CN108920754B - Structural plane control slope stability dynamic evaluation method based on strain softening shearing constitutive model and displacement change - Google Patents
Structural plane control slope stability dynamic evaluation method based on strain softening shearing constitutive model and displacement change Download PDFInfo
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Abstract
The invention provides a structural plane control slope stability dynamic evaluation method based on a strain softening shearing constitutive model and displacement change. The method comprises the steps of landslide investigation, stress analysis, establishment of an anti-skid force calculation model, calculation of load shedding of an empty surface, determination of a structural surface shear constitutive equation, construction of a structural surface control slope body motion equation, calculation of a displacement process curve of a potential sliding body and the like. The method can dynamically judge the real-time stability state of the structural surface control slope by combining with the field deformation monitoring data. The convergence of displacement is calculated according to the sliding body, and the long-term stability of the structural surface control rock slope can be predicted to a certain extent.
Description
Technical Field
The invention relates to the technical field of geological disaster prediction, in particular to a rock slope stability evaluation method based on a displacement development process.
Background
The existing slope geological disaster treatment design generally adopts a static design based on specifications, and has the obvious defect that a geologic body is regarded as a rigid body, and the deformation and damage mechanism of the geologic body and the process of geological disaster inoculation are not fully considered. Although the catastrophe evolution process and the action mechanism of the rock high slope are very complex, the macroscopic expression of the catastrophe evolution process and the action mechanism of the rock high slope is that the slope body is deformed, and the deformed part and the deformation are continuously changed along with the development of the catastrophe process. The instability process of the rock slope has a time-varying effect, namely, the whole deformation process shows obvious aging deformation. According to the aging deformation process obtained by field monitoring, the stability state of the side slope can be judged. However, in China, on one hand, the problems of wide distribution of landslide disasters, engineering prevention and control, mechanism research, prediction and forecast and the like need to be solved urgently, almost all work is carried out by relying on landslide monitoring data, on the other hand, the method is deficient in a theoretical calculation method of deformation of a supportless slope, a small amount of research is concentrated on an engineering numerical method or experience estimation is carried out according to an actual measurement value, the reliability is low, and the method is different from the actual situation. Under the condition, a theoretical calculation method for deformation of the slope body of the non-support slope is established, and the significance of the slope stability evaluation method based on the deformation process is great.
Disclosure of Invention
The invention aims to provide a structural plane control slope stability dynamic evaluation method based on a strain softening shearing constitutive model and displacement change, so as to solve the problems in the prior art.
The technical scheme adopted for achieving the purpose of the invention is that the dynamic evaluation method for controlling the slope stability of the structural plane based on the strain softening shearing constitutive model and the displacement change comprises the following steps:
1) and (5) carrying out landslide investigation on the control slope of the structural surface to be evaluated.
2) And (4) taking excavation unloaded load as the starting force of slope deformation, and carrying out stress analysis on the potential sliding body of the slope to be evaluated.
3) And establishing a structural surface sliding resistance calculation model considering strain softening.
4) And calculating the unloading load of the potential sliding body face caused by excavation.
5) And determining the shear constitutive equation of the structural plane.
6) And (5) constructing a structural plane control slope body motion equation.
7) And calculating a displacement process curve of the potential sliding body.
8) And comparing and analyzing the on-site deformation monitoring data with the potential slide displacement process curve, and judging the displacement development trend of the structural surface control slope to be evaluated.
9) And (4) according to the convergence of the calculated displacement of the potential sliding body, predicting the long-term stability of the structural surface control slope to be evaluated.
Further, in step 3), the strain softening shear constitutive equation obtained by considering the strain softening structural surface is as follows:
in the formula, FRThe sliding resistance, kN, provided for the structural surface. k is the shear stiffness, Pa/m. u is the potential slider displacement, m. u. of*And b, determining according to the direct shear test result of the rock mass structural plane. u. of*Is the characteristic displacement, m. And b is the equation coefficient of the dimensionless parameter.
Further, in the step 4), the potential slide body face dump load caused by excavation is calculated by the formula (2).
Wherein F' is the unloading load of the potential sliding body face, kN. W is the potential weight of the slider, kN. L is the structural plane sliding length, m. Beta is the structural plane inclination angle. c is the cohesive force of the soft structural surface Pa.
The angle of friction in the structural plane is degree.
Further, in step 3), the structural constitutive equation of the structural surface is:
in the formula u0To initiate displacement for the potential slider, m.
Further, the landslide investigation in the step 1) comprises determining a landslide area range, and collecting and summarizing landslide deformation characteristic data and hydrographic and geological engineering condition data.
Further, the hydrological and geological engineering conditions comprise geological and landform data, geotechnical physical and mechanical property data, ground stress data, meteorological hydrological data and construction operation data near the side slope.
Further, the self weight of the potential sliding body is shown as formula (4):
wherein gamma is the rock mass weight of the potential sliding body, N/m3. h is the fracture depth, m. Alpha is the slope inclination angle of the controlled slope of the structural plane to be evaluated.
The technical effects of the invention are undoubted:
A. the real-time stability state of the structural surface control slope can be dynamically judged by combining with the field deformation monitoring data;
B. the stability stage of the structural surface control side slope can be determined, and certain theoretical guiding significance is provided for how to take reinforcement and protection measures to avoid landslide and instability disaster accidents;
C. the method can predict the development trend of the potential slip body displacement of the structural surface control side slope, and can predict the long-term stability of the structural surface control rock side slope to a certain extent according to the convergence of the potential slip body calculation displacement.
Drawings
FIG. 1 is a flow chart of an evaluation method;
FIG. 2 is a schematic diagram of potential slider displacement calculations;
FIG. 3 is a schematic diagram of a strain softening shear constitutive model calculation;
FIG. 4 is a schematic illustration of a slip resistance calculation;
FIG. 5 is a diagram illustrating potential slider displacement calculations.
Detailed Description
The present invention is further illustrated by the following examples, but it should not be construed that the scope of the above-described subject matter is limited to the following examples. Various substitutions and alterations can be made without departing from the technical idea of the invention and the scope of the invention is covered by the present invention according to the common technical knowledge and the conventional means in the field.
Example 1:
the embodiment discloses a structural surface control slope stability dynamic evaluation method based on a strain softening shearing constitutive model and displacement change, aiming at the current situation that the existing non-support slope deformation theoretical calculation method is lost and the reliability is lower by empirical estimation according to an actual measurement value, and the method is used for calculating the sliding process of an upper dangerous rock body so as to determine the stable state of the upper dangerous rock body and predict the displacement of the upper dangerous rock body.
In this embodiment, a cutting slope in the open area is selected as the structural surface to control the rock slope. Under the influence of slope toe excavation, stability is reduced, bedding face collapse and slip instability occur, so that upper rock masses are in danger of being empty to form dangerous rock masses, and a slope top unloading zone has a crack, so that the stability of the dangerous rock masses in the danger of being empty is analyzed. Referring to fig. 1, the dynamic evaluation method for slope excavation deformation stability control by structural surface based on the strain softening shearing constitutive model comprises the following steps:
1) and (5) carrying out landslide investigation on the control slope of the structural surface to be evaluated. And controlling the side slope to be evaluated to carry out landslide investigation. Determining the range of a landslide area, and collecting and summarizing landslide deformation characteristic data and hydrographic and geological engineering condition data. The hydrological and geological engineering conditions comprise geological and landform data, geotechnical physical and mechanical property data, ground stress data, meteorological hydrological data and construction operation data near a side slope. Through field investigation and comprehensive analysis, the slope toe of the side slope is cut and excavated, so that the rock side slope slides along the surface of the rock layer locally. The landslide is in a transverse shape on a plane, the rear edge mainly controls the fracture extension length and the cutting height of a slope toe, the rock stratum surface is an outward-inclined structure surface, the side slope easily slides along the rock stratum surface, and therefore the main control structure surface is the layer surface. According to the results obtained from the on-site investigation, the rock mass weight gamma is 25.5 multiplied by 103N/m3Internal friction angle of rock mass layer in natural state
Is 11.3 degrees and the cohesive force c is 5.75 multiplied by 103Pa, internal friction angle in saturated state
9.5 DEG, and a cohesive force c' of 4.1X 103Pa. In addition, the slope height is 21.5m, the slope angle alpha is 34.0 degrees, the adjacent space height is 4.6m, the crack depth h is 4.1m, the sliding length L of the structural surface is 30.1m, the inclination angle of the structural surface is 33.0 degrees, and the shearing rigidity k of the elastic deformation stage of the structural surface is 4.3 multiplied by 106Pa/m。
2) And (4) taking excavation unloading load as the starting force of the slope deformation, and carrying out stress analysis on the potential sliding body of the slope to be evaluated.
And selecting a slope body with the slope trend in unit length for research, and establishing a coordinate system along the structural surface and the normal direction thereof by taking the structural surface and the fracture intersection point as the origin, so that the structural surface controls the slope to be generalized into the geological model shown in the figure 2. Wherein the potential slide body face dump load caused by excavation is calculated by the formula (1). The calculation starting point of the displacement of the potential sliding body of the structural surface control slope is obtained by carrying out Newton iteration numerical solution calculation on the formula (2). Referring to fig. 4, the structural surface sliding resistance calculation constitutive model can be calculated by equation (3). The dead weight for a potential sliding body can be calculated by equation (4):
wherein W is the dead weight of the potential sliding body, and N. Beta is the structural plane inclination angle. c is structural surface cohesion, Pa.
The angle of friction in the structural plane is degree. L is the structural plane sliding length, m.
In the formula u0Starting shift, m. And k is the shear stiffness of the structural plane, Pa/m.
Where u is the displacement of the potential runner, m. u. of1The initial displacement, m, for the plastic flow phase.
In the formula (I), the compound is shown in the specification,gamma is the rock mass gravity of potential sliding mass, N/m3. h is the fracture depth, m. Alpha is the slope inclination angle of the controlled slope of the structural plane to be evaluated.
3) And establishing a structural surface sliding resistance calculation model considering strain softening.
The sliding resistance and sliding displacement relationship which can be provided by the structural surface can be expressed by the following formula (5):
FR＝λu·exp[(-au)b] (5)
in the formula, λ, a and b are coefficients of equation (1), where λ is in units of N/m, a is in units of m, and b is a dimensionless parameter. u is the potential slider displacement, m.
Order to
Then formula (5) is converted into:
in the formula u*Is the characteristic displacement, m.
The derivation is carried out on the formula (6),
when u is 0, equation (7) satisfies
Wherein k is shear stiffness, Pa/m. L is the structural plane sliding length, m. At this time, it is obvious from the above formula that, in the elastic deformation stage at which shearing starts, the product of the shear stiffness of the structural surface and the action area is λ, and thus,
the mixture is obtained by finishing the raw materials,
wherein z is the shear thickness, m. G is the shear modulus, Pa. l is the structural plane length, m. Assuming that the shear deformation varies linearly in the tangential and normal directions, the right side of the pair of symmetries is from 0 to z for z and l, respectively0And 0 to L are subjected to definite integration to obtain
In the formula, z0To calculate the structural face interlayer thickness, m. Substituting equation (11) into equation (8) to obtain
Substituting it into equation (7) and replacing the shear stiffness k for large deformation analysis with that for small deformation
Obtaining a strain softening shear constitutive equation of
Extreme value is obtained for equation (13) to
Then
The displacement u corresponding to the peak value of the sliding resistance is obtained by arrangement1In order to realize the purpose,
at this time, the peak value of the slip resistance is:
in the above formula, the parameter b reflects the softening property of the material, and the larger the value of b, the stronger the shear softening property, and the parameter u*And b can be determined according to the direct shear test result of the rock mass structural plane. In this example, b is 1.85, u*The characteristic displacement was taken to be 0.002 m.
4) And calculating the unloading load of the potential sliding body face caused by excavation. When the excavation unloading amount value is calculated, the excavated part of rock-soil mass is treated as a leading edge retaining wall of a potential sliding body, and according to technical specification of building slope engineering (GB50330-2013), the unloading load of a potential sliding body face caused by excavation can be calculated by the following formula:
wherein W is the potential self weight of the sliding body, kN. L is the structural plane sliding length, m. Beta is the structural plane inclination angle. c is the cohesive force of the soft structural surface Pa.
The angle of friction in the structural plane is degree.
5) Determining a structural surface shear constitutive equation used for calculating the anti-sliding force under the excavation unloading condition. Assuming that the total anti-slip force is reduced by F ' due to the excavation dump load being F ', the anti-slip force calculation model curve shows, wherein the excavation dump load F ' can be calculated according to equation (17). The slope body is in a static state before excavation, namely the anti-sliding force provided by the structural surface and the excavation free surface is equal to the gliding force, so that the stress state is at a point (u, F), and when the slope angle excavation unloading load F' is carried out, the stress state of the potential sliding body is changed into (u, F)0Point F-F'), whereinThe sliding force F is the sum of,
F＝Wsinβ (18)
substituting equation (18) into equation (13) can calculate the initial displacement point u of the potential sliding body0The solution is carried out and the solution is carried out,
the equation of the above formula is a transcendental equation, and the equation is obtained by sorting the equation,
order to
Then u0That is, the solution of equation f (u) ═ 0, newton's iteration method can be used to start the displacement of potential sliding body u0And (6) performing calculation. Since the root of the equation f (u) ═ 0 needs to be estimated when the numerical calculation is performed by the newton iteration method, the root of the equation f (u) ═ 0 can be estimated by calculating f' (u) and analyzing the increase and decrease of the function f (u), and u can be estimated according to the following steps0And (3) solving:
a) selecting an approximate root of equation f (u) 0 as u1Calculating f1＝f(u1)，f′1＝f′(u1)。
b) According to the formula
Iterative calculation is carried out once to obtain a new approximate value u2Calculating f2＝f(u2)、f′2＝f′(u2)。
c) If u2Satisfies | delta | < epsilon1Or | f2|＜ε2(ε1、ε2To allow error), the iterative computation is terminated, in u2As solved forThe root of (2).
d) If the iteration number reaches the preset number N or f' is 0, the approximate root is re-established, otherwise (u)2,f2,f′2) Instead of (u)1,f1,f′1) Substituting into step (b) to perform iterative calculation again. Calculating to obtain displacement calculation initial displacement point u0After that, the structural plane constitutive equation becomes:
6) and (3) from the aspect of kinematics, constructing a sliding displacement model of the potential sliding body of the control side slope of the structural plane to be evaluated.
Within the time bin dt, the slider motion satisfies Newton's second law, i.e.
That is, for the elastic deformation phase, the structural plane controlled slope body displacement control equation caused by excavation is described by equation (24):
wherein, F is W sin beta,
substituting equations (13), (18) into equation (24) and arranging to obtain:
separating variables from the equation
Integral to the right side of equation
It is verified that the double integral on the left side of the equation does not have a primary function represented by an initial function, so that a method of numerical integration for u from 0 to u is consideredtAnd (5) performing fixed integration processing. Order to
The equation form is arranged as
The numerical integration method is to perform discretization processing on the continuous function, and the double numerical integration is to perform discretization processing on the continuous function twice, which is easy to cause larger error of a calculation result. Thus two single integrations are used here to handle the double integration problem. The double integral to the right of the above equation is written as the product of two single integrals as follows,
order to
Substituting equation (30) into equation (29) yields
The numerical product of equation (31) is here performed using the newton-cotts method. The integration interval [0, u ] of the two integration functions in equation (31)t]Are divided into n, m, etcDivide, calculate step length
Selecting equidistant nodes
Wherein i is 0,1.. n, j is 0,1.. m, constructing an interpolation type quadrature function,
in the above-mentioned formula, the compound has the following structure,
for the Countes coefficients, a transform u is introducedi＝xl1，uj＝yl2Then there is
Since the integrand in equation (33) is a polynomial of degree n and m, respectively, no substantial difficulty is encountered in solving equation (33) by integration, and therefore equation (33) can be written as:
7) according to the sliding displacement model in the step 6), taking n-m-7 and combining initial conditions
And u is 0, t is 0, the above formula is solved numerically, and a displacement process curve of the potential sliding body is obtained through calculation. The displacement process curve of the potentially unstable dangerous rock mass in the present embodiment is shown in fig. 4.
8) And comparing and analyzing the on-site deformation monitoring data with the potential slide displacement process curve, and judging the displacement development trend of the structural surface control slope to be evaluated.
9) And (4) according to the convergence of the calculated displacement of the potential sliding body, predicting the long-term stability of the structural surface control slope to be evaluated. Through comparative analysis with displacement monitoring data of a reconnaissance design unit on dangerous rock masses, the dangerous rock masses are not supported at present and have the risk of sliding instability on bedding surfaces, but the potential sliding mass displacement finally tends to be stable, the time required for stabilization is about 1430h, and the final horizontal displacement is 0.0038 m.
It is worth to be noted that, in this embodiment, from a factor inducing instability of a rock slope excavated from a side slope, excavation dump load is used as a starting force for the instability deformation of the side slope, a stress analysis is performed on a potential instability block of the rock side slope controlled by a typical structural surface, a motion equation of displacement of the slope is established, and mathematical description of long-term stability of the structural surface controlled side slope from the angle of displacement of the slope is realized. Compared with other calculation means, the method can quantitatively describe the sliding displacement process of the potentially unstable rock mass at the upper part of the rock slope caused by excavation, can predict the long-term stability of the rock slope, can evaluate the state of the slope stability by combining displacement monitoring data of a construction site, can provide reference for selection of rock slope reinforcement time and mode in actual engineering, and has certain practical value. The slope stability can be accurately judged to a certain extent and the long-term strength can be predicted.
Claims (4)
1. The structural plane control slope stability dynamic evaluation method based on the strain softening shearing constitutive model and the displacement change is characterized by comprising the following steps of:
1) carrying out landslide investigation on the control slope of the structural surface to be evaluated;
2) taking excavation unloading load as the starting force of the slope deformation, and carrying out stress analysis on the potential sliding body of the slope to be evaluated;
3) establishing a structural surface sliding resistance calculation model considering strain softening; the strain softening shear constitutive equation is as follows:
in the formula, FRThe skid resistance, kN, provided for the structural surface; k is shear stiffness, Pa/m; l is the sliding length of the structural surface, m; u is the potential sliding mass displacement, m; u. of*B, determining according to the direct shear test result of the rock mass structural plane; u. of*Is the characteristic displacement, m; b is an equation coefficient of a dimensionless parameter;
4) calculating the potential dump load of the sliding body on the free face caused by excavation according to the formula (2);
in the formula, F' is the unloading load of the potential sliding body face, kN; w is the potential self weight of the sliding body, kN; l is the sliding length of the structural surface, m; beta is the structural plane inclination angle, °; c is the cohesive force of the soft structural surface Pa;
the angle of internal friction of the structural surface is degree;
5) when the load F' is unloaded in the slope angle excavation, the stress state of the potential sliding body changes; determining a structural surface shear constitutive equation under the excavation unloading condition as shown in a formula (3);
in the formula, FR' is the sliding resistance under the condition of excavation unloading, kN; k is shear stiffness, Pa/m; l is the sliding length of the structural surface, m; u is the potential slider displacement, m; u. of0Starting displacement for potential sliding mass, m; u. of*B, determining according to the direct shear test result of the rock mass structural plane; u. of*Is the characteristic displacement, m; b is an equation coefficient of a dimensionless parameter;
6) constructing a structural plane control side slope body motion equation;
7) calculating a displacement process curve of the potential sliding body;
8) comparing and analyzing the on-site deformation monitoring data with the potential slide displacement process curve, and judging the displacement development trend of the structural surface control slope to be evaluated;
9) and (4) according to the convergence of the calculated displacement of the potential sliding body, predicting the long-term stability of the structural surface control slope to be evaluated.
2. The structural surface control slope stability dynamic evaluation method based on the strain softening shearing constitutive model and the displacement change according to claim 1, characterized in that: the landslide investigation in the step 1) comprises determining a landslide area range, and collecting and summarizing landslide deformation characteristic data and hydrographic and geological engineering condition data.
3. The structural surface control slope stability dynamic evaluation method based on the strain softening shearing constitutive model and the displacement change as claimed in claim 2, characterized in that: the hydrological and geological engineering conditions comprise geological landform data, geotechnical physical and mechanical property data, ground stress data, meteorological hydrological data and construction operation data near a side slope.
4. The structural surface control slope stability dynamic evaluation method based on the strain softening shearing constitutive model and the displacement change according to claim 1, characterized in that: the self weight of the potential sliding body is shown as the formula (4):
wherein gamma is the rock mass weight of the potential sliding body, N/m3(ii) a h is the fracture depth, m; l is the sliding length of the structural surface, m; beta is the structural plane inclination angle, °; alpha is the slope inclination angle of the control slope of the structural plane to be evaluated.
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