CN108763833B - Method for calculating deflection of foundation pit supporting pile in consideration of soil resistance sudden change - Google Patents
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Abstract
The invention relates to a method for calculating foundation pit supporting pile deflection considering soil resistance mutation, belonging to the field of geotechnical engineering calculation methods, and the technical scheme of the invention is as follows: and deducing a pile body deflection differential equation, determining a rock-soil composite formation resistance function, segmenting the pile body, and simultaneously establishing each segmented differential equation to calculate the pile body deflection. The method mainly considers that the rock-soil resistance function has sudden change at the rock-soil interface, and also considers that the support deflection is influenced by the excavation process, the pile body is calculated in sections by utilizing the section independent coordinates and the like, so that the method can be more suitable for the actual condition of the engineering, reduces the calculation error of the stress deformation of the supporting structure, ensures the calculation of the deflection of the supporting pile to be more accurate, and ensures the construction safety.
Description
Technical Field
The invention belongs to the field of geotechnical engineering calculation methods, and particularly relates to a method for calculating the deflection of a foundation pit supporting pile by considering soil resistance mutation.
Background
In various supporting structures of a deep foundation pit, a row pile-steel support supporting form is widely applied. The stressed deformation of the enclosure structure is one of the key points of the stability control of the foundation pit and is also a key concern in the design and construction process of the foundation pit.
At present, in the calculation method of the internal force and the deformation of a pile-support supporting structure system in a foundation pit, for the purpose of simple calculation, the rock-soil resistance modulus is mostly seen as a form of continuous distribution along the depth direction of a pile body. However, in practical engineering, underground geological distribution is complex, physical and mechanical properties among soil layers are different to a certain extent, and particularly, in geological conditions with soil layers and rock layers, the geotechnical resistance modulus can not be seen as a continuously distributed function any more and should be considered in sections.
On the other hand, most of the existing calculation methods simply consider the supporting structure as a rod structure, influence of the excavation process of the foundation pit is not considered, the supporting structure seems to exist before excavation, and changes of supporting counter force and structural deformation of the foundation pit along with the excavation process of the foundation pit are not considered.
The defects cause serious calculation errors and potential safety hazards to engineering implementation.
Disclosure of Invention
In order to reduce the calculation error and enable the calculation result to be closer to the actual situation, the invention provides a foundation pit supporting pile deflection calculation method considering soil resistance mutation, and the deflection of the foundation pit supporting pile can be calculated more accurately.
The invention discloses a method for calculating the deflection of a foundation pit supporting pile in consideration of soil resistance mutation, which adopts the following technical scheme:
step (1): deducing a pile body deflection differential equation below an excavation surface;
step (2): deducing a pile body deflection differential equation above an excavation surface;
and (3): determining a rock-soil composite formation resistance function p which has a sudden change as p (x, y);
and (4): segmenting the pile body by using a segmentation independent coordinate method considering the influence of the excavation process;
and (5): simultaneously calculating the deflection of the pile body by the differential equation of each section;
further, in the step (1), the following pile body bending differential equation of the excavation surface is as follows:
wherein q (x) is a loading function, associated with depth x and external loading; p (x, y) represents a rock-soil foundation reaction force function, and the distribution of the p (x, y) is closely related to the depth x of the pile body and the deformation size y of the pile.
Further, in the step (2), the bending differential equation of the pile body above the excavation surface is as follows:
wherein q is0The size of the trapezoidal short side load of the lateral trapezoidal load of the rock and soil mass outside the foundation pit is represented, n0Showing that the load is distributed triangularly with depthThe magnitude of the slope of the change in degree x.
Further, in the step (3), the value of the rock-soil composite formation resistance function p ═ p (x, y) is as follows:
wherein x is less than t and represents a soil layer, and x is more than or equal to t and represents a rock stratum; m is1And m2Is a proportionality coefficient related to soil texture; n is an index related to the depth x, and different n values represent different soil resistance distribution forms; b0And (4) representing the calculated width of the force deformation in the pile body.
Further, in step (4), the definition considering the influence of the excavation process is as follows:
before each support is erected, a certain initial displacement is generated at the corresponding position. At each supporting and erecting position, the actual elastic compression deformation of the pile body is the total pile body displacement calculated at a certain moment minus the initial displacement of the pile body at the supporting position.
Further, in the step (4), the definition of the piecewise independent coordinate method is as follows:
the method comprises the steps of taking supporting and other supporting structure positions, soil layer interfaces, rock-soil interfaces and excavation surface positions as branch nodes, segmenting a pile body structure into a plurality of pile units, respectively establishing independent Cartesian coordinate systems for the pile units, and establishing pile body deflection differential equations in segments.
Further, in the step (5), the expression of the deflection of the pile body above the excavation surface is as follows:
according to the segmented independent coordinate method, if the foundation pit supporting structure has n supports, the pile body above the excavation surface can be divided into n +1 sections of pile unit bodies, and n +1 segmented deflection differential equation sets are listed according to the step (1).
Further, in the step (5), the following pile deflection expression of the excavation surface is as follows:
when rock strata and soil layers exist below the excavation face, the pile body can be divided into 2 sections. According to the step (1), the deflection equation of the pile body in the soil can be listed as follows:
the differential equation of pile body deflection in the rock stratum is as follows:
wherein p islRepresents the pile side load, p, in the soil layer below the excavation face of the foundation pit due to the gravity of the upper soil bodyl' represents a pile-side load in a rock stratum generated below a excavation face of a foundation pit due to the gravity of an upper soil body, bsTo calculate the width.
Further, in the step (5), the method for calculating the pile body deflection comprises the following steps:
n +1 differential equations above the excavation surface and 2 differential equations below the excavation surface are combined into a differential equation set with n +3 differential equations, and the differential equations of all the sections are solved according to the boundary condition of the pile end, the deformation continuity at the sections of the pile body and the static balance condition.
The invention has the advantages that:
under the geological conditions of both soil layers and rock layers, the rock-soil resistance modulus is seen as a form of discontinuous distribution along the depth direction of the pile body, and the rock-soil resistance function of the rock-soil interface has sudden change. The influence of the excavation process of the foundation pit is considered, and the internal force and the deformation of the pile-support supporting structure are continuously changed along with the propulsion of the working condition. And (3) segmenting the pile body structure into a plurality of pile units, and establishing a pile body deflection differential equation in a segmented manner. The improvement of the above points can be closer to the actual situation of the engineering, the error in the calculation process of the stress deformation of the foundation pit supporting pile is reduced, and the powerful guarantee is provided for the safe construction.
Description of the drawings:
FIG. 1 is a flow chart of the calculation of the present invention.
Fig. 2 is a schematic diagram of the pile body stress direction and the unit body stress balance under the excavation surface.
Fig. 3 is a schematic diagram of the coordinate direction of the pile body above the excavation surface and the trapezoidal stress form.
FIG. 4 is a segmented schematic of the resistance modulus.
The specific implementation mode is as follows:
in the following, embodiments are explained in more detail by means of the attached drawings. It is noted that the technology and terminology referred to herein are the same as those commonly understood by one of ordinary skill in the art to which this patent pertains.
A method for calculating foundation pit supporting pile deflection considering soil resistance sudden change is shown in figure 1, and the specific implementation mode is as follows:
firstly, deducing a pile body deflection differential equation below an excavation surface.
The relation between the bending moment M and the shearing force Q is Q ═ dM/dx, then:
the schematic diagram of the stress of the pile body below the excavation surface of the foundation pit and the direction of the calculation coordinate are shown in figure 2. According to the relation between deflection and bending moment in mechanics of materials, the second order differential (d) of deflection y2y)/(dx2) The sign is usually opposite to the bending moment M, and the deflection unit mm of the pile is different from the length unit M of the pile body by three orders of magnitude, so that the horizontal displacement curve of the pile body is generally flat, and the first-order differential of the deflection y is squared to obtain (dy/dx)2The value is substantially negligible compared to 1, the bending differential equation can be written approximately as:
if the pile body structure of the analysis section is assumed to be a straight pile with a uniform cross section, the inertia moment I of the pile body is a constant, and the bending rigidity EI (E represents the elastic modulus of the pile material) of the pile structure is a constant. Thus, a pile body deflection differential equation below the excavation surface is obtained:
wherein q (x) is a loading function, associated with depth x and external loading; p (x, y) represents a rock-soil foundation reaction force function, and the distribution of the p (x, y) is closely related to the depth x of the pile body and the deformation size y of the pile.
And secondly, deducing a pile body deflection differential equation above the excavation surface.
As shown in fig. 3, it is assumed that the pile body above the excavation face is subjected to lateral pressure in a linear distribution form under external load and lateral rock-soil pressure, that is, the function of change with the depth x can be expressed as:
as can be seen from the above formula, the stress distribution form of the pile body above the excavation surface can be regarded as a trapezoidal load action, namely the load is formed by uniformly distributing loads q0With a triangularly distributed load n0Are combined, wherein n is0The slope of the triangular distribution load with the change of the depth x is shown, n0＝(qx-q0)/x。
The differential equation of the pile body deflection above the excavation surface is as follows:
wherein q is0The size of the trapezoidal short side load of the lateral trapezoidal load of the rock and soil mass outside the foundation pit is represented, n0The magnitude of the slope of the triangular distribution load as a function of depth x is shown.
And thirdly, determining a rock-soil composite formation resistance function p as p (x, y).
The resistance function p (x, y) is a resistance distribution function in an opposite direction generated by the rock-soil body due to flexural deformation after the pile body under the excavation surface is stressed. When the pile body is stressed to generate deflection, if the deflection is y, the influence factor of the resistance function is represented by a resistance modulus K, and at the moment, the form of the resistance function p (x, y) can be represented as follows:
p(x,y)＝Kb0y
due to the large difference in physical and mechanical properties between the rock formation and the soil layer, the resistance modulus K should be considered in the rock formation and the soil layer, respectively. Resistance modulus K in soil layer is K1＝m1xn(ii) a The resistance modulus K in the rock formation is constant, namely: k2＝m2。
The resistance modulus segmented schematic diagram is shown in fig. 4, and a rock-soil composite formation resistance function p is expressed as p (x, y) as follows:
wherein x is less than t and represents a soil layer, and x is more than or equal to t and represents a rock stratum; m is1And m2Is a proportionality coefficient related to soil texture; n is an index related to the depth x, and different n values represent different soil resistance distribution forms; b0And (4) representing the calculated width of the force deformation in the pile body.
And fourthly, segmenting the pile body by using a segmentation independent coordinate method considering the influence of the excavation process.
Before each support is erected, a certain initial displacement is generated at the corresponding position. At each supporting position, the actual elastic compression deformation of the pile body is the sum of the pile body displacement calculated at a certain moment minus the initial displacement of the pile body at the supporting position. In the subsequent steps, when the deflection of the pile body is solved by utilizing the boundary conditions, the deformation continuity of the pile body segments and the static balance conditions, the support deflection change in the excavation process needs to be considered.
The method comprises the steps of taking supporting and other supporting structure positions, soil layer interfaces, rock-soil interfaces and excavation surface positions as branch nodes, segmenting a pile body structure into a plurality of pile units, respectively establishing independent Cartesian coordinate systems for the pile units, and establishing pile body deflection differential equations in segments.
Fifthly, calculating the deflection of the pile body by simultaneous differential equations of all the sections.
According to the segmented independent coordinate method, if the foundation pit supporting structure has n supports, the pile body above the excavation surface can be divided into n +1 sections of pile unit bodies, and n +1 segmented deflection differential equation sets can be respectively listed according to the step one.
When rock strata and soil layers exist below the excavation face, the pile body can be divided into 2 sections. According to the second step, the deflection equation of the pile body in the soil can be listed as follows:
the differential equation of pile body deflection in the rock stratum is as follows:
wherein p islRepresents the pile side load, p, in the soil layer below the excavation face of the foundation pit due to the gravity of the upper soil bodyl' represents a pile-side load in a rock stratum generated below a excavation face of a foundation pit due to the gravity of an upper soil body, bsTo calculate the width.
N +1 differential equations above the excavation surface and 2 differential equations below the excavation surface are combined into a differential equation set with n +3 differential equations.
Pile body deflection equations above and below the excavation surface are four-order constant coefficient linear homogeneous differential equations, and the general solution of the differential equations can be solved by a method of stepwise differentiation. Each differential equation has 4 undetermined parameters, and the differential equation set comprising n +3 differential equations has 4(n +3) undetermined parameters in total.
According to the boundary conditions of the pile end (the pile top is a free end, the pile bottom is a fixed end), the deformation continuity of the pile body subsection and the static balance condition: 4 parameter equations can be obtained under the boundary conditions of the top end and the bottom end of the pile body, n +2 nodes are shared by n supports and rock-soil interfaces, 4(n +2) parameter equations can be obtained according to the node deformation continuous condition and the force balance condition, and then 4+4(n +2) ═ 4(n +3) parameter equations can be obtained in total.
4(n +3) parameter equations can be used for solving 4(n +3) undetermined parameters, and further the solution of the whole deflection differential equation of the pile body can be obtained.
Claims (5)
1. A method for calculating the deflection of a foundation pit supporting pile in consideration of soil resistance mutation is characterized by comprising the following steps:
step (1): deducing a pile body deflection differential equation below an excavation surface;
step (2): deducing a pile body deflection differential equation above an excavation surface;
and (3): determining a rock-soil composite formation resistance function p which has a sudden change as p (x, y);
and (4): segmenting the pile body by using a segmentation independent coordinate method considering the influence of the excavation process;
and (5): simultaneously calculating the deflection of the pile body by the differential equation of each section;
in the step (1), the following pile body bending differential equation of the excavation surface is as follows:
wherein q (x) is a load function of the soil mass load above the excavation surface acting on the pile body below the excavation surface; p (x, y) represents a rock-soil foundation reaction force function, and the distribution condition of the function is closely related to the depth x of the pile body and the deformation size y of the pile;
in the step (2), the bending differential equation of the pile body above the excavation surface is as follows:
wherein q is0The size of the trapezoidal short side load of the lateral trapezoidal load of the rock and soil mass outside the foundation pit is represented, n0The slope magnitude of the triangular distribution load along with the change of the depth x is shown;
in the step (3), the value of the rock-soil composite formation resistance function p (x, y) is as follows:
wherein x is less than t and represents a soil layer, and x is more than or equal to t and represents a rock stratum; m is1And m2Is a proportionality coefficient related to soil texture; n is an index related to the depth x, and different n values represent different soil resistance distribution forms; b0Representing the calculation width of the force deformation in the pile body;
in the step (5), the expression of the deflection of the pile body below the excavation surface is as follows:
when rock strata and soil layers exist below the excavation surface, the pile body is divided into 2 sections; according to the step (2), the deflection equation of the pile body in the soil can be listed as follows:
the differential equation of pile body deflection in the rock stratum is as follows:
wherein, PlRepresents the pile side load P generated below the excavation surface of the foundation pit due to the gravity action of the upper soil body in the soil layerl' represents a pile-side load in a rock stratum generated below a excavation face of a foundation pit due to the gravity of an upper soil body, bsTo calculate the width.
2. The method for calculating the deflection of the foundation pit supporting pile considering the sudden change of the soil resistance as claimed in claim 1, wherein the method comprises the following steps: in the step (4), the definition considering the influence of the excavation process is as follows:
before each support is erected, a certain initial displacement is generated at the corresponding position of each support; at each supporting and erecting position, the actual elastic compression deformation of the pile body is the total pile body displacement calculated at a certain moment minus the initial displacement of the pile body at the supporting position.
3. The method for calculating the deflection of the foundation pit supporting pile considering the sudden change of the soil resistance as claimed in claim 1, wherein the method comprises the following steps: in the step (4), the definition of the piecewise independent coordinate method is as follows:
the method comprises the steps of taking the position of a supporting structure, a soil layer interface, a rock-soil interface and an excavation surface of a support as sub-nodes, segmenting a pile body structure into a plurality of pile units, respectively establishing independent Cartesian coordinate systems for the pile units, and establishing a pile body deflection differential equation in a segmented manner.
4. The method for calculating the deflection of the foundation pit supporting pile considering the sudden change of the soil resistance as claimed in claim 1, wherein the method comprises the following steps: in the step (5), the expression of the deflection of the pile body above the excavation surface is as follows:
according to the segmented independent coordinate method, if the foundation pit supporting structure has n supports, the pile body above the excavation surface is divided into n +1 sections of pile unit bodies, and n +1 segmented deflection differential equation sets are respectively listed according to the step (1).
5. The method for calculating the deflection of the foundation pit supporting pile considering the sudden change of the soil resistance as claimed in claim 1, wherein the method comprises the following steps: in the step (5), the method for calculating the pile body deflection comprises the following steps:
n +1 differential equations above the excavation surface and 2 differential equations below the excavation surface are combined into a differential equation set with n +3 differential equations, and the differential equations of all the sections are solved according to the boundary condition of the pile end, the deformation continuity at the sections of the pile body and the static balance condition.
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