CN104268380B - Long-term stability prediction method for three-dimensional creep slope - Google Patents

Abstract

The invention discloses a long-term stability prediction method for a three-dimensional creep slope. The long-term stability prediction method comprises the steps of selecting a specific three-dimensional creep slope to be predicted, discretizing the three-dimensional creep slope, establishing a xiyuan model of a soil-rock mass and a strength reduction method, and obtaining the relationship between the shear force of the bottom surface of a bar column and key point vertical displacements Delta0 and solving the key point vertical displacements Delta0 corresponding to different time, and the like, and the relationship between the long-term slide displacement of the three-dimensional creep slope and the changes of a reduction coefficient can be obtained, thus obtaining the long-term stability coefficient of the three-dimensional creep slope. The long-term stability prediction method disclosed by the invention has the following advantages that: the creep characteristics of the soil-rock mass and the slide displacement information of the three-dimensional creep slope are considered, the calculation accuracy is improved, and the long-term stability prediction result of the three-dimensional creep slope is more reliable.

Description

A kind of long-time stability Forecasting Methodology of three-dimensional creep side slope

Technical field

The invention belongs to geological disaster Control Technology field is and in particular to a kind of long-time stability of three-dimensional creep side slope are pre- Survey method.

Background technology

Research at home and abroad is still few at present for the creep of geotechnical slope, but because rock behavio(u)r is included with Rock And Soil rheological behavior Research not leads to be delayed construction or even the precedent of project failure is too numerous to enumerate, and Italian tile is according to high (Vajont) storehouse bank creep Destruction is one of them.In all previous international conference since the 1st International Rock mechanics meeting in 1966, have many with regard to The paper of Mineral rheology Journal of Sex Research.In the 1st International Rock mechanics meeting, Zischinsky rheological model describes height The deformation of side slope, and point out that the creep of Rock And Soil plays an important role in high-wall slope deformation.

Engineering practice is shown with research, the destruction of geotechnical slope engineering and unstability, is not to excavate in many cases Occurs immediately after being formed, ground body stress and deformation are to change over and constantly adjust, the process that it adjusts often needs Continue a longer period.Slope creep refers to form the rock mass of side slope and the soil body in weight stress and with horizontal stress Based on tectonic stress field in the presence of, the deformation property continuing to increase in time.The reason produce slope deforming is multi-party Face, geologic process, subsurface flow, temperature change, vegetation effect etc. can produce the macroscopic deformation of side slope.But with regard to Rock And Soil Itself, side slope time dependent deformation is mainly caused by Rock And Soil creep, therefore, during research slope deforming, should Pay special attention to the creep propertieses of material of rock and soil and the substantial connection of slope creep characteristic.

Property analysis to creep side slope, is mainly also limited to analysis of two-dimensional creep slope problem at present, for example, " considers rock The long-term slope stability study of native creep propertieses ", Jiang Haifei, Hu Bin, Liu Qiang, Wang Xingang, metal mine, 2013 years the 12nd Phase, page 131～157, describe the Strength Reduction Method using considering ground creep propertieses and Shiyan building yard side slope is entered Line position is moved and is calculated, and has obtained creep curve under different reduction coefficients for the monitoring point.But the slope project problem of nature is led to Often there is three-dimensional feature, therefore with the method for two-dimentional creep side slope come analyzing three-dimensional creep side slope, exist substantially with actual situation Difference, thus obtained slide displacement result is necessarily unreliable, and the reliability obtaining can not fully meet engine request.

Content of the invention

For the difference of the method for analyzing stability presence with two-dimentional creep side slope for the prior art and virtual condition, the present invention Technical problem to be solved is exactly to provide a kind of long-time stability Forecasting Methodology of three-dimensional creep side slope, and it can be in conjunction with three-dimensional The displacement of slope sliding, calculates the coefficient of stability obtaining this three-dimensional slope, thus improving forecasting reliability.

The technical problem to be solved is realized by such technical scheme, and it includes following steps：

Step 1, selected three-dimensional creep side slope specifically to be predicted, determine the geometry of this three-dimensional slope and its Potential failure surface Size, Potential failure surface and side slope surface equation is represented, determines the soil body index parameter of ground；

Step 2, by three-dimensional creep side slope discretization, three-dimensional creep side slope is m row and n row bar post by Vertical derivative, each Bar post is defined as [i, j] by line number i being located and row number j；It is assumed that the bar intercolumniation active force of line direction and horizontal plane angle be ± α is it is assumed that the bar intercolumniation active force of column direction and horizontal plane angle are ± β；

Step 3, introducing Strength Reduction Method, reduction coefficient is RF, and mole coulomb criterion, to calculate resisting for a long time of Rock And Soil Cut intensity；Further according to visco-elastoplastic model, determine the pass between the shearing of [i, j] bar post bottom surface and the shear displacemant of this post System；Using the displacement coordination condition of each bar post after discrete, obtain shearing force and the vertical position of key point of [i, j] bar post bottom surface Move Δ₀Relation；

The equilibrium equation of step 4, the equilibrium equation according to 3 power and three moment, and combine cutting of [i, j] bar post bottom surface Power and the relational expression of key point vertical displacement, set up one and contain unknown number α, β, Δ₀, the non-linear side of RF and creep time t Journey group；Solve equation group, obtain different reduction coefficients and the vertical displacement Δ of key point corresponding to the different moment₀；And then Obtain the relation of the long-term vertical displacement of this three-dimensional creep side slope under different reduction coefficients；The long-term vertical displacement of key point is suddenly at increasing Corresponding reduction coefficient RF value is the coefficient of stability of this three-dimensional creep side slope, thus judging the steady in a long-term of this three-dimensional creep side slope Property.

Because the present invention is after three-dimensional creep side slope discretization, according to the balance side of 3 equilibrium equations and three moment Journey, and consider the slide displacement amount of three-dimensional creep side slope, obtains the long-term of this three-dimensional creep side slope under different reduction coefficients The relation of slide displacement.Thus judging the long term stabilization factor of this three-dimensional creep side slope.In addition, all modeling process can program Change, be easy to operate and program, realize the prediction of three-dimensional creep slope sliding displacement by computer, greatly reducing artificial Amount of calculation.So it is an advantage of the invention that：Consider the creep propertieses of Rock And Soil and the slide displacement information of creep side slope, improve Computational accuracy, the long-time stability of three-dimensional creep side slope predict the outcome more reliable.

Brief description

The brief description of the present invention is as follows：

Fig. 1 is the side slope Potential failure surface of one embodiment of the present of invention and the profile on side slope surface；

Fig. 2 is three-dimensional creep side slope discretization structure chart；

Fig. 3 is the stress model figure of discretization bar post；

Fig. 4 is the visco-elastoplastic model schematic diagram of Rock And Soil；

Fig. 5 is the key point vertical displacement Δ under the different reduction coefficients of embodiment₀Time dependent graph of a relation；

Fig. 6 is the graph of a relation with reduction coefficient for the long-term vertical displacement of key point of embodiment.

Specific embodiment

The invention will be further described with reference to the accompanying drawings and examples：

Step 1, select three-dimensional creep side slope specifically to be predicted, determine three-dimensional creep side slope Potential failure surface shape and Side slope body physical dimension, side slope surface and Potential failure surface equation are represented；The parameter on side slope surface has side slope inclined-plane in water Projected length l in plane, projected length H of side slope inclined-plane in the vertical direction；The parameter of Potential failure surface is according to actual several What shape determines, and determines the soil body index parameter of ground；

The expression formula on side slope surface is

$\left\{\begin{array}{cc}{z}_1=0,& (x<0)\\ z_1=x,& (0\&le;x\&le;20)\\ z_1=20,& (x>20)\end{array}\right.---\left(1\right)$

The expression formula of Potential failure surface is：

$\frac{x^2}{{20}^2}+\frac{{(y-40)}^2}{{40}^2}+\frac{{(z-20)}^2}{{20}^2}=1---\left(2\right)$

The three-dimensional creep side slope of the present embodiment, as shown in figure 1, its side slope surface is inclined plane, takes its inclination angle to be 45 °, side The horizontal direction on slope inclined-plane be projected as 20m, in the vertical direction be projected as 20m；Slip-crack surface is spheroid slip-crack surface, if y On direction, the semi-major axis of slip-crack surface width is 40m；The half shaft length in x, z direction is 20m.The material of rock and soil of this side slope be each to Same sex homogeneous material, its index parameter is：Cohesive strength c=10kPa, internal friction angleUnit weight γ=22.0kN/m³.

Step 2, by this three-dimensional creep side slope body discretization

As shown in Fig. 2 by three-dimensional creep side slope discretization.This three-dimensional creep side slope is 200 row and 200 row by Vertical derivative Bar post.Each post is defined as [i, j] by line number i being located and row number j；It is assumed that the bar intercolumniation active force of line direction and horizontal plane Angle is ± α it is assumed that the bar intercolumniation active force of column direction and horizontal plane angle are ± β.The stress model of [i, j] bar post is as schemed Shown in 3.

Step 3, set up the visco-elastoplastic model of Rock And Soil；

(1) Strength Reduction Method (reduction coefficient is RF) and mole coulomb criterion, are introduced

Set up the visco-elastoplastic model of Rock And Soil as shown in figure 4, the visco-elastoplastic model parameter of the Rock And Soil of three-dimensional creep side slope For G₁=43 × 10⁶Pa, G₂=37 × 10⁶Pa, η₁=3.739 × 10¹²Pa s, η₂=3.739 × 10¹²Pa·s.This Rock And Soil Long-term Shear Strength be τ_long, Long-term Shear Strength is the 70% of shearing strength, then Long-term Shear Strength is τ_longFor：

Wherein σ^i,jDirect stress for [i, j] bar post bottom surface.

Introduce Strength Reduction Method, the Rock And Soil Long-term Shear Strength after reduction is：

WhereinFor the Rock And Soil Long-term Shear Strength after the bottom surface reduction of [i, j] bar post.

So, the long-term shearing resistance after the bottom surface reduction of [i, j] bar post is：

$S_{\mathrm{long},r}^{i,j}=\frac{{\mathrm{\&tau;}}_{\mathrm{long},r}^{i,j}{\&CenterDot;A}^{i,j}}{n_z^{\text{i,j}}}---\left(5\right)$

Wherein,Long-term shearing resistance after the bottom surface reduction of [i, j] bar post, A^i,jCross section for [i, j] bar post It is long-pending,Component in z-axis for the unit vector for [i, j] bar post bottom surface normal force.

(2), determine the relation between the shearing force of [i, j] bar post bottom surface and the shear displacemant of this post

The mathematic(al) representation of the visco-elastoplastic model of Rock And Soil in side slope bar post is as follows,

A () is as the shearing S on Potential failure surface^i,jLess than long-term shearing resistanceWhen,

$\frac{b^{i,j}{G}_1{\mathrm{\&eta;}}_1}{G_1+G_2}\frac{d{\mathrm{\&Delta;}}^{i,j}\left(t\right)}{\mathrm{dt}}+\frac{b^{i,j}{G}_1{G}_2{\mathrm{\&eta;}}_1}{G_1+G_2}{\mathrm{\&Delta;}}^{i,j}\left(t\right)=S^{i,j}---\left(6\right)$

b^i,jIt is the width of [i, j] bar post line direction, and have boundary condition Δ^i,j(0)=0, [i, j] can be obtained Relation between the shearing of bar post bottom surface and the shear displacemant of this post is：

${\mathrm{\&Delta;}}^{i,j}\left(t\right)=\frac{(G_1+G_2)S^{i,j}}{b{G}_1{G}_2}(1-e^{-\frac{G_2}{{\mathrm{\&eta;}}_1}t})---\left(7\right)$

Δ in formula^i,jT () is the shear displacemant of [i, j] bar post bottom surface, S^i,jFor the shearing of [i, j] bar post bottom surface, G₁, G₂, η₁, η₂For the parameter in visco-elastoplastic model, t is the time that creep occurs.

B () is as the shearing S on Potential failure surface^i,jMore than or equal to long-term shearing resistanceWhen,

$\frac{G_1{G}_2}{{\mathrm{\&eta;}}_1{\mathrm{\&eta;}}_2}(S^{i,j}-S_{\mathrm{long},r}^{i,j})=\frac{b^{i,j}{G}_1}{{\mathrm{\&eta;}}_2}\frac{d{\mathrm{\&Delta;}}^{i,j}\left(t\right)}{\mathrm{dt}}+\frac{b^{i,j}{G}_1{G}_2{\mathrm{\&eta;}}_1}{G_1+G_2}\frac{G_1}{G_1-\frac{G_1{G}_2}{G_1+G_2}}\frac{d^2{\mathrm{\&Delta;}}^{i,j}\left(t\right)}{d{t}^2}---\left(8\right)$

And there is boundary condition Δ^i,j(0)=0 HeCan obtain the shearing of [i, j] bar post bottom surface with Relation between the shear displacemant of this post is：

${\mathrm{\&Delta;}}^{i,j}\left(t\right)=\frac{G_2(S^{i,j}-S_{\mathrm{long},r}^{i,j})}{b{\mathrm{\&eta;}}_1}(t+\frac{G_2{\mathrm{\&eta;}}_2}{G_1}{e}^{-\frac{G_1}{G_2{\mathrm{\&eta;}}_1}}+\frac{G_2{\mathrm{\&eta;}}_2}{G_1})---\left(9\right)$

(3) shearing force and the key point vertical displacement Δ of [i, j] bar post bottom surface, are determined₀The relation of (t)

According to the rigid assumption of side slope body, discrete each bar post meets certain compatibility conditions, i.e. the horizontal position of each bar post Phase shift etc..

The key point selecting this three-dimensional creep side slope first (is assumed to be [1, j₀] bar post, its vertical displacement is Δ₀(t)), that This three-dimensional creep horizontal displacement of slope is：

${\mathrm{\&Delta;}}_h\left(t\right)={\mathrm{\&Delta;}}_h^{1,j_0}\left(t\right)=\frac{{\mathrm{\&Delta;}}_0\left(t\right)\&CenterDot;l_x^{1,j_0}}{l_z^{1,j_0}}---\left(10\right)$

WhereinFor the horizontal displacement of [1, j0] bar post, Δ_hHorizontal displacement (the i.e. level of this side slope for all posts Displacement),For [1, j₀] bar post bottom surface shearing force component on x, z direction for the unit vector.

So, the shear displacemant of [i, j] bar post bottom surfaceCan obtain：

${\mathrm{\&Delta;}}^{i,j}\left(t\right)=\frac{{\mathrm{\&Delta;}}_h\left(t\right)}{l_x^{i,j}}=\frac{l_x^{1,j_0}\&CenterDot;{\mathrm{\&Delta;}}_v^{1,j_0}\left(t\right)}{l_x^{i,j}\&CenterDot;l_z^{1,j_0}}=\frac{l_x^{1,j_0}\&CenterDot;{\mathrm{\&Delta;}}_0\left(t\right)}{l_x^{i,j}\&CenterDot;l_z^{1,j_0}}---\left(11\right)$

Formula (11) is updated to formula (7) respectively and (9) obtain：

A () is as the shearing S on slip-crack surface^i,jLess than long-term shearing resistanceWhen,

$\frac{l_x^{1,j_0}}{l_x^{i,j}\&CenterDot;l_z^{1,j_0}}{\mathrm{\&Delta;}}_0\left(t\right)=\frac{(G_1+G_2)S^{i,j}}{b{G}_1{G}_2}(1-e^{-\frac{G_2}{{\mathrm{\&eta;}}_1}t})---\left(12\right)$

B () is as the shearing S on slip-crack surface^i,jMore than long-term shearing resistanceWhen,

$\frac{l_x^{1,j_0}}{l_x^{i,j}\&CenterDot;l_x^{1,j_0}}{\mathrm{\&Delta;}}_0\left(t\right)=\frac{G_2(S^{i,j}-S_{\mathrm{long},r}^{i,j})}{b{\mathrm{\&eta;}}_1}(t+\frac{G_2{\mathrm{\&eta;}}_2}{G_1}{e}^{-\frac{G_1}{G_2{\mathrm{\&eta;}}_2}}+\frac{G_2{\mathrm{\&eta;}}_2}{G_1})---\left(13\right)$

The equilibrium equation of step 4, the equilibrium equation according to 3 power and three moment, and combine cutting of [i, j] bar post bottom surface Power and the relational expression of key point vertical displacement, set up one and contain unknown number α, β, Δ₀, the Nonlinear System of Equations of RF and t；Solve Equation group, obtains different reduction coefficients and the vertical displacement Δ of key point corresponding to the different moment₀；And then obtain different foldings Subtract the relation of the long-term vertical displacement of this three-dimensional creep side slope under coefficient；The long-term vertical displacement of key point corresponding reduction at increasing suddenly Coefficients R F value is the coefficient of stability of this three-dimensional creep side slope, thus judging the long-time stability of this three-dimensional creep side slope.

(1), determine the relation between the shearing force of [i, j] bar post bottom surface and the shear displacemant of this post

The stress model of [i, j] bar post as shown in figure 3, on [i, j] bar post bottom surface the unit vector of normal direction force direction be

$\stackrel{\&RightArrow;}{n}=(n_x^{i,j},n_y^{i,j},n_z^{i,j})=(-\frac{1}{\mathrm{\&Delta;}}\frac{\&PartialD;f}{\&PartialD;x},-\frac{1}{\mathrm{\&Delta;}}\frac{\&PartialD;f}{\&PartialD;y},\frac{1}{\mathrm{\&Delta;}})---\left(14\right)$

In formula, f is the function of slip-crack surface,For the unit vector of normal direction force direction on bar post bottom surface, wherein It is component on x, y, z direction for this vector respectively,

The unit vector in bar post bottom surface up cut shear direction is

$\stackrel{\&RightArrow;}{l}=(l_x^{i,j},l_y^{i,j},l_z^{i,j})=\frac{1}{{\mathrm{\&Delta;}}^{\&prime;}}(\mathrm{1,0},\frac{\&PartialD;f}{\&PartialD;x})---\left(15\right)$

In formula,For the unit vector of bar post bottom surface shearing force, whereinIt is this vector respectively in x, y, z direction On component, ${\mathrm{\&Delta;}}^{\&prime;}=\sqrt{1+{\left(\frac{\&PartialD;f}{\&PartialD;x}\right)}^2}.$

According to the balance of three axial forces, each post can be set up equation below：

The equilibrium equation of power is in the x-direction：

N^i,jn_x+S^i,jl_x+ΔG^i,jCos β=0 (16)

The equilibrium equation of power in the y-direction：

N^i,jn_y+S^i,jl_y+ΔQ^i,jCos α=0 (17)

The equilibrium equation of power in the z-direction：

N^i,jn_z+S^i,jl_z+ΔG^i,jsinβ+ΔQ^i,jsinα-W^i,j=0 (18)

Respectively simultaneous formula (16)～(18) and formula (12) or (13) obtain the normal force of [i, j] bar post bottom surface and shearing with The relational expression of key point vertical displacement.

(1) as the shearing S on slip-crack surface^i,jLess than long-term shearing resistanceWhen,

The normal force of [i, j] bar post bottom surface and shearing and key point vertical displacement Δ₀Relation be：

$\begin{array}{c}{N}^{i,j}=-\frac{l_x^{1,j_0}{l}_x^{i,j}\cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\&CenterDot;{\mathrm{\&Delta;}}_0+l_x^{1,j_0}{l}_y^{i,j}\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}\&CenterDot;{\mathrm{\&Delta;}}_0}{k_1{l}_z^{1,j_0}{l}_x^{i,j}(n_x^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}+n_y^{i,j}\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}-n_z^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;})}\\ +\frac{l_x^{1,j_0}{l}_z^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}\&CenterDot;{\mathrm{\&Delta;}}_0-k_1{l}_z^{1,j_0}{l}_x^{i,j}{W}^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}}{k_1{l}_z^{1,j_0}{l}_x^{i,j}(n_x^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}+n_y^{i,j}\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}-n_z^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;})}\end{array}---\left(19\right)$

$S^{i,j}=\frac{l_x^{1,j_0}\&CenterDot;{\mathrm{\&Delta;}}_0}{k_1{l}_z^{1,j_0}{l}_x^{i,j}}---\left(20\right)$

$k_1=\frac{(G_1+G_2)}{b{G}_1{G}_2}(1-e^{-\frac{G_2}{{\mathrm{\&eta;}}_1}})---\left(21\right)$

(2) as the shearing S on slip-crack surface^i,jMore than or equal to long-term shearing resistanceWhen,

The normal force of [i, j] bar post bottom surface and shearing and key point vertical displacement Δ₀Relation be：

$\begin{array}{c}{N}^{i,j}=\frac{W^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}}{-n_x^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}-n_y^{i,j}\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}+n_z^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}}\\ +\frac{(-l_x^{1,j_0}\&CenterDot;{\mathrm{\&Delta;}}_0-k_2{l}_z^{1,j_0}{l}_x^{i,j}{S}_{\mathrm{long},r}^{i,j})(-l_x^{i,j}\cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}-l_y^{i,j}\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}\&CenterDot;{\mathrm{\&Delta;}}_0+l_z^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}\&CenterDot;{\mathrm{\&Delta;}}_0)}{k_2{l}_z^{1,j_0}{l}_x^{i,j}(-n_x^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}-n_y^{i,j}\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}+n_z^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;})}\end{array}---\left(22\right)$

$S^{i,j}=\frac{l_x^{1,j_0}\&CenterDot;{\mathrm{\&Delta;}}_0+k_2{l}_z^{1,j_0}{l}_x^{i,j}{S}_{\mathrm{long},r}^{i,j}}{k_2{l}_x^{1,j_0}{l}_x^{i,j}}---\left(23\right)$

$k_2=\frac{G_2}{b{\mathrm{\&eta;}}_1}(t+\frac{G_2{\mathrm{\&eta;}}_2}{G_1}{e}^{-\frac{G_1}{G_2{\mathrm{\&eta;}}_2}}+\frac{G_2{\mathrm{\&eta;}}_2}{G_1})---\left(24\right)$

In formula (19)～(24), N^i,jAnd S^i,jIt is respectively normal force and the shearing of [i, j] bar post bottom surface,Point It is not the component on x, y, z direction for the unit vector of [i, j] bar post bottom surface shearing force,For [1, j₀] bar post bottom surface Component on x, z direction for the unit vector of shearing force,It is normal direction force direction on [i, j] bar post bottom surface respectively Component on x, y, z direction for the unit vector, W^i,jThe weight of [i, j] bar post.

By normal force N^i,jWith shearing S^i,jIt is updated to the torque equilibrium equation of 3 coordinate axess, the equilibrium equation of moment is as follows,

Side slope is around the torque equilibrium equation of x-axis：

$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}[-(N^{i,j}{n}_{i,j}^y+S^{i,j}{l}_{i,j}^y)z_{i,j}^G+(N^{i,j}{n}_{i,j}^z+S^{i,j}{l}_{i,j}^z)y_{i,j}^G-W^{i,j}{y}_{i,j}^H]=0---\left(25\right)$

Side slope is around the torque equilibrium equation of y-axis：

$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}[(N^{i,j}{n}_{i,j}^x+S^{i,j}{l}_{i,j}^x)z_{i,j}^G-(N^{i,j}{n}_{i,j}^z+S^{i,j}{l}_{i,j}^z)y_{i,j}^G+W^{i,j}{y}_{i,j}^H]=0---\left(26\right)$

Side slope is around the torque equilibrium equation of z-axis：

$\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}[-(N^{i,j}{n}_{i,j}^x+S^{i,j}{l}_{i,j}^x)y_{i,j}^G+(N^{i,j}{n}_{i,j}^y+S^{i,j}{l}_{i,j}^y)x_{i,j}^G]=0---\left(27\right)$

One group of Nonlinear System of Equations can be set up, be designated as：

$\left\{\begin{array}{c}{F}_1(\mathrm{\&alpha;},\mathrm{\&beta;},{\mathrm{\&Delta;}}_0,\mathrm{RF},t)=0\\ F_2(\mathrm{\&alpha;},\mathrm{\&beta;},{\mathrm{\&Delta;}}_0,\mathrm{RF},t)=0\\ F_3(\mathrm{\&alpha;},\mathrm{\&beta;},{\mathrm{\&Delta;}}_0,\mathrm{RF},t)=0\end{array}\right.---\left(28\right)$

By giving different moment value t, and solve Nonlinear System of Equations (25), when obtaining different under different reduction coefficients Carve corresponding key point vertical displacement Δ₀.Prepare a computer program, substitute into relevant parameter, the key point of this embodiment can be obtained Vertical displacement Δ₀Time dependent relation.As shown in figure 5, vertical coordinate is key point vertical displacement Δ₀, abscissa is change Time, the key point vertical displacement Δ under the different reduction coefficients of graphical representation₀Time dependent graph of a relation.Further Ground, as shown in fig. 6, vertical coordinate is key point long-term vertical displacement, abscissa is the reduction coefficient of change, and graphical representation is closed The long-term vertical displacement of key point is with the graph of a relation of reduction coefficient.As seen from Figure 6, the long-term vertical displacement of key point is in reduction coefficient Have, after more than 0.42, the trend sharply increasing, according to " considering the long-term slope stability study of ground creep propertieses ", Jiang Hai Fly, Hu Bin, Liu Qiang, Wang Xingang, metal mine, the 12nd phase in 2013, page 131～157, can determine whether that the three-dimensional of this embodiment is compacted The long term stabilization factor becoming side slope is 0.42.

Claims (2)

1. a kind of long-time stability Forecasting Methodology of three-dimensional creep side slope, including step 1, selectes creep side specifically to be predicted Slope, determines three-dimensional slope and its physical dimension of Potential failure surface, and Potential failure surface and side slope surface equation are represented；Determine The soil body index parameter of ground；

Step 2, by three-dimensional creep side slope body discretization, three-dimensional creep side slope is m row and n row bar post by Vertical derivative, each Post is defined as [i, j] by line number i being located and row number j；It is assumed that the bar intercolumniation active force of line direction and horizontal plane angle are ± α, It is assumed that the bar intercolumniation active force of column direction and horizontal plane angle are ± β；

Step 3, introducing Strength Reduction Method, reduction coefficient is RF, and mole coulomb criterion, and the long-term shearing resistance to calculate Rock And Soil is strong Degree：

WhereinFor the Long-term Shear Strength of [i, j] bar post bottom surface,For the direct stress of [i, j] bar post bottom surface,For rock The internal friction angle of the soil body, c is the cohesive strength of Rock And Soil；

Introduce Strength Reduction Method, the Rock And Soil Long-term Shear Strength after reduction is：

WhereinFor the Rock And Soil Long-term Shear Strength after the bottom surface reduction of [i, j] bar post；

So, the long-term shearing resistance after the bottom surface reduction of [i, j] bar post is：

$S_{long,r}^{i,j}=\frac{{\mathrm{\&tau;}}_{long,r}^{i,j}{A}^{i,j}}{n_z^{i,j}}$

WhereinLong-term shearing resistance after the bottom surface reduction of [i, j] bar post, A^i,jFor the cross-sectional area of [i, j] bar post,For Component in z-axis for the unit vector of [i, j] bar post bottom surface normal force；

Further according to visco-elastoplastic model, determine the relation between the shearing of [i, j] bar post bottom surface and the shear displacemant of this post；Profit With the displacement coordination condition of each bar post after discrete, obtain shearing force and the key point vertical displacement Δ of [i, j] bar post bottom surface₀ Relation；

It is characterized in that, the visco-elastoplastic model in side slope bar post is divided into two parts：

(1) as the shearing S on Potential failure surface^i,jLess than the long-term shearing resistance after the bottom surface reduction of [i, j] bar postWhen, obtain Relation between the shearing and the shear displacemant of this post of [i, j] bar post bottom surface is：

${\mathrm{\&Delta;}}^{i,j}\left(t\right)=\frac{(G_1+G_2)S^{i,j}}{{\mathrm{bG}}_1{G}_2}\left(1-e^{-\frac{G_2}{{\mathrm{\&eta;}}_1}t}\right)$

Δ in formula^i,jT () is the shear displacemant of [i, j] bar post bottom surface, S^i,jFor the shearing of [i, j] bar post bottom surface, G₁, G₂, η₁, η₂For the parameter in visco-elastoplastic model, t is the time that creep occurs, and b is the width of bar post line direction；

(2) as the shearing S on Potential failure surface^i,jDuring more than or equal to long-term shearing resistance after the bottom surface reduction of [i, j] bar postThe relation obtaining between the shearing of [i, j] bar post bottom surface and the shear displacemant of this post is：

${\mathrm{\&Delta;}}^{i,j}\left(t\right)=\frac{G_2(S^{i,j}-S_{long,r}^{i,j})}{{\mathrm{b\&eta;}}_1}\left(t+\frac{G_2{\mathrm{\&eta;}}_2}{G_1}{e}^{-\frac{G_1}{G_2{\mathrm{\&eta;}}_2}t}+\frac{G_2{\mathrm{\&eta;}}_2}{G_1}\right)$

WhereinFor the long-term shearing resistance after the bottom surface reduction of [i, j] bar post, S^i,jShearing for [i, j] bar post bottom surface；

The equilibrium equation of step 4, the equilibrium equation according to 3 power and three moment, and combine [i, j] bar post bottom surface shearing with The relational expression of key point vertical displacement, sets up one and contains unknown number α, β, Δ₀, the Nonlinear System of Equations of RF and creep time t； Solve equation group, obtain different reduction coefficients and the vertical displacement Δ of key point corresponding to the different moment₀；And then obtain not Relation with the long-term vertical displacement of this three-dimensional creep side slope under reduction coefficient；The long-term vertical displacement of key point is suddenly corresponding at increasing Reduction coefficient RF value is the coefficient of stability of this three-dimensional creep side slope, thus judging the long-time stability of this three-dimensional creep side slope.

2. a kind of long-time stability Forecasting Methodology of three-dimensional creep side slope according to claim 1, is characterized in that：In step In 4, relational expression between the shearing of the equilibrium equation of three power of simultaneous and bar post bottom surface and the shear displacemant of this post, obtain The normal force of [i, j] bar post bottom surface and the relation of shearing and key point vertical displacement：

(1) as the shearing S on Potential failure surface^i,jLess than the long-term shearing resistance after the bottom surface reduction of [i, j] bar postWhen,

The normal force of [i, j] bar post bottom surface and shearing and key point vertical displacement Δ₀Relation be：

$\begin{array}{c}{N}^{i,j}=-\frac{l_x^{1,j_0}{l}_x^{i,j}\cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}\&CenterDot;{\mathrm{\&Delta;}}_0+l_x^{1,j_0}{l}_y^{i,j}\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}\&CenterDot;{\mathrm{\&Delta;}}_0}{k_1{l}_z^{1,j_0}{l}_x^{i,j}\left(n_x^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}+n_y^{i,j}\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}-n_z^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}\right)}\\ +\frac{l_x^{1,j_0}{l}_z^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}\&CenterDot;{\mathrm{\&Delta;}}_0-k_1{l}_z^{1,j_0}{l}_x^{i,j}{W}^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}}{k_1{l}_z^{1,j_0}{l}_x^{i,j}\left(n_x^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}+n_y^{i,j}\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}-n_z^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}\right)}\end{array}$

$S^{i,j}=\frac{l_x^{1,j_0}{\mathrm{\&Delta;}}_0}{k_1{l}_z^{1,j_0}{l}_x^{i,j}}$

Wherein

(2) as the shearing S on Potential failure surface^i,jMore than or equal to the long-term shearing resistance after the bottom surface reduction of [i, j] bar post When,

The normal force of [i, j] bar post bottom surface and shearing and key point vertical displacement Δ₀Relation be：

$\begin{array}{c}{N}^{i,j}=\frac{W^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}}{-n_x^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}-n_y^{i,j}\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}+n_z^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}}\\ +\frac{(-l_x^{1,j_0}\&CenterDot;{\mathrm{\&Delta;}}_0-k_2{l}_z^{1,j_0}{l}_x^{i,j}{S}_{long,r}^{i,j})(-l_x^{i,j}\cos \mathrm{\&alpha;}\sin \mathrm{\&beta;}-l_y^{i,j}\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}\&CenterDot;{\mathrm{\&Delta;}}_0+l_z^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}\&CenterDot;{\mathrm{\&Delta;}}_0)}{k_2{l}_z^{1,j_0}{l}_x^{i,j}\left(-n_x^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}-n_y^{i,j}\sin \mathrm{\&alpha;}\cos \mathrm{\&beta;}+n_z^{i,j}\cos \mathrm{\&alpha;}\cos \mathrm{\&beta;}\right)}\end{array}$

$S^{i,j}=\frac{l_x^{1,j_0}\&CenterDot;{\mathrm{\&Delta;}}_0+k_2{l}_z^{1,j_0}{l}_x^{i,j}{S}_{long,r}^{i,j}}{k_2{l}_z^{1,j_0}{l}_x^{i,j}}$

Wherein

In various above, N^i,jAnd S^i,jIt is respectively normal force and the shearing of [i, j] bar post bottom surface,Be respectively [i, J] bar post bottom surface shearing force component on x, y, z direction for the unit vector,For [1, j₀] bar post bottom surface shearing force Component on x, z direction for the unit vector,Be respectively normal direction force direction on [i, j] bar post bottom surface unit to Component on x, y, z direction for the amount, W^i,jIt is the weight of [i, j] bar post.