CN101514553A - Soil slope stability analysis method based on limit equilibrium theory and stress analysis - Google Patents

Abstract

The present invention discloses a soil slope stability analysis method based on limit equilibrium theory and stress analysis, wherein the method comprises the following steps: 1) respectively preinstalling two slip surface starting points on the slope base and the next-to-top position of slope; 2) preinstalling a plurality of slip surface starting points on natural interface of slope between the two slip surface starting points; 3) setting the preinstalled safety factor corresponding with each slip surface starting point, and calculating out the critical slip surface corresponding to each slip surface starting point through calculating the found preinstalled safety factor satisfying the condition; and 4) selecting the critical slip surface with least preinstalled safety factor as the critical slip surface of whole soil slope, wherein the least preinstalled safety factor is used as the stability safety factor of whole slope. The soil slope stability analysis method of the invention has the following beneficial effects: (1) no requirement for pre-supposing the shape or position of slip surface, and only requirement for supposing the starting point position of slip surface (namely the position of so-called slip surface shear crack); and (2) translation of problem for searching the critical slip surface to the problem for searching the position of critical shear crack, and overcoming the problems of leaked solution or a plurality of solutions in the traditional method.

Description

Slope stability analysis method based on limit equilibrium theory and stress analysis

Technical field

The present invention relates to a kind of Soil Slope Stability analytical technology, relate in particular to a kind of slope stability analysis method based on limit equilibrium theory and stress analysis.

Background technology

In the soil mechanics, slope stability analysis is that soil pressure and bearing capacity of foundation soil grow up simultaneously with two other branch.The method that coulomb and Rankine are analyzed soil pressure was generalized in bearing capacity of foundation soil and the slope stability analysis limit equilibrium method that Here it is afterwards.In Soil Slope Stability was analyzed, although also have other method such as finite element, the limit equilibrium method was owing to have theoretical simple, clear concept and many advantages such as grasps and being had a preference for by vast engineering and researcher easily.

The calculation procedure of classical limit balance method can reduce for two steps: at first be slip-crack surface of supposition, calculate the safety factor of side slope along this face generation unstability; Be to seek minimum safety factor then, just seek critical sliding surface.

In order to calculate the safety factor of side slope, suppose that slope soil enters state of limit equilibrium because of certain disturbance factor from present stable state.At this moment, an imaginary slip-crack surface appears in the sloping body.On this sliding surface, the normal stress of every bit and shear stress all satisfy Mohr-Coulomb strength criterion.

Fellenius has proposed the circular arc Sliding analysis method of slope stability analysis, just Sweden's arc method in nineteen twenty-seven.In this method, slip-crack surface is assumed to circular arc, and the normal stress of native bar bottom surface is counted as the projection of native bar gravity in native bar bottom surface normal direction, does not occur when therefore square is got in the center of circle, and amount of calculation is simplified greatly.But this method can not satisfy all static balance condition owing to ignored the effect of power between bar.When slip-crack surface was not circular arc, this method was no longer suitable.

The Bishop method is the development on Sweden arc method basis, and this method supposes that also slip-crack surface is a circular arc, but it has considered power between bar.Vertical force balance and equalising torque by native bar are released the formula of finding the solution safety factor.The Bishop method is a a progressive step than Sweden arc method owing to considered power between bar, for the homogeneous slight slope, generally believes that at present this method can obtain more reasonably separating.But sliding surface is the range of application that the supposition of circular arc has limited this method.

Janbu method supposition slip surface shape is an arbitrary shape, and the position of action point (being the line of thrust position) of power is known between the supposition bar.To each native bar, can list two equations of static equilibrium and a torque equilibrium equation, therefore belong to rigorous method.But the supposition of its line of thrust must meet the requirement of reasonableness of power between bar.Although the sliding surface of this method is an arbitrary shape, supposition, so this method in advance is only applicable to the slope stability analysis that position of slip surface, form are all determined substantially.

Uneven thrust TRANSFER METHOD be according to the broken line slide plane with the sliding mass piecemeal, suppose interblock power make a concerted effort parallel with a last soil block bottom surface.This method is only carried out piecemeal to gliding mass, and does not have itemize, thereby amount of calculation reduces greatly.Equally, this method also is only applicable to the Analysis of Slope Stability that position of slip surface, form are all determined substantially.

The slope stability analysis method that belongs to limit equilibrium method category is a lot, more than only enumerated several typical methods, from above analysis as can be known: the classical limit equilibrium method, no matter be that the supposition sliding surface is a circular arc, or arbitrary shape; No matter being rigorous method, also is non-rigorous method, all must at first suppose the form (as Fellenius method and Bishop method) of sliding surface, perhaps supposes form and position (as the Janbu method and the uneven thrust TRANSFER METHOD) of sliding surface simultaneously.When the slight slope structure is complicated, such as the slight slope that constitutes by multilayer soil and be subjected to underground water and the situation of external loads effect, the form of actual sliding surface and position can not determine in advance probably that all at this moment, the integrity problem of classical limit balance method has just highlighted.

Summary of the invention

The present invention proposes a kind of slope stability analysis method based on limit equilibrium theory and stress analysis, its step is as follows: 1) preset two slip-crack surface starting points (rule of thumb value is chosen two endpoint locations that may become the slip-crack surface starting point on the side slope) in the sloping end and the domatic nearly Po Ding position of side slope respectively; 2) again on the side slope between two slip-crack surface starting points in the step 1) nature interface, adopt 0.618 method to preset a plurality of slip-crack surface starting points; 3) the pairing default safety factor of each slip-crack surface starting point is set, finds the default safety factor that satisfies condition, try to achieve the pairing critical slip surface of each slip-crack surface starting point by calculating; 4) choose the critical slip surface of the critical slip surface of default safety factor minimum as whole slight slope, this minimum default safety factor is as the buckling safety factor of whole side slope.

In the step 3), the method for calculating the pairing critical slip surface of single slip-crack surface starting point comprises:

At a certain slip-crack surface starting point (comprising two slip-crack surface starting points of initial setting and the slip-crack surface starting point of determining by 0.618 method), the default safety factor and the native bar width of the slip-crack surface of this slip-crack surface starting point correspondence are set, try to achieve the theoretical safety factor of slip-crack surface by calculating, whether the difference of judging theoretical safety factor and default safety factor is in error range: if resulting slip-crack surface is the critical slip surface through this slip-crack surface starting point; If not, reset default safety factor and calculate its theoretical safety factor, until the default safety factor of difference in error range that finds with theoretical safety factor; Aforementioned part is to the text summarization of the method for calculating the pairing critical slip surface of single slip-crack surface starting point, carries out as follows when quantitatively calculating:

Represent native bar scope with the quadrangle that DABC surrounded,

(1) the default safety factor of establishing the slip-crack surface of a certain slip-crack surface starting point correspondence is F _s, native bar width is b _i, native bar width is the horizontal range that B point and A are ordered on the native bar;

On the DA limit of (2) first native bars, D, A point overlaps, and is designated as the A point, and this A point is the slip-crack surface starting point; Set up the equilibrium equation of the first native bar and find the solution, determine the BC section endpoint location of the first native bar, also promptly determine the DA section endpoint location of the second native bar; This part can further be refined as following steps:

The A of [1] first native bar, D point overlaps, and promptly A, D point normal stress satisfies σ ' ₁ ⁰=σ ' ₁, determine according to following formula:

In the formula, c ' ₁It is the weighted average of each soil layer effective cohesion intercept in the first native bar AB segment limit;

It is the weighted average of each soil layer effective angle of inner friction in the first native bar AB segment limit;

F _sBe default safety factor.

[2] σ ' ₁ ⁰, σ ' ₁, F _s, b _iAs known quantity substitution equilibrium equation (parameter that relates in the equilibrium equation is more, but can represent with the known quantity in each step), separate the B point normal stress σ ' of the native bar of winning ₂, C point normal stress σ ' ₂ ⁰, AB section and horizontal direction angle α ₁

[3] known B point and the A horizontal range of ordering can be determined B point position in conjunction with following formula result of calculation,

Y _AB＝b _i·tan(α ₁)

In the formula, Y _ABThe vertical distance of ordering for B point and A.

[4] C point position is determined by following method:

The BC slope is

Can unique definite BC section and the intersection point C at side slope nature interface;

Determine δ according to following formula ₂,

In the formula,

It is the weighted average of each the soil layer angle of internal friction in the BC segment limit of interface between the bar of the 1st native bar and the 2nd native bar;

δ ₂It is the angle of interface BC section and vertical curve between the bar of the 1st native bar and the 2nd native bar;

The first native bar BC section B, C point position and normal stress thereof are the second native bar AD section A, D point position and normal stress thereof.

(3) determine the DA section endpoint location of i native bar according to the correlation computations result of i-1 native bar, set up the equilibrium equation of i native bar and find the solution; Determine the DA section endpoint location of i+1 native bar; This part can be refined as following steps:

The B point of [1] i-1 native bar is the A point position of i native bar, and the C point position of i-1 native bar is the D point position of i native bar; The B point normal stress of i-1 native bar is the A point normal stress σ ' of i native bar _i, the C point normal stress of i-1 native bar is the D point normal stress σ ' of i native bar _i ⁰

[2] σ ' _i, σ ' _i ⁰, F _s, b _iAs known quantity substitution equilibrium equation, solve the B point normal stress σ ' of i native bar _I+1, C point normal stress σ ' _I+1 ⁰, AB section and horizontal direction angle α _i

[3] known B point combines following formula result of calculation with horizontal range that A is ordered and can determine B point position,

Y _AB＝b _i·tan(α _i)

In the formula, Y _ABThe vertical distance of ordering for B point and A;

[4] C point position is determined by following method:

The BC slope is

Can unique definite BC section and the intersection point C at side slope nature interface;

Determine δ according to following formula _I+1,

In the formula,

Be i native bar with the bar of i+1 native bar between the weighted average of angle of internal friction of interior each soil layer of interface BC segment limit;

δ _I+1It is the angle of individual native bar interface BC section of i native bar and i+1 and vertical curve.

(4) establishing i+1 native bar is last native bar, and then the DA section endpoint location of i+1 native bar is determined by the correlation computations result of i native bar;

B, C point overlaps on the BC limit of i+1 native bar, is designated as the C point, and this C point is the terminal point of slip-crack surface, sets up the equilibrium equation of i+1 native bar; Obtain theoretical safety factor F ' _sC point position with i+1 native bar; Refinement is as follows:

[1] establishing i+1 native bar is last native bar, then the DA limit endpoint location of i+1 native bar and D point, A point normal stress σ ' _I+1 ⁰, σ ' _I+1Correlation computations result by i native bar determines;

B, C point overlaps on the BC limit of [2] i+1 native bars, and promptly B, C point normal stress satisfies ${\mathrm{\σ}}_{i+2}^{\′0}={\mathrm{\σ}}_{i+2}^{\′},$ Be designated as the C point;

[3] σ ' _I+1, σ ' _I+1 ⁰, b _iAs known quantity substitution equilibrium equation, simultaneously the F in the equilibrium equation _sReplace with F ' _s, and with F ' _sFind the solution as unknown number, solve the C point normal stress σ ' of i+1 native bar _I+2 ⁰(also be B point normal stress σ ' _I+2), theoretical safety factor F ' _sAngle α with AB section and horizontal direction _I+1

[4] C point position is determined by following method:

The slope of the AC section of i+1 native bar is tan (α _I+1), can unique definite AC section and the intersection point C point (B, C point overlaps, and is designated as the C point) at side slope nature interface, the C point is the slip-crack surface terminal point.

The curve that the AB section of slip-crack surface starting point and slip-crack surface terminal point and middle native bar (i.e. second native bar to the i native bar) is linked to be, be this time calculate at the pairing slip-crack surface of default slip-crack surface starting point;

(5) relatively more default safety factor F _sWith theoretical safety factor F ' _sDifference whether in error range: if resulting slip-crack surface was the critical slip surface of default slip-crack surface starting point; If not, repeating step (1) is to (5), until default safety factor F _sWith theoretical safety factor F ' _sDifference in error range till.

The equilibrium equation that relates in the preceding method comprises: the torque equilibrium equation that the horizontal direction equation of static equilibrium, the vertical direction equation of static equilibrium and each native bar A are ordered,

The horizontal direction equation of static equilibrium:

$+{\stackrel{\‾}{c}}_{i+1}^{\′}{d}_{i+1}\sin {\mathrm{\δ}}_{i+1}-Q_i-H_i=0$

The vertical direction equation of static equilibrium:

$+{\stackrel{\‾}{c}}_{i+1}^{\′}{d}_{i+1}\cos {\mathrm{\δ}}_{i+1}-W_i-V_i=0$

The torque equilibrium equation that each native bar A is ordered:

In the formula, F _sBe default safety factor, when calculating the first native bar and middle native bar, with F _sPreset value substitution equation calculate; When finding the solution last native bar, with the F in the above-mentioned formula _sReplace with F ' _s, and with F ' _sFind the solution as unknown number;

b _iBe the horizontal projection length of i native bar AB section;

d _iIt is the interface length between the individual native bar of i native bar and i-1;

d _I+1It is the interface length between the individual native bar of i native bar and i+1;

L ' _iBe i total pore space, native bar bottom surface water pressure U _iThe distance that application point is ordered to A;

x _iThe center of gravity that is i native bar arrives the horizontal range that A is ordered;

y _iThe center of gravity that is i native bar arrives the vertical distance that A is ordered;

Z ' _iBe total pore space, the interface water pressure PW between the individual native bar of i native bar and i-1 _iThe distance that application point is ordered to A;

Z ' _I+1Be total pore space, the interface water pressure PW between the individual native bar of i+1 native bar and i _I+1The distance that application point is ordered to B;

α _iIt is the angle of i native bar AB section and horizontal direction;

It is the weighted average of each soil layer effective angle of inner friction in i the native bar AB segment limit;

It is the weighted average of interior each the soil layer effective angle of inner friction of AD segment limit of i native bar;

It is the weighted average of interior each the soil layer effective angle of inner friction of BC segment limit of i native bar;

C ' _iIt is the weighted average of each soil layer effective cohesion intercept in i the native bar AB segment limit;

It is the weighted average of interior each the soil layer effective cohesion intercept of AD segment limit of i native bar;

It is the weighted average of interior each the soil layer effective cohesion intercept of BC segment limit of i native bar;

σ ' _iBe the A point normal stress of i native bar;

σ ' _i ⁰Be the D point normal stress of i soil bar;

σ ' _I+1Be the B point normal stress of i native bar;

σ ' _I+1 ⁰Be the C point normal stress of i soil bar;

δ _iBe i native bar with the individual native bar of i-1 between the interface and the angle between vertical curve;

δ _I+1Be i native bar with the individual native bar of i+1 between the interface and the angle between vertical curve;

U _iBe i total pore space, native bar bottom surface water pressure;

PW _iIt is total pore space, the interface water pressure between the individual native bar of i native bar and i-1;

PW _I+1It is total pore space, the interface water pressure between the individual native bar of i+1 native bar and i;

Q _iBe horizontal seismic force;

H _iFor native bar end face level to load, the level that promptly acts on native bar DC face is to load;

W _iBe native bar gravity;

V _iBe native bar end face vertical load.

Useful technique effect of the present invention is: (1) need not to suppose in advance the form or the position of slip-crack surface, only need suppose the start position (just so-called sliding surface cuts the position of mouth) of slip-crack surface; (2) search problem with critical slip surface is converted into the critical search problem that cuts mouthful position, has overcome the problem that the leakage in the conventional method is separated or separated more.

Description of drawings

Fig. 1: the native bar of multilayer heterogeneous body slight slope is divided schematic diagram;

Fig. 2: native bar is by the force analysis figure of total stress;

Fig. 3: native bar is by the force analysis figure of effective stress;

The specific embodiment

Main points of the present invention can be summarized as follows: 1, native bar is divided: native bar is divided in computational process and is progressively realized, rather than ready-portioned before calculating (being different from the division methods of the whole bag of tricks of the prior art to native bar): native bar interface is a clinoplain, and the angle between itself and vertical curve is the function along each soil layer angle of internal friction weighted average at native bar interface.

2, basic assumption: the normal stress and the shear stress of (1) native bar interface and bottom surface are linear distribution; (2), act on the normal stress equal and opposite in direction of native bar interface and bottom surface at native bar interface and bottom surface intersection point place; (3) stress state of native bar interface and bottom surface can be the equilibrium state that reaches capacity simultaneously, and promptly the safety factor along native bar interface and bottom surface generation destruction equates; Also can be the equilibrium state that do not reach capacity simultaneously, promptly can be unequal along the safety factor of native bar interface and bottom surface generation destruction, but both functional relations are determined.

3, basic theories: the power (comprising muscle power and face power) that acts on arbitrary native bar satisfies three equilibrium equations, that is: (1) horizontal direction equation of static equilibrium simultaneously; (2) the vertical direction equation of static equilibrium; (3) each native bar A torque equilibrium equation of ordering; Each equation includes total stress and two kinds of forms of effective stress, referring to Fig. 2,3.

The concrete equation of effective stress method is as follows:

The horizontal direction equation of static equilibrium,

$+{\stackrel{\‾}{c}}_{i+1}^{\′}{d}_{i+1}\sin {\mathrm{\δ}}_{i+1}-Q_i-H_i=0$

The vertical direction equation of static equilibrium,

$+{\stackrel{\‾}{c}}_{i+1}^{\′}{d}_{i+1}\cos {\mathrm{\δ}}_{i+1}-W_i-V_i=0$

The torque equilibrium equation that each native bar A is ordered,

In the formula, F _sBe default safety factor, when calculating the first native bar and middle native bar, with F _sPreset value substitution equation calculate; When finding the solution last native bar, with the F in the above-mentioned formula _sReplace with F ' _s, and with F ' _sFind the solution as unknown number;

b _iBe the horizontal projection length of i native bar AB section;

d _iIt is the interface length between the individual native bar of i native bar and i-1;

d _I+1It is the interface length between the individual native bar of i native bar and i+1;

L ' _iBe i total pore space, native bar bottom surface water pressure U _iThe distance that application point is ordered to A;

x _iThe center of gravity that is i native bar arrives the horizontal range that A is ordered;

y _iThe center of gravity that is i native bar arrives the vertical distance that A is ordered;

Z ' _iBe total pore space, the interface water pressure PW between the individual native bar of i native bar and i-1 _iThe distance that application point is ordered to A;

Z ' _I+1Be total pore space, the interface water pressure PW between the individual native bar of i+1 native bar and i _I+1The distance that application point is ordered to B;

α _iIt is the angle of i native bar AB section and horizontal direction;

It is the weighted average of each soil layer effective angle of inner friction in i the native bar AB segment limit;

It is the weighted average of interior each the soil layer effective angle of inner friction of AD segment limit of i native bar;

It is the weighted average of interior each the soil layer effective angle of inner friction of BC segment limit of i native bar;

C ' _iIt is the weighted average of each soil layer effective cohesion intercept in i the native bar AB segment limit;

It is the weighted average of interior each the soil layer effective cohesion intercept of AD segment limit of i native bar;

It is the weighted average of interior each the soil layer effective cohesion intercept of BC segment limit of i native bar;

σ ' _iBe the A point normal stress of i native bar;

σ ' _i ⁰Be the D point normal stress of i soil bar;

σ ' _I+1Be the B point normal stress of i native bar;

σ ' _I+1 ⁰Be the C point normal stress of i soil bar;

δ _iBe i native bar with the individual native bar of i-1 between the interface and the angle between vertical curve;

δ _I+1Be i native bar with the individual native bar of i+1 between the interface and the angle between vertical curve;

U _iBe i total pore space, native bar bottom surface water pressure;

PW _iIt is total pore space, the interface water pressure between the individual native bar of i native bar and i-1;

PW _I+1It is total pore space, the interface water pressure between the individual native bar of i+1 native bar and i;

Q _iBe horizontal seismic force;

H _iFor native bar end face level to load, the level that promptly acts on native bar DC face is to load;

W _iBe native bar gravity;

V _iBe native bar end face vertical load.

According to the equilibrium relation of above-mentioned formula, just can determine the critical slip surface and the safety factor thereof of a certain slip-crack surface starting point correspondence, concrete steps are as follows:

Referring to Fig. 1, represent native bar scope with the quadrangle that DABC surrounded,

(1) the default safety factor of establishing the slip-crack surface of a certain slip-crack surface starting point correspondence is F _s, native bar width is b _i, native bar width is the horizontal range that B point and A are ordered on the native bar;

On the DA limit of (2) first native bars, D, A point overlaps, and is designated as the A point, and this A point is the slip-crack surface starting point; Set up the equilibrium equation of the first native bar and find the solution, determine the BC section endpoint location of the first native bar, also promptly determine the DA section endpoint location of the second native bar; This part can further be refined as following steps:

The A of [1] first native bar, D point overlaps, and promptly A, D point normal stress satisfies σ ' ₁ ⁰=σ ' ₁, determine according to following formula:

In the formula, c ' ₁It is the weighted average of each soil layer effective cohesion intercept in the first native bar AB segment limit;

It is the weighted average of each soil layer effective angle of inner friction in the first native bar AB segment limit;

F _sBe default safety factor.

[2] σ ' ₁ ⁰, σ ' ₁, F _s, b _iAs known quantity substitution equilibrium equation, separate the B point normal stress σ ' of the native bar of winning ₂, C point normal stress σ ' ₂ ⁰, AB section and horizontal direction angle α ₁

[3] known B point and the A horizontal range of ordering can be determined B point position in conjunction with following formula result of calculation,

Y _AB＝b _i·tan(α ₁)

In the formula, Y _ABThe vertical distance of ordering for B point and A.

[4] C point position is determined by following method:

The BC slope is

Can unique definite BC section and the intersection point C at side slope nature interface;

Determine δ according to following formula ₂,

In the formula,

It is the weighted average of each the soil layer angle of internal friction in the BC segment limit of interface between the bar of the 1st native bar and the 2nd native bar;

δ ₂It is the angle of interface BC section and vertical curve between the bar of the 1st native bar and the 2nd native bar;

The first native bar BC section B, C point position and normal stress thereof are the second native bar AD section A, D point position and normal stress thereof.

(3) determine the DA section endpoint location of i native bar according to the correlation computations result of i-1 native bar, set up the equilibrium equation of i native bar and find the solution; Determine the DA section endpoint location of i+1 native bar; This part can be refined as following steps:

The B point of [1] i-1 native bar is the A point position of i native bar, and the C point position of i-1 native bar is the D point position of i native bar; The B point normal stress of i-1 native bar is the A point normal stress σ ' of i native bar _i, the C point normal stress of i-1 native bar is the D point normal stress σ ' of i native bar _i ⁰

[2] σ ' _i, σ ' _i ⁰, F _s, b _iAs known quantity substitution equilibrium equation, solve the B point normal stress σ ' of i native bar _I+1, C point normal stress σ ' _I+1 ⁰, AB section and horizontal direction angle α _i

[3] known B point combines following formula result of calculation with horizontal range that A is ordered and can determine B point position,

Y _AB＝b _i·tan(α _i)

In the formula, Y _ABThe vertical distance of ordering for B point and A;

[4] C point position is determined by following method:

The BC slope is

Can unique definite BC section and the intersection point C at side slope nature interface;

Determine δ according to following formula _I+1,

In the formula,

Be i native bar with the bar of i+1 native bar between the weighted average of angle of internal friction of interior each soil layer of interface BC segment limit;

δ _I+1It is the angle of individual native bar interface BC section of i native bar and i+1 and vertical curve.

(4) establishing i+1 native bar is last native bar, and then the DA section endpoint location of i+1 native bar is determined by the correlation computations result of i native bar;

B, C point overlaps on the BC limit of i+1 native bar, is designated as the C point, and this C point is the terminal point of slip-crack surface, sets up the equilibrium equation of i+1 native bar; Obtain theoretical safety factor F ' _sC point position with i+1 native bar; Refinement is as follows:

[1] establishing i+1 native bar is last native bar, then the DA limit endpoint location of i+1 native bar and D point, A point normal stress σ ' _I+1 ⁰, σ ' _I+1Correlation computations result by i native bar determines;

B, C point overlaps on the BC limit of [2] i+1 native bars, and promptly B, C point normal stress satisfies ${\mathrm{\σ}}_{i+2}^{\′0}={\mathrm{\σ}}_{i+2}^{\′},$ Be designated as the C point;

[3] σ ' _I+1, σ ' _I+1 ⁰, b _iAs known quantity substitution equilibrium equation, simultaneously the F in the equilibrium equation _sReplace with F ' _s, and with F ' _sFind the solution as unknown number, solve the C point normal stress σ ' of i+1 native bar _I+2 ⁰, theoretical safety factor F ' _sAngle α with AB section and horizontal direction _I+1

[4] C point position is determined by following method:

The slope of the AC section of i+1 native bar is tan (α _I+1), can unique definite AC section and the intersection point C point at side slope nature interface, the C point is the slip-crack surface terminal point.

The curve that the AB section of slip-crack surface starting point and slip-crack surface terminal point and middle native bar (i.e. second native bar to the i native bar) is linked to be, be this time calculate at the pairing slip-crack surface of default slip-crack surface starting point;

(5) relatively more default safety factor F _sWith theoretical safety factor F ' _sDifference whether in error range: if resulting slip-crack surface was the critical slip surface of default slip-crack surface starting point; If not, repeating step (1) to (5) (during repeating step (1), F _sMust reset b _iCan reset also and can continue to use previous setting), until default safety factor f _sWith theoretical safety factor F ' _sDifference in error range till.

Preceding method is the computational methods at pairing critical slip surface of single slip-crack surface starting point and default safety factor thereof, for the security evaluation of whole slight slope, also needs the different critical slip-crack surface and the safety factor of different slip-crack surface starting point correspondences are taken all factors into consideration.

When considering, should carry out as follows: 1) respectively in default two the slip-crack surface starting points in the sloping end and domatic nearly Po Ding position of side slope as the complete scheme of slope stability analysis; 2) again on the side slope between two slip-crack surface starting points in the step 1) nature interface, adopt 0.618 method (Fibonacci method) to preset a plurality of slip-crack surface starting points; 3) the default safety factor of each slip-crack surface starting point is set respectively, determines the default safety factor and the critical slip surface that satisfy condition by calculating; 4) from pairing critical slip surface of each slip-crack surface starting point and default safety factor thereof, choose the critical slip surface of the critical slip surface of default safety factor minimum as whole upward slope, the default safety factor of the minimum of this moment is as the buckling safety factor of whole slight slope.

By the elaboration of front to the inventive method, the most basic difference is can to sum up the present invention and prior art: existing Method all must at first be supposed the form of sliding surface or suppose simultaneously form and the position of sliding surface, and method of the present invention need not in advance Suppose form or the position of sliding surface, only need suppose that sliding surface cuts the position (being the slip-crack surface starting point) of mouth, with the search of critical slip surface Problem is converted into the critical search problem that cuts mouthful position, has avoided leakage solution or the problem of separating in the conventional method more.

Claims (8)

1, a kind of slope stability analysis method based on limit equilibrium theory and stress analysis, it is characterized in that: it comprises: 1) respectively in default two the slip-crack surface starting points in the sloping end and domatic nearly Po Ding position of side slope; 2) again on the side slope between two slip-crack surface starting points in the step 1) nature interface, default a plurality of slip-crack surface starting points; 3) the pairing default safety factor of each slip-crack surface starting point is set, finds the default safety factor that satisfies condition, try to achieve the pairing critical slip surface of each slip-crack surface starting point by calculating; 4) choose the critical slip surface of the critical slip surface of default safety factor minimum as whole slight slope, this minimum default safety factor is as the buckling safety factor of whole side slope.

2, the slope stability analysis method based on limit equilibrium theory and stress analysis according to claim 1 is characterized in that: step 2) comprising: on the nature of the side slope between two slip-crack surface starting points interface, with the default a plurality of slip-crack surface starting points of 0.618 method.

3, the slope stability analysis method based on limit equilibrium theory and stress analysis according to claim 1, it is characterized in that: step 3) comprises:

At a certain slip-crack surface starting point, the default safety factor and the native bar width of the slip-crack surface of this slip-crack surface starting point correspondence are set, try to achieve the theoretical safety factor of slip-crack surface by calculating, whether the difference of judging theoretical safety factor and default safety factor is in error range: if resulting slip-crack surface is the critical slip surface through this slip-crack surface starting point; If not, reset default safety factor and calculate its theoretical safety factor, until the default safety factor of difference in error range that finds with theoretical safety factor.

4, the slope stability analysis method based on limit equilibrium theory and stress analysis according to claim 3, it is characterized in that: these method concrete steps are as follows:

Represent native bar scope with the quadrangle that DABC surrounded,

(1) the default safety factor F of the slip-crack surface of a certain slip-crack surface starting point correspondence is set _sWith native bar width b _i, native bar width is the horizontal range that B point and A are ordered on the native bar;

On the DA limit of (2) first native bars, D, A point overlaps, and is designated as the A point, and this A point is the slip-crack surface starting point; Set up the equilibrium equation of the first native bar and find the solution, determine the BC section endpoint location of the first native bar, also promptly determine the DA section endpoint location of the second native bar;

(3) determine the DA section endpoint location of i native bar according to the correlation computations result of i-1 native bar, set up the equilibrium equation of i native bar and find the solution; Determine the DA section endpoint location of i+1 native bar;

(4) establishing i+1 native bar is last native bar, and then the DA section endpoint location of i+1 native bar is determined by the correlation computations result of i native bar;

B, C point overlaps on the BC limit of i+1 native bar, is designated as the C point, and this C point is the terminal point of slip-crack surface, sets up the equilibrium equation of i+1 native bar; Obtain theoretical safety factor F ' _sC point position with i+1 native bar;

The curve that the AB section of slip-crack surface starting point and slip-crack surface terminal point and middle native bar is linked to be, be this time calculate at the pairing slip-crack surface of default slip-crack surface starting point;

(5) relatively more default safety factor F _sWith theoretical safety factor F ' _sDifference whether in error range: if resulting slip-crack surface was the critical slip surface of default slip-crack surface starting point; If not, repeating step (1) is to (5), until default safety factor F _sWith theoretical safety factor F ' _sDifference in error range till.

5, the slope stability analysis method based on limit equilibrium theory and stress analysis according to claim 4, it is characterized in that: the equilibrium equation of foundation comprises: the torque equilibrium equation that the horizontal direction equation of static equilibrium, the vertical direction equation of static equilibrium and each native bar A are ordered

The horizontal direction equation of static equilibrium:

$+{\stackrel{\‾}{c}}_{i+1}^{\′}{d}_{i+1}\sin {\mathrm{\δ}}_{i+1}-Q_i-H_i=0$

The vertical direction equation of static equilibrium:

$+{\stackrel{\‾}{c}}_{i+1}^{\′}{d}_{i+1}\cos {\mathrm{\δ}}_{i+1}-W_i-V_i=0$

The torque equilibrium equation that each native bar A is ordered:

In the formula, F _sBe default safety factor, when calculating the first native bar and middle native bar, with F _sPreset value substitution equation calculate; When finding the solution last native bar, with the F in the above-mentioned formula _sReplace with F ' _s, and with F ' _sFind the solution as unknown number;

b _iBe the horizontal projection length of i native bar AB section;

d _iIt is the interface length between the individual native bar of i native bar and i-1;

d _I+1It is the interface length between the individual native bar of i native bar and i+1;

L ' _iBe i total pore space, native bar bottom surface water pressure U _iThe distance that application point is ordered to A;

x _iThe center of gravity that is i native bar arrives the horizontal range that A is ordered;

y _iThe center of gravity that is i native bar arrives the vertical distance that A is ordered;

Z ' _iBe total pore space, the interface water pressure PW between the individual native bar of i native bar and i-1 _iThe distance that application point is ordered to A;

Z ' _I+1Be total pore space, the interface water pressure PW between the individual native bar of i+1 native bar and i _I+1The distance that application point is ordered to B;

α _iIt is the angle of i native bar AB section and horizontal direction;

It is the weighted average of each soil layer effective angle of inner friction in i the native bar AB segment limit;

It is the weighted average of interior each the soil layer effective angle of inner friction of AD segment limit of i native bar;

It is the weighted average of interior each the soil layer effective angle of inner friction of BC segment limit of i native bar;

C ' _iIt is the weighted average of each soil layer effective cohesion intercept in i the native bar AB segment limit;

C ' _iIt is the weighted average of interior each the soil layer effective cohesion intercept of AD segment limit of i native bar;

C ' _I+1It is the weighted average of interior each the soil layer effective cohesion intercept of BC segment limit of i native bar;

σ ' _iBe the A point normal stress of i native bar;

σ ' _i ⁰Be the D point normal stress of i soil bar;

σ ' _I+1Be the B point normal stress of i native bar;

σ ' _I+1 ⁰Be the C point normal stress of i soil bar;

δ _iBe i native bar with the individual native bar of i-1 between the interface and the angle between vertical curve;

δ _I+1Be i native bar with the individual native bar of i+1 between the interface and the angle between vertical curve;

U _iBe i total pore space, native bar bottom surface water pressure;

PW _iIt is total pore space, the interface water pressure between the individual native bar of i native bar and i-1;

PW _I+1It is total pore space, the interface water pressure between the individual native bar of i+1 native bar and i;

Q _iBe horizontal seismic force;

H _iFor native bar end face level to load, the level that promptly acts on native bar DC face is to load;

W _iBe native bar gravity;

V _iBe native bar end face vertical load.

6, the slope stability analysis method based on limit equilibrium theory and stress analysis according to claim 4 is characterized in that: in the step (2), determine DA section (the i.e. the first native bar BC section) endpoint location of the second native bar according to following method:

The A of [1] first native bar, D point overlaps, and promptly A, D point normal stress satisfies ${\mathrm{\σ}}_1^{\′0}={\mathrm{\σ}}_1^{\′},$ Determine according to following formula:

In the formula, c ' ₁It is the weighted average of each soil layer effective cohesion intercept in the first native bar AB segment limit;

It is the weighted average of each soil layer effective angle of inner friction in the first native bar AB segment limit;

F _sBe default safety factor.

[2] σ ' ₁ ⁰, σ ' ₁, F _s, b _iAs known quantity substitution equilibrium equation, separate the B point normal stress σ ' of the native bar of winning ₂, C point normal stress σ ' ₂ ⁰, AB section and horizontal direction angle α ₁

[3] known B point and the A horizontal range of ordering can be determined B point position in conjunction with following formula result of calculation,

Y _AB＝b _i·tan(α ₁)

In the formula, Y _ABThe vertical distance of ordering for B point and A.

[4] C point position is determined by following method:

The BC slope is

Can unique definite BC section and the intersection point C at side slope nature interface;

Determine δ according to following formula ₂,

In the formula, It is the weighted average of each the soil layer angle of internal friction in the BC segment limit of interface between the bar of the 1st native bar and the 2nd native bar;

δ ₂It is the angle of interface BC section and vertical curve between the bar of the 1st native bar and the 2nd native bar;

The first native bar BC section B, C point position and normal stress thereof are the second native bar AD section A, D point position and normal stress thereof.

7, the slope stability analysis method based on limit equilibrium theory and stress analysis according to claim 4 is characterized in that: in the step (3), determine the DA section endpoint location of i+1 native bar according to following method:

The B point of [1] i-1 native bar is the A point position of i native bar, and the C point position of i-1 native bar is the D point position of i native bar; The B point normal stress of i-1 native bar is the A point normal stress σ ' of i native bar _i, the C point normal stress of i-1 native bar is the D point normal stress σ ' of i native bar _i ⁰

[2] σ ' _i, σ ' _i ⁰, F _s, b _iAs known quantity substitution equilibrium equation, solve the B point normal stress σ ' of i native bar _I+1, C point normal stress σ ' _I+1 ⁰, AB section and horizontal direction angle α _i

[3] known B point combines following formula result of calculation with horizontal range that A is ordered and can determine B point position,

Y _AB＝b _i·tan(α _i)

In the formula, Y _ABThe vertical distance of ordering for B point and A;

[4] C point position is determined by following method:

The BC slope is

Can unique definite BC section and the intersection point C at side slope nature interface;

Determine δ according to following formula _I+1,

In the formula, Be i native bar with the bar of i+1 native bar between the weighted average of angle of internal friction of interior each soil layer of interface BC segment limit;

δ _I+1It is the angle of individual native bar interface BC section of i native bar and i+1 and vertical curve.

8, the slope stability analysis method based on limit equilibrium theory and stress analysis according to claim 4 is characterized in that: in the step (4), determine the C point position of last native bar according to following method:

[1] establishing i+1 native bar is last native bar, then the DA limit endpoint location of i+1 native bar and D point, A point normal stress σ ' _I+1 ⁰, σ ' _I+1Correlation computations result by i native bar determines;

B, C point overlaps on the BC limit of [2] i+1 native bars, and promptly B, C point normal stress satisfies ${\mathrm{\σ}}_{i+2}^{\′0}={\mathrm{\σ}}_{i+2}^{\′},$ Be designated as the C point;

[3] σ ' _I+1, σ ' _I+1 ⁰, b _iAs known quantity substitution equilibrium equation, simultaneously the F in the equilibrium equation _sReplace with F ' _s, and with F ' _sFind the solution as unknown number, solve the C point normal stress σ ' of i+1 native bar _I+2 ⁰, theoretical safety factor F ' _sAngle α with AB section and horizontal direction _I+1

[4] C point position is determined by following method:

The slope of the AC section of i+1 native bar is tan (α _I+1), can unique definite AC section and the intersection point C point at side slope nature interface, the C point is the slip-crack surface terminal point.

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