{\mathrm{\σ}}_i\cos {\mathrm{\α}}_i---\left(7\right)$

The skid resistance and the sliding force of potential gliding mass are respectively:

$T_I=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{T}_i$ $T_i^{,}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{T}_i^{,}---\left(8\right)$

The stability factor of potential gliding mass is:

In the formula, r is a rock mass unit weight, α _iBe the angle between cell cube base mid point normal and the gravity vertical, ε _iBe the horizontal strain value of arbitrfary point in the cell cube, ε _IjBe the vertical strain value of arbitrfary point in the cell cube, C,

E is respectively rock mass cohesiveness, angle of internal friction and elastic modulus.

Because:

Then (9) formula is:

(10) formula is the theoretical formula that slope stability is calculated under underground and the Subaerial comprehensive mining effect.Wherein

With Can obtain according to following method.

Can derive following parameters by (5) formula:

(1) along the horizontal strain of any direction

(2) the sinking distribution coefficient of on the strike principal section and tendency principal section:

$c_x=\left\{\right[\mathrm{erf}\left(\stackrel{\‾}{\mathrm{\π}}\frac{x}{R_z}\right)+1]-[\mathrm{erf}(\stackrel{\‾}{\mathrm{\π}}(x-L_x)/R_z)+1\left]\right\}/2---\left(12\right)$

$c_{\text{y}}=\left\{\right[\mathrm{erf}\left(\stackrel{\‾}{\mathrm{\π}}\frac{y}{R_z}\right)+1]-[\mathrm{erf}(\stackrel{\‾}{\mathrm{\π}}(y-L_y)/R_z)+1\left]\right\}/2---\left(13\right)$

(3) inclination and distortion

$i_x=\frac{w_{\max }}{R_z}[e^{-\mathrm{\π}\frac{x^2}{R_z^2}}-e^{-\mathrm{\π}\frac{{(x-L_x)}^2}{R_z^2}}],$ $i_y=\frac{w_{\max }}{R_z}\left[e^{-\mathrm{\π}\frac{y^2}{R_z^2}}{-e}^{-\mathrm{\π}\frac{{(y-L_y)}^2}{R_z^2}}\right]---\left(14\right)$

(4) move horizontally

$u_x={\mathrm{bw}}_{\max }[e^{-\mathrm{\π}\frac{x^2}{R_z^2}}-e^{-\mathrm{\π}\frac{{(x-L_x)}^2}{R_z^2}}]$ $u_y={\mathrm{bw}}_{\max }[e^{-\mathrm{\π}\frac{y^2}{R_z^2}}-e^{-\mathrm{\π}\frac{{(y-L_y)}^2}{R_z^2}}]$

(15)

(5) curvature distortion

$k_x=-2\mathrm{\π}\frac{w_{\max }}{R_z}[\frac{x}{R_z}{e}^{-\mathrm{\π}\frac{x^2}{R_z^2}}-\frac{x-L_x}{R_z}{e}^{-\mathrm{\π}\frac{{(x-L_x)}^2}{R_z^2}}]$ (16)

$k_y=-2\mathrm{\π}\frac{w_{\max }}{R_z}[\frac{y}{R_z}{e}^{-\mathrm{\π}\frac{y^2}{R_z^2}}-\frac{y-L_y}{R_z}{e}^{-\mathrm{\π}\frac{{(y-L_y)}^2}{R_z^2}}]$

In the formula, L _x, L _yBe respectively the horizontal projection value of the exploitation length of on the strike and across strike, all the other symbols are identical with the front.

Horizontal strain along the derivative of any direction is:

$\frac{\mathrm{d\ϵ}}{\mathrm{d\ρ}}=\frac{1}{E}(\frac{\mathrm{d\σ}}{\mathrm{d\ρ}}-u\frac{{\mathrm{d\σ}}_j}{\mathrm{d\ρ}})=\frac{1}{E}(\frac{\mathrm{d\σ}}{\mathrm{d\ρ}}-u\frac{{\mathrm{d\σ}}_j}{\mathrm{dz}}\frac{\mathrm{dz}}{\mathrm{d\ρ}})=\frac{1}{E}(\frac{\mathrm{d\σ}}{\mathrm{d\ρ}}-\mathrm{utg\β}\frac{{\mathrm{d\σ}}_j}{\mathrm{d\ρ}})---\left(17\right)$

Vertically strain to the derivative of the degree of depth is:

$\frac{{\mathrm{d\ϵ}}_j}{\mathrm{dz}}=\frac{1}{E}(\frac{{\mathrm{d\σ}}_j}{\mathrm{dz}}-u\frac{\mathrm{d\σ}}{\mathrm{dz}})=\frac{1}{E}(\frac{{\mathrm{d\σ}}_j}{\mathrm{dz}}-u\frac{\mathrm{d\σ}}{\mathrm{d\ρ}}\frac{\mathrm{d\ρ}}{\mathrm{dz}})=\frac{1}{E}(\frac{{\mathrm{d\σ}}_j}{\mathrm{dz}}-\frac{u}{\mathrm{tg\β}}\frac{\mathrm{d\σ}}{\mathrm{d\ρ}})---\left(19\right)$

In the formula, β is the rock stratum angle of critical deformation.

Can calculate the stability factor of potential gliding mass on the arbitrary section according to (1)～(20) formula.

Claims (2)

1. slope rock mass method for estimating stability, be not only applicable to side slope rock stability evaluation under the underground and open-air compound mining influence, equally also be applicable to the evaluation of underground mining to slope, mountain area, hills body, railway bed stability, it mainly may further comprise the steps:

Get a block abcd, and appoint therein and get a cell cube; Because in underground mining influence territory, the cell cube both sides produce unbalanced move horizontally and cell cube produces unbalanced sedimentation up and down, make to produce horizontal strain and vertically strain in the cell cube; Wherein undergroundly adopt caused horizontal stress and be:

$\mathrm{\ϵ}=\frac{1}{E}(\mathrm{\σ}-{\mathrm{\μ\σ}}_j)---\left(1\right)$

$\mathrm{\σ}=E\·\mathrm{\ϵ}=E\·b\frac{d^{2}W\left(\mathrm{\ρ}\right)}{d{\mathrm{\ρ}}^2}---\left(2\right)$

In the formula, b is a displacement factor, and E is the rock mass elastic modulus, and W (ρ) is the sinking value in cell cube left side, and opposite side sinking value is W (ρ+Δ ρ).

The sedimentation of cell cube top and bottom is inconsistent and vertical stress that produce is:

${\mathrm{\ϵ}}_j=\frac{1}{E}({\mathrm{\σ}}_j-\mathrm{\μ\σ})---\left(3\right)$

${\mathrm{\σ}}_j=E\·\mathrm{\ϵ}=E\frac{\mathrm{dW}\left(z\right)}{\mathrm{dz}}---\left(4\right)$

In the formula, E is the rock mass elastic modulus, and W (z), W (z-Δ z) are the sinking value of cell cube top and bottom.

Generally under underground mining influence, the sinking value of arbitrfary point is on the different depth of ground:

$w(x,y)=\frac{W_{\max }}{R_z}{\∫\∫}_e-\mathrm{\π}(x^2+y^2)\mathrm{dxdy}{Z}_i---\left(5\right)$

In the formula, W _MaxFor being Z in the degree of depth _tMaximum sinking value on the plane, R _zFor being Z in the degree of depth _iMaximum effect radius on the plane, A are productive area.

The skid resistance of bar block:

The sliding force of bar block:

$T_{\mathrm{Ii}}=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Δz}}_{\mathrm{ij}}{\mathrm{\Δ\ρ}}_i\·r\sin {\mathrm{\α}}_i+{\mathrm{\Δ\ρ}}_i\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\σ}}_{\mathrm{ij}}\sin {\mathrm{\α}}_i+\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\mathrm{\Δz}}_{\mathrm{ij}}{\mathrm{\σ}}_i\cos {\mathrm{\α}}_i---\left(7\right)$

The skid resistance and the sliding force of potential gliding mass are respectively:

$T_I=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{T}_i$ $T_i^{,}=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{T}_i^{,}---\left(8\right)$

The stability factor of potential gliding mass is:

In the formula, r is a rock mass unit weight, α _iBe the angle between cell cube base mid point normal and the gravity vertical, ε _iBe the horizontal strain value of arbitrfary point in the cell cube, ε _IjBe the vertical strain value of arbitrfary point in the cell cube, C,

E is respectively rock mass cohesiveness, angle of internal friction and elastic modulus.

Because:

Then (9) formula is:

(10) formula is the theoretical formula that slope stability is calculated under underground and the Subaerial comprehensive mining effect.Wherein

With

Can obtain according to following method.

Can derive following parameters by (5) formula:

(1) along the horizontal strain of any direction

(2) the sinking distribution coefficient of on the strike principal section and tendency principal section:

$c_x=\left\{\right[\mathrm{erf}\left(\stackrel{\‾}{\mathrm{\π}}\frac{x}{R_z}\right)+1]-[\mathrm{erf}(\stackrel{\‾}{\mathrm{\π}}(x-L_x)/R_z)+1\left]\right\}/2---\left(12\right)$

$c_{\text{y}}=\left\{\right[\mathrm{erf}\left(\stackrel{\‾}{\mathrm{\π}}\frac{y}{R_z}\right)+1]-[\mathrm{erf}(\stackrel{\‾}{\mathrm{\π}}(y-L_y)/R_z)+1\left]\right\}/2---\left(13\right)$

(3) inclination and distortion

$i_x=\frac{w_{\max }}{R_z}[e^{-\mathrm{\π}\frac{x^2}{R_z^2}}-e^{-\mathrm{\π}\frac{{(x-L_x)}^2}{R_z^2}}],$ $i_y=\frac{w_{\max }}{R_z}\left[e^{-\mathrm{\π}\frac{y^2}{R_z^2}}{-e}^{-\mathrm{\π}\frac{{(y-L_y)}^2}{R_z^2}}\right]---\left(14\right)$

(4) move horizontally

$u_x={\mathrm{bw}}_{\max }[e^{-\mathrm{\π}\frac{x^2}{R_z^2}}-e^{-\mathrm{\π}\frac{{(x-L_x)}^2}{R_z^2}}]$ $u_y={\mathrm{bw}}_{\max }[e^{-\mathrm{\π}\frac{y^2}{R_z^2}}-e^{-\mathrm{\π}\frac{{(y-L_y)}^2}{R_z^2}}]$

(5) curvature distortion

$k_x=-2\mathrm{\π}\frac{w_{\max }}{R_z}[\frac{x}{R_z}{e}^{-\mathrm{\π}\frac{x^2}{R_z^2}}-\frac{x-L_x}{R_z}{e}^{-\mathrm{\π}\frac{{(x-L_x)}^2}{R_z^2}}]$ (16)

$k_y=-2\mathrm{\π}\frac{w_{\max }}{R_z}[\frac{y}{R_z}{e}^{-\mathrm{\π}\frac{y^2}{R_z^2}}-\frac{y-L_y}{R_z}{e}^{-\mathrm{\π}\frac{{(y-L_y)}^2}{R_z^2}}]$

In the formula, L _x, L _yBe respectively the horizontal projection value of the exploitation length of on the strike and across strike, all the other symbols are identical with the front.

Horizontal strain along the derivative of any direction is:

$\frac{\mathrm{d\ϵ}}{\mathrm{d\ρ}}=\frac{1}{E}(\frac{\mathrm{d\σ}}{\mathrm{d\ρ}}-u\frac{{\mathrm{d\σ}}_j}{\mathrm{d\ρ}})=\frac{1}{E}(\frac{\mathrm{d\σ}}{\mathrm{d\ρ}}-u\frac{{\mathrm{d\σ}}_j}{\mathrm{dz}}\frac{\mathrm{dz}}{\mathrm{d\ρ}})=\frac{1}{E}(\frac{\mathrm{d\σ}}{\mathrm{d\ρ}}-\mathrm{utg\β}\frac{{\mathrm{d\σ}}_j}{\mathrm{d\ρ}})---\left(17\right)$

Vertically strain to the derivative of the degree of depth is:

$\frac{{\mathrm{d\ϵ}}_j}{\mathrm{dz}}=\frac{1}{E}(\frac{{\mathrm{d\σ}}_j}{\mathrm{dz}}-u\frac{\mathrm{d\σ}}{\mathrm{dz}})=\frac{1}{E}(\frac{{\mathrm{d\σ}}_j}{\mathrm{dz}}-u\frac{\mathrm{d\σ}}{\mathrm{d\ρ}}\frac{\mathrm{d\ρ}}{\mathrm{dz}})=\frac{1}{E}(\frac{{\mathrm{d\σ}}_j}{\mathrm{dz}}-\frac{u}{\mathrm{tg\β}}\frac{\mathrm{d\σ}}{\mathrm{d\ρ}})---\left(19\right)$

In the formula, β is the rock stratum angle of critical deformation.

2. the method for claim 1 is primarily characterized in that the derivation to formula 10,19,20.

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