CN115659586A - Earthquake slope permanent displacement calculation method based on random concave-convex slope surface - Google Patents
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Abstract
The invention discloses a method for calculating permanent displacement of an earthquake slope based on a random concave-convex slope surface, and particularly relates to the technical field of earthquake slope stability. Comprises inputting relevant parameters; randomly generating and acquiring a slope surface with irregular geometry; obtaining the critical sliding surface parameters of the side slope in the limit state by optimizing and solving the safety coefficient by combining a limit analysis upper limit method and a strength reduction method; assuming that the critical sliding surface does not change any more in the earthquake process, constructing a dynamic balance equation of the side slope through a virtual work principle to obtain the angular acceleration of the side slope; and carrying out secondary integration on the angular acceleration within a small time period, and obtaining the horizontal permanent displacement at the slope toe of the side slope in the whole earthquake process through accumulation and superposition. By adopting the technology, the irregular geometric slope surface side slope permanent displacement considering the slope top tension damage under the action of real horizontal and vertical seismic motions can be quickly obtained, the problems that the slope body tension damage is not considered in the seismic slope stability analysis theory and the actual horizontal seismic motion and the vertical seismic motion are not in a definite proportional relation in the seismic process are solved, and the method can be used for more accurately calculating the seismic stability of the irregular slope surface side slope.
Description
Technical Field
The invention relates to the technical field of seismic slope stability, in particular to a seismic slope permanent displacement calculation method based on random concave-convex slope surfaces.
Background
In recent years, with the gradual progress of the tibetan railway engineering, the problem of slope stability is inevitably involved in the development of infrastructure construction in fragile ecological environment, complex geological conditions and strong active fracture areas. In the theoretical method of slope stability analysis, only linear, convex and concave slope forms are considered in most methods. However, in practical engineering, the slope surface of the side slope mostly presents an irregular concave-convex shape, the concave-convex characteristics of the slope surface have a certain influence on the stability of the side slope, and the conclusion of the influence rule of the concave-convex characteristics of the slope surface on the stability of the side slope is not uniform. The concave-convex characteristics of the slope surface relate to the stability of the slope and further relate to a slope-releasing excavation scheme in engineering. In addition, in the conventional seismic stability research using permanent displacement as an evaluation index, only a horizontal seismic acceleration-time-course curve is considered, or a certain proportional relation between vertical seismic acceleration and horizontal seismic acceleration is assumed. However, the actual horizontal earthquake motion and the vertical earthquake motion are not in a definite proportion in the earthquake process. Therefore, the slope permanent displacement calculation method capable of considering the irregular geometric slope and the real horizontal-vertical seismic dynamic coupling effect has theoretical and practical significance.
Disclosure of Invention
The invention aims to provide a method for calculating permanent displacement of an earthquake slope based on a random concave-convex slope surface, and solves the problem that the slope stability analysis theory does not consider that actual horizontal earthquake motion and vertical earthquake motion do not have a definite proportional relation in the earthquake process.
In order to achieve the purpose, the technical scheme of the invention is as follows: a method for calculating permanent displacement of an earthquake slope based on random concave-convex slopes comprises the following steps:
s1, inputting dimensionless parameters u of soil mass gravity gamma, cohesive force c, internal friction angle phi, slope vertex angle alpha, slope height H and rock and soil mass tensile strength;
s2, setting the number n of the broken lines on the slope surface and the ratio of the height of each broken line to the height of the slope as a i The included angle between each section of broken line and the horizontal line is beta i By randomly generating a i 、β i Acquiring an irregular slope surface of a side slope;
s3, combining a limit analysis upper limit method and a strength reduction method, and obtaining critical sliding surface parameters of the side slope in a limit state by optimizing and solving a safety coefficient;
s4, assuming that the critical sliding surface does not change any more in the earthquake process, constructing a dynamic balance equation of the side slope through a virtual work principle, and further acquiring the angular acceleration of the side slope;
and S5, carrying out secondary integration on the angular acceleration within a small time period, and further obtaining the horizontal permanent displacement of the slope toe of the side slope in the whole earthquake process through accumulation and superposition.
Further, the specific method of step S2:
s21, setting the number of broken lines forming the slope surface to be n (n =1,2,3, 4- ·), and setting a i And beta i The constraint conditions that are satisfied;
and S22, randomly generating a slope broken line according to the constraint conditions in the step S21.
Further, the constraint condition of step S21 satisfies the following formula:
further, the specific method of step S3:
s31, combining a limit analysis upper limit method and a strength reduction method to obtain a calculation formula of the slope safety coefficient;
s32, substituting real horizontal and vertical seismic acceleration at the time t, wherein t is more than or equal to 0, and calculating a safety coefficient;
s33, when the safety factor F s If the sum is less than or equal to 1.0, the step S34 is entered, otherwise, the step T = t + d is returned t And returning to the step S32;
s34, assuming that the safety factor is at a time step d t Internally linear, and at time t n Optimizing and obtaining a safety factor F s(n) (k v(n) ，k h(n) ) Less than or equal to 1.0, and recording the previous time step t (n-1) Slope safety factor F s(n-1) (k v(n-1) ，k h(n-1) )>1.0, obtaining F by linear interpolation s K when =1.0 h(s) And k v(s) ；
S35, mixing k h(s) And k v(s) And substituting the parameters into a safety coefficient calculation equation to obtain the critical sliding surface parameters.
Further, the slope safety factor in step S31 is calculated as follows:
in the above formula, F s In order to ensure the safety factor,
is the internal energy dissipation coefficient, k h Is the horizontal seismic acceleration coefficient, k v Is the vertical seismic acceleration coefficient, f 1 ～f n+2 ，f 1 '～f n+2 '，t 1 ～t 3 ，t 1 '～t 3 ' are external power coefficients;
the calculation formula of the internal energy dissipation rate coefficient is as follows:
the external power coefficient f 1 ～f n+2 The calculation formula of (c) is:
the external power coefficient f 1 '～f n+2 ' is calculated as:
the external power coefficient t 1 ～t 3 The calculation formula of (2) is as follows:
the external power coefficient t 1 '～t 3 The formula for calculation of' is:
further, k in step S34 h(s) And k v(s) The calculation formula of (2) is as follows:
further, the power balance equation of the slope in step S4 is:
in the above formula, W is the gravity of the sliding body, and l is the distance from the gravity center of the sliding body to the point P of the rotating gravity center;
the calculation formula of the weight of the sliding body is as follows:
the calculation formula of the distance from the center of gravity of the sliding body to the point P of the rotating center of gravity is as follows:
further, the calculation formula of the horizontal permanent displacement in step S5 is:
compared with the prior art, the beneficial effect of this scheme:
the scheme considers the irregular slope surface form of the side slope in the actual engineering and the real horizontal-vertical seismic dynamic coupling effect, so that the calculation of the permanent displacement of the side slope under the action of the earthquake is more accurate, and a foundation is laid for the evaluation method of the permanent displacement of the side slope in the actual engineering.
Drawings
FIG. 1 is a flow chart of a method for calculating permanent displacement of an earthquake slope based on a random concave-convex slope surface according to the invention;
FIG. 2 is a slope failure mode diagram of the seismic slope permanent displacement calculation method based on random concave-convex slopes according to the present invention;
FIG. 3 is a diagram of an irregular slope surface and a critical failure surface of a slope according to an embodiment of the present invention;
fig. 4 is a permanent displacement analysis diagram in an embodiment of the present invention.
Detailed Description
The invention is explained in more detail below by means of specific embodiments:
examples
As shown in figures 1 and 2: a method for calculating permanent displacement of an earthquake slope based on random concave-convex slopes comprises the following steps:
s1, inputting soil mass gravity gamma, cohesive force c, an internal friction angle phi, a slope vertex angle alpha, a slope height H and dimensionless parameters u considering the tensile strength of a rock and soil mass;
s2, setting the number n of the broken lines on the slope surface and the ratio of the height of each broken line to the height of the slope as a i The included angle between each section of broken line and the horizontal line is beta i By randomly generating a i 、β i And acquiring the irregular slope surface of the side slope. The specific method comprises the following steps:
s21, setting the number of broken lines forming the slope surface to be n (n =1,2,3, 4- ·), and setting a i And beta i The constraint condition is satisfied, and the constraint condition satisfies the following formula:
and S22, randomly generating a slope broken line according to the constraint conditions in the step S21.
S3, combining a limit analysis upper limit method and a strength reduction method, considering real horizontal and vertical earthquake dynamic acceleration, and obtaining critical sliding surface parameters of the side slope in a limit state by optimizing and solving a safety coefficient; the specific method comprises the following steps:
s31, combining a limit analysis upper limit method and a strength reduction method to obtain a calculation formula of the slope safety coefficient; the calculation formula of the slope safety coefficient is as follows:
in the above formula, F s In order to be a safety factor,
is the internal energy dissipation coefficient, k h Is the horizontal seismic acceleration coefficient, k v Is the vertical seismic acceleration coefficient, f 1 ～f n+2 ，f 1 '～f n+2 '，t 1 ～t 3 ，t 1 '～t 3 ' are external power coefficients;
the calculation formula of the internal energy dissipation rate coefficient is as follows:
external power coefficient f 1 ～f n+2 The calculation formula of (2) is as follows:
coefficient of external power f 1 '～f n+2 The formula for calculation of' is:
external power systemNumber t 1 ～t 3 The calculation formula of (c) is:
external power coefficient t 1 '～t 3 ' is calculated as:
s32, substituting real horizontal and vertical seismic acceleration at the time t, wherein t is more than or equal to 0, and calculating a safety coefficient;
s33, when the safety factor F s If the sum is less than or equal to 1.0, the step S34 is entered, otherwise, the step T = t + d is returned t And returns to step S32;
s34, assuming that the safety factor is in a time step d t Internally linear, and at time t n Optimizing and obtaining a safety factor F s(n) (k v(n) ，k h(n) ) Less than or equal to 1.0, and recording the previous time step t (n-1) Slope safety factor F s(n-1) (k v(n-1) ，k h(n-1) )>1.0, obtaining F by linear interpolation s K when =1.0 h(s) And k v(s) (ii) a Wherein k is h(s) And k v(s) The calculation formula of (c) is:
s35, adding k h(s) And k v(s) And substituting the parameters into a safety coefficient calculation equation to obtain the critical sliding surface parameters.
And S4, assuming that the critical sliding surface does not change any more in the earthquake process, constructing a dynamic balance equation of the side slope through a virtual work principle, and further acquiring the angular acceleration of the side slope. The dynamic balance equation of the side slope is as follows:
in the above formula, W is the gravity of the sliding body, and l is the distance from the gravity center of the sliding body to the point P of the rotating gravity center;
the calculation formula of the weight of the sliding body is as follows:
the calculation formula of the distance from the center of gravity of the sliding body to the point P of the rotating center of gravity is as follows:
s5, carrying out secondary integration on the diagonal acceleration within a tiny time period, and further obtaining the horizontal permanent displacement of the slope toe of the side slope in the whole earthquake process through accumulation and superposition, wherein the calculation formula of the horizontal permanent displacement is as follows:
case (1): and carrying out the example analysis of the permanent displacement of the slope with n =10 fold lines on the slope surface under the action of the earthquake. The method of the embodiment is adopted to randomly generate the irregular geometric slope parameters as follows: beta is a 1 ～β 10 ＝71.49,28.01,47.57,14.91,54.18,23.67,58.87,62.03,67.33,40.55，a i And (1/n). Considering the tension failure of the top of the slope, the relevant parameters are phi =20 degrees, c =25kPa, gamma =21kN/m3, alpha =5 degrees and H =15m. The earthquake chooses Imperial Valley earthquake motion. The slope irregular slope, the critical failure plane are shown in fig. 3, and the permanent displacement analysis is shown in fig. 4.
The above are merely examples of the present invention and common general knowledge of known specific structures and/or characteristics of the schemes has not been described herein in more detail. It should be noted that, for those skilled in the art, without departing from the structure of the present invention, several variations and modifications can be made, which should also be considered as the protection scope of the present invention, and these will not affect the effect of the implementation of the present invention and the utility of the patent. The scope of the claims of the present application shall be determined by the contents of the claims, and the description of the embodiments and the like in the specification shall be used to explain the contents of the claims.
Claims (8)
1. A method for calculating permanent displacement of an earthquake slope based on random concave-convex slopes is characterized by comprising the following steps: the method comprises the following steps:
s1, inputting dimensionless parameters u of soil mass gravity gamma, cohesive force c, internal friction angle phi, slope vertex angle alpha, slope height H and rock and soil mass tensile strength;
s2, setting the number n of the broken lines on the slope surface and the ratio of the height of each broken line to the height of the slope as a i The included angle between each section of broken line and the horizontal line is beta i By randomly generating a i 、β i Acquiring a slope surface with irregular geometry;
s3, combining a limit analysis upper limit method and a strength reduction method, and obtaining critical sliding surface parameters of the side slope in a limit state through optimizing and solving a safety coefficient;
s4, assuming that the critical sliding surface does not change any more in the earthquake process, constructing a dynamic balance equation of the side slope through a virtual work principle, and further acquiring the angular acceleration of the side slope;
and S5, carrying out secondary integration on the angular acceleration within a small time period, and further obtaining the horizontal permanent displacement of the slope toe of the side slope in the whole earthquake process through accumulation and superposition.
2. The method for calculating the permanent displacement of the earthquake slope based on the random concave-convex slope surface as claimed in claim 1, wherein: the specific method of step S2:
s21, setting the number of broken lines forming the slope surface to be n (n =1,2,3, 4- ·), and setting a i And beta i A constraint condition to be satisfied;
and S22, randomly generating a slope broken line according to the constraint condition in the step S21.
3. The method for calculating the permanent displacement of the seismic slope based on the random concave-convex slope surface as claimed in claim 2, characterized in that: the constraint condition of step S21 satisfies the following formula:
4. the method for calculating the permanent displacement of the seismic slope based on the random concave-convex slope surface as claimed in claim 1, wherein: the specific method of step S3:
s31, combining a limit analysis upper limit method and a strength reduction method to obtain a calculation formula of the slope safety coefficient;
s32, substituting the real horizontal and vertical seismic acceleration at the time t, wherein t is more than or equal to 0, and calculating a safety coefficient;
s33, when the safety factor F is reached s When the value is less than or equal to 1.0, the step S34 is entered, otherwise, the step T = t + d is returned t And returns to step S32;
s34, assuming that the safety factor is at a time step d t Internally linear, and at time t n Optimizing and obtaining a safety factor F s(n) (k v(n) ，k h(n) ) Less than or equal to 1.0, and recording the previous time step length t (n-1) Slope safety factor F s(n-1) (k v(n-1) ，k h(n-1) )>1.0, obtaining F by linear interpolation s K at =1.0 h(s) And k v(s) ；
S35, adding k h(s) And k v(s) And substituting the parameters into a safety coefficient calculation equation to obtain the critical sliding surface parameters.
5. The method for calculating the permanent displacement of the earthquake slope based on the random concave-convex slope surface as claimed in claim 4, wherein: the calculation formula of the slope safety coefficient in the step S31 is as follows:
in the above formula, F s In order to be a safety factor,
is the internal energy dissipation coefficient, k h Is the horizontal seismic acceleration coefficient, k v Is the vertical seismic acceleration coefficient, f 1 ～f n+2 ，f 1 '～f n+2 '，t 1 ～t 3 ，t 1 '～t 3 ' are external power coefficients;
the calculation formula of the internal energy dissipation rate coefficient is as follows:
the external power coefficient f 1 ～f n+2 The calculation formula of (2) is as follows:
the external power coefficient f 1 '～f n+2 ' is calculated as:
the external power coefficient t 1 ～t 3 The calculation formula of (2) is as follows:
the external power coefficient t 1 '～t 3 The formula for calculation of' is:
6. the method for calculating the permanent displacement of the earthquake slope based on the random concave-convex slope surface as claimed in claim 4, wherein: k in step S34 h(s) And k v(s) The calculation formula of (2) is as follows:
7. the method for calculating the permanent displacement of the earthquake slope based on the random concave-convex slope surface as claimed in claim 1, wherein: the dynamic balance equation of the side slope in the step S4 is as follows:
in the above formula, W is the gravity of the sliding body, and l is the distance from the gravity center of the sliding body to the point P of the rotating gravity center;
the calculation formula of the weight of the sliding body is as follows:
the calculation formula of the distance from the center of gravity of the sliding body to the point P of the rotating center of gravity is as follows:
8. the method for calculating the permanent displacement of the seismic slope based on the random concave-convex slope surface as claimed in claim 1, wherein: the calculation formula of the horizontal permanent displacement in the step S5 is as follows:
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