CN103469780B - A kind of computational methods of Gravity Dam Foundation stability against deep sliding critical slip surface - Google Patents
A kind of computational methods of Gravity Dam Foundation stability against deep sliding critical slip surface Download PDFInfo
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Abstract
The invention discloses a kind of computational methods of Gravity Dam Foundation stability against deep sliding critical slip surface, belong to gravity dam stability analysis field, the present invention is directed to the slow weak structural face that inclines of Gravity Dam Foundation not appear, but cutting off of possible generating portion downstream basement rock and produce the situation of slip, downstream basement rock is cut off the location variable of destruction sliding surface as optimized variable, using gravity dam against sliding in deep safety factor as object function, simultaneously with etc. safety factor normal equation for constraints, set up the nonlinear mathematics programming model that gravity dam against sliding in deep is analyzed, and use Mathematical Planning optimized algorithm to solve minimum value that downstream rock mass cuts off the least favorable critical sliding surface of destruction and the safety factor of its correspondence, the inventive method has definite conception, computational accuracy high, the analysis of gravity dam against sliding in deep can be applied to.
Description
Technical field
The present invention relates to the computational methods of Gravity Dam Foundation stability analysis, particularly a kind of computational methods of Gravity Dam Foundation stability against deep sliding critical sliding surface, belong to Gravity Dam Foundation stability analysis technical field.
Background technology
Gravity dam is the hydraulic structure that the skid resistance relying on deadweight to produce carrys out dash, is a kind of common dam type in Hydraulic and Hydro-Power Engineering.Because gravity dam has good safety and economy, it is widely used in water conservancy and hydropower industry.Along with the increase day by day of the development and construction scale of construction of hydropower facilities, the gravity dam site with complete basement rock is fewer and feweri, and most of gravity dam is all built on the batholith of complex geologic conditions, and therefore the Against Sliding Stability problem of the complicated dam foundation of gravity dam becomes and becomes increasingly conspicuous.There is a large amount of weak structural face in Gravity Dam Foundation rock mass, when acting on the load on dam body and rock mass and reaching certain value, the compound sliding surface that the dam foundation can form along one or more weak structural face destroys.According to the difference of Gravity Dam Foundation weak structural face occurrence, Gravity Dam Foundation deep implication destroys can be divided into Four types: monocline shearing slip destruction, diclinic shearing slip destruction, tail rock drag body squeeze and destroy and tail rock drag body bulge fracture.In this Four types, modal type is: monocline shearing slip destroys, diclinic shearing slip destroys.
Monocline shearing slip destroys and belongs to single sliding surface situation, and its calculating is fairly simple, and the general Against Sliding Stability formula slided along foundation plane with reference to gravity dam calculates.Diclinic sliding stability is analyzed comparatively monocline shearing slip and is destroyed complicated, and its computational methods mainly contain three kinds: passive resisting force method, etc. method of safety coefficients, and residual thrust method.The design of gravity dam specification that its medium method of safety coefficients is water conservancy industry is adopted.Etc. the main thought of method of safety coefficients be: employing Shear Strength formula adjusts the factor of safety against sliding on two sliding surfaces respectively, and makes these two safety factor equal, then adopts the value of iterative method determination safety factor.
The calculating of following two class stability against deep sliding is mainly can be used for: the first kind is that dam body drives one block of basement rock along low-angle dip and two continuously slide planes slips of appearing etc. method of safety coefficients; Equations of The Second Kind is that the slow weak structural face that inclines of the dam foundation is not appeared, also without compressible stratum, but the cutting off and produce slip of possible generating portion downstream basement rock.The safety factor of Against Sliding Stability directly can be calculated for method of safety coefficients such as first kind situation application; But for Equations of The Second Kind situation, the plane of disruption of downstream basement rock is generally difficult to determine, the method for designing of present stage is generally the plane of disruption first supposing a downstream basement rock, then carries out sliding stability analysis, but the method can not determine the plane of disruption of worst downstream basement rock.
Based on above-mentioned analysis, do not appear for the slow weak structural face that inclines of the dam foundation, but may cutting off of generating portion downstream basement rock and produce the situation of slip, the present invention proposes a kind of Gravity Dam Foundation diclinic slip critical slope langth sliding surface computational methods.
Summary of the invention
The object of this invention is to provide a kind of Gravity Dam Foundation diclinic slip critical slope langth sliding surface computational methods, and obtain the dam foundation and delay the weak structural face that inclines and do not appear and the portion downstream basement rock least favorable critical slope langth sliding surface cutting off and slide, for design of gravity dam, dam foundation stability calculates provides a kind of new ways and means.
General principle of the present invention is: do not appear for the slow weak structural face that inclines of Gravity Dam Foundation, but cutting off of possible generating portion downstream basement rock and produce the situation of slip, downstream basement rock is cut off the location variable of destruction sliding surface as optimized variable, using gravity dam against sliding in deep safety factor as object function, simultaneously based on etc. method of safety coefficients constraints, set up the nonlinear mathematics programming model that gravity dam against sliding in deep is analyzed, and use Mathematical Planning optimized algorithm to solve minimum value that downstream rock mass cuts off the least favorable critical sliding surface of destruction and the safety factor of its correspondence.
When the present invention solves the nonlinear mathematics programming model of gravity dam deep implication destruction critical sliding surface, with gravity dam against sliding in deep safety factor for object function (solving its minimum value), cut off the critical sliding surface position of destruction for optimized variable with gravity dam downstream rock mass, simultaneously with etc. safety factor equation for constraints.
The technical scheme of Gravity Dam Foundation diclinic slip critical slope langth sliding surface computational methods of the present invention is carried out successively according to the following steps:
1, the relevant parameter that Gravity Dam Foundation stability against deep sliding calculates is drafted.
According to the actual conditions of gravity dam, draft its calculating parameter, mainly comprise: gravity dam dam body geometric parameter, basement rock geometric parameter, material parameter (comprising the unit weight of dam body, basement rock and weak structural face, cohesive force, friction factor), parameters of loading information.
2, the nonlinear mathematics programming model that gravity dam against sliding in deep is analyzed is set up
(1) force analysis of gravity dam against sliding in deep calculating
Do not appear according to the slow weak structural face that inclines of Gravity Dam Foundation, portion downstream basement rock is cut off and produces the diclinic slip force diagram (as shown in Figure 1) of slip, in Fig. 1: ADC is Foundation Base of Gravity Dam, AB is the slow weak structural face that inclines, BC is the destruction sliding surface that downstream basement rock is cut off, and BD is the interface of slide block ABD, BCD; The meaning of other symbols is specific as follows:
---act on the vertical component of whole load on dam body (not comprising uplift pressure, lower same), kN;
---act on the horizontal component of whole load on dam body, kN;
,
---be respectively the vertical of rock mass ABD, BCD weight, kN;
,
---be respectively the Shear friction factor of AB, BC slide plane;
,
---be respectively the Shear cohesive force of AB, BC slide plane, kPa;
,
---be respectively the area of AB, BC slide plane, m
2;
,
---be respectively the angle of AB, BC slide plane and horizontal plane;
,
,
---be respectively the uplift pressure on AB, BC, BD face, kN;
---be respectively the active force on BD face, KN;
---the active force on BD face
with the angle of horizontal plane, from being relatively taken as 0 degree safely.
The main purpose of the inventive method determines the position of the critical slope langth sliding surface BC that downstream basement rock is cut off, and therefore establishes the position coordinates of C point
for optimized variable.According to gravity dam dam body geometric parameter, basement rock geometric parameter, material parameter, the parameters of loading initially drafted, variable known in above-mentioned variable is:
,
,
,
,
,
,
,
,
,
,
, and
,
,
,
for known variables, and be the position coordinates of C point
function, that is:
,
,
,
.
(2) object function
For gravity dam against sliding in deep problem, general definition safety factor is:
.The present invention is by Gravity Dams Against Sliding Stability safety factor
as object function, and seek the minimum value that it corresponds to downstream rock mass critical slope langth sliding surface BC.
(3) the method for safety coefficients constraint equation such as
Gravity dam shown in Fig. 1 occur double inclined plane sliding failure time, according to etc. safety factor law theory, ABD slide block and BCD slide block should have identical safety factor, then ABD, BCD slide block should meet following constraint equation:
Adopt Shear Strength formula can obtain the buckling safety factor of ABD sillar
value:
Equally, Shear Strength formula is adopted can to obtain the buckling safety factor of BCD sillar
value:
According to etc. method of safety coefficients, make the buckling safety factor of ABD sillar
equal the buckling safety factor of BCD sillar
:
(4) the nonlinear mathematics programming model of Gravity Dam Foundation diclinic slip critical slope langth sliding surface is solved
The nonlinear mathematics programming model solving Gravity Dam Foundation diclinic slip critical slope langth sliding surface is object function with safety factor, etc. safety factor normal equation as constraints.Mathematical Modeling expression is:
3, the safety factor of critical slope langth sliding surface and correspondence thereof is solved
The Mathematical Modeling more than obtained is a nonlinear mathematics programming model, the present invention adopts sequential quadratic programming algorithm (Sequential Quadratic Programming Method) to carry out solving of nonlinear mathematics programming model, and result of calculation comprises the factor against sliding of critical slope langth sliding surface that downstream basement rock cuts off and correspondence thereof.
Feature of the present invention is: based on the gravity dam against sliding in deep theory of computation, the location parameter of the destruction sliding surface cut off by downstream basement rock is as optimized variable, using gravity dam against sliding in deep safety factor as object function, and based on etc. method of safety coefficients constraints, set up the nonlinear mathematics programming model that gravity dam against sliding in deep is analyzed, use Mathematical Planning optimized algorithm to solve downstream rock mass and cut off the least favorable critical sliding surface of destruction and the safety factor minimum value of its correspondence.The method can be accurate, easy calculate gravity dam deep layer unstability time the critical slope langth sliding surface cut off of downstream basement rock and the minimum safety factor of correspondence thereof, there is definite conception, computational accuracy high.
The present invention has following beneficial effect:
1, existing gravity dam specification for gravity dam against sliding in deep analyze regulation adopt etc. method of safety coefficients be generally only applicable to the known situation of sliding surface, the slow weak structural face that inclines of the dam foundation is not appeared, also without compressible stratum, but cutting off of possible generating portion downstream basement rock and produce the situation of slip, the plane of disruption of downstream basement rock is generally difficult to the method for safety coefficients such as employing and determines.The minimum safety factor of the least favorable critical slope langth sliding surface that the inventive method adopts Optimization Method downstream basement rock to cut off and correspondence thereof.
2, the inventive method definite conception, computational accuracy is high, engineer applied is easy, can be applied to the analysis of gravity dam against sliding in deep.
Accompanying drawing explanation
Fig. 1 is Gravity Dam Foundation deep layer unstability diclinic sliding-modes schematic diagram of the present invention;
Fig. 2 is the Technology Roadmap of the inventive method;
Fig. 3 is embodiment of the present invention side slope schematic diagram;
In figure: ADC is Foundation Base of Gravity Dam; AB is the slow weak structural face that inclines; BC is the destruction sliding surface that downstream basement rock is cut off; BD is the interface of slide block ABD, BCD.
Detailed description of the invention
Below by drawings and Examples, the present invention is described in further detail, but protection scope of the present invention is not limited to described content.
Embodiment 1: this Gravity Dam Foundation diclinic slip critical slope langth sliding surface computational methods (see figure 2), concrete operations are as follows:
1, the relevant parameter that Gravity Dam Foundation stability against deep sliding calculates is drafted
The present embodiment is gravity dam as shown in Figure 3, height of dam is 50.0 m, width at dam crest 5.0 m, dam bottom width degree is 40 m, and the downstream face gradient is 1:0.778, upstream normal pool level is 47.0 m, the level of tail water is 0.0 m, ADC is foundation plane, and AB is a slow weak structural face that inclines, its inclination angle is 16.7 °, and BC is the slip-crack surface that downstream basement rock is cut off; The coordinate that A, B, D are 3 is respectively: A(0,0), B(50 ,-15), D(50,0), C point coordinates
for unknown quantity undetermined; Due to foundation plane be horizontal plane and C point must be positioned at D point right side, therefore get
,
.
Dam body is concrete, and concrete density is 2400kg/m
3, basement rock rock mass unit weight is 2500kg/m
3; The shear strength parameter of the slow weak structural face AB that inclines is:
,
; Basement rock shear strength parameter is
,
.
2, the nonlinear mathematics programming model that gravity dam against sliding in deep is analyzed is set up, build model time with the safety factor of gravity dam against sliding in deep for object function, with etc. safety factor normal equation for constraint equation, cut off the critical sliding surface location variable of destruction for optimized variable with gravity dam downstream rock mass;
(1) according to above parameter and composition graphs 1, Fig. 3, carry out the force analysis of Gravity Dams Against Sliding Stability calculating, wherein ADC is Foundation Base of Gravity Dam, AB is the slow weak structural face that inclines, BC is the destruction sliding surface that downstream basement rock is cut off, BD is the interface of slide block ABD, BCD, and the meaning of other symbols is specific as follows:
---act on the vertical component of whole load on dam body (not comprising uplift pressure, lower same), kN;
---act on the horizontal component of whole load on dam body, kN;
,
---be respectively the vertical of rock mass ABD, BCD weight, kN;
,
---be respectively the Shear friction factor of AB, BC slide plane;
,
---be respectively the Shear cohesive force of AB, BC slide plane, kPa;
,
---be respectively the area of AB, BC slide plane, m
2;
,
---be respectively the angle of AB, BC slide plane and horizontal plane;
,
,
---be respectively the uplift pressure on AB, BC, BD face, kN;
---be respectively the active force on BD face, KN;
---the active force on BD face
with the angle of horizontal plane, from being relatively taken as 0 degree safely;
If the position coordinates of C point
for optimized variable; According to gravity dam dam body parameter, basement rock geometric parameter, material parameter, the parameters of loading initially drafted, variable known in above-mentioned variable is:
,
,
,
,
,
,
,
,
,
,
, and
,
,
,
for known variables, and be the position coordinates of C point
function, that is:
,
,
,
;
(2) object function
For gravity dam against sliding in deep problem, general definition safety factor is:
, by Gravity Dams Against Sliding Stability safety factor
as object function, and seek the safety factor corresponding to downstream rock mass critical slope langth sliding surface BC
minimum value;
(3) when there is double inclined plane and sliding in the gravity dam shown in Fig. 1, ABD, BCD slide block should meet following constraint equation:
Adopt Shear Strength formula can obtain the buckling safety factor of ABD sillar
value:
Equally, Shear Strength formula is adopted can to obtain the buckling safety factor of BCD sillar
value:
According to etc. method of safety coefficients, make the buckling safety factor of ABD sillar
equal the buckling safety factor of BCD sillar
:
(4) the nonlinear mathematics programming model of Gravity Dam Foundation diclinic slip critical slope langth sliding surface is solved
The object function of combined mathematical module, constraints, formed and solve gravity dam downstream rock mass to cut off the nonlinear mathematics programming model of the safety factor destroying critical slip surface and correspondence thereof as follows:
3, the safety factor of critical slope langth sliding surface and correspondence thereof is solved
Adopt Sequential Quadratic Programming method to solve above-mentioned nonlinear mathematics programming model, result of calculation is: downstream basement rock cuts off the coordinate of the critical sliding surface C point of destruction for (0.0,76.74645), the inclination angle of critical sliding surface BC sliding surface
, the length of critical sliding surface BC is 30.6655 m, and the gravity dam against sliding in deep safety factor minimum value corresponding to critical sliding surface BC is
, the active force between sillar ABD and sillar BCD
.
Claims (1)
1. Gravity Dam Foundation diclinic slip critical slope langth sliding surface computational methods, it is characterized in that: do not appear for the slow weak structural face that inclines of Gravity Dam Foundation, but cutting off of possible generating portion downstream basement rock and produce the situation of slip, downstream basement rock is cut off the location variable of destruction sliding surface as optimized variable, using gravity dam against sliding in deep safety factor as object function, simultaneously based on etc. method of safety coefficients constraints, set up the nonlinear mathematics programming model that gravity dam against sliding in deep is analyzed, and use Mathematical Planning optimized algorithm to solve minimum value that downstream rock mass cuts off the least favorable critical sliding surface of destruction and the safety factor of its correspondence,
Said method carries out according to the following steps:
(1) according to the actual conditions of gravity dam, determine calculating parameter, calculating parameter comprises gravity dam dam body geometric parameter, basement rock geometric parameter, material parameter, parameters of loading, and wherein material parameter comprises unit weight, cohesive force, the friction factor of dam body, basement rock and weak structural face;
(2) the nonlinear mathematics programming model that gravity dam against sliding in deep is analyzed is set up, build model time with the safety factor of gravity dam against sliding in deep for object function, with etc. safety factor normal equation for constraint equation, cut off using gravity dam downstream rock mass and destroy the location variable of critical sliding surface as optimized variable;
The force analysis that A, gravity dam against sliding in deep calculate
Do not appear for the slow weak structural face that inclines of Gravity Dam Foundation, portion downstream basement rock is cut off and produces the diclinic slip of slip, carries out the force analysis of diclinic sliding-modes;
B, by the safety factor of gravity dam against sliding in deep
as object function, and seek the minimum value that it corresponds to downstream rock mass critical slope langth sliding surface, wherein
;
C, with etc. safety factor normal equation for constraint equation;
D, solve the nonlinear mathematics programming model of Gravity Dam Foundation diclinic slip critical slope langth sliding surface, Mathematical Modeling expression is:
Wherein as shown in Figure 1:
---act on the vertical component of whole load on dam body, do not comprise uplift pressure, kN;
---act on the horizontal component of whole load on dam body, do not comprise uplift pressure, kN;
,
---be respectively the vertical of rock mass ABD, BCD weight, do not comprise uplift pressure, kN;
,
---be respectively the Shear friction factor of AB, BC slide plane;
,
---be respectively the Shear cohesive force of AB, BC slide plane, do not comprise uplift pressure, kPa;
,
---be respectively the area of AB, BC slide plane, m
2;
,
---be respectively the angle of AB, BC slide plane and horizontal plane;
,
,
---be respectively the uplift pressure on AB, BC, BD face, kN;
---be respectively the active force on BD face, KN;
---the active force on BD face
with the angle of horizontal plane, from being relatively taken as 0 degree safely;
(3) safety factor of critical slope langth sliding surface and correspondence thereof is solved
Adopt sequential quadratic programming algorithm to carry out solving of nonlinear mathematics programming model, result of calculation comprises the factor against sliding of critical slope langth sliding surface that downstream basement rock cuts off and correspondence thereof
.
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