CN117744219A - Active soil pressure calculation method and system considering rigidity of cantilever retaining wall - Google Patents
Active soil pressure calculation method and system considering rigidity of cantilever retaining wall Download PDFInfo
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Abstract
The invention relates to the technical field of civil engineering, in particular to an active soil pressure calculation method considering the rigidity of a cantilever retaining wall. The method comprises the following steps: determining retaining wall materials and section parameters, and obtaining soil physical and mechanical data; analyzing the correlation between the active soil pressure and the soil displacement according to the soil physical and mechanical data; obtaining a displacement-related active soil pressure calculation model according to the correlation; obtaining an active soil pressure distribution model according to the physical and mechanical data of the soil body and the acting effect of the rigidity of the retaining wall; and establishing a rigidity-related active soil pressure calculation model by combining the displacement-related active soil pressure calculation model and the active soil pressure distribution model. In order to calculate the soil pressure more accurately, the invention provides an active soil pressure calculation method considering the rigidity of the cantilever type retaining wall in consideration of the influence of the rigidity of the retaining wall on the soil pressure, so as to obtain a more accurate soil pressure calculation result.
Description
The invention relates to the technical field of civil engineering, in particular to an active soil pressure calculation method and system considering the rigidity of a cantilever retaining wall.
Background
At present, in the calculation process of the active soil pressure of the cantilever type soil retaining structure, the classical soil pressure theory is generally used for solving the active soil pressure. However, the classical soil pressure theory ignores the influence of the rigidity of the retaining wall on the soil pressure, the classical soil pressure method assumes that the retaining wall is completely rigid, and the soil body reaches a limit balance state, so that the calculated soil pressure is in linear distribution, the value of the active soil pressure is smaller, and the calculation result of the classical soil pressure theory is obviously different from the situation in the actual engineering.
In practice, the cantilevered retaining wall may flex, resulting in a redistribution of active earth pressure. Because the displacement variation of the retaining wall is small, the soil body is usually in an unlimited state, and the rigidity of the retaining wall can influence the displacement of the soil body, thereby influencing the active soil pressure on the retaining wall. Therefore, establishing an active soil pressure calculation formula related to the stiffness of the cantilever retaining wall to obtain a soil pressure calculation result close to the actual working condition is an important problem to be solved in the current engineering.
Disclosure of Invention
Aiming at the defects of the existing method and the defects of practical application, the invention obtains the soil pressure calculation result which is closer to the practical working condition in order to make up the defects of the classical soil pressure theory, establishes an active soil pressure calculation model in consideration of the rigidity of the cantilever retaining wall, and obtains more accurate soil pressure calculation result, thereby optimizing the design and improving the safety and stability of the engineering. The first aspect of the invention provides an active soil pressure calculation method considering the rigidity of a cantilever type retaining wall, which comprises the following steps of determining retaining wall materials and section parameters and obtaining physical and mechanical data of soil; analyzing the correlation between the active soil pressure and the soil displacement according to the soil physical and mechanical data; obtaining a displacement-related active soil pressure calculation model according to the correlation; obtaining an active soil pressure distribution model according to the physical and mechanical data of the soil body and the acting effect of the rigidity of the retaining wall; and establishing a rigidity-related active soil pressure calculation model by combining the displacement-related active soil pressure calculation model and the active soil pressure distribution model. According to the method, the effect of the physical and mechanical data of the soil body and the rigidity of the retaining wall are combined, the rigidity-related active soil pressure distribution model is built, the influence of various factors on the active soil pressure is comprehensively considered, the accuracy and the reliability of a calculation result are improved, and the actual working condition situation is further accurately reflected.
Optionally, the analyzing the correlation between the active soil pressure and the soil displacement according to the soil physical and mechanical data includes: presetting active soil pressure and soil displacement to be linearly related according to the soil physical and mechanical data; constructing a correlation analysis model of active soil pressure and soil displacement based on the linear correlation; and analyzing the correlation of the active soil pressure and the soil displacement through the correlation analysis model. The invention presets that the active soil pressure and the soil displacement are in linear correlation, builds a correlation analysis model of the active soil pressure and the soil displacement based on the linear correlation, can better reveal the internal rule between the active soil pressure and the soil displacement, simplifies the analysis flow, expands the practical application range, ensures that the invention is easier to be applied in practical engineering practice, and provides effective guidance for the engineering practice.
Optionally, the correlation analysis model of the active soil pressure and the soil displacement satisfies the following relationship:
wherein k is a Represents the relativity of soil pressure and soil displacement, K represents the linear coefficient of active soil pressure, S represents soil displacement, K 0 Representing the coefficient of static soil pressure on the retaining wall,S a represents the active limit displacement value, K of the soil body a Representing the coulomb initiative soil pressure coefficient. The invention introduces the related coefficient to describe the relation between the active soil pressure and the soil displacement more accurately, uses the mathematical model to analyze the relativity, can simplify the calculation process between the active soil pressure and the soil displacement, and improves the calculation efficiency.
Optionally, the obtaining a displacement-related active soil pressure calculation model according to the correlation includes: constructing a displacement-related active soil pressure calculation model of any depth of the retaining wall according to the correlation; the displacement-related active soil pressure calculation model meets the following relation:
wherein P is a Represents the active soil pressure, K related to displacement at any depth of the retaining wall a Represents the coulomb initiative soil pressure coefficient, K 0 Representing the static soil pressure coefficient on the retaining wall, S representing the soil displacement, z representing the depth of the soil, S a Represents the active limit displacement value of the soil body,indicating the average weight of the earth fill behind the retaining wall. The displacement-related active soil pressure model considers the influence of various factors on the active soil pressure, and can more accurately describe the relation between the active soil pressure and the soil displacement so as to improve the accuracy of a calculation result.
Optionally, the obtaining the active soil pressure distribution model according to the physical and mechanical data of the soil body and the acting effect of the rigidity of the retaining wall includes: analyzing the acting effect of the rigidity of the retaining wall and obtaining the displacement condition of the rigidity of the cantilever retaining wall; and obtaining a displacement curve function of the cantilever type retaining wall according to the displacement condition. According to the invention, the effect of the rigidity of the retaining wall is analyzed, the displacement condition of the rigidity of the cantilever retaining wall is obtained, and then the displacement curve function is obtained according to the displacement condition, so that more accurate and comprehensive guidance can be provided for engineering practice, and the optimization design and the improvement of engineering efficiency are facilitated.
Optionally, the displacement curve function satisfies the following relationship:
wherein s (z) represents the displacement curve of the cantilever type retaining wall, z represents the depth of soil body, L represents the height of the retaining wall, A represents the rigidity correlation coefficient of the cantilever type retaining wall, s max Representing the displacement value of the top of the cantilever type retaining wall. The invention considers the relation between the soil depth and the retaining wall height, introduces the parameters such as the rigidity related coefficient and the like, is beneficial to more accurately predicting and controlling the behavior of the retaining wall, and provides guidance for engineering practice.
Optionally, the obtaining the active soil pressure distribution model according to the physical and mechanical data of the soil body and the acting effect of the rigidity of the retaining wall includes: constructing an active soil pressure distribution model according to the displacement curve function and the soil physical and mechanical data; the active soil pressure distribution model meets the following relations:
wherein P is a (z) represents the distribution result of the active soil pressure, C 1 The quadratic coefficient of the active soil pressure distribution function is represented, z represents the depth of soil body, L represents the height of retaining wall, and C 2 The first order coefficients representing the active earth pressure distribution function,indicating the average weight of the earth fill behind the retaining wall. According to the invention, the distribution condition of the active soil pressure is calculated through the mathematical model, so that the distribution results of the active soil pressure at different depths of the retaining wall can be obtained quickly, the efficiency of engineering design can be improved, and quick and accurate decision support can be provided for engineering practice.
Optionally, the establishing the stiffness-related active soil pressure calculation model in combination with the displacement-related active soil pressure calculation model and the active soil pressure distribution model includes: setting displacement conditions of the rigidity of the cantilever retaining wall, wherein the displacement conditions comprise a first displacement condition and a second displacement condition; establishing an active soil pressure calculation model of a first model based on the first displacement condition, the displacement-related active soil pressure calculation model and the active soil pressure distribution model; and establishing an active soil pressure calculation model of a second model based on the second displacement condition, the displacement-related active soil pressure calculation model and the active soil pressure distribution model. The invention combines the displacement related active soil pressure calculation model and the active soil pressure distribution model, can calculate the active soil pressure more accurately, is beneficial to improving the reliability of calculation results, and provides more accurate data support for engineering practice
Optionally, the active soil pressure calculation model of the first model satisfies the following relationship:
wherein P is a1 (z) represents the first active soil pressure, K, related to the stiffness 0 Representing the static soil pressure coefficient, K, on the retaining wall a Represents the coulomb initiative soil pressure coefficient, S a Representing the active limit displacement value s of the soil body max Represents the displacement value of the top of the cantilever type retaining wall, L represents the height of the retaining wall, A represents the rigidity-related coefficient of the cantilever type retaining wall,the average gravity of the earth filled behind the retaining wall is shown, and z represents the depth of the earth.
The active soil pressure calculation model of the second model meets the following relation:
wherein P is a2 (z) represents a stiffness-dependent second active earth pressure, K a Representing the coulomb initiative earth pressure coefficient,represents the average gravity of the earth filled behind the retaining wall, z represents the depth of the earth, z a ' represents critical height, K of limit state of soil body 0 Representing the static soil pressure coefficient on the retaining wall, S a Representing the active limit displacement value s of the soil body max The displacement value of the top of the cantilever type retaining wall is represented by L, the height of the retaining wall is represented by L, and the stiffness-related coefficient of the cantilever type retaining wall is represented by A.
In a second aspect, the present invention also provides an active soil pressure calculation system taking into account the stiffness of a cantilever type retaining wall, capable of efficiently performing the active soil pressure calculation method taking into account the stiffness of a cantilever type retaining wall, the system comprising an input device, a processor, an output device and a memory, wherein the input device, the processor, the output device and the memory are connected to each other, the memory comprises a computer readable storage medium according to the first aspect of the present invention, the memory is used for storing a computer program, the computer program comprises program instructions, and the processor is configured to call the program instructions. The system provided by the invention has compact structure and strong applicability, and greatly improves the operation efficiency.
Drawings
FIG. 1 is a flow chart of an active soil pressure calculation method taking into account the stiffness of a cantilever retaining wall according to the present invention;
FIG. 2 is a schematic diagram of the relationship between active soil pressure and soil displacement for filtering stiffness of a cantilever retaining wall according to the present invention;
FIG. 3 is a schematic view of a first displacement scenario taking into account the stiffness of a cantilevered retaining wall according to the present invention;
FIG. 4 is a schematic view of a second displacement scenario taking into account the stiffness of the cantilevered retaining wall of the present invention;
FIG. 5 is a schematic view of the approximate differential deflection of the present invention taking into account the stiffness of the cantilever retaining wall;
fig. 6 is a schematic structural view of an active soil pressure calculation system considering stiffness of a cantilever type retaining wall according to the present invention.
Detailed Description
Specific embodiments of the invention will be described in detail below, it being noted that the embodiments described herein are for illustration only and are not intended to limit the invention. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be apparent to one of ordinary skill in the art that: no such specific details are necessary to practice the invention. In other instances, well-known circuits, software, or methods have not been described in detail in order not to obscure the invention.
Throughout the specification, references to "one embodiment," "an embodiment," "one example," or "an example" mean: a particular feature, structure, or characteristic described in connection with the embodiment or example is included within at least one embodiment of the invention. Thus, the appearances of the phrases "in one embodiment," "in an embodiment," "one example," or "an example" in various places throughout this specification are not necessarily all referring to the same embodiment or example. Furthermore, the particular features, structures, or characteristics may be combined in any suitable combination and/or sub-combination in one or more embodiments or examples. Moreover, those of ordinary skill in the art will appreciate that the illustrations provided herein are for illustrative purposes and that the illustrations are not necessarily drawn to scale.
Referring to fig. 1, in order to make up for the defect of classical soil pressure theory, the invention combines the rigidity of the cantilever type retaining wall, establishes an active soil pressure calculation model with related rigidity, can better predict and control the behavior of the retaining wall, and provides more accurate and reliable decision support for engineering practice. The invention provides an active soil pressure calculation method considering the rigidity of a cantilever type retaining wall, which comprises the following steps of:
S1, determining retaining wall materials and section parameters, and obtaining soil physical and mechanical data, wherein the concrete implementation steps and related contents are as follows:
first, a retaining wall material is determined. The retaining wall material needs to be determined by comprehensively considering various factors, including but not limited to engineering requirements, design specifications, material properties, construction conditions, engineering budget, environmental factors and the like, further, the requirements of different retaining wall materials on the construction conditions are different, and the environment where the retaining wall is located can influence the selection of the retaining wall material. Only by comprehensively considering various factors, the most suitable retaining wall material can be selected, and the safety and stability of the retaining wall are ensured.
Then, a cross-sectional parameter associated with the retaining wall is determined. Since the section parameters of the retaining wall are adapted to the soil pressure distribution, the proper section shape and size are formulated according to the soil pressure distribution condition so as to better disperse and transfer the soil pressure. On the other hand, different materials have different mechanical properties, and the section parameters need to be selected according to the properties of the materials. For example, concrete and reinforced concrete have high compressive strength, and are suitable for rectangular or trapezoidal cross sections; the wood has better flexibility and is suitable for adopting triangular or other curve-shaped cross sections. In addition, the cross-section parameters related to the retaining wall also need to be considered, and other factors including but not limited to environmental factors, load conditions, geological conditions and the like can be considered, so that the accuracy and the reliability of the cross-section parameters of the retaining wall can be ensured only by comprehensively considering the interference of other factors.
Finally, the physical and mechanical data of the soil body are obtained. The on-site investigation is a key step for acquiring physical and mechanical data of the soil body, and can intuitively understand the geological conditions, physical properties and mechanical properties of the soil body through the on-site investigation, so that an important reference basis is provided for the subsequent active soil pressure analysis; moreover, acquiring a soil sample is an important link for acquiring physical and mechanical data of a soil body, and a representative soil sample is required to be selected and processed to acquire related data of the physical and mechanical data of the soil body; the obtained soil physical and mechanical data needs to be analyzed and preprocessed in detail, useful information can be extracted, and important basis is provided for retaining wall pressure calculation and soil displacement analysis.
In the embodiment, when determining the retaining wall material and the section parameters, the influence of factors such as engineering geological conditions, load conditions, environmental conditions and the like is considered; the data are preprocessed and stored when the physical and mechanical data of the soil body are obtained, the above selection condition is only one selectable condition of the invention, and in other embodiments, the material determination method and the data acquisition mode can be flexibly selected according to actual requirements so as to ensure the accuracy and the reliability of related data.
S2, analyzing the correlation between the active soil pressure and the soil displacement according to the soil physical and mechanical data, wherein the concrete implementation steps and the related contents are as follows:
in the embodiment, based on the physical and mechanical parameters of the soil body, the linear correlation between the active soil pressure and the soil body displacement is preset, then a correlation analysis model of the active soil pressure and the soil body displacement is constructed according to the linear correlation conditions, and the correlation of the active soil pressure and the soil body displacement can be rapidly analyzed by using the correlation analysis model.
Referring to fig. 2, where S represents a stationary state of the retaining wall, a represents an effective limit state of the retaining wall, and the relationship between the active soil pressure and the soil displacement is linearly related, it can be represented by a straight line, which is represented by a broken line in fig. 1, and it is known that the active soil pressure increases with the increase of the soil displacement.
Based on fig. 2, the correlation analysis model of the active soil pressure and the soil displacement can be known, and the following relationship is satisfied:
wherein k is a Represents the relativity of soil pressure and soil displacement, K represents the linear coefficient of active soil pressure, S represents soil displacement, K 0 Representing the static soil pressure coefficient on the retaining wall, S a Represents the active limit displacement value, K of the soil body a Representing the coulomb initiative soil pressure coefficient.
The correlation between the soil pressure and the soil displacement refers to the relationship between the displacement of the soil and the soil pressure under the action of the soil pressure, and if the soil pressure and the soil displacement are in a linear relationship, namely, along with the increase of the soil pressure, the soil displacement can be correspondingly increased, so that the method can be used for predicting and controlling the displacement condition of the soil.
The linear coefficient of the active soil pressure refers to that under the action of the active soil pressure, the relation between the soil displacement and the soil pressure can be represented by a straight line, the slope of the straight line is the linear coefficient of the active soil pressure, the coefficient can be used for describing the linear relation between the active soil pressure and the soil displacement, and the linear coefficient has important significance for predicting and controlling the soil displacement.
Soil displacement refers to the change of the soil in the space position under the action of external force, and is usually represented as horizontal displacement, vertical displacement or both, and in practical engineering application, monitoring and analysis of the soil displacement are very important, and the soil displacement can influence the stability and safety of the engineering.
The static soil pressure coefficient of the retaining wall refers to the pressure of the soil to the wall when the retaining wall is static and the soil body is in an elastic balance state. Further, in this embodiment, the static soil pressure coefficient on the retaining wall is analyzed, and the Jaky static soil pressure coefficient calculation formula commonly used in engineering is adopted:
Wherein K is 0 Representing the coefficient of static soil pressure on the retaining wall,indicating the internal friction angle of the earth-filled behind the retaining wall. The internal friction angle of the earth filling behind the retaining wall refers to the friction resistance between earth filling particles, and is one of the characteristics of resisting shear damage of the soil body. The magnitude of the internal friction angle is related to factors such as the shape, size, surface condition, water content of the filler particles.
When the retaining wall material is selected or designed, the soil pressure acting on the retaining wall needs to be determined, and further parameters such as the material, the reinforcing bars, the section size and the like of the retaining wall are reasonably determined, so that the stability and the safety of the retaining wall are ensured, and the actual application value of the retaining wall rigidity active soil pressure calculation method is facilitated.
The active limit displacement value of the soil body refers to the displacement of the soil body when the soil body breaks the wedge body completely in the process of deviating from the soil body displacement of the retaining wall. The active limit displacement value may be affected by a variety of factors including, but not limited to, the physical and mechanical properties of the soil body, stress states, boundary conditions, and the like.
The coulomb active soil pressure coefficient refers to an active soil pressure coefficient calculated according to the coulomb soil pressure theory. The coulomb soil pressure is based on the equilibrium condition of the force system when the earth body is in the limit equilibrium state behind the wall, and the soil pressure calculation theory is derived from the static equilibrium condition of the wedge body when a sliding body wedge body is formed. The soil pressure coefficient obtained by the equilibrium theory is called an active soil pressure coefficient.
The coulomb initiative soil pressure coefficient satisfies the following relationship:
wherein K is a Representing the coulomb initiative earth pressure coefficient,the internal friction angle of the filled soil behind the retaining wall is shown, and delta is the friction angle between the retaining wall and the soil body.
According to the internal friction angle of the rear filling soil of the retaining wall, the friction angle between the retaining wall and the soil body obtains the active soil pressure coefficient of the storage, and the soil pressure born by the retaining wall can be rapidly determined, so that corresponding measures are taken to improve the stability of the retaining wall. The stability of the retaining wall can be improved by increasing the parameters such as the height, the width and the like of the retaining wall or adopting more proper filling materials.
The coulomb active soil pressure coefficient reflects the resistance of the soil body under the action of the active soil pressure, and on the other hand, when the soil body is acted by the active soil pressure, the stress distribution and the deformation can be generated in the soil body, so that the displacement of the soil body is caused, and the correlation between the active soil pressure and the displacement of the soil body can be more accurately analyzed based on the coulomb active soil pressure coefficient.
Furthermore, in this embodiment, the correlation between the active soil pressure and the soil displacement is analyzed according to various parameters, which is only an optional condition of the present invention, and in other embodiments or some embodiments, the correlation may be adjusted according to engineering requirements and actual conditions, so as to ensure the accuracy of the analysis result of the soil physical and mechanical data.
S3, obtaining a displacement-related active soil pressure calculation model according to the correlation between the active soil pressure and the soil displacement, wherein the specific implementation steps and the related contents are as follows:
in the embodiment, according to the physical and mechanical data of the soil body and the correlation between the active soil pressure and the soil body displacement, an active soil pressure calculation model related to the displacement at any depth of the retaining wall can be constructed.
The displacement-related active soil pressure calculation model meets the following relation:
wherein P is a Represents the active soil pressure, K related to displacement at any depth of the retaining wall a Represents the coulomb initiative soil pressure coefficient, K 0 Representing the static soil pressure coefficient on the retaining wall, S representing the soil displacement, z representing the depth of the soil, S a Represents the active limit displacement value of the soil body,indicating the average weight of the earth fill behind the retaining wall.
The active soil pressure related to the displacement of the retaining wall at any depth refers to the active soil pressure generated by the displacement of the soil body at any depth of the retaining wall, the active soil pressure is closely related to the displacement of the soil body, and when the soil body is displaced, the active soil pressure is also changed.
The depth of the soil body refers to the distance from the earth's surface to a certain depth in the ground, i.e. the dimension of the soil body in the vertical direction. The depth of the soil body determines the distribution condition of the soil pressure born by the retaining wall, and the soil pressure can be gradually increased along with the increase of the depth of the soil body, so that larger acting force is generated on the retaining wall due to the increase of the weight and the lateral pressure of the soil body.
The average weight of the earth-filled soil behind the retaining structure refers to the average volume weight of the earth-filled soil, the value of the average weight directly reflects the density of the earth-filled soil, and the average weight of the earth-filled soil is an important parameter in the process of designing and actually using the retaining wall and directly influences the soil pressure on the retaining wall.
In the embodiment, the active soil pressure related to displacement at any depth of the retaining wall is analyzed by combining a plurality of parameters, so that the magnitude of the active soil pressure can be obtained more accurately, and further data support is provided for a later rigidity related active pressure calculation method.
Furthermore, in this embodiment, an active soil pressure model related to displacement at any depth of the retaining wall is built based on the soil physical and mechanical data, and the algorithm design method of this embodiment is widely applied to other related fields, and in one or some other embodiments, a similar model building method may be adopted, so as to further realize practical application value of related mathematical models.
S4, obtaining an active soil pressure distribution model according to the physical and mechanical data of the soil body and the action effect of the rigidity of the retaining wall, wherein the concrete implementation steps and the related contents are as follows:
the effect of the rigidity of the retaining wall is analyzed, and the displacement condition of the rigidity of the cantilever retaining wall is obtained, and the concrete contents are as follows:
In this embodiment, the displacement mode of the stiffness of the cantilever retaining wall is simplified, and two displacement situations can be approximately obtained: the first displacement condition is that the displacement value of the top of the cantilever retaining wall is smaller than or equal to the active limit displacement value; the first displacement condition is that the displacement value of the top of the cantilever type retaining wall is larger than the active limit displacement value.
In an alternative embodiment, when the cantilevered retaining wall top displacement value is less thanWhen the active limit displacement value is equal to the active limit displacement value, please refer to fig. 3, wherein X represents the displacement of the retaining wall, Z represents the depth of the retaining wall, L represents the height of the retaining wall, S a Representing the active limit displacement value s of the soil body max Representing the displacement value of the top of the cantilever type retaining wall.
In another alternative embodiment, when the cantilever type retaining wall top displacement value is greater than the active limit displacement value, please refer to fig. 4, wherein X represents the displacement of the retaining wall, Z represents the depth of the retaining wall, L represents the height of the retaining wall, S a Representing the active limit displacement value s of the soil body max Representing the displacement value of the top of the cantilever type retaining wall.
In this embodiment, the curve change diagrams shown in fig. 3 and fig. 4 are only an alternative schematic diagram, and do not represent the actual deformation situation of the retaining wall, and in order to more accurately understand and describe the curve deformation situation of the retaining wall, extensive analysis and research are required, and verification and solution are performed by using related formulas.
In an alternative embodiment, the deformation of the retaining wall is simplified in order to solve the displacement of the cantilevered retaining wall. In the embodiment it is assumed that the bottom of the cantilever retaining wall is completely fixed, so the bottom displacement is directly regarded as zero. In addition, the deformation between the retaining wall and the filling soil is completely coordinated, which means that the retaining wall structure and the soil body cannot be separated in the construction and operation processes. The simplified model can reduce the calculation amount and improve the calculation efficiency, and for a complex retaining wall structure, if a detailed finite element analysis or other advanced numerical methods are adopted, the calculation process can be very time-consuming, and the simplified model of the embodiment can provide a quick approximate solution to meet the time requirement in engineering.
Common cantilever type retaining wall structures, including but not limited to cantilever type retaining walls, since the cantilever type retaining wall structure generally needs to ensure stability of a wall body through the embedment of a bottom plate and the soil covered on the bottom plate, a wall bottom can be regarded as a fixed end with almost no displacement, which helps to simplify an analysis process.
For the problem of deformation coordination between the cantilever type retaining wall and the filled earth, it can be assumed that the contact between them is continuous, and the compressive deformation and lateral displacement of the filled earth are limited by the cantilever type retaining wall under the self-weight of the filled earth, so that the coordination between the cantilever type retaining wall and the filled earth can be ensured.
In this embodiment, by considering the lateral rigidity of the cantilever retaining wall, the deformation coordination with the filling soil, and the simplification to the plane strain problem, only one optional condition of the present invention is considered, and in other or other embodiments, the retaining wall may be replaced according to engineering requirements and retaining wall, so as to simplify the solving process of the displacement situation of the retaining wall.
The displacement curve function of the cantilever retaining wall is obtained according to the displacement conditions shown in fig. 3 and 4, and is implemented as follows:
in the embodiment, the cantilever retaining wall is simplified into the cantilever beam with the bottom fixedly connected, deflection analysis is carried out on the cantilever beam, so that displacement and deformation conditions of the cantilever retaining wall can be described more accurately, response and stability of the retaining wall under different load conditions can be further studied by establishing a deflection approximate differential equation, and the deflection approximate differential equation meets the following relation:
EIS″(z)＝-M(z)
Where S' (z) represents the second derivative of the deflection of the cantilevered retaining wall, EI represents the flexural stiffness of the retaining wall, and z represents the depth of the soil mass. The deflection approximate differential equation is expressed in the form of a mathematical formula, so that the structure and parameters of the equation can be directly displayed, and mathematical deduction and calculation are facilitated. According to the displacement-related active soil pressure calculation model, when S>S a Under the condition of (1), the active soil pressure and the soil displacement show linear distributionThe method comprises the steps of carrying out a first treatment on the surface of the S is less than or equal to S a In order to obtain more intuitively relevant data and expression of the deflection approximate differential equation, please refer to fig. 5, wherein P represents the active soil pressure distribution of the cantilever retaining wall.
The deflection approximation differential equation based on the cantilever type retaining wall in the present embodiment describes the relationship between the displacement and the load pressure, and the displacement curve function satisfies the following relationship:
wherein s (z) represents the displacement curve of the cantilever type retaining wall, z represents the depth of soil body, L represents the height of the retaining wall, A represents the correlation coefficient of the rigidity of the cantilever type retaining wall, and s max Representing the displacement value of the top of the cantilever type retaining wall.
The displacement curve of the cantilever type retaining wall refers to the deformation condition of the retaining wall after being stressed, and can be plotted as a displacement curve according to displacement, force and deformation as coordinate axes. The displacement curve can reflect the displacement change condition of the retaining wall under different load pressures, so that the stability and safety of the retaining wall can be evaluated. For a cantilevered retaining wall, the displacement curve generally includes a horizontal displacement curve and a vertical displacement curve. The horizontal displacement curve represents the displacement variation of the retaining wall in the horizontal direction, and the vertical displacement curve represents the displacement variation of the retaining wall in the vertical direction.
The stiffness related coefficient of the cantilever type retaining wall refers to a parameter that the stiffness of the retaining wall changes along with the load pressure in the stress process, and the coefficient can reflect the relation between the stiffness of the retaining wall and the load pressure and can also be used for predicting the displacement change of the retaining wall under different pressures. If the rigidity correlation coefficient is larger, the rigidity of the retaining wall is smaller, and the nonlinearity degree of the displacement curve is stronger; if the stiffness correlation coefficient is smaller, the stiffness of the retaining wall is larger, and the displacement curve is more approximate to linear distribution.
The displacement value of the top of the cantilever type retaining wall refers to the vertical displacement of the top of the retaining wall after being stressed. This displacement value can be obtained by measuring the change in distance between the top of the retaining wall and the reference point. In the cantilever type retaining wall structure, the top displacement value is an important parameter, which can reflect the stability and safety of the retaining wall, and if the top displacement value is too large, the retaining wall may be unstable, thereby causing a safety problem. In another aspect, the displacement value of the top of the cantilever type retaining wall is related to the shape and slope of the displacement curve, when the retaining wall is subjected to external pressure, the rigidity of the retaining wall changes, so that each part of the retaining wall is displaced, the displacement value of the top reflects the deformation condition of the top of the retaining wall, and the shape of the displacement curve describes the displacement distribution and change rule of the whole retaining wall.
In this embodiment, the specific content of the displacement curve function construction is as follows:
according to the displacement curve function and the soil physical and mechanical data, an active soil pressure distribution model is constructed, and further, in the embodiment, the distribution form of the active soil pressure is assumed to be fitted through a polynomial function with more than two times, so that the distribution condition and the change rule of the active soil pressure on the retaining wall can be described more accurately. In addition, the polynomial function has better fitting capacity and adaptability, and can better describe complex soil pressure distribution forms.
The active soil pressure distribution model meets the following relation:
wherein P is a (z) represents the distribution result of the active soil pressure, C 1 The quadratic coefficient of the active soil pressure distribution function is represented, z represents the depth of soil body, L represents the height of retaining wall, and C 2 The first order coefficients representing the active earth pressure distribution function,indicating the average weight of the earth fill behind the retaining wall.
The distribution result of the active soil pressure refers to the distribution of the active soil pressure on the retaining wall.
The relation number of the active soil pressure distribution refers to a correlation coefficient between the distribution of the active soil pressure on the retaining wall and factors such as wall geometry, soil properties and the like, and is used for describing the distribution rule of the active soil pressure on the retaining wall and the influence degree of different factors on the active soil pressure distribution. By using the active soil pressure distribution correlation coefficient, it is possible to calculate the active soil pressure more accurately and guide the design and optimization of the retaining wall.
The depth of the soil body refers to the thickness of the soil layer from the surface layer to a certain depth of the ground, that is, the vertical distance from a certain point in the soil body to the soil surface. In practical engineering, the depth of soil body is an important parameter, and has important significance for calculating the dead weight stress of the soil, determining the embedded fixed depth, evaluating the ground stress condition and the like.
The height of the retaining wall refers to the vertical distance from the top of the retaining wall to the bottom surface of the foundation, i.e., the height of the retaining wall. The height of the retaining wall is determined according to the design and actual requirements of the retaining wall, and the factors such as stability and load of the retaining wall are required to be comprehensively considered for reasonable design and construction.
Next, according to the above-described dynamic soil pressure distribution model, the magnitude of the resultant force of the soil pressure acting on the soil retaining structure and the position of the point of action of the resultant force can be deduced. The active soil pressure distribution model is combined with the geometric shape and the stress condition of the soil retaining structure, so that the magnitude and the action point of the resultant force of the soil pressure can be determined, and further the strength analysis and the stability evaluation of the soil retaining structure are carried out.
In this embodiment, the resultant force of the soil pressure satisfies the following relationship:
wherein E is α (z) represents the resultant force of the soil pressure, z represents the depth of the soil body, L represents the height of the retaining wall, and P a (z) shows the distribution result of the active soil pressure.
Further, according to the moving soil pressure distribution model, the resultant force of the soil pressure satisfies the following relationship:
wherein E is α (z) represents the resultant force of the soil pressure, C 1 A quadratic coefficient representing an active soil pressure distribution function, z represents the depth of soil body, C 2 The first order coefficients representing the active earth pressure distribution function,the average gravity of the earth fill behind the retaining wall is shown, and L is the height of the retaining wall.
In this embodiment, the action point of the soil pressure resultant force satisfies the following relationship:
wherein Z is α Represents the action point of the soil pressure, L represents the height of the retaining wall, z represents the depth of soil mass, and P a (z) shows the distribution result of the active soil pressure.
Further, according to the above-described dynamic soil pressure distribution model, the soil pressure resultant force action points satisfy the following relationship:
wherein Z is α Indicating the action point of the soil pressure and the pressure combination force C 1 A quadratic coefficient representing an active soil pressure distribution function, z represents the depth of soil body, C 2 The first order coefficient representing the active soil pressure distribution function, L representing the height of the retaining wall.
Then, based on the magnitude of the resultant force of the earth pressure on the retaining wall structure and the point of action, the equation of bending moment of the retaining wall in the depth direction can be further deduced. Based on the bending moment distribution conditions of the retaining wall structure at different depth positions can be described, and the bending effect of the soil pressure on the retaining wall is reflected.
In this embodiment, the equation of bending moment of the retaining wall in the depth direction satisfies the following relationship:
M(z)＝E α ×Z α
wherein M (z) represents a bending moment of the retaining wall in the depth direction, E α (Z) represents the resultant force of the soil pressure, Z α Indicating the point of action of the earth pressure force.
Further, the correlation function of the resultant force of the soil pressure and the action point of the resultant force of the soil pressure is carried in, and the bending moment equation of the retaining wall along the depth direction at this time satisfies the following relation:
wherein M (z) represents a bending moment of the retaining wall in the depth direction, C 1 The quadratic coefficient of the active soil pressure distribution function, C 2 The first order coefficients representing the active earth pressure distribution function,the average gravity of the earth fill behind the retaining wall is shown, and L is the height of the retaining wall.
In this embodiment, the integral operation will also be performed on the deflection approximation differential equation of the cantilever retaining wall. And the preliminary retaining wall displacement curve expression is deduced through a certain conversion formula by combining the retaining wall flexible line, the related integral constant and the conversion formula, and the related operation expression formula is simplified, so that the subsequent data deduction and application development are facilitated.
The correlation coefficient of the stiffness of the cantilever retaining wall is also extracted in the embodiment, and the following relation is satisfied;
Wherein A represents the rigidity-related coefficient of the cantilever type retaining wall, EI represents the bending rigidity of the retaining wall, C 1 The quadratic coefficient of the active soil pressure distribution function, C 2 A coefficient of a first order term representing an active soil pressure distribution function, L representing the height of the retaining wall,the average gravity of the earth filled behind the retaining wall is shown, and z represents the depth of the earth.
And combining the correlation coefficient of the stiffness of the cantilever retaining wall with the preliminary displacement curve expression, and obtaining a final retaining wall displacement curve function through certain mathematical deduction. In this embodiment, the stiffness characteristic of the retaining wall can be more accurately described by optimizing and simplifying the displacement curve function of the retaining wall by introducing the stiffness correlation coefficient, so as to obtain a more accurate displacement curve function, and the displacement curve function can intuitively represent the displacement variation condition of the retaining wall under different pressures, thereby being beneficial to the practical application of the active soil pressure calculation method considering the stiffness of the cantilever retaining wall, and further analyzing the stability and safety of the retaining wall.
S5, combining the displacement-related active soil pressure calculation model and the active soil pressure distribution model to establish a rigidity-related active soil pressure calculation model, wherein the concrete implementation steps and the related contents are as follows:
The displacement condition of the stiffness of the cantilever type retaining wall is set in the embodiment, and mainly comprises a first displacement condition and a second displacement condition, wherein the displacement value of the top of the cantilever type retaining wall is the first displacement condition when the displacement value of the top of the cantilever type retaining wall is smaller than or equal to the active limit displacement value of a soil body, and the displacement condition of the retaining wall under the first displacement condition can be more intuitively understood by combining with fig. 3; when the displacement value of the top of the cantilever type retaining wall is larger than the active limit displacement value of the soil body, the displacement value is the second displacement condition, and the displacement condition of the retaining wall under the second displacement condition can be more intuitively understood by combining with fig. 4.
In an alternative embodiment, an active soil pressure calculation model of the first model is established by combining the first displacement condition, the displacement related active soil pressure calculation model and the active soil pressure distribution model, and the implementation is as follows;
under the first deflection condition of the rigidity of the cantilever type retaining wall, the whole displacement of the retaining wall is relatively small and does not exceed the limit displacement value of the soil body, so that the soil body behind the retaining wall does not reach the limit state and still stays in a stable or acceptable range, and excessive disturbance or damage to the soil body can be avoided.
The active soil pressure calculation model of the first model satisfies the following relationship:
Wherein P is a1 (z) represents the first active soil pressure, K, related to the stiffness 0 Representing the static soil pressure coefficient, K, on the retaining wall a Represents the coulomb initiative soil pressure coefficient, S a Representing the active limit displacement value s of the soil body max Represents the displacement value of the top of the cantilever type retaining wall, L represents the height of the retaining wall, A represents the rigidity-related coefficient of the cantilever type retaining wall,the average gravity of the earth filled behind the retaining wall is shown, and z represents the depth of the earth.
In the embodiment, the correlation coefficient of the stiffness of the retaining wall and the physical property parameters of the soil body are considered, the interaction relation between the retaining wall and the soil body can be reflected more accurately, in addition, the displacement curve of the retaining wall and the active soil pressure distribution model under the first deflection condition are combined, the displacement and the soil pressure distribution condition of the retaining wall under different loads are considered more comprehensively, and further, the reliability and the accuracy of the stiffness correlation active soil pressure calculation method are ensured.
In another alternative embodiment, an active soil pressure calculation model of the second model is established by combining the second displacement condition, the displacement related active soil pressure calculation model and the active soil pressure distribution model, and the implementation of the active soil pressure calculation model is as follows;
in the second displacement of the stiffness of the cantilever type retaining wall, the maximum displacement value of the top of the retaining wall is smaller than the limit displacement value of the soil body, so that the integral structure of the retaining wall is in a relatively stable state. However, in the upper region of the retaining wall, the soil has reached a corresponding limit state, indicating that the soil in that region has lost shear capacity and is in a near failure state. In contrast, in the lower region of the soil retaining structure, the soil remains in an unlimited state, i.e. the soil in the region still has the capacity of shearing, and the breaking critical point is not reached.
Under the second displacement condition, the critical height of the soil body reaching the limit state needs to be determined, and the critical height can be analyzed and calculated through the physical property, the pressure condition, the boundary constraint and other factors of the soil body.
And the critical height of the soil mass limit state is used as a demarcation point of the active soil pressure, so that the active soil pressure calculation model of the second model meets the following relation:
wherein P is a2 (z) represents a stiffness-dependent second active earth pressure, K a Representing the coulomb initiative earth pressure coefficient,represents the average gravity of the earth filled behind the retaining wall, z represents the depth of the earth, z a ' represents critical height, K of limit state of soil body 0 Representing the static soil pressure coefficient on the retaining wall, S a Representing the active limit displacement value s of the soil body max The displacement value of the top of the cantilever type retaining wall is represented by L, the height of the retaining wall is represented by L, and the stiffness-related coefficient of the cantilever type retaining wall is represented by A.
In the embodiment, the critical height of the soil limit state is firstly analyzed and calculated in detail based on the factors such as the physical property of the soil, the pressure condition, the boundary constraint and the like, and the critical height of the soil limit state can be determined more accurately, so that more accurate and reliable data support is provided for calculating the active soil pressure of the retaining wall with related rigidity. On the other hand, the detailed analysis and calculation are carried out on the related factors, so that the action condition of the related influence factors on the rigidity related active soil pressure can be considered more comprehensively, and a more accurate and reliable active soil pressure calculation result is obtained.
Furthermore, the construction of the stiffness-related active soil pressure calculation model based on the stiffness of the cantilever retaining wall in the embodiment is only an optional condition of the invention, and in other embodiments or some embodiments, the optimization and adjustment can be performed according to the retaining structure and the actual requirements, so that the active soil pressure can be better calculated, and the accuracy of the active soil pressure result is ensured.
In this embodiment, in order to make up for the deficiency of classical soil pressure theory, the invention combines the cantilever type retaining wall rigidity to establish a rigidity-related active soil pressure calculation model, and calculates the active soil pressure and controls the retaining wall-related behavior by using the model.
The active soil pressure calculation model related to rigidity of the embodiment considers the influence of the rigidity of the retaining wall on the soil pressure, thereby more accurately reflecting the displacement and stress distribution of the retaining wall under the action of external pressure, and based on the model, the behavior of the retaining wall can be more accurately predicted, including but not limited to the stability, the deformation degree, the damage condition and the like of the retaining wall structure.
On the other hand, in this embodiment, the displacement condition of the retaining wall is divided into different displacement conditions according to the relative relationship between the top displacement value and the soil mass limit displacement value of the cantilever retaining wall, and the pressure condition of the retaining wall at different stages can be more accurately estimated according to the different displacement conditions, so as to further ensure the practicality and safety of the retaining wall structure.
Specifically, in an alternative embodiment, when the top displacement value of the retaining wall is smaller than or equal to the active limit displacement value of the soil body, the retaining wall is in a relatively stable state, and the soil body does not reach the limit state, so that the rigidity of the retaining wall has less influence on the soil pressure; in another alternative embodiment, when the top displacement value of the retaining wall is greater than the active limit displacement value of the soil body, the influence of the stiffness of the retaining wall on the soil pressure is gradually increased, and at this time, the rapid prediction of the pressure and the control of the related behavior of the retaining wall can be performed according to the active soil pressure calculation model related to the stiffness.
The active soil pressure calculation model with related rigidity can better calculate soil pressure, provides more accurate and reliable decision support for engineering practice, is beneficial to improving the design level and safety of the retaining wall, and provides new ideas and methods for research and development of related fields.
Referring to fig. 6, in an alternative embodiment, to be able to efficiently perform the active soil pressure calculation method taking the stiffness of the cantilever-type retaining wall into consideration provided by the present invention, the present invention further provides an active soil pressure calculation system taking the stiffness of the cantilever-type retaining wall into consideration, which includes a processor, an input device, an output device, and a memory, the processor, the input device, the output device, and the memory being connected to each other, wherein the memory is used for storing a computer program including program instructions configured to invoke the program instructions to perform the active soil pressure calculation method taking the stiffness of the cantilever-type retaining wall into consideration as provided by the present invention, and specific steps of the related embodiments. The active soil pressure calculation system considering the rigidity of the cantilever type retaining wall has the advantages of complete, objective and stable structure, overcomes the defects of the classical soil pressure theory method and the defects of practical application, improves the accuracy of the soil pressure calculation result according to the active soil pressure calculation model related to the rigidity, and improves the overall applicability and the practical application capability of the invention.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some or all of the technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit of the invention, and are intended to be included within the scope of the appended claims and description.
Claims (10)
1. An active soil pressure calculation method considering the rigidity of a cantilever retaining wall is characterized by comprising the following steps:
determining retaining wall materials and section parameters, and obtaining soil physical and mechanical data;
analyzing the correlation between the active soil pressure and the soil displacement according to the soil physical and mechanical data;
obtaining a displacement-related active soil pressure calculation model according to the correlation;
obtaining an active soil pressure distribution model according to the physical and mechanical data of the soil body and the acting effect of the rigidity of the retaining wall;
and establishing a rigidity-related active soil pressure calculation model by combining the displacement-related active soil pressure calculation model and the active soil pressure distribution model.
2. The method for calculating the active soil pressure considering the rigidity of the cantilever type retaining wall according to claim 1, wherein the analyzing the correlation between the active soil pressure and the soil displacement according to the soil physical and mechanical data comprises:
presetting active soil pressure and soil displacement to be linearly related according to the soil physical and mechanical data;
constructing a correlation analysis model of active soil pressure and soil displacement based on the linear correlation;
and analyzing the correlation of the active soil pressure and the soil displacement through the correlation analysis model.
3. The method for calculating the active soil pressure considering the rigidity of the cantilever type retaining wall according to claim 2, wherein the correlation analysis model of the active soil pressure and the soil displacement satisfies the following relationship:
wherein k is a Represents the relativity of soil pressure and soil displacement, K represents the linear coefficient of active soil pressure, S represents soil displacement, K 0 Representing the static soil pressure coefficient on the retaining wall, S a Represents the active limit displacement value, K of the soil body a Representing the coulomb initiative soil pressure coefficient.
4. The method for calculating the active soil pressure taking into account the stiffness of the cantilever type retaining wall according to claim 1, wherein the obtaining a displacement-dependent active soil pressure calculation model from the correlation comprises:
Constructing a displacement-related active soil pressure calculation model of any depth of the retaining wall according to the correlation;
the displacement-related active soil pressure calculation model meets the following relation:
wherein P is a Represents the active soil pressure, K related to displacement at any depth of the retaining wall a Represents the coulomb initiative soil pressure coefficient, K 0 Representing the static soil pressure coefficient on the retaining wall, S representing the soil displacement, z representing the depth of the soil, S a Represents the active limit displacement value of the soil body,indicating the average weight of the earth fill behind the retaining wall.
5. The method for calculating the active soil pressure considering the rigidity of the cantilever type retaining wall according to claim 4, wherein the step of obtaining the active soil pressure distribution model according to the physical and mechanical data of the soil body and the acting effect of the rigidity of the retaining wall comprises the steps of:
analyzing the acting effect of the rigidity of the retaining wall and obtaining the displacement condition of the rigidity of the cantilever retaining wall;
and obtaining a displacement curve function of the cantilever type retaining wall according to the displacement condition.
6. The method for calculating the active soil pressure considering the stiffness of the cantilever type retaining wall according to claim 5, wherein the displacement curve function satisfies the following relationship:
Wherein s (z) represents the displacement curve of the cantilever type retaining wall, z represents the depth of soil body, L represents the height of the retaining wall, A represents the rigidity correlation coefficient of the cantilever type retaining wall, s max Representing the displacement value of the top of the cantilever type retaining wall.
7. The method for calculating the active soil pressure considering the rigidity of the cantilever type retaining wall according to claim 6, wherein the step of obtaining the active soil pressure distribution model according to the physical and mechanical data of the soil body and the acting effect of the rigidity of the retaining wall comprises the steps of:
constructing an active soil pressure distribution model according to the displacement curve function and the soil physical and mechanical data;
the active soil pressure distribution model meets the following relations:
wherein P is a (z) represents the distribution result of the active soil pressure, C 1 The quadratic coefficient of the active soil pressure distribution function is represented, z represents the depth of soil body, L represents the height of retaining wall, and C 2 The first order coefficients representing the active earth pressure distribution function,indicating the average weight of the earth fill behind the retaining wall.
8. The method of claim 1, wherein the combining the displacement-dependent active soil pressure calculation model and the active soil pressure distribution model to build a stiffness-dependent active soil pressure calculation model comprises:
Setting displacement conditions of the rigidity of the cantilever retaining wall, wherein the displacement conditions comprise a first displacement condition and a second displacement condition;
establishing an active soil pressure calculation model of a first model based on the first displacement condition, the displacement-related active soil pressure calculation model and the active soil pressure distribution model;
and establishing an active soil pressure calculation model of a second model based on the second displacement condition, the displacement-related active soil pressure calculation model and the active soil pressure distribution model.
9. The method for calculating the active soil pressure taking into account the stiffness of the cantilever type retaining wall according to claim 8, wherein the method for calculating the active soil pressure taking into account the stiffness of the cantilever type retaining wall comprises the steps of;
the first model of the active soil pressure calculation model satisfies the following relationship:
wherein P is a1 (z) represents the first active soil pressure, K, related to the stiffness 0 Representing the static soil pressure coefficient, K, on the retaining wall a Represents the coulomb initiative soil pressure coefficient, S a Representing the active limit displacement value s of the soil body max Represents the displacement value of the top of the cantilever type retaining wall, L represents the height of the retaining wall, A represents the rigidity-related coefficient of the cantilever type retaining wall,the average gravity of the earth filled behind the retaining wall is shown, and z represents the depth of the earth.
The active soil pressure calculation model of the second model meets the following relation:
wherein P is a2 (z) represents a stiffness-dependent second active earth pressure, K a Representing the coulomb initiative earth pressure coefficient,represents the average gravity of the earth filled behind the retaining wall, z represents the depth of the earth, z a ′ Represents critical height, K of soil limit state 0 Representing the static soil pressure coefficient on the retaining wall, S a Representing the active limit displacement value s of the soil body max The displacement value of the top of the cantilever type retaining wall is represented by L, the height of the retaining wall is represented by L, and the stiffness-related coefficient of the cantilever type retaining wall is represented by A.
10. An active earth pressure calculation system taking into account the stiffness of a cantilever retaining wall, characterized in that the system comprises a processor, an input device, an output device and a memory, which are interconnected, wherein the memory is adapted to store a computer program comprising program instructions, the processor being configured to invoke the program instructions to perform the active earth pressure calculation method taking into account the stiffness of a cantilever retaining wall according to any of claims 1-9.
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