CN112270102B - Multi-parameter non-equal-proportion reduction safety coefficient calculation method based on energy principle - Google Patents
Multi-parameter non-equal-proportion reduction safety coefficient calculation method based on energy principle Download PDFInfo
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Abstract
The invention discloses a method for calculating a safety coefficient of multi-parameter non-equal proportional reduction based on an energy principle, which comprises the following steps: determining the geometric dimension and the distribution characteristic of the strength material of the calculation model; determining a numerical method and establishing a numerical model; collecting mechanical parameters of a related material, and determining a degradation function of the material; determining reduction time, reduction proportion and reduction step length of different parameters or materials according to the degradation function; performing parameter reduction to reduce the geotechnical structure to a limit state; calculating the evolution of dissipation energy of a geotechnical structure system and calculating the weight values of different reduction parameters; and solving a safety coefficient reduction overall process evolution curve. The invention provides a convenient and feasible solving method for quantitatively evaluating the safety of the whole process of the life of the geotechnical structure and predicting the service life of the tunnel, and actively promotes the progress of the safety quantitative evaluation technology in the fields of geotechnical engineering, tunnels and underground engineering.
Description
Technical Field
The invention belongs to the fields of geotechnical engineering, tunnel and underground engineering, and particularly relates to a multi-parameter non-equal proportion reduction safety coefficient calculation method based on an energy principle.
Background
At present, the methods commonly used for stability analysis of geotechnical engineering, tunnels and underground engineering mainly comprise a limit analysis method (an upper limit method and a lower limit method), a limit balance method and a strength reduction method. Compared with a limit analysis method and a limit balance method, the strength reduction method has the following advantages: on one hand, the whole damage process can be monitored and observed without presupposing the form and position of a fracture surface and the internal force among the strip blocks; on the other hand, complex situations such as seismic forces, pore water pressure, and supporting structures can be calculated. With the improvement of computer performance and the development of numerical calculation software, the method is widely applied to stability analysis of geotechnical engineering, tunnels and underground engineering by a plurality of researchers.
The traditional strength reduction method is usually based on the principle of molar-coulomb strength and the concept of strength reserve, and adopts an equal proportion reduction mode, namely the strength parameters of cohesive force c and internal friction angle
And obtaining new cohesive force and an internal friction angle by adopting the same reduction coefficient, then enabling the geotechnical structure to reach a limit state by gradually increasing the reduction coefficient, and defining the reduction coefficient at the moment as a safety Factor (FOS). In fact, a large number of experiments show that the degradation rate and the degradation degree of the strength parameters of the geotechnical materials are different when the geotechnical materials are degraded, and the strength parameters of the geotechnical structures are different and dynamically changed in contribution to maintaining the stability of the geotechnical structures during instability. In addition, for geotechnical engineering, various geotechnical materials or supporting structures are often involved, and the attenuation rate and degree of mechanical parameters between different geotechnical materials and between the geotechnical materials and the supporting materials are different. Therefore, it is important to study the multiparameter non-equal proportional reduction between different mechanical parameters and between different materials of the same material, wherein the number of reduction parameters may be two or more, depending on the selected strength criteria and the number of reduction materials.
The research on the unequal proportion reduction method (also called as the double reduction method) of the two parameters mainly aims at the geotechnical engineering structure of homogeneous materials, and currently mainly comprises a mathematical mean value method, a strength reduction path method, a limit balance method, a reference geotechnical structure method and the like. In the conventional non-equal-proportion reduction method, the reduction ratio is generally preset
Then, one stable rock-soil structure is reduced to a limit state at one time according to a reduction ratio k, then the safety coefficient of the current state of the rock-soil structure relative to the limit state is calculated, the safety reserve of the current state of the rock-soil structure relative to the limit state is reflected, and the problem of calculating the whole-process evolution of the safety coefficient along with the reduction path is rarely noticed. In fact, the mechanical parameters of the rock-soil mass and the supporting material usually undergo degradation processes with different degrees and dynamic changes under the action of the external environment, and the destructive evolution process of the rock-soil structure is objective. Corresponding to the parameter reduction, on one hand, the process of parameter degradation is the process of parameter reduction; on the other hand, the reduction paths of different parameters in the parameter reduction process are variable, namely not necessarily linear, the contributions of the different parameters to the stability of the geotechnical structure in the whole reduction process are different and dynamically changed, and the safety coefficient is dynamically evolved along with the reduction paths in the process of reducing the geotechnical structure from the initial state to the limit state. In addition, for engineering technicians, the engineering technicians not only need to care about the safety factor of the geotechnical structures at the present stage, but also need to know the safety factor evolution rule of the overall process of the reduction of the geotechnical structures, so that appropriate time can be selected for targeted reinforcement.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a multi-parameter non-equal proportion reduction safety coefficient calculation method based on an energy principle.
The invention discloses a method for calculating the safety coefficient of multi-parameter unequal proportional reduction based on an energy principle, which comprises the following steps of:
step 1: determining the boundary range, the geometric parameters and the material distribution characteristics of the geotechnical structure calculation model;
step 2: establishing a numerical calculation model, carrying out grid division, and determining a material constitutive model;
and step 3: determining initial key mechanical parameters related to the material and a degradation function thereof by adopting a mechanical test;
and 4, step 4: determining the reduction time of the mechanical parameters, and determining the reduction proportion and the reduction step length of the mechanical parameters according to the degradation function obtained in the step 3;
and 5: defining the limit state of the geotechnical structure, and determining the instability criterion;
step 6: performing parameter reduction to reduce the geotechnical structure to a limit state;
and 7: the contribution degree of different mechanical parameters for maintaining the stability of the rock-soil structure in the reduction process is used as the weighted value of the reduction coefficient of the mechanical parameters;
and step 8: obtaining a safety coefficient calculation method of the multi-parameter unequal proportion reduction of the geotechnical structure by theoretical derivation according to the weighted values in the step 7;
and step 9: and (5) solving to obtain a safety coefficient reduction overall process evolution curve of the geotechnical structure considering the parameter reduction process correlation according to the safety coefficient calculation method in the step (8).
Further, the geotechnical structure is a side slope or a tunnel and underground engineering.
Further, the geotechnical structure is a non-support geotechnical engineering structure or a support geotechnical engineering structure.
Further, in the step 3, the related materials comprise rock-soil mass, concrete and steel; the initial key mechanical parameters refer to deformation parameters and strength parameters; the deformation parameters are elastic modulus and Poisson ratio; the strength parameters are cohesive force and internal friction angle.
Further, step 4 specifically includes: determining reduction time of different mechanical parameters of the same strength material and reduction time of different strength materials; and determining the reduction proportion among different parameters and the reduction step length of each parameter according to the form or the degradation rate of the mechanical parameter degradation function.
Further, plastic region through, strain through, displacement mutation and energy mutation are selected as instability criteria in the step 5.
Further, in step 7, the method using the contribution of different mechanical parameters to maintain the stability of the rock-soil structure in the reduction process as the weight value of the mechanical parameter reduction comprises:
in the formula (I), the compound is shown in the specification,
reducing the weight of the contribution of the jth mechanical parameter of the ith material to the variation of the dissipation energy of the geotechnical structure system;
the dissipation energy increment of the geotechnical structure system after the jth mechanical parameter reduction of the ith material in a certain reduction process is obtained; delta E d The dissipation energy increment of the rock-soil structure system after the reduction of all the mechanical parameters of all the materials in a certain reduction process is obtained; σ is the stress tensor,. epsilon e In order to be a tensor of elastic strain,
U total ═ σ: d epsilon, total strain energy; v is the volume of the reduction unit.
Further, in step 8, the method for calculating the safety coefficient of the multi-parameter unequal proportion reduction of the geotechnical structure comprises the following steps:
in the formula: FOS (k-1) is a comprehensive safety coefficient of the rock-soil structure in a state of k-1; SRF i j Is the reduction coefficient of the jth mechanical parameter of the ith material; n is the reduction times, l is the material quantity, and m is the mechanical parameter quantity; FOS (n) is the residual safety coefficient of the rock-soil structure after reducing for n times, and FOS (n) is more than or equal to 1.0; f (SRF) i j ) The method is a harmonic average value of the reduction coefficient, represents a common action part of the reduction coefficient during non-equal proportional reduction, and reflects the influence of nonlinearity and correlation of the reduction parameter during common reduction on the comprehensive safety coefficient.
Compared with the prior art, the invention has the beneficial technical effects that:
firstly, for geotechnical engineering, the degradation rate and degree of different mechanical parameters of materials are different when the materials are degraded, and the contributions of the different mechanical parameters to the maintenance of the stability of the geotechnical structure are different and dynamically changed in the destabilization process. Moreover, geotechnical engineering often involves multiple geotechnical materials or supporting structures, and the attenuation rate and degree of mechanical parameters between different geotechnical materials and between the geotechnical materials and the supporting materials are different. The calculation method of the invention can consider the multi-parameter non-equal proportion reduction among different parameters of the same material and among different strength materials, and has clear physical significance.
The second, the existing non-equal proportion reduction method is that the reduction ratio of the strength parameter is preset usually, then a stable geotechnical structure is reduced to the limit state once according to the reduction ratio, then the safety factor of the initial state of the geotechnical structure relative to the limit state is calculated, the safety reserve of the initial state relative to the limit state is reflected, and the whole process evolution calculation problem of the safety factor along with the reduction path is rarely concerned. The calculation method of the invention considers the process correlation of parameter reduction, and can obtain the whole process evolution rule of the safety coefficient along with the reduction path and the weight of contribution of the mechanical parameters to maintaining the stability of the rock-soil structure in the whole reduction process. The degradation function is linked with time, and the residual life of the rock-soil structure in the service process can be predicted.
Thirdly, the time-lapse decay curve of the safety coefficient of the whole process of the service life of the tunnel obtained by the solving method can effectively provide a basis for determining the maintenance and reinforcement time of the operation tunnel and making and selecting the maintenance and reinforcement scheme.
And fourthly, the solving method provided by the invention is convenient and easy to implement, and actively promotes the progress of the safety quantitative evaluation technology in the field of tunnels and underground engineering.
Drawings
FIG. 1 is a flow chart of the operation of the present invention.
Detailed Description
The invention is described in further detail below with reference to the figures and the detailed description.
The method for calculating the safety coefficient of the multi-parameter unequal proportional reduction based on the energy principle is shown in figure 1 and comprises the following steps:
step 1: determining the boundary range, the geometric parameters and the material distribution characteristics of the geotechnical structure calculation model;
step 2: establishing a numerical calculation model, carrying out grid division, and determining a material constitutive model;
and step 3: determining initial key mechanical parameters related to the material and a degradation function thereof by adopting a mechanical test;
and 4, step 4: determining the reduction time of the mechanical parameters, and determining the reduction proportion and the reduction step length of the mechanical parameters according to the degradation function obtained in the step 3;
and 5: defining the limit state of the geotechnical structure and determining the instability criterion of the geotechnical structure;
step 6: performing parameter reduction to reduce the geotechnical structure to a limit state;
and 7: the contribution degree of different mechanical parameters for maintaining the stability of the rock-soil structure in the reduction process is used as the weighted value of the reduction coefficient of the mechanical parameters;
and 8: obtaining a safety coefficient calculation method of the multi-parameter unequal proportion reduction of the geotechnical structure by theoretical derivation according to the weighted values in the step 7;
and step 9: and (4) solving to obtain a safety coefficient reduction overall process evolution curve of the geotechnical structure considering the parameter reduction process correlation according to the safety coefficient calculation method in the step 8.
Further, the geotechnical structure is a side slope or a tunnel and underground engineering.
Further, the geotechnical structure is a non-support geotechnical engineering structure or a support geotechnical engineering structure.
Further, in the step 3, the materials comprise rock-soil mass, concrete and steel; the initial key mechanical parameters refer to deformation parameters and strength parameters; the deformation parameters are elastic modulus and Poisson ratio; the strength parameters are cohesive force and internal friction angle.
Further, step 4 specifically includes: determining reduction time of different mechanical parameters of the same strength material and reduction time of different strength materials; and determining the reduction proportion among different parameters and the reduction step length of each parameter according to the form or the degradation rate of the mechanical parameter degradation function.
Further, in the step 5, plastic region through, strain through, displacement mutation and energy mutation are selected as instability criteria.
Further, in step 7, the method using the contribution of different mechanical parameters to maintain the stability of the rock-soil structure in the reduction process as the weight value of the mechanical parameter reduction comprises:
in the formula (I), the compound is shown in the specification,
reducing the weight of the contribution of the jth mechanical parameter of the ith material to the variation of the dissipation energy of the geotechnical structure system;
the dissipation energy increment of the geotechnical structure system after the jth mechanical parameter reduction of the ith material in a certain reduction process is obtained; delta E d The dissipation energy increment of the rock-soil structure system after the reduction of all the mechanical parameters of all the materials in a certain reduction process is obtained; σ is the stress tensor,. epsilon e In order to be the tensor of elastic strain,
U total ═ σ: d epsilon, total strain energy; v is the volume of the reduction unit.
Further, in step 8, the method for calculating the safety coefficient of the multi-parameter unequal proportion reduction of the geotechnical structure comprises the following steps:
in the formula: FOS (k-1) is the comprehensive safety coefficient of the rock-soil structure in the state of k-1; SRF i j Is the reduction coefficient of the jth mechanical parameter of the ith material; n is the reduction times, l is the material quantity, and m is the mechanical parameter quantity; FOS (n) is the residual safety coefficient of the rock-soil structure after reducing for n times, and FOS (n) is more than or equal to 1.0; f (SRF) i j ) The method is characterized in that a harmonic mean value of the reduction coefficient represents a common action part of the reduction coefficient during non-equal proportional reduction, and reflects the influence of nonlinearity and correlation of the reduction parameter during common reduction on the comprehensive safety coefficient.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not intended to limit the present invention in any way, and all simple modifications, equivalent variations and modifications made to the above embodiments according to the technical spirit of the present invention are within the scope of the present invention.
Claims (3)
1. The method for calculating the safety coefficient of multi-parameter unequal proportion reduction based on the energy principle is characterized by comprising the following steps of:
step 1: determining the boundary range, the geometric parameters and the material distribution characteristics of the geotechnical structure calculation model;
and 2, step: establishing a numerical calculation model, carrying out grid division, and determining a material constitutive model;
and step 3: determining initial key mechanical parameters related to the material and a degradation function thereof by adopting a mechanical test;
the related materials comprise rock-soil mass, concrete and steel; the initial key mechanical parameters refer to deformation parameters and strength parameters; the deformation parameters are elastic modulus and Poisson ratio; the strength parameters are cohesive force and internal friction angle;
and 4, step 4: determining the reduction time of the mechanical parameters, and determining the reduction proportion and the reduction step length of the mechanical parameters according to the degradation function obtained in the step 3;
determining reduction time of different mechanical parameters of the same strength material and reduction time of different strength materials; determining reduction proportions among different parameters and reduction step length of each parameter according to the form or the degradation rate of a mechanical parameter degradation function;
and 5: defining the limit state of the geotechnical structure and determining the instability criterion of the geotechnical structure;
selecting plastic region through, strain through, displacement mutation and energy mutation as instability criterion;
and 6: performing parameter reduction to reduce the geotechnical structure to a limit state;
and 7: the contribution degree of different mechanical parameters for maintaining the stability of the rock-soil structure in the reduction process is used as the weighted value of the reduction coefficient of the mechanical parameters;
the method for taking the contribution degree of different mechanical parameters for maintaining the stability of the rock-soil structure in the reduction process as the weighted value of the mechanical parameter reduction comprises the following steps:
in the formula (I), the compound is shown in the specification,
reducing the weight of the contribution to the variation of the dissipated energy of the geotechnical structure system for the jth mechanical parameter of the ith material;
the dissipation energy increment of the geotechnical structure system after the jth mechanical parameter reduction of the ith material in a certain reduction process is obtained; delta E d The increment of the dissipated energy of the rock-soil structure system after the reduction of all the mechanical parameters of all the materials in a certain reduction process; σ is the stress tensor,. epsilon e In order to be the tensor of elastic strain,
is the total strain energy; v is the volume of the reduction unit;
and 8: obtaining a safety coefficient calculation method of the multi-parameter unequal proportion reduction of the rock-soil structure according to the weighted values in the step 7;
the method for calculating the safety coefficient of the multi-parameter unequal proportion reduction of the geotechnical structure comprises the following steps:
in the formula: FOS (k-1) is the comprehensive safety coefficient of the rock-soil structure in the state of k-1; SRF i j Is the reduction coefficient of the jth mechanical parameter of the ith material; n is the reduction times, l is the material quantity, and m is the mechanical parameter quantity; FOS (n) is the residual safety coefficient of the rock-soil structure after reducing for n times, and FOS (n) is more than or equal to 1.0; f (SRF) i j ) Representing a common action part of the reduction coefficients during non-equal-proportion reduction for a harmonic average value of the reduction coefficients, and reflecting the influence of nonlinearity and correlation of the reduction parameters during common reduction on the comprehensive safety coefficient;
and step 9: and (5) solving to obtain a safety coefficient reduction overall process evolution curve of the geotechnical structure considering the parameter reduction process correlation according to the safety coefficient calculation method in the step (8).
2. The method for calculating the safety coefficient of the multiparameter unequal proportion reduction according to claim 1, wherein the geotechnical structures are slopes or tunnels and underground engineering.
3. The energy-principle-based method for calculating the safety factor of multiparameter unequal proportion reduction according to claim 1, wherein the geotechnical structures are unsupported geotechnical structures or supported geotechnical structures.
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