CN113935098A - Foundation pit support active soil pressure calculation method based on slip surface shape correction - Google Patents
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Abstract
The invention relates to a foundation pit support active soil pressure calculation method based on slip surface shape correction. The method comprises the following steps: determining design parameters of a foundation pit supporting structure and physical and mechanical parameters of a soil body; determining a displacement mode of a supporting structure; determining a relational expression of the displacement of the supporting structure along with the change of the depth; determining a relational expression of the friction angle and the displacement; assuming that the shape of a soil body slip crack surface in a limit state is a logarithmic spiral; and establishing an equation according to the force balance by adopting a horizontal layer analysis method, and finally obtaining an expression of the shape of the slip surface and the size of the active soil pressure, the resultant force and the position of the resultant force action point. By adopting the foundation pit support active soil pressure calculation method based on the shape correction of the slip fracture surface, the obtained soil pressure is more accurate and reasonable in distribution, the calculation formula is simple and practical, the method can be suitable for different types of support structures in foundation pit engineering, is beneficial to reasonable design and construction of the foundation pit engineering, and has certain popularization and application values.
Description
Technical Field
The invention relates to the technical field of geotechnical engineering, in particular to a foundation pit support active soil pressure calculation method based on slick surface shape correction.
Background
At present, in the design calculation of a foundation pit supporting structure, the traditional Rankine soil pressure theory and the Coulomb soil pressure theory are clear in mechanical concept and simple and convenient in calculation process, and the safety coefficient is introduced to basically reflect the size and the distribution rule of the soil pressure, so that the design calculation of the soil pressure in the actual engineering is usually the first choice.
The classical soil pressure theory is provided based on a rigid retaining wall in a translation mode, the soil pressure can be accurately solved only when a wall body is displaced for a certain distance until a soil body generates shearing damage and reaches a limit balance state, a calculated linear slip crack surface does not completely accord with the shape of an actual soil body slip crack surface, and the obtained linear soil pressure distribution can not completely reflect the actual stress state of the retaining wall. In practical engineering, the displacement of the wall body is far smaller than the displacement value of the wall body reaching the limit state, the soil pressure borne by the wall body is often between the static soil pressure and the active (passive) limit soil pressure, and the retaining wall is in the non-limit state. Therefore, for the research on the soil pressure actually acting on the supporting structure, in addition to the characteristics of the soil body, the factors of the structure, such as the strength, the supporting form, the displacement mode, the slip plane and the like, should be considered.
At present, the research on the soil pressure on a supporting structure is not perfect enough, most of the soil pressure is built on the basis of a rigid retaining wall, the application in actual engineering is lacked, and a relatively complete soil pressure calculation model based on a curve slip fracture surface needs to be found, so that the design theory and the construction level of a foundation pit supporting structure are improved to a certain extent.
Disclosure of Invention
The invention mainly aims at the defects of the classical soil pressure theory and provides a foundation pit supporting structure active soil pressure calculation method based on slip surface shape correction.
In order to achieve the technical purpose, the method for calculating the active soil pressure of the foundation pit support based on the shape correction of the slip fracture surface is characterized by comprising the following steps of:
the method comprises the following steps: determining design parameters of a foundation pit supporting structure and physical and mechanical parameters of a soil body, comprising the following steps of: excavating a foundation pit by a depth h; heavy gamma, cohesive force c, internal friction angle of soil
Uniformly distributing loads q on the surface of the soil body by using a friction angle delta between the foundation pit supporting structure and the soil body;
step two: determining a displacement mode of a supporting structure according to a displacement curve of the supporting structure;
step three: assuming that a displacement curve of a supporting structure is in a parabola form, taking three special points of the top, the bottom and the maximum displacement of the structure, and obtaining a relational expression of displacement S and depth Z for any displacement curve:
in the formula: m and n are parameters reflecting the shape of the curve, and there are:
Son the upper partHorizontally displacing the top of the supporting structure;
Slower partHorizontally displacing the bottom of the supporting structure;
Smthe maximum horizontal displacement of the supporting structure;
Zmis the depth corresponding to the maximum displacement；
Step four: determining the relation between the friction angle and the displacement, and obtaining the play value of the internal friction angle of any displacement of the soil body by means of the stress Mohr circle
External friction angle exertion value deltamThe calculation formula (c) is as follows:
in the formula: rfTaking 0.75-1.0 as a destruction ratio;
eta is the effective displacement area ratio of the supporting structure;
step five: assuming that the shape of the soil body slip crack surface in the limit state can be represented by a logarithmic spiral, the included angle between any tangent line of a point on the slip crack surface and the horizontal direction can be obtained:
in the formula: theta is an included angle between any point on the slip crack surface and the vertical direction;
parameters taking into account the influence of displacements
Step six: taking a triangular soil wedge formed after the supporting structure in the limit state for analysis, dividing the types of horizontal micro-elements according to the displacement mode of the supporting structure by means of a horizontal layer analysis method, establishing horizontal and vertical differential equations according to the balance of force and simplifying the equations to obtain:
boundary conditions: when y is 0, σy＝q；
In the formula: l isOn the upper partTaking L as the length of the upper surface of the infinitesimal bodyOn the upper part＝Heωθsinθ；
σyThe vertical pressure of the top surface of the micro element body; sigmawThe intensity of the soil pressure borne by the supporting structure;
k is the lateral active soil pressure coefficient:
beta is the included angle between the small main stress plane of the soil body unit and the horizontal plane:
n is the ratio of large and small main stresses:
step seven: according to (ii), the value is exerted by the internal and external friction angles
And deltamReplacement of soil pressure parameters in
And delta to obtain a calculation formula of the soil pressure under different displacements and corresponding to the y point sigmayThe differential equation of the values is solved by the Runge Kutta method.
The further technical scheme of the invention is as follows: the soil body is non-cohesive soil, and the surface of the soil body is horizontal.
The further technical scheme of the invention is as follows: the calculation formula of the effective displacement area ratio eta of the supporting structure in the fourth step is as follows:
Sataking 3.75-6H per mill for the displacement of the supporting side soil body when the supporting side soil body reaches the limit state;
h is the length of the foundation pit supporting structure; z1、Z2Is an equation S(z)＝SaTwo solutions of (a);
the other parameters in the above formula are the same as the relevant parameters in claim 1.
The further technical scheme of the invention is as follows: the formula for calculating the soil pressure under different displacements obtained in the seventh step is as follows, and the relevant parameters in the following formula are the same as those in claim 1:
the invention has the following excellent technical scheme: and seventhly, programming solution is carried out by adopting Matlab software based on a Runge Kutta method.
The further technical scheme of the invention is as follows: and obtaining the soil pressure resultant force E according to a formula (I) according to the calculation method, wherein the relevant parameters in the formula (I) are consistent with the relevant parameters:
the further technical scheme of the invention is as follows: the method further comprises the following steps of calculating the torque of the soil pressure on the wall bottom according to a formula (c), wherein relevant parameters in the formula (c) are consistent with the relevant parameters:
the further technical scheme of the invention is as follows: and the distance between the resultant action point of soil pressure and the wall bottom is calculated according to a formula (I), and the related parameters in the formula (I) are consistent with the related parameters:
in the formula: n is the number of equal layers along the wall height;
Δ y is high per aliquot, Δ y ═ H/n.
The invention has the beneficial effects that: by adopting the foundation pit support active soil pressure calculation method based on the shape correction of the slip fracture surface, the influence of displacement on the soil pressure can be considered, the assumption of the slip fracture surface of the soil body is more practical, the main stress deflection caused by the soil arch effect is considered in calculation and analysis, the obtained soil pressure is more accurate and reasonable in distribution, the calculation formula is simple and practical, the method can be suitable for different types of support structures in foundation pit engineering, the reasonable design and construction of the foundation pit engineering are facilitated, and the method has certain popularization and application values.
Drawings
FIG. 1 is a schematic flow chart of the active computing method of the present invention;
FIG. 2 is a model for calculation and analysis of active soil pressure of a foundation pit supporting structure;
FIG. 3 is a graph showing the displacement curves of the supporting structure in the example under various working conditions;
FIG. 4 is a graph of active earth pressure distribution as a function of displacement for the examples;
FIG. 5 is a graph of a slip surface in an example;
in the figure: 1-ground, 2-supporting structure, 3-supporting structure displacement mode, 4-foundation pit bottom surface, and 5-slip surface.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and embodiments, wherein fig. 1 to 5 are drawings of the embodiments of the present invention, and are simplified for the purpose of concisely and clearly illustrating the embodiments of the present invention. It should be understood, however, that the scope of the embodiments of the present invention is not limited to the embodiments, and the embodiments may be implemented in various forms. These embodiments are provided so that this disclosure will be thorough and complete.
The embodiment of the invention provides a foundation pit support active soil pressure calculation method based on slick fracture surface shape correction, which is characterized in that aiming at the defects of the traditional soil pressure theoretical calculation method, the active soil pressure accurate calculation method considering the slick fracture surface shape is designed, referring to figure 1, the parameters in different formulas in the embodiment are consistent, and the concrete steps are as follows:
the method comprises the following steps: determining design parameters of a foundation pit supporting structure and physical and mechanical parameters of a soil body, comprising the following steps of: excavating a foundation pit by a depth h; heavy gamma, cohesive force c, internal friction angle of soil
Uniformly distributing loads q on the surface of the soil body by using a friction angle delta between the foundation pit supporting structure and the soil body;
step two: determining a displacement mode of the supporting structure according to the displacement curve of the supporting structure;
step three: simplifying the displacement mode, and assuming that the displacement mode of the supporting structure only has four modes of cantilever type, inward convex type, skirting type and combined type, and any displacement mode can be obtained by combining the first three basic displacement modes; simplifying the displacement mode into a parabolic form, and taking three special points at the top, the bottom and the maximum displacement position of the structure, obtaining a relational expression of the displacement S and the depth Z:
in the formula: s(z)Horizontally displacing the supporting structure;
z is the depth below the ground;
m and n are parameters reflecting the shape of the curve, and there are:
Son the upper partFor supporting the top water of the structurePerforming horizontal displacement;
Slower partHorizontally displacing the bottom of the supporting structure;
Smthe maximum horizontal displacement of the supporting structure;
Zmthe depth corresponding to the maximum displacement.
Step four: determining the relation between friction angle and displacement, and setting the internal friction angle in non-limit state
The external friction angle delta is not fully exerted, and the exerted value is
δmThe triaxial test with unloading stress path is used to compare the lateral displacement process of the soil body behind the wall in the active state and make an improved stress Mohr circle, and the existing parameters are used to obtain the internal friction angle play value of any displacement of the soil body in the quasi-active state
External friction angle exertion value deltamThe calculation formula (c) is as follows:
in the formula: rfTaking 0.75-1.0 as a destruction ratio;
eta is the ratio of the horizontal displacement value of a certain point in the height range of the supporting structure to the limit displacement value required for reaching the active limit state;
for a foundation pit supporting structure with a complex displacement form, the friction angle parameter of the filling soil
δmThe method is not only influenced by displacement, but also related to the height of the wall, and the intermediate state of the displacement of the supporting structure is reflected by replacing the displacement ratio with the effective displacement area ratio;
coefficient of intermediate state
SaTaking 3.75-6H per mill for the displacement of the supporting side soil body when the supporting side soil body reaches the limit state;
h is the length of the foundation pit supporting structure;
Z1、Z2is an equation S(z)＝SaTwo solutions of (a).
Step five: the shape of the soil body slip crack surface in the assumed limit state can be represented by a logarithmic spiral, and is represented by a polar coordinate equation:
the included angle between any tangent of any point on the slip crack surface and the horizontal direction can be obtained by deriving the formula:
in the formula: theta is an included angle between any point on the slip crack surface and the vertical direction;
parameters taking into account the influence of displacements
Step six: analyzing a triangular soil wedge body formed by a combined displacement mode supporting structure in an extreme state, dividing the analysis model into three types of horizontal micro-elements by adopting a horizontal layer analysis method according to the relative motion trend of the triangular soil wedge body as shown in a figure 2;
respectively establishing horizontal and vertical differential equations of three types of infinitesimal bodies according to the balance of forces, and simultaneously simplifying the equations to obtain:
boundary conditions: when y is 0, σy＝q；
In the formula: l isOn the upper partIs a micro-element bodyThe length of the upper surface is taken as L according to the relation of logarithmic spiral slip crack surfaceOn the upper part＝Heωθsinθ；
σyThe vertical pressure of the top surface of the micro element body;
σwthe intensity of the soil pressure borne by the supporting structure;
k is the lateral active soil pressure coefficient:
beta is the included angle between the small main stress plane of the soil body unit and the horizontal plane:
n is the ratio of large and small main stresses:
step seven: according to the formula II, the value is exerted by the internal and external friction angles
And deltamSoil pressure parameter in substitution formula
And delta, obtaining a soil pressure calculation formula under different displacements:
corresponding to the y point sigma for the above formulaySolving the differential equation of the value by a numerical method, programming by Matlab software based on a Runge Kutta method, performing trial calculation on the assumption of a reasonable theta value to obtain different active soil pressure distributions, wherein the maximum resultant force value is an active soil pressure calculation value, and further obtaining the soil pressure resultant force E:
moment M of soil pressure to wall bottom:
the distance h between the soil pressure resultant force action point and the wall bottom is as follows:
in the formula: n is the number of equal layers along the wall height;
Δ y is high per aliquot, Δ y ═ H/n.
The soil body is non-cohesive soil, and the surface of the soil body is horizontal.
For supporting structures in other displacement modes, the active soil pressure can be changed by changing ZmThe method is realized by the size of the pressure sensor, and Rankine or Coulomb pressure theory calculation can be directly adopted for the supporting structure in the translation mode.
The following is described in comparison with a specific embodiment: the method takes a single anchor pile model test of a certain sandy soil foundation pit as an object, the pile length H is 2m, and the soil filling weight gamma is 16kN/m3Angle of internal friction
The external friction angle delta is 20 degrees, and the single anchor plate anchor is supportedAt a depth of 0.2 m. The foundation pit is excavated for three times, each excavation is 0.3m, and displacement and soil pressure values at different depths under different working conditions are recorded respectively.
The active soil pressure in the height range of the support pile is calculated by the calculation method, firstly, the displacement test value is substituted into a formula I, a relational expression of the displacement S and the depth Z is solved, and further, a comparison graph of the fitting result of the pile body displacement curve under each working condition and the test actual measurement data is obtained as shown in figure 3.
Substitute the first into the second to obtain
δm＝18.3°。
Thirdly, solving a differential equation by a numerical method, and assuming a theta value to perform trial calculation to obtain active soil pressure distribution under different displacements; the calculated result of the invention is compared with the Coulomb pressure theory calculated result and the experimental measured data, the comparison chart is shown in figure 4, the calculated potential slip crack surface is compared with the classical soil pressure theory calculated result, and the comparison chart is shown in figure 5.
As can be seen from the graphs of FIG. 4 and FIG. 5, the displacement curve equation of the invention has better fitting compared with the test result and smaller explanation error, and can reflect the change relation of the horizontal displacement of the pile body along with the depth; the active soil pressure calculation result of the invention is basically consistent with the test result, the soil pressure obtained by theory is in R-shaped nonlinear distribution along the depth, and the phenomena that the soil pressure near the wall top is increased and the soil pressure near the middle part is reduced due to the soil arch effect can be reflected. Compared with the Coulomb soil pressure theory, the calculation result is safer, and the magnitude and the distribution rule of the soil pressure acting on the support pile in the inward convex displacement mode can be reflected more truly; when the pit is excavated to the bottom, the range of the potential slip crack surface calculated by the method is smaller than the theoretical result of the classical soil pressure, and the method is more practical compared with the traditional method.
Finally, the above-described embodiments are intended to be illustrative only and not to be limiting, and although the present invention has been described in detail by way of the foregoing examples, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit of the invention and without departing from the scope of the invention as defined by the appended claims.
Claims (8)
1. A foundation pit support active soil pressure calculation method based on slip surface shape correction is characterized by comprising the following steps:
the method comprises the following steps: determining design parameters of a foundation pit supporting structure and physical and mechanical parameters of a soil body, comprising the following steps of: excavating a foundation pit by a depth h; heavy gamma, cohesive force c, internal friction angle of soil
Uniformly distributing loads q on the surface of the soil body by using a friction angle delta between the foundation pit supporting structure and the soil body;
step two: determining a displacement mode of a supporting structure according to a displacement curve of the supporting structure;
step three: assuming that a displacement curve of a supporting structure is in a parabola form, taking three special points of the top, the bottom and the maximum displacement of the structure, and obtaining a relational expression of displacement S and depth Z for any displacement curve:
in the formula: m and n are parameters reflecting the shape of the curve, and there are:
Son the upper partHorizontally displacing the top of the supporting structure;
Slower partHorizontally displacing the bottom of the supporting structure;
Smthe maximum horizontal displacement of the supporting structure;
Zmthe depth corresponding to the maximum displacement;
step four: determining the relation between friction angle and displacement, and obtaining soil by means of stress Mohr circleValue of internal friction angle for any displacement of body
External friction angle exertion value deltamThe calculation formula (c) is as follows:
in the formula: rfTaking 0.75-1.0 as a destruction ratio;
eta is the effective displacement area ratio of the supporting structure;
step five: assuming that the shape of the soil body slip crack surface in the limit state can be represented by a logarithmic spiral, the included angle between any tangent line of a point on the slip crack surface and the horizontal direction can be obtained:
in the formula: theta is an included angle between any point on the slip crack surface and the vertical direction;
parameters taking into account the influence of displacements
Step six: taking a triangular soil wedge formed after the supporting structure in the limit state for analysis, dividing the types of horizontal micro-elements according to the displacement mode of the supporting structure by means of a horizontal layer analysis method, establishing horizontal and vertical differential equations according to the balance of force and simplifying the equations to obtain:
boundary conditions: when y is 0, σy＝q；
In the formula: l isOn the upper partTaking L as the length of the upper surface of the infinitesimal bodyOn the upper part＝Heωθsinθ；
σyThe vertical pressure of the top surface of the micro element body;
σwthe intensity of the soil pressure borne by the supporting structure;
k is the lateral active soil pressure coefficient:
beta is the included angle between the small main stress plane of the soil body unit and the horizontal plane:
n is the ratio of large and small main stresses:
step seven: according to (ii), the value is exerted by the internal and external friction angles
And deltamSoil pressure parameter in substitution formula
And delta to obtain a calculation formula of the soil pressure under different displacements and corresponding to the y point sigmayThe differential equation of the values is solved by the Runge Kutta method.
2. The foundation pit support active soil pressure calculation method based on the slip fracture surface shape correction as claimed in claim 1, wherein: the soil body is non-cohesive soil, and the surface of the soil body is horizontal.
3. The method for calculating the active soil pressure of the foundation pit support based on the shape correction of the slip fracture surface of claim 1, wherein the effective displacement area ratio η of the support structure in the fourth step is calculated according to the following formula:
Sataking 3.75-6H per mill for the displacement of the supporting side soil body when the supporting side soil body reaches the limit state;
h is the length of the foundation pit supporting structure;
Z1、Z2is an equation S(z)＝SaThe other parameters in the above formula are the same as the relevant parameters in claim 1.
4. The active soil pressure calculation method for foundation pit support based on slip surface shape correction according to claim 1, wherein the soil pressure calculation formula under different displacements obtained in the seventh step is as follows, and the relevant parameters in the following formula are the same as those in claim 1:
5. the foundation pit support active soil pressure calculation method based on slip surface shape correction according to claim 1, characterized by comprising the following steps: and seventhly, programming solution is carried out by adopting Matlab software based on a Runge Kutta method.
6. The active soil pressure calculation method for foundation pit support based on shape correction of the slip fracture surface as claimed in claim 1, further comprising obtaining a soil pressure resultant force E according to a formula (I) according to the calculation method, wherein the relevant parameters in the formula (I) are the same as those in claim 1:
7. the method for calculating the active soil pressure of the foundation pit support based on the shape correction of the slip surface of claim 1, further comprising the step of calculating the moment of the soil pressure on the wall bottom according to a formula (c), wherein the related parameters in the formula (c) are the same as the related parameters in claim 1:
8. the active earth pressure calculation method for foundation pit support based on slip surface shape correction according to claim 1, characterized by further comprising the following steps of calculating the distance between the resultant action point of earth pressure and the wall bottom according to a formula (i): :
in the formula: n is the number of equal layers along the wall height;
Δ y is high per aliquot, Δ y ═ H/n.
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| CN115935482A (en) * | 2022-12-26 | 2023-04-07 | 山东建筑大学 | Method and system for calculating active supporting force of tunnel under-passing existing structure |
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