CN111931273B - Rapid calculation method for slope safety coefficient theoretical value - Google Patents
Rapid calculation method for slope safety coefficient theoretical value Download PDFInfo
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- CN111931273B CN111931273B CN202010687539.4A CN202010687539A CN111931273B CN 111931273 B CN111931273 B CN 111931273B CN 202010687539 A CN202010687539 A CN 202010687539A CN 111931273 B CN111931273 B CN 111931273B
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Abstract
The invention discloses a method for quickly calculating a theoretical value of a safety coefficient of a side slope, which comprises the steps of defining a scale factor; selecting different grid division heights according to the known side slope height and obtaining a plurality of groups of different scale factors; establishing a plurality of slope stability calculation models with the same residual calculation conditions except different scale factors; solving the model to obtain slope safety coefficients corresponding to the slope stability calculation models; performing data fitting on the slope safety coefficient to obtain a slope safety coefficient fitting type; and obtaining a final side slope safety coefficient theoretical value according to the side slope safety coefficient fitting mode. The method for rapidly calculating the theoretical value of the safety coefficient of the side slope, provided by the invention, not only can theoretically calculate the theoretical value of the safety coefficient of the side slope, but also has the advantages of rapid calculation process, high reliability, good practicability, simplicity and easiness.
Description
Technical Field
The invention belongs to the field of civil engineering, and particularly relates to a method for quickly calculating a theoretical value of a safety coefficient of a side slope.
Background
The side slope is a slope with a certain slope. The mountain land area is wide in China and the civil construction industry is developed, so that a large number of natural slopes and artificial slopes exist. Slope instability (landslide) generally threatens the life and property safety of people and brings huge economic losses, such as traffic interruption, river channel blockage, urban burying, engineering construction obstruction and the like, so the problem of slope stability is always a research hotspot in the field of geotechnical engineering.
The analysis methods of the slope stability are numerous, but the purpose of the analysis methods is not only to quickly determine the safety coefficient of the slope and the position of a potential sliding surface. At present, numerical simulation methods such as a limit balance method LEM and an intensity reduction method SRM are the mainstream for calculating the safety coefficient of the side slope. The LEM calculates the safety coefficient of the side slope based on the method of the balance of the bending moment, force or shearing strength of the slip surface at the moment of damage, and the SRM defines the ratio of the initial value of the strength parameter of the side slope to the critical value as the safety coefficient. Compared with LEM, the SRM does not need to set the shape and the position of a potential sliding surface in advance, can reflect the gradual slope damage process, and can obtain a calculation result similar to that of LEM, so that the SRM is widely applied to actual engineering.
The SRM is adopted to calculate the slope safety coefficient, grid division needs to be carried out on a slope calculation model, and the size of the divided grid can have certain influence on the safety coefficient calculation result. At present, a theoretical basis of grid division is not found, so that common slope stability calculation results have certain artificial subjectivity, and the safety factors of different slopes are not comparable. On the other hand, the actual soil particle size is fine, if the grid division size is set to be the same order of magnitude as the soil particles, the most accurate slope safety coefficient can be obtained, but the extremely high requirements on the computer performance are also provided. Therefore, a method for quickly calculating the theoretical value of the safety coefficient of the side slope does not exist at present.
Disclosure of Invention
The invention aims to provide a method for quickly calculating the theoretical value of the safety coefficient of the side slope, which is high in reliability, good in practicability, simple and easy to implement.
The invention provides a method for rapidly calculating a theoretical value of a safety coefficient of a side slope, which comprises the following steps:
s1, defining a scale factor;
s2, selecting different grid division heights according to the known slope height, so as to obtain a plurality of groups of different scale factors;
s3, establishing a plurality of slope stability calculation models with the same residual calculation conditions except different scale factors according to the set calculation models and slope parameters;
s4, carrying out numerical operation on the plurality of slope stability calculation models established in the step S3 to obtain slope safety coefficients corresponding to the slope stability calculation models;
s5, performing data fitting on the slope safety coefficients corresponding to the slope stability calculation models obtained in the step S4 to obtain a slope safety coefficient fitting type;
and S6, calculating to obtain a final theoretical value of the side slope safety coefficient according to the side slope safety coefficient fitting type obtained in the step S5.
The scale factor in step S1 is specifically defined as a ratio of the height of the divided grid to the height of the slope, and η = h grid /H slope (ii) a Eta is a scale factor, h grid To divide the height of the grid, H slope Is the height of the side slope.
Step S3, establishing a plurality of slope stability calculation models with the same residual calculation conditions except different scale factors, wherein the slope parameters all adopt the following parameter values:
density ρ =1.93 in g · cm -3 ；
Elastic modulus E =56.5 in MPa;
poisson ratio u =0.4;
cohesion c =25, in η Pa;
internal friction angle phi =20 °;
establishing a calculation model by adopting the optimal side slope geometric dimension;
and establishing at least three slope stability calculation models with the same residual calculation conditions except different scale factors eta.
The optimal slope geometric dimension establishes a calculation model, specifically, the length of the left boundary of the slope calculation model from the toe is 1.5 times of the slope height, the length of the right boundary of the slope calculation model from the shoulder is 2.5 times of the slope height, and the thickness of the foundation of the slope calculation model is 1 time of the slope height.
And S4, solving the slope stability calculation models established in the step S3 to obtain the slope safety coefficients corresponding to the slope stability calculation models, specifically, solving the slope stability calculation models by adopting a strength reduction dichotomy to obtain the slope safety coefficients corresponding to the slope stability calculation models.
The method for solving the slope stability calculation model by adopting the intensity reduction dichotomy specifically comprises the following steps of:
A. creating an array M and global variables A, B and N; the array M is used for storing the value of the slope safety coefficient, the global variable A is used as the upper limit value of the calculation interval and is initialized to 0, the global variable B is used as the lower limit value of the calculation interval and is initialized to 0, and the N is the cycle number and is initialized to 0;
B. bringing in a slope stability calculation model and calculation parameters;
C. judging whether the cycle number N is larger than or equal to 1:
if N is more than or equal to 1, taking A as the upper limit value of the calculation interval and taking B as the lower limit value of the calculation interval;
if N is less than 1, not operating;
D. solving a currently brought slope stability calculation model to obtain a slope safety coefficient and an amplitude value to an intermediate variable S, and storing the slope safety coefficient to an array M;
E. modifying the value of A to be S and modifying the value of B to be kxS; k is a reduction factor less than 1;
F. the value of the number of cycles N is increased by 1;
G. judging whether all slope stability calculation models are calculated:
if yes, outputting a final array M to obtain all slope safety coefficient values;
and if not, deleting the slope stability calculation model brought currently, and returning to the step B.
And S6, calculating to obtain a final theoretical value of the side slope safety coefficient according to the side slope safety coefficient fitting formula obtained in the step S5, specifically calculating to obtain a coordinate value of an intersection point of the side slope safety coefficient fitting formula and a y axis in a coordinate axis, and calculating to obtain the theoretical value of the side slope safety coefficient according to the side slope safety coefficient fitting formula.
The method for rapidly calculating the theoretical value of the safety coefficient of the side slope, provided by the invention, not only can theoretically calculate the theoretical value of the safety coefficient of the side slope, but also has the advantages of rapid calculation process, high reliability, good practicability, simplicity and easiness.
Drawings
FIG. 1 is a schematic process flow diagram of the process of the present invention.
Fig. 2 is a schematic diagram of an embodiment of the method of the present invention when quadrilateral mesh partitioning is employed.
FIG. 3 is a schematic diagram of an embodiment of the method of the present invention when triangular mesh partitioning is employed.
FIG. 4 is a schematic diagram of a calculation flow for solving a slope stability calculation model by using a strength reduction dichotomy in the method of the present invention.
FIG. 5 is a schematic diagram of a relationship between a slope safety factor and a scale factor in an embodiment of the method of the present invention.
Detailed Description
FIG. 1 shows a schematic flow chart of the method of the present invention: the invention provides a method for rapidly calculating a theoretical value of a safety coefficient of a side slope, which comprises the following steps:
s1, defining a scale factor; specifically, the scale factor is defined as the ratio of the height of the divided grid to the height of the side slope, and eta = h grid /H slope (ii) a Eta is a scale factor, h grid To divide the height of the grid, H slope Is the height of the side slope;
s2, selecting different grid division heights according to the known slope height, so as to obtain a plurality of groups of different scale factors;
s3, establishing a plurality of slope stability calculation models with the same residual calculation conditions except different scale factors (which can be in FLAC) according to the set calculation models and slope parameters 3D Establishing the model in numerical calculation software); specifically, the slope parameters all adopt the following parameters:
density ρ =1.93 in g · cm -3 ；
Elastic modulus E =56.5 in MPa;
poisson ratio u =0.4;
cohesion c =25, in η Pa;
internal friction angle phi =20 °;
establishing a calculation model by adopting the optimal slope geometric dimension, wherein the length of the left boundary of the slope calculation model from the toe is 1.5 times of the slope height, the length of the right boundary of the slope calculation model from the shoulder is 2.5 times of the slope height, and the thickness of the foundation of the slope calculation model is 1 time of the slope height;
establishing at least three slope stability calculation models with the same residual calculation conditions except different scale factors eta;
s4, solving the plurality of slope stability calculation models established in the step S3 to obtain slope safety coefficients corresponding to the slope stability calculation models; solving the slope stability calculation models by adopting a strength reduction dichotomy method so as to obtain slope safety coefficients corresponding to the slope stability calculation models;
in specific implementation, the following steps are adopted for solving:
A. creating an array M and global variables A, B and N; the array M is used for storing the value of the safety coefficient of the side slope, the global variable A is used as the upper limit value of the calculation interval and is initialized to 0, the global variable B is used as the lower limit value of the calculation interval and is initialized to 0, and the N is the cycle number and is initialized to 0;
B. introducing a slope stability calculation model and calculation parameters;
C. judging whether the cycle number N is larger than or equal to 1:
if N is more than or equal to 1, taking A as the upper limit value of the calculation interval and taking B as the lower limit value of the calculation interval;
if N is less than 1, not operating;
D. solving a currently brought slope stability calculation model to obtain a slope safety coefficient and an amplitude value to an intermediate variable S, and storing the slope safety coefficient to an array M;
E. modifying the value of A to be S and modifying the value of B to be kxS; k is a reduction factor less than 1;
F. the value of the number of cycles N is increased by 1;
G. judging whether all slope stability calculation models are calculated:
if yes, outputting a final array M to obtain all slope safety coefficient values;
if not, deleting the slope stability calculation model brought currently, and returning to the step B;
s5, performing data fitting on the slope safety coefficients corresponding to the slope stability calculation models obtained in the step S4 to obtain a slope safety coefficient fitting type;
s6, calculating to obtain a final theoretical value of the side slope safety coefficient according to the side slope safety coefficient fitting type obtained in the step S5; specifically, a coordinate value of an intersection point of the slope safety coefficient fitting formula and a y axis in a coordinate axis is obtained through calculation, and then a slope safety coefficient theoretical value is obtained through calculation according to the slope safety coefficient fitting formula.
The process and feasibility of the present invention are further illustrated below with reference to one example:
firstly, introducing a dimensionless coefficient scale factor eta;
then, selecting different grid division heights according to the known side slope heights to obtain a plurality of groups of scale factor eta values, and sequencing according to the size;
establishing a plurality of slope stability calculation models with the same residual calculation conditions except different scale factors; meanwhile, in order to evaluate the influence of different grid shape conditions, two groups of slope calculation models (shown in fig. 2 and 3) are respectively established by pure triangular divided grids and pure quadrilateral divided grids;
solving the model; wherein k is a reduction coefficient less than 1; the method can be determined according to the value density of eta when the fine safety coefficient is calculated: if eta is dense, k can be a larger value to reduce the calculation interval, thereby reducing the calculation time; otherwise, reducing the value of k;
carrying out statistical treatment on the obtained slope safety coefficient, drawing a slope safety coefficient change rule graph under different scale factors, and obtaining a corresponding change rule function expression through data fitting; as can be seen from fig. 5, the functional expression of the pure triangulated mesh correspondence curve is Fs =1.74-0.86 × 0.08 η Adjusting R 2 =0.987; the function expression of the corresponding curve of the pure quadrilateral division grid is as follows: fs =1.26-0.39 × 0.10 η Adjusting R 2 =0.983; the fitting curve is very close to the calculation result of Fs, and the fitting result can be considered to be effective;
finally, defining the intersection point of the function curve and the ordinate as a theoretical value of the safety coefficient of the side slope, wherein the specific value can be obtained according to a function expression: let η =0, then Fs corresponding to the pure triangular divided mesh and the pure quadrilateral divided mesh are 0.88 and 0.87, respectively, which are substantially equal, which indicates that the method of the present invention can not only avoid subjectivity in the divided mesh size, but also eliminate calculation errors in the shape.
The side slope safety coefficient theoretical value calculated by the method can be used for accurately calculating the safety coefficient in the stability analysis of the actual side slope engineering. The theoretical value eliminates the artificial subjectivity of calculating the safety coefficient of the side slope by using a numerical calculation method in actual engineering, can reduce the calculation error caused by the grid division problem to the maximum extent, obtains the accurate safety coefficient, reflects the most real stable condition of the side slope, and can play an important guiding role in the design construction and stability evaluation of the engineering side slope.
Claims (5)
1. A method for rapidly calculating a theoretical value of a safety coefficient of a side slope comprises the following steps:
s1, defining a scale factor;
s2, selecting different grid division heights according to the known slope heights so as to obtain a plurality of groups of different scale factors;
s3, establishing a plurality of slope stability calculation models with the same residual calculation conditions except different scale factors according to the set calculation models and slope parameters;
s4, solving the plurality of slope stability calculation models established in the step S3 to obtain slope safety coefficients corresponding to the slope stability calculation models; solving the slope stability calculation models by adopting a strength reduction dichotomy method so as to obtain slope safety coefficients corresponding to the slope stability calculation models;
in specific implementation, the following steps are adopted for solving:
A. creating an array M and global variables A, B and N; the array M is used for storing the value of the slope safety coefficient, the global variable A is used as the upper limit value of the calculation interval and is initialized to 0, the global variable B is used as the lower limit value of the calculation interval and is initialized to 0, and the N is the cycle number and is initialized to 0;
B. bringing in a slope stability calculation model and calculation parameters;
C. judging whether the cycle number N is larger than or equal to 1:
if N is more than or equal to 1, taking A as the upper limit value of the calculation interval and taking B as the lower limit value of the calculation interval;
if N is less than 1, not operating;
D. solving a currently brought slope stability calculation model to obtain a slope safety coefficient and an amplitude value to an intermediate variable S, and storing the slope safety coefficient to an array M;
E. modifying the value of A to be S and modifying the value of B to be kxS; k is a reduction factor less than 1;
F. the value of the number of cycles N is increased by 1;
G. judging whether all slope stability calculation models are calculated:
if yes, outputting a final array M to obtain all slope safety coefficient values;
if not, deleting the slope stability calculation model brought currently, and returning to the step B;
s5, performing data fitting on the slope safety coefficients corresponding to the slope stability calculation models obtained in the step S4 to obtain a slope safety coefficient fitting type;
and S6, calculating to obtain a final theoretical value of the side slope safety coefficient according to the side slope safety coefficient fitting type obtained in the step S5.
2. The method for rapidly calculating the theoretical value of the safety factor of the side slope according to claim 1, wherein the scale factor in step S1, specifically, the scale factor is defined as a ratio of a height of a divided grid to a height of the side slope, and η = h grid /H slope (ii) a Eta is a scale factor, h grid To divide the height of the grid, H slope Is the height of the side slope.
3. The method for rapidly calculating the theoretical value of the safety coefficient of the side slope according to claim 2, wherein the step S3 is characterized in that a plurality of side slope stability calculation models with the same residual calculation conditions except for different scale factors are established, and specifically, the side slope parameters all adopt the following parameter values:
density ρ =1.93 in g · cm -3 ；
Elastic modulus E =56.5 in MPa;
poisson ratio u =0.4;
cohesive force c =25, in units of η Pa;
internal friction angle phi =20 °;
establishing a calculation model by adopting the optimal side slope geometric dimension;
and establishing at least three slope stability calculation models with the same residual calculation conditions except different scale factors eta.
4. The method for rapidly calculating the theoretical value of the safety coefficient of the side slope according to claim 3, wherein the optimal geometric dimension of the side slope establishes a calculation model, specifically, the length of the distance from the left boundary to the toe of the side slope calculation model is 1.5 times of the slope height, the length of the distance from the right boundary to the shoulder of the side slope calculation model is 2.5 times of the slope height, and the thickness of the foundation of the side slope calculation model is 1 time of the slope height.
5. The method for rapidly calculating the theoretical value of the side slope safety coefficient according to claim 4, wherein the final theoretical value of the side slope safety coefficient is calculated according to the side slope safety coefficient fit obtained in the step S6, specifically, a coordinate value of an intersection point of the side slope safety coefficient fit and a y axis in a coordinate axis is calculated, and then the theoretical value of the side slope safety coefficient is calculated according to the side slope safety coefficient fit.
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| WO2018018661A1 (en) * | 2016-07-29 | 2018-02-01 | 深圳朝伟达科技有限公司 | Display method of interactive stability display system for rock slope |
| CN110909488A (en) * | 2019-12-06 | 2020-03-24 | 中南大学 | High-efficiency slope reliability analysis method |
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| CN110489826B (en) * | 2019-07-30 | 2022-12-20 | 石家庄铁道大学 | Rock slope safety coefficient calculation method and device and terminal equipment |
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| WO2018018661A1 (en) * | 2016-07-29 | 2018-02-01 | 深圳朝伟达科技有限公司 | Display method of interactive stability display system for rock slope |
| CN110909488A (en) * | 2019-12-06 | 2020-03-24 | 中南大学 | High-efficiency slope reliability analysis method |
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