CN112487675A - Slope reinforcement measure evaluation method based on uncoordinated model - Google Patents
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Abstract
The invention discloses a slope reinforcement measure evaluation method based on an uncoordinated model, which comprises the following steps of: 1) determining an object, establishing a discrete model, and inputting related data; 2) solving the local coordinates of the beam unit; 3) determining a displacement coordination relationship between the beam unit and the equal parameter unit; 4) establishing a system control equation, and performing interactive solution between the equal parameter units and the beam units; 5) post-processing the calculation result; 6) outputting a result; 7) and (4) calculating the strength of the reinforcing member according to the body type and the material parameters of the reinforcing member, and evaluating the effect of a reinforcing measure. The method can solve the problems of complex modeling, excessive grid quantity and low solving precision when the isoparametric unit is used for simulating the slope reinforcing member, can simplify the process of establishing the model for evaluating the slope reinforcing effect, reduces the requirement of the calculation precision on the grid density, and can directly calculate the internal force of the reinforcing member.
Description
Technical Field
The invention relates to the technical field of slope stability numerical analysis, in particular to a slope reinforcement measure evaluation method based on an uncoordinated model.
Background
The high slope is a natural or artificial structure commonly seen in civil engineering and hydraulic engineering. The stability of the slope is important during the operation of the project, and therefore the slope is usually reinforced with reinforcement members. The common reinforcing measures for high slopes include anti-slide piles, anchoring holes and other rod system members. When the slope reinforcing member is buried in a rock body, the boundary condition is complex, the slope reinforcing member can be subjected to acting forces such as axial force, tangential force, bending moment and the like, and when the reinforcing measure is evaluated, if the internal force of the reinforcing member can be directly obtained, the effect of the reinforcing measure can be more truly evaluated.
For example, the Chinese invention patent application (publication number: CN109117586A) discloses a bedding rock slope three-dimensional geological model establishment and stability evaluation method in 2019, the method constructs a slope three-dimensional geological model by means of three-dimensional geological modeling software through geological element expression, and carries out slope stability evaluation through a scientific and reasonable three-dimensional calculation model, compared with the existing specification, the calculation result obtained by adopting the method is more reasonable and reliable, and the engineering treatment cost can be saved; however, this method does not fully take into account the simulation of the reinforcement elements during the modeling, mainly for the slip of the slope itself.
The Chinese patent application (publication number: CN111310356A) discloses a reverse arch retaining wall stability evaluation method suitable for loess slope reinforcement in 2020, which comprises the following steps: establishing a slope stability analysis model under a rainfall condition; establishing a slope stability analysis model under a load condition; establishing a slope stability analysis model under a coupling condition; improving a slope stability analysis model under a coupling condition, increasing anchoring parameters, and establishing a slope stability analysis model under a reinforcement measure; establishing a reverse arch type retaining wall structure according to a slope stability analysis model under reinforcement measures; and analyzing the structure of the inverted arch retaining wall, and judging the reasonability of the slope stability analysis model under the reinforcement measure. Although the reinforcement measure is considered in the evaluation method, the reinforcement measure size and the prestress are just substituted into the slope stability evaluation model after reinforcement to obtain the slope stability evaluation coefficient after reinforcement, and the parameter values of the reinforcement such as axial force, shearing force and bending moment cannot be directly obtained.
In addition, when the reinforcing effect of the slope reinforcing measure is evaluated, the finite element method is widely applied as the most common numerical calculation method, and the grid division is carried out on a plurality of three-dimensional geological models by using the finite element method. However, because the slope structure is usually complex, and the difference between the body types of the reinforcing member and the rock mass is large, when the isoparametric unit model is subdivided, the slope structure and the shape of the reinforcing member are considered at the same time, so that the subdivision of the model mesh has high difficulty. The equal parameter units are used for simulating slender structures such as anti-slide piles and anchoring holes, the rigidity of a reinforcing member is easy to amplify, the precision achieved by utilizing the rod system structure calculation can be achieved only by needing fine enough grids, and the number of units of the whole model is very large from the viewpoint of coordination. Furthermore, when the isoparametric unit is used for simulating the reinforcing member, the axial force, the shearing force and the bending moment cannot be directly obtained, and the rod system unit can be directly calculated to obtain the axial force, the shearing force and the bending moment. However, when the equal parameter unit and the beam unit have the same solving system, the displacement modes of the equal parameter unit and the beam unit need to be coordinated and interactive solving is carried out.
Disclosure of Invention
The invention aims to provide a slope reinforcement measure evaluation method based on an uncoordinated model, which aims to simplify the establishment of the model and reduce the requirement of calculation precision on grid density while fully considering the simulation of rod system units such as reinforcement members.
In order to achieve the purpose, the invention adopts the technical scheme that:
a slope reinforcement measure evaluation method based on an uncoordinated model comprises the following steps:
step (1): determining an object, establishing a discrete model of the object, wherein the discrete model comprises isoparametric units and beam units, and inputting related data;
step (2): solving the local coordinates of the beam unit;
and (3): determining a displacement coordination relationship between the beam unit and the equal parameter unit;
and (4): establishing a system control equation, and performing interactive solution between the equal parameter units and the beam units;
and (5): post-processing the calculation result;
and (6): outputting a result;
and (7): and calculating the strength of the reinforcing member according to the body type and material parameters of the reinforcing member, and evaluating the effect of slope reinforcement measures.
The method for evaluating the slope reinforcement measures utilizes the displacement mode of the beam unit and according to the local coordinates of the beam unit nodes in the surrounding rock mass equal-parameter units, the relationship between the node displacement of the rotation of the rod system reinforcement members such as the anti-slide piles and the anchoring holes and the node displacement of the equal-parameter units is established, the relationship is further substituted into a finite element overall control equation to be solved, and the internal force of the members is output and evaluated. When the integral model is subjected to grid division, the soil body isoparametric units and the beam units of the reinforcing member can be respectively divided, coordination does not need to be considered, the difficulty of model establishment can be simplified, the requirement of calculation precision on grid density is reduced, and meanwhile, the accuracy and precision of final evaluation are not influenced.
Further, the objects comprise side slopes, bedrocks (rock masses, foundations and the like), reinforcing members and the like, the side slopes and the bedrocks are dispersed into equal parameter units, the reinforcing members are dispersed into beam units, and models of the equal parameter units and the beam units are respectively constructed and then combined to form the discrete models; the associated data includes load information, loading step size, constraint information, and material information, wherein the material information of the reinforcement member in turn includes geometric information, such as cross-sectional area and moment of inertia.
Further, in the step (2), the relationship between the node of the beam unit after being dispersed and the surrounding isoparametric unit is as follows: (1) the nodes are positioned in the equal parameter units and comprise nodes which are superposed, positioned on edges, surfaces or in the equal parameter units; (2) located outside the isoparametric unit; the position relation between the node of the beam unit and the equal parameter unit can be judged by utilizing the position of the local coordinate of the node of the beam unit in a certain equal parameter unit; the global coordinates of any point in the equal reference unit can be expressed by a local coordinate-related shape function as:
in the formula, Ni(xi, η, ζ), related to local coordinates; n is the number of nodes of the equal parameter unit;
when the overall coordinate of one point is known, solving the corresponding local coordinate of the point by a Newton iteration method; the local coordinate for the nth iteration is (xi, eta, zeta)nThe (n + 1) th iteration process is as follows:
further, in the step (3), the node displacement of the beam unit includes translational displacement and rotational displacement, and the node displacement of the equal parameter unit only has translational displacement; the adopted displacement mode does not consider the relative displacement between the pile and the soil;
the set of beam elements near the isoparametric element is represented by { B } ═ B {1 b2 … bm},
Wherein m is the total number of nodes of the beam unit, and for any node biCan find out the node biAll the equal parameter units { E }, are expressed as { E } ═ E }1 e2 … eiIn which eiIs the total number of equal parameter units containing the node;
let xyz be a global coordinate system, and the node biLocal coordinate system of associative unitIn (1)The transformation matrix between the local coordinates and the global coordinates is [ R ] for the axial direction of the beam unit]Expressed as:
correspondingly, any point in the global coordinate system is shifted toAnd { U } - { U v w }T(ii) a Definition biIn isoparametric unit ejThe local coordinate is (xi, eta, zeta)ejNode b according to the characteristics of the isoparametric unitiCan be displaced by unit ejThe node displacement interpolation is obtained, and the expression is as follows:
the node biIs expressed as an isoparametric unit ejIs a linear combination of the node displacements of (a),for the rotational displacement under the local coordinate system, the following relationship exists between the node rotational displacement of the beam unit and the node translational displacement of the equal parameter unit:
isoparametric unit ejZhong-ren point (xi, eta, zeta)ejCan utilize isoparametric unit ejThe node displacement is obtained by interpolation through a shape function, so that the following steps are provided:
the average translational displacement and the average rotational displacement of the nodes of the beam units are as follows:
when the system is solved as a whole,andthe two expressions are converted into an expression under a global coordinate system, and the expression is as follows:
further, in the step (4), the overall system control equation is KU ═ F, where K is an overall stiffness matrix, U is an overall node displacement array, and F is an overall node load array; displacement and load are interacted between the isoparametric unit and the beam unit; the load is mainly the self-weight load of the side slope and is dispersed to the equal parameter unit.
Further, in the step (5), the post-processing includes performing displacement field and stress field interpolation on the isoparametric unit model, and performing global-local coordinate system conversion on the internal force of the beam unit.
Further, in the step (6), the output results include an overall displacement field cloud picture output, an overall stress field cloud picture output, a reinforcement member shear force picture output, a reinforcement member axial force picture output and a reinforcement member bending moment picture output.
Further, in the step (7), the strength of the member is calculated by a material mechanics method; the evaluation of the effect of the reinforcement measures should compare the numerically calculated internal force of the component with the theoretical strength of the component.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a slope reinforcement measure evaluation method based on an uncoordinated model from the interactive calculation of displacement modes of a beam (rod system) unit and an equal parameter unit, wherein the relationship between node displacement of a rod system reinforcement member such as an anti-slide pile and an anchoring hole, which comprises a corner (rotation), and node displacement of the equal parameter unit is established by utilizing the displacement mode of the beam unit, and is further substituted into an overall control equation to solve, and the internal force of the member is output and evaluated; the method provided by the invention improves the calculation precision and reduces the difficulty of grid division, can respectively divide the soil body equal parameter units and the beam units of the reinforcement member when the integral model is subjected to grid division, does not need to consider harmony, can simplify the process of model establishment, reduces the requirement of the calculation precision on the grid density, can directly calculate the internal force of the reinforcement member, and compares the internal force with the theoretical strength.
Drawings
FIG. 1 is a flow chart of a method for evaluating a slope reinforcement measure based on an uncoordinated model according to the present invention;
FIG. 2 is a diagram of an iso-parametric unit model of a slope in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a reinforcement beam unit for a slope according to an embodiment of the present invention;
figure 4 is a shear diagram of a No. 6 stake of a particular embodiment of the invention;
FIG. 5 is a bending moment diagram of a No. 6 slide pile according to an embodiment of the present invention;
figure 6 is an axial diagram of a No. 6 friction pile in a specific embodiment of the invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it is obvious that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, a method for evaluating a slope reinforcement measure based on an uncoordinated model includes the following steps:
step (1): determining an object, establishing a discrete model of the object, wherein the discrete model comprises isoparametric units and beam units, and inputting related data;
step (2): solving the local coordinates of the beam unit;
and (3): determining a displacement coordination relationship between the beam unit and the equal parameter unit;
and (4): establishing a system control equation, and performing interactive solution between the equal parameter units and the beam units;
and (5): post-processing the calculation result;
and (6): outputting a result;
and (7): and calculating the strength of the reinforcing member according to the body type and material parameters of the reinforcing member, and evaluating the effect of slope reinforcement measures.
The following is described in detail according to a flow chart:
step one, determining a rock slope as an analysis object, wherein 6 deep slide-resistant piles and 7 anchoring holes are arranged in the rock slope; as shown in the attached figure 2, the slope rock mass is discretely set as a model of the isoparametric unit; as shown in fig. 3, the bar system reinforcing members are discretely set as a model of the beam unit;
and secondly, solving the local coordinates of the beam unit, wherein the overall coordinates of any point in the equal parameter unit can be expressed as the following shape function related to the local coordinates:
in the formula, Ni(xi, η, ζ), related to local coordinates; n is the number of equal parameter unit nodes; knowing the overall coordinate, and solving the corresponding local coordinate by a Newton iteration method; the local coordinate for the nth iteration is (xi, eta, zeta)nThe (n + 1) th iteration process is as follows:
thirdly, determining a displacement coordination relationship between the beam unit and the equal parameter unit; solving the translation displacement and the rotation displacement of the node under the global coordinate system:
and fourthly, establishing a system control equation, and interactively solving between the equal parameter unit and the beam unit. The overall system control equation is
KU=F
K is an integral rigidity matrix, U is an integral node displacement array, and F is an integral node load array; the displacement and the load are interacted between the equal parameter unit and the beam unit; the load is mainly the self-weight load of the side slope and is dispersed on the isoparametric unit.
And fifthly, interpolating a displacement field and a stress field of the slope isoparametric unit model, and performing integral-local coordinate system conversion on the internal force of the beam unit of the reinforcing member.
And sixthly, outputting results, namely outputting an overall displacement field cloud picture, outputting an overall stress field cloud picture, outputting a reinforcing member shear force picture, outputting a reinforcing member axial force picture and outputting a reinforcing member bending moment picture. When the method provided by the invention is used for simulating the slope reinforcing member, the internal force of the member can be directly obtained through theoretical calculation. Taking the number 6 slide-resistant pile as a typical representative, a shear diagram is shown in figure 4, a shaft diagram is shown in figure 5, and a bending moment diagram is shown in figure 6.
Seventhly, calculating the strength of the reinforcing member according to the body type and material parameters of the reinforcing member, and evaluating the effect of a reinforcing measure; and calculating the bearing capacity of the slide-resistant pile according to a material mechanics method, and comparing the calculation result with the calculation result of the invention to find that the internal force of the slide-resistant pile and the anchoring hole is less than the bearing capacity, so that the reinforcing member is in a safe state.
Through the steps, the calculation accuracy is improved, the difficulty of grid division is reduced, the soil body equal parameter units and the beam units of the reinforcement member are respectively divided when the integral model is subjected to grid division, coordination does not need to be considered, the process of model establishment can be simplified, the requirement of the calculation accuracy on grid density is reduced, the internal force of the reinforcement member can be directly calculated and obtained, and the internal force is compared with the theoretical strength.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (8)
1. A slope reinforcement measure evaluation method based on an uncoordinated model is characterized by comprising the following steps:
step (1): determining an object, establishing a discrete model of the object, wherein the discrete model comprises isoparametric units and beam units, and inputting related data;
step (2): solving the local coordinates of the beam unit;
and (3): determining a displacement coordination relationship between the beam unit and the equal parameter unit;
and (4): establishing a system control equation, and performing interactive solution between the equal parameter units and the beam units;
and (5): post-processing the calculation result;
and (6): outputting a result;
and (7): and calculating the strength of the reinforcing member according to the body type and material parameters of the reinforcing member, and evaluating the effect of slope reinforcement measures.
2. The method for evaluating the slope reinforcement measure based on the uncoordinated model according to claim 1, wherein the object comprises a slope, bedrock and a reinforcement member, the slope and the bedrock are discrete into the equal parameter units, the reinforcement member is discrete into beam units, and the discrete model is formed by respectively constructing models of the equal parameter units and the beam units and then combining the models; the associated data includes load information, loading step size, constraint information, and material information, wherein the material information of the reinforcement member in turn includes geometric information, such as cross-sectional area and moment of inertia.
3. The method for evaluating a slope strengthening measure based on an uncoordinated model according to claim 1, wherein in the step (2), the relationship between the nodes of the beam units after being discretized and the surrounding isoparametric units is as follows: (1) the nodes are positioned in the equal parameter units and comprise nodes which are superposed, positioned on edges, surfaces or in the equal parameter units; (2) located outside the isoparametric unit; the position relation between the node of the beam unit and the equal parameter unit can be judged by utilizing the position of the local coordinate of the node of the beam unit in a certain equal parameter unit; the global coordinates of any point in the equal reference unit can be expressed by a local coordinate-related shape function as:
in the formula, Ni(xi, η, ζ), related to local coordinates; n is the number of nodes of the equal parameter unit;
when the overall coordinate of one point is known, solving the corresponding local coordinate of the point by a Newton iteration method; the local coordinate for the nth iteration is (xi, eta, zeta)nThe (n + 1) th iteration process is as follows:
4. the method for evaluating the slope strengthening measure based on the uncoordinated model according to claim 1, wherein in the step (3), the node displacement of the beam unit comprises translational displacement and rotational displacement, and the node displacement of the equal parameter unit only comprises translational displacement;
the set of beam elements near the isoparametric element is represented by { B } ═ B {1 b2…bm},
Wherein m is the total number of nodes of the beam unit, and for any node biCan find out the node biAll the equal parameter units { E }, are expressed as { E } ═ E }1 e2…eiIn which eiIs the total number of equal parameter units containing the node;
let xyz be a global coordinate system, and the node biLocal coordinate system of associative unitIn (1)The transformation matrix between the local coordinates and the global coordinates is [ R ] for the axial direction of the beam unit]Expressed as:
correspondingly, any point under the global coordinate systemIs displaced byAnd { U } - { U v w }T(ii) a Definition biIn isoparametric unit ejThe local coordinate is (xi, eta, zeta)ejNode b according to the characteristics of the isoparametric unitiCan be displaced by unit ejThe node displacement interpolation is obtained, and the expression is as follows:
the node biIs expressed as an isoparametric unit ejIs a linear combination of the node displacements of (a),for the rotational displacement under the local coordinate system, the following relationship exists between the node rotational displacement of the beam unit and the node translational displacement of the equal parameter unit:
isoparametric unit ejZhong-ren point (xi, eta, zeta)ejCan utilize isoparametric unit ejThe node displacement is obtained by interpolation through a shape function, so that the following steps are provided:
the average translational displacement and the average rotational displacement of the nodes of the beam units are as follows:
when the system is solved as a whole,andthe two expressions are converted into an expression under a global coordinate system, and the expression is as follows:
5. the method for evaluating a slope strengthening measure based on an uncoordinated model according to claim 1, wherein in the step (4), the overall system control equation is KU ═ F, where K is an overall stiffness matrix, U is an overall node displacement array, and F is an overall node loading array; displacement and load are interacted between the isoparametric unit and the beam unit; the load is the self-weight load of the side slope and is dispersed to the equal parameter units.
6. The method for evaluating a slope strengthening measure based on an uncoordinated model according to claim 1, wherein in the step (5), the post-processing includes performing displacement field and stress field interpolation on the isoparametric unit model, and performing global-local coordinate system conversion on the internal force of the beam unit.
7. The method for evaluating a slope strengthening measure based on an uncoordinated model according to claim 1, wherein in the step (6), the output results comprise an overall displacement field cloud picture output, an overall stress field cloud picture output, a strengthening member shear force picture output, a strengthening member axial force picture output and a strengthening member bending moment picture output.
8. The non-coordinated model based slope reinforcement measure evaluation method according to claim 1, wherein in the step (7), the calculation member strength is calculated by a material mechanics method; the evaluation of the effect of the slope reinforcement measures should compare the numerically calculated internal force of the component with the theoretical strength of the component.
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CN111310356A (en) * | 2020-03-04 | 2020-06-19 | 山西水务集团建设投资有限公司 | Reverse-arch retaining wall stability evaluation method suitable for loess slope reinforcement |
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