CN110457855A - It is partially flooded with the analytic method of the critical reservoir level analysis of c '-φ ' homogeneous slope - Google Patents
It is partially flooded with the analytic method of the critical reservoir level analysis of c '-φ ' homogeneous slope Download PDFInfo
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Abstract
Side of the present invention provides one kind and is partially flooded withThe analytic method of the critical reservoir level analysis of homogeneous slope, assuming that circular arc failure mechanism, it is solved using closing, consider soil body entirety equalising torque between side slope face and sliding surface, Side Slope Safety Coefficient explicit expression is obtained, by the fmincon Multi-dimensional constraint optimization algorithm built in Matlab, establishment optimization calculates main program and objective function subprogram, constraint function subprogram are calculated, critical circle center is found, and solves safety coefficient.This method belongs to statically problem, and obtained calculation formula is explicit expression, and formula is simple, and can reflect leads to critical reservoir level Producing reason, more fully understands influence of the SEA LEVEL VARIATION to slope stability is partially flooded with, makes up the deficiency of existing other methods.
Description
Technical field
The invention belongs to geotechnical engineering Analysis of Slope Stability fields, and in particular to one kind is partially flooded with c '-φ ' homogeneous side
The analytic method of the critical reservoir level analysis in slope.
Background technique
Being partially flooded with side slope may be considered a kind of water level descending at slow speed situation, it is assumed that water level line and reservoir level exist in side slope
It is equal in any case, remain horizontal situation.C '-φ ' homogeneous slope is partially flooded in the water level condition of above-mentioned level
It is lower there are a critical reservoir level, this phenomenon passes through Finite Element by Lane and Griffiths (1997) first and sends out
Existing, Side Slope Safety Coefficient reaches minimum value at this time, means that side slope has maximum unstable failure risk.Then several researchers use
Different methods is further discussed the critical reservoir level problem for being partially flooded with side slope, including Griffiths and Lane
(1999), Lane and Griffiths (2000) uses Finite Element and limit equilibrium method comparative study, Bromhead et
Al. (1999), Baker et al. (2005) use limit equilibrium method, Viratjandr and Michalowski (2006)
And Michalowski (2009) is studied using limit analysis method.
The geometric shape of problem is detailed in Fig. 1, slope height H, and slope angle is expressed as cot β, to the depth of lower part competent bed
Degree rate is D, and horizontal water level is defined as water level decreasing rate dW/H。
Being partially flooded with the critical reservoir level analysis essence of side slope is Analysis of Slope Stability, analysis side during water level decreasing
Water level when the safety coefficient minimum of slope, i.e., critical reservoir level.Be developed so far at the beginning of the last century, method for analyzing stability there are commonly
Limit equilibrium method, Strength Reduction of FEM, limit analysis method.
Developing earliest limit equilibrium method, there are many methods, are defined using identical safety coefficient and apply standing balance side
Journey solves safety coefficient, can be divided into two classes: Dan Gangti analytic method, slices method.
Traditional single rigid Limit Equilibrium analytic method, including infinite slopes, logarithmic spiral side slope, Sweden Arc Method, wherein
Sweden Arc Method is directed to circular arc failure mechanism, and φ=0 does not drain cohesive slope.Single rigid Limit Equilibrium mould that the present invention establishes
Type is different from above-mentioned model.
Limit Equilibrium Method mainly include Bishop approach, Morgenstein-Price method, Sarma method,
Spencer method etc..The soil body is divided into many vertical sticks by slices method, to each stick column balancing equation and is solved, and is indeterminate
Problem needs to make inter-slice force it is assumed that statically indeterminate problem is made to become statically problem to solve safety coefficient.In the above method,
Except Bishop approach, other methods calculation formula is implied expression formula, needs to iteratively solve.
Since Limit Equilibrium Method needs to make inter-slice force additionally it is assumed that so that statically indeterminate problem becomes statically problem
To solve safety coefficient；The calculation formula of most methods is implied expression formula, needs to iteratively solve.Above-mentioned two feature makes
Stability solution, which is difficult to reflect, leads to critical reservoir level Producing reason.
Finite Element is a kind of numerical method for solving Practical Project problem and problem in science.Finite Element is applied to
Analysis of Slope Stability, the paper of early stage be found in Smith&Hobbs (1974), Zienkiewicz et al (1975),
Griffiths (1980), subsequent Strength Reduction of FEM are suggested, and start to be widely used in Analysis of Slope Stability
(e.g.Griffths,1989；Potts et al.,1990；Matsui&San,1992；Griffths&Lane,1999).It is limited
Material nonlinearity, geometrical non-linearity can be considered in first Strength Reduction Method, and relatively traditional limit equilibrium method has the side slope solved
Stability result is more acurrate, does not need to make inter-slice force it is assumed that also not needing in advance to carry out the form of failure mechanics and position
Assuming that the advantages of.
Finite Element is a kind of numerical method for solving partial differential equation, although having the slope stability result solved
The above-mentioned advantage such as more acurrate, but solution procedure is more abstract, more complicated, so that stability solution, which is difficult to reflect, leads to critical library
Water level Producing reason.
Limit analysis method is a kind of ENERGY METHOD applied to Analysis of Slope Stability.The soil body is considered as a kind of reason by this method
Think plastic material, abides by associated flow rule.Under above-mentioned native behavior idealized conditions, there are two plasticity Bound theorems
(lower bound and the upper bound) (Drucker et al.1952；Chen 1975).Under the frame of two plasticity Bound theorems, it can be based on
Slices method and Finite Element establish Limit Analysis formula, solve Side Slope Safety Coefficient.
Limit analysis method needs based on slices method are iterated calculating, the Limit Analysis based on Finite Element,
Has the characteristics that Finite Element, solution procedure is abstract, complicated, causes critical reservoir level to produce so that stability solution is difficult to reflect
Raw reason.
Summary of the invention
The method of the present invention is using a kind of new limiting equilibrium list rigid body analytic method, it is assumed that circular arc failure mechanism.This method is adopted
It is solved with closing, the method that similar Pantelidis and Griffiths (2013) is proposed considers soil between side slope face and sliding surface
Body entirety equalising torque, obtains Side Slope Safety Coefficient explicit expression, is optimized by the fmincon Multi-dimensional constraint built in Matlab
Algorithm, establishment optimization calculates main program and objective function subprogram, constraint function subprogram are calculated, and finds in critical circle
The heart, and solve safety coefficient.The method for analyzing stability belongs to statically problem, and obtained calculation formula is explicit expression, public
Formula is simple, and can reflect leads to critical reservoir level Producing reason, more fully understands SEA LEVEL VARIATION to being partially flooded with stability of slope
The influence of property, makes up the deficiency of existing other methods.
Specific technical solution are as follows:
It is partially flooded with the analytic method of the critical reservoir level analysis of c '-φ ' homogeneous slope, comprising the following steps:
Step 1: given homogeneous slope circular arc failure mechanism is assumed；
Step 2: establishing single rigid Limit Equilibrium Model, single rigid Limit Equilibrium Model is related to sliding block gravity W,
Act on the water pressure V in slope surfacep1, act on the water pressure V on slope foot horizontal planep2, the shear strength parameters of the soil body are effectively viscous
Poly- power c ', effective angle of inner friction φ ', side slope pore water pressure u, and all power is projected on circular sliding surface, so as to
In calculating slip moment and the moment of resistance；
Step 3: being destroyed for side slope circular arc, defined using the safety coefficient FS according to equalising torque, square journey (1):
MRFor the moment of resistance, MOFor slip moment；
Step 4: being partially flooded with shown in homogeneous slope safety coefficient explicit expression such as equation (2):
In above formula, R is sliding radius of circle, and α is to destroy the diagonal half of the round heart, and c ' is effective cohesion intercept, and φ ' is effective
Angle of friction, Wt,Vp1,t Vp2,tRespectively gravity W, water pressure Vp1、Vp2Tangential component, Wn,Vp1,n Vp2,nRespectively gravity W,
Water pressure Vp1、Vp2Normal component of force, U be pore water pressure u resultant force；
Step 5: establishment optimization calculates main program and mesh by the fmincon Multi-dimensional constraint optimization algorithm built in Matlab
Scalar functions subprogram, constraint function subprogram are calculated, and critical circle center is found, and are then based on safety shown in equation (2)
The safety coefficient FS under the conditions of a certain water level is calculated in coefficient explicit expression；
Step 6: the safety coefficient FS under the conditions of different water levels are calculated, makes FS-dW/ H curve, it is slow to obtain water level
Minimum safety factor FS and critical reservoir level during speed decline；
Step 7: analyzing explicit algorithm as a result, finding each active force respectively to the contribution of safety coefficient, obtain causing critical
The basic reason that reservoir level generates.
Being partially flooded with c '-φ ' homogeneous slope, there are a critical reservoir levels under water level descending at slow speed case conditions, at this time
Side Slope Safety Coefficient reaches minimum value, means that side slope has maximum unstable failure risk.It is partially flooded with the critical reservoir level of side slope point
Analysis essence is Analysis of Slope Stability problem, usually one complicated non-linear implicit calculating.To avoid common limiting equilibrium
The iterative calculation of slices method and the complicated abstract numerical value of other methods (FInite Element, limit analysis method) calculate, and the present invention is given
It is assumed that establishing a kind of new single rigid Limit Equilibrium Model, the whole equalising torque of satisfaction uses homogeneous slope circular arc failure mechanism
A kind of analytical technique of closing solution, obtains Side Slope Safety Coefficient explicit expression, obtains difference using Matlab optimization method
Under the conditions of water level critical slip circle circle the center of circle and Side Slope Safety Coefficient, find critical reservoir level, study and find out cause part flood
No the basic reason of the critical reservoir level of c '-φ ' homogeneous slope.
It is flat to establish a kind of new single rigid body limit under the premise of given homogeneous slope circular arc failure mechanism is assumed by the present invention
Weigh model, meets whole equalising torque, is solved using a kind of closing, obtain Side Slope Safety Coefficient explicit expression shown in equation (2)
Formula avoids the iterative calculation of common Limit Equilibrium Method and the numerical value calculating that other methods complexity is abstract；Using being based on
The safety coefficient calculation method of Matlab optimization, avoids traditional safety coefficient searching method, verified calculated result is accurate
Reliably.The explicit algorithm formula simple, intuitive obtained by the method for the invention, can find out the basic reason for causing critical reservoir level
It is to act on the destabilizing effect of the internal void pressure of soil strength and the stabilization of the external hydrostatic water pressure power acted in slope surface
Growth and decline between effect compensate for the deficiency of other methods.
Detailed description of the invention
Fig. 1 be the prior art side slope under the conditions of water level descending at slow speed stability problem geometric shape figure；
Fig. 2 is that of the invention acting on is partially flooded with the power schematic diagram on side slope round destructed surface；
Fig. 3 is the flow chart of the method for the present invention；
Fig. 4 is the method for the present invention to the proof diagram for not draining cohesive slope stability diagram；
Fig. 5 is proof diagram of the method for the present invention to anhydrous c '-φ ' homogeneous slope stability diagram；
Fig. 6 is embodiment difference water level decreasing rate dwThe safety coefficient FS of/H
(cot β=2, c '/(γ H)=0.05, φ '=20 ° and D=1.0)；
Fig. 7 is embodiment difference water level decreasing rate dwThe safety coefficient FS of/H
(cot β=4, c '/(γ H)=0.05, φ '=10 ° and D=1.0).
Specific embodiment
It is described in conjunction with the embodiments technical solution of the present invention.
Present invention assumes that side slope circular arc failure mechanism, establishes a kind of new single rigid Limit Equilibrium Model, which is related to
Sliding block gravity W acts on the water pressure V in slope surfacep1, act on the water pressure V on slope foot horizontal planep2, the shear strength of the soil body
Parameter c ', φ ', side slope pore water pressure u, and all power is projected on circular sliding surface, calculate slip moment and resistance
Torque is detailed in Fig. 2.
As shown in figure 3, complete technical solution is as follows:
Step 1: given homogeneous slope circular arc failure mechanism is it is assumed that the failure mechanism is that people are common, relative to logarithm
Spiral failure mechanism is more simple, as shown in Figure 2.
Step 2: establishing a kind of new single rigid Limit Equilibrium Model, meet whole equalising torque.Traditional single rigid body pole
Limit balance model, including infinite slopes, logarithmic spiral side slope, Sweden Arc Method, single rigid Limit Equilibrium mould that the present invention establishes
Type is different from above-mentioned model.Single rigid Limit Equilibrium Model that the present invention establishes is related to sliding block gravity W, acts on the water in slope surface
Pressure Vp1, act on the water pressure V on slope foot horizontal planep2, the shear strength parameters effective cohesion intercept c ' of the soil body, effectively in rub
Wipe angle φ ', side slope pore water pressureu, and all power is projected on circular sliding surface, in order to calculate slip moment and
The moment of resistance is detailed in Fig. 2.
Step 3: being destroyed for side slope circular arc, defined using the safety coefficient according to equalising torque, square journey (1):
MRFor the moment of resistance, MOFor slip moment.
Step 4: being partially flooded with shown in homogeneous slope safety coefficient explicit expression such as equation (2):
In above formula, R is sliding radius of circle, and α is that the diagonal half of the round heart is destroyed shown in Fig. 2, and c ' is effective cohesion intercept,
φ ' is effective angle of friction, Wt,Vp1,t Vp2,tRespectively gravity W, water pressure Vp1、Vp2Tangential component, Wn,Vp1,n Vp2,nRespectively
For gravity W, water pressure Vp1、Vp2Normal component of force, U be pore water pressure u resultant force.
Step 5: establishment optimization calculates main program and mesh by the fmincon Multi-dimensional constraint optimization algorithm built in Matlab
Scalar functions subprogram, constraint function subprogram are calculated, and critical circle center is found, and are then based on safety shown in equation (2)
The safety coefficient FS under the conditions of a certain water level is calculated in coefficient explicit expression.
Step 6: the safety coefficient FS under the conditions of different water levels are calculated, makes FS-dW/ H curve, application example are detailed
See Fig. 6,7, finally obtains minimum safety factor FS and critical reservoir level during water level descending at slow speed.
Step 7: analyzing explicit algorithm as a result, finding each active force respectively to the contribution of safety coefficient, obtain causing critical
The basic reason that reservoir level generates.
The comprehensive verification of the method for the present invention and Matlab program by following three aspects, is then applied to be partially flooded with side
The critical reservoir level on slope is analyzed.Below under three kinds of different situations: not draining clay homogeneous slope (a)；(b) anhydrous c '-φ '
Homogeneous slope；(c) it is partially flooded with c '-φ ' homogeneous slope；The verifying of slope stability figure can be used as the inventive method by simple
To complicated application example.
(a) to document Terzaghi, K., Peck, R.B., and Mesri, G. (1996) .Soil Mechanics in
Figure 35 .3 form in Engineering Practice, Third Edition.John Wiley&Sons, Inc., New York.
Derive from document Taylor, D.W. (1937) " Stability of earth slopes. " J.Boston Soc.Civil
Eng.,24(3).Reprinted in:Contributions to Soil Mechanics 1925to 1940,Boston
The cohesive slope stability diagram that do not drain in Society of Civil Engineers, 337-386. is verified, to institute
Some slope angle β and depth rate D, obtain fabulous consistency, as shown in Figure 4.
(b) to document Michalowski, R.L. (2002) .Stability charts for uniform slopes
.J.Geotech.Geoenviron.Eng., 128 (4), the anhydrous c '-φ ' homogeneous slope stability of Fig. 3 (a) in 351-355.
Figure is verified, the side slope of side slope angle beta≤45 °, and consistency is good；The side slope of 45 ° of β≤60 ° < of opposite side slope angle optimizes journey
Sequence provides the safety coefficient slightly more higher than stability diagram in document；The side slope of 60 ° of side slope angle beta >, optimum results are than stablizing
Property figure is more higher.Based on above-mentioned verifying as shown in Figure 5, this method and Matlab program are defined in slope angle β≤45 °
Range.
(c) to the verifying for being partially flooded with side slope with horizontal water level, will optimization program and Strength Reduction of FEM and
Simplified Bishop limit equilibrium method, is verified for following two situation, the first situation c '/(γ H)=0.05,
φ '=20 °, β=2 cot, D=1, as shown in Figure 6；Second situation c '/(γ H)=0.05, φ '=10 °, β=4 cot, D=
1, as shown in Figure 7.Two kinds of situations show that an apparent minimum safety factor FS, critical reservoir level appear in -0.7 < dw/H
In < -0.6 range.Finite elements result be may be noted that between optimization and Bishop approach, although finite elements
Method and optimization result are in -1.0 < dw/ H < -0.7 range reaches unanimity.
In three kinds of methods, optimum results provide minimum safety coefficient always.
Calculating research is normalized in the displaying of result to simplify the calculation, and calculating introduces following three characteristics: text
Offer Taylor, D.W. (1937) " Stability of earth slopes. " J.Boston Soc.Civil Eng., 24
(3).Reprinted in:Contributions to Soil Mechanics 1925to 1940,Boston Society
The stabilization number c proposed in of Civil Engineers, 337-386.u/ (γ H) (see Fig. 4) and document Bell, J.M.
(1966).Dimensionless parameters for homogeneous earth slopes.J.Soil
Mech.Found.Div., number c '/(γ Htan φ ') is stablized in Am.Soc.Civ.Eng., 92 (5), the amendment proposed in 51-65.
With amendment coefficient of stability FS/tan φ ' (see Fig. 5).
Claims (2)
1. being partially flooded with the analytic method of the critical reservoir level analysis of c '-φ ' homogeneous slope, which comprises the following steps:
Assuming that circular arc failure mechanism, is closed using single rigid Limit Equilibrium Model and solved, soil body body force between side slope face and sliding surface is considered
Square balance, obtains Side Slope Safety Coefficient explicit expression, finds critical circle center by Matlab Multi-dimensional constraint optimization algorithm, and
Solve safety coefficient.
2. according to claim 1 be partially flooded withThe analytic method of the critical reservoir level analysis of homogeneous slope, feature
It is, comprising the following steps:
Step 1: given homogeneous slope circular arc failure mechanism is assumed；
Step 2: establishing single rigid Limit Equilibrium Model, single rigid Limit Equilibrium Model is related to sliding block gravity W, acts on
Water pressure V in slope surfacep1, act on the water pressure V on slope foot horizontal planep2, the shear strength parameters effective cohesion intercept of the soil body
C ', effective angle of inner friction φ ', side slope pore water pressure u, and all power is projected on circular sliding surface；
Step 3: being destroyed for side slope circular arc, defined using the safety coefficient FS according to equalising torque, square journey (1):
MRFor the moment of resistance, MOFor slip moment；
Step 4: being partially flooded with shown in homogeneous slope safety coefficient explicit expression such as equation (2):
In above formula, R is sliding radius of circle, and α is to destroy the diagonal half of the round heart, and c ' is effective cohesion intercept, and φ ' is effectively friction
Angle, Wt,Vp1,t Vp2,tRespectively gravity W, water pressure Vp1、Vp2Tangential component, Wn,Vp1,n Vp2,nRespectively gravity W, hydraulic pressure
Power Vp1、Vp2Normal component of force, U be pore water pressure u resultant force；
Step 5: establishment optimization calculates main program and target letter by the fmincon Multi-dimensional constraint optimization algorithm built in Matlab
Number subprogram, constraint function subprogram are calculated, and are found critical circle center, are then based on safety coefficient shown in equation (2)
The safety coefficient FS under the conditions of a certain water level is calculated in explicit expression；
Step 6: the safety coefficient FS under the conditions of different water levels are calculated, makes FS-dW/ H curve, obtains water level descending at slow speed
Minimum safety factor FS and critical reservoir level in the process；
Step 7: analyzing explicit algorithm as a result, finding each active force respectively to the contribution of safety coefficient, obtain leading to critical library water
The basic reason that position generates.
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