CN111139876B - Method for calculating limit bearing capacity of sludge soft soil foundation pile group by dynamic compaction replacement of broken stones - Google Patents

Method for calculating limit bearing capacity of sludge soft soil foundation pile group by dynamic compaction replacement of broken stones Download PDF

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CN111139876B
CN111139876B CN201910913097.8A CN201910913097A CN111139876B CN 111139876 B CN111139876 B CN 111139876B CN 201910913097 A CN201910913097 A CN 201910913097A CN 111139876 B CN111139876 B CN 111139876B
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stress
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刘文连
李鸿翔
张国海
韩鹏伟
贺加乐
吴胤龙
秦勇光
郝勇
眭素刚
高楠
张劼
周志恒
张腾龙
华明亮
李泽
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China Nonferrous Metals Industry Kunming Survey And Design Institute Co ltd
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    • E—FIXED CONSTRUCTIONS
    • E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
    • E02D—FOUNDATIONS; EXCAVATIONS; EMBANKMENTS; UNDERGROUND OR UNDERWATER STRUCTURES
    • E02D33/00—Testing foundations or foundation structures
    • E—FIXED CONSTRUCTIONS
    • E02—HYDRAULIC ENGINEERING; FOUNDATIONS; SOIL SHIFTING
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    • E02D3/00—Improving or preserving soil or rock, e.g. preserving permafrost soil
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Abstract

The invention discloses a method for calculating the limit bearing capacity of sludge soft soil foundation pile groups by broken stone dynamic compaction replacement, which comprises the following steps: step 1, drawing up basic parameters of a sludge soft soil foundation subjected to stone crushing and dynamic compaction replacement treatment; 2, using a limited unit discrete gravel dynamic compaction to replace the treated sludge soft soil foundation; step 3, calculating the pore water pressure of the finite element node; step 4, establishing a linear programming model of the ultimate bearing capacity of the pile group of the silt soft soil foundation after the stone breaking dynamic compaction replacement treatment according to the Pan family shining maximum principle; and 5, solving a linear programming model of the ultimate bearing capacity of the pile group of the silt soft soil foundation by using an interior point algorithm to obtain the ultimate bearing capacity of the pile group of the silt soft soil foundation. The method establishes a mathematical programming model for solving the limit bearing capacity of the grouped piles of the coastal sludge soft soil foundation subjected to the broken stone dynamic compaction replacement treatment, solves the mathematical programming model through an interior point algorithm to obtain the limit bearing capacity of the foundation, and can calculate the stress field and point safety coefficient distribution rule of the foundation.

Description

Method for calculating limit bearing capacity of sludge soft soil foundation pile group by dynamic compaction replacement of broken stones
Technical Field
The invention relates to the technical field of foundation treatment, in particular to a calculation method for limit bearing capacity of sludge soft soil foundation pile groups through dynamic compaction replacement of broken stones.
Background
In coastal areas of China, stratums are mainly formed by coastal facies deposition and delta facies deposition, and a large amount of silt soft soil with uneven thickness is distributed below the ground surface. The silt soil is mainly characterized by containing a large amount of organic humus, being dark gray in color, having natural water content of 40-70 percent, a pore ratio of more than 1 and low volume weight. The silt soil has very low strength and high compressibility. The building is built on the coastal silt foundation, the bearing capacity of the natural foundation generally cannot meet the design requirement, and the coastal silt foundation generally needs to be subjected to foundation treatment. The currently mainstream method for treating the muddy soil foundation comprises the following steps: the method comprises a replacement filling method, a pile foundation method, a pre-compaction consolidation method, a broken stone dynamic compaction replacement filling method and the like. The broken stone dynamic compaction and replacement filling method is a novel method for treating the sludge soft soil foundation in recent years, has the characteristics of high construction speed, low cost and high bearing capacity of the foundation after treatment, and has better reinforcement effect because the sludge soil among the piles is compacted and the broken stone pile foundation forms pile group effect after the sludge soil foundation is treated by the broken stone dynamic compaction and replacement filling method. Due to the complexity of treating the silt soil foundation by a broken stone dynamic compaction and replacement filling method, the ultimate bearing capacity of the treated silt soft soil foundation is generally determined by using a field test method, and a high-efficiency numerical method for calculating the ultimate bearing capacity of pile groups of the silt soil foundation is lacked.
In view of the above, the invention provides a method for calculating the ultimate bearing capacity of the pile group of the silt soft soil foundation by the dynamic compaction replacement of broken stones based on the highest emitting principle of panhomer, so that the ultimate bearing capacity of the pile group of the coastal silt soft soil foundation after the dynamic compaction replacement of the broken stones can be obtained, and the distribution rule of the stress field and the point safety coefficient of the foundation can be obtained.
Disclosure of Invention
The invention aims to provide a method for calculating the ultimate bearing capacity of silt soft soil foundation pile groups through broken stone dynamic compaction replacement, so as to obtain the ultimate bearing capacity of coastal silt soft soil foundation pile groups and provide a new method for calculating the foundation bearing capacity.
In order to solve the technical problems, the invention adopts the following technical scheme:
the method for calculating the limit bearing capacity of the sludge soft soil foundation pile group through dynamic compaction replacement of broken stones comprises the following steps:
step 1, drawing up basic parameters of a sludge soft soil foundation subjected to stone crushing and dynamic compaction replacement treatment;
2, using a limited unit discrete gravel dynamic compaction to replace the treated sludge soft soil foundation;
step 3, calculating the pore water pressure of the finite element node;
step 4, establishing a linear programming model of the ultimate bearing capacity of the pile group of the silt soft soil foundation after the stone breaking dynamic compaction replacement treatment according to the Pan family shining maximum principle;
and 5, solving a linear programming model of the ultimate bearing capacity of the pile group of the silt soft soil foundation by using an interior point algorithm to obtain the ultimate bearing capacity of the pile group of the silt soft soil foundation.
Further, step 6, calculating the main stress and the maximum shear stress of the soil body of the silt soft soil foundation; and 7, calculating the point safety coefficient of the soil body of the sludge soft soil foundation, and drawing a point safety coefficient isoline.
Further, the basic parameters of the silt soft soil foundation subjected to the stone crushing, dynamic compaction and replacement treatment in the step 1 are drawn up and include: the method comprises the following steps of arranging a tamping replacement gravel pile group pile scheme, replacing depth and replacing range of gravel piles, volume weight and shearing resistance parameters of in-situ foundation soil after dynamic tamping replacement, and foundation underground water level information.
Further, the step 2 specifically comprises: constructing a stress field of a foundation, using three-node finite unit discrete gravel dynamic compaction to replace the treated sludge soft soil foundation, setting an overall coordinate system (x, y), wherein the x axis is horizontally right, the y axis is vertically upward, and under the overall coordinate system, any finite unit e in a foundation soil body is provided with three nodes which are a first node 1, a second node 2 and a third node 3; the ith node of the e-th finite element has an effective positive stress in the x-direction
Figure GDA0003056818490000021
Effective positive stress in the y-direction
Figure GDA0003056818490000022
And shear stress
Figure GDA0003056818490000023
Wherein i is 1,2, 3; meanwhile, each node has pore water pressure action, and the ith node of the e finite element has pore water pressure action
Figure GDA0003056818490000024
Wherein i is 1,2, 3.
Further, the step 3 of calculating the pore water pressure of the finite element node is specifically as follows: supposing that the underground water in the base is a static water level, the seepage field in the foundation is a stable seepage field, and the pore water pressure of the node of the finite unit is calculated according to the following formula:
Figure GDA0003056818490000025
in the formula:
Figure GDA0003056818490000026
the ith node of the e-th finite element is acted upon by the pore water pressure, gammawIs the volume weight of the water and is,
Figure GDA0003056818490000027
is the vertical coordinate of the ith node of the e-th finite element, HwIs the ground water level of the foundation, i is 1,2,3, e is (1, …, N)e)，NeIs the number of limited units in a silt soft soil foundation.
Further, the step 4 specifically includes: constructing stress fields and objective functions of finite elements according to the Pan family shining maximum value principle, specifically: firstly, establishing a pile group ultimate bearing capacity objective function; establishing a balance equation constraint condition of the limited foundation soil unit; establishing stress continuous constraint conditions of the common edges of the limited units of the foundation soil body; establishing yield constraint conditions of limited foundation soil units; establishing static force boundary constraint conditions of the limited foundation soil units; and sixthly, establishing a linear programming model of the ultimate bearing capacity of the sludge soft soil foundation pile group after the broken stone dynamic compaction replacement treatment.
Further, the step 4 specifically includes: establishing a pile group ultimate bearing capacity objective function: according to the panhomer shining maximum principle, the maximum value of the uniformly distributed load acting on the surface of the foundation pile needs to be solved, so that the objective function is as follows:
Maximize:Pd (2)
in the formula: maximize means "max"; pdEvenly distributed loads acting on the surface of foundation pile groups;
establishing a balance equation constraint condition of the limited foundation soil body unit:
Aeσe＝Bepe+Ce (3)
in the formula: e ═ 1, …, Ne)，NeIs the number of finite elements in the foundation;
Figure GDA0003056818490000031
Figure GDA0003056818490000032
Figure GDA0003056818490000033
Figure GDA0003056818490000034
are 6 shape function coefficients of a triangle finite element e, respectively;
Figure GDA0003056818490000035
effective positive stress along the x direction of a first node, a second node and a third node of the finite element e respectively;
Figure GDA0003056818490000036
effective positive stress along the y direction of a first node, a second node and a third node of the finite element e respectively;
Figure GDA0003056818490000037
the shear stress of the first node, the second node and the third node of the finite element e respectively;
Figure GDA0003056818490000038
the pore water pressure of the first node, the second node and the third node of the finite element e respectively;
Aeis the area of finite element e; gamma rayeIs the volume weight of finite element e;
establishing stress continuous constraint conditions of the common edges of the limited units of the foundation soil body;
Figure GDA0003056818490000039
in the formula: d ═ 1, …, Nd)，NdIs the number of common edges of the finite element in the foundation;
Figure GDA00030568184900000310
Figure GDA00030568184900000311
Figure GDA00030568184900000312
θdis the inclination angle of the common edge of the limited unit, and is positive anticlockwise;
Figure GDA00030568184900000313
effective positive stress of a first node, a second node, a third node and a fourth node which are respectively a common edge d of the finite element along the x direction;
Figure GDA00030568184900000314
effective positive stress along the y direction of a first node, a second node, a third node and a fourth node which are respectively a common edge d of the finite element;
Figure GDA00030568184900000315
the shear stress of a first node, a second node, a third node and a fourth node which are the common edge d of the finite element respectively;
establishing yield constraint conditions of the limited foundation soil units:
Anσn＝Bn (5)
in the formula: n ═ 1, …, Nz)，NzIs the number of finite element nodes in the foundation;
Figure GDA0003056818490000041
Figure GDA0003056818490000042
Figure GDA0003056818490000043
Ck＝2sin(2kπ/p)；
Figure GDA0003056818490000044
k is (1, …, p), and p is the number of the edges of the regular polygon linearized under the molar coulomb yield condition of the foundation soil material;
Figure GDA0003056818490000045
is the effective positive stress of the nth node in the x direction;
Figure GDA0003056818490000046
is the effective positive stress of the nth node in the y direction;
Figure GDA0003056818490000047
is the shear stress of the nth node;
Figure GDA0003056818490000048
is the internal friction angle of the nth node; c. CnIs the cohesion of the nth node;
establishing a static force boundary constraint condition of the limited unit of the foundation soil body:
the static boundary conditions on the boundary without the external load action on the surface of the foundation are as follows:
Figure GDA0003056818490000049
in the formula: b ═ 1, …, Nb)，NbIs the number of finite elements on the foundation boundary without external load;
Figure GDA00030568184900000410
Figure GDA00030568184900000411
Figure GDA00030568184900000412
respectively effective positive stress along the x direction of two nodes close to the boundary in the finite element b on the boundary;
Figure GDA00030568184900000413
respectively effective positive stress along the y direction of two nodes close to the boundary in the finite element b on the boundary;
Figure GDA00030568184900000414
respectively the shear stress of two nodes close to the boundary in the limited unit b on the boundary;
θbthe inclination angle of a connecting line of two nodes of the limited unit b close to the boundary on the boundary is positive anticlockwise;
uniformly distributing load action P on the surface of foundation pile groupdThe static boundary conditions on the boundary of (1) are as follows:
Figure GDA00030568184900000415
in the formula: s ═ 1, …, Ns)，NsThe number of limited units with uniformly distributed load action on the boundary of the foundation;
Figure GDA0003056818490000051
Figure GDA0003056818490000052
Figure GDA0003056818490000053
Figure GDA0003056818490000054
respectively effective positive stress along the x direction of two nodes close to the boundary in the finite element s on the boundary;
Figure GDA0003056818490000055
respectively effective positive stress along the y direction of two nodes close to the boundary in the finite element s on the boundary;
Figure GDA0003056818490000056
respectively the shear stress of two nodes close to the boundary in the finite element s on the boundary;
θsthe inclination angle of a connecting line of two nodes of the boundary, which is close to the finite element s on the boundary, is positive anticlockwise; pdIs the uniform load acting on the surface of the foundation pile group.
Establishing a linear programming model of the ultimate bearing capacity of the sludge soft soil foundation pile groups after the broken stone dynamic compaction replacement treatment:
Figure GDA0003056818490000057
further, the step 5 specifically includes: (1) with stress σ of finite elementeAs decision variable, limit load PdFor the objective function, the constraints include: the method comprises the following steps of (1) balancing equation constraint conditions of limited foundation units, stress continuous constraint conditions of common edges of the limited foundation units and speed boundary conditions of the limited foundation units;
(2) taking an initial penalty factor of a linear programming model for solving the limit bearing capacity of the pile group of the silt soft soil foundation, and defining an allowable error;
(3) taking an initial point in a feasible region;
(4) constructing a penalty function of the linear programming model, and solving an extreme point of the penalty function by using an unconstrained optimization method from an initial point;
(5) and (4) performing loop iteration calculation, and if the iteration error is smaller than the defined allowable error, terminating the iteration and obtaining the optimal solution of the ultimate bearing capacity of the foundation.
Further, the step 6 specifically includes: (1) the principal stress of the nodes of finite elements in the foundation soil is calculated according to the following formula:
Figure GDA0003056818490000061
in the formula: n ═ 1, …, Nz)，NzIs the number of finite element nodes in the foundation;
Figure GDA0003056818490000062
is the effective positive stress of the nth node in the x direction;
Figure GDA0003056818490000063
is the effective positive stress of the nth node in the y direction;
Figure GDA0003056818490000064
is the shear stress of the nth node;
Figure GDA0003056818490000065
is the first principal stress of the nth node,
Figure GDA0003056818490000066
is the second principal stress of the nth node.
(2) The maximum node shear stress of the limited units in the foundation soil body is calculated according to the following formula:
Figure GDA0003056818490000067
in the formula: n ═ 1, …, Nz)，NzIs the number of finite element nodes in the foundation;
Figure GDA0003056818490000068
is the first principal stress of the nth node,
Figure GDA0003056818490000069
is the second principal stress of the nth node,
Figure GDA00030568184900000610
is the maximum shear stress at the nth node.
(3) And drawing a main stress contour line and a maximum shear stress contour line of the foundation soil body.
Preferably, the step 7 specifically comprises: (1) the point safety factors of the nodes of the limited units in the foundation soil body are calculated according to the following formula:
Figure GDA00030568184900000611
in the formula: n ═ 1, …, Nz)，NzIs the number of finite element nodes in the foundation;
Figure GDA00030568184900000612
is the effective positive stress of the nth node in the x direction;
Figure GDA00030568184900000613
is the effective positive stress of the nth node in the y direction;
Figure GDA00030568184900000614
is the shear stress of the nth node;
Figure GDA00030568184900000615
is the internal friction angle of the nth node; c. CnIs the cohesion of the nth node.
(2) And drawing a point safety factor contour map according to the point safety factors of the limited unit nodes in the foundation soil body.
Compared with the prior art, the invention can at least produce one of the following beneficial effects: according to the method, a coastal sludge soft soil foundation subjected to broken stone dynamic compaction replacement is taken as a research object, a finite element discrete foundation soil body is used based on the Panjia maximum value principle, a mathematical programming model for solving the ultimate bearing capacity of the group piles of the coastal sludge soft soil foundation subjected to broken stone dynamic compaction replacement is established, the mathematical programming model is solved through an interior point algorithm to obtain the ultimate bearing capacity of the foundation, and a stress field and a point safety coefficient distribution rule of the foundation can be calculated.
Drawings
FIG. 1 is a step diagram of the present invention.
Fig. 2 is a schematic diagram of a limited unit of a silt soft soil foundation.
Fig. 3 is a schematic view of a common edge d between adjacent finite elements of a silt soft soil foundation.
Fig. 4 schematic diagram of the silt soft soil foundation treated by the stone crushing, dynamic compaction and replacement in the embodiment 1.
FIG. 5 is a schematic discrete diagram of a limited unit of the silt soft soil foundation of example 1;
figure 6 is a pore water pressure contour line of a finite element node of the silt soft soil foundation in embodiment 1.
Figure 7 first principal stress contour of a silt soft soil foundation of example 1.
Figure 8 second principal stress contour of silt soft soil foundation of example 1.
Fig. 9 maximum shear stress contour of the silt soft soil foundation of example 1.
Figure 10 point safety factor contours for silt soft soil foundations of example 1.
Wherein, 1-a first node, 2-a second node, 3-a third node, 4-a fourth node, 5-a common edge d, 6-a finite element e, 7-plain filling, 8-silt, 9-medium sand and 10-gravel pile.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Fig. 1 to fig. 10 show a schematic diagram of a calculation method for limit bearing capacity of a pile group of a silt soft soil foundation by the dynamic compaction replacement of crushed stones, and one embodiment is listed below by combining an illustration.
Example 1:
the method for calculating the limit bearing capacity of the sludge soft soil foundation pile group through dynamic compaction replacement of broken stones comprises the following steps:
step 1, drawing up basic parameters of a sludge soft soil foundation subjected to stone crushing and dynamic compaction replacement treatment;
2, using a limited unit discrete gravel dynamic compaction to replace the treated sludge soft soil foundation;
step 3, calculating the pore water pressure of the finite element node;
step 4, establishing a linear programming model of the ultimate bearing capacity of the pile group of the silt soft soil foundation after the stone breaking dynamic compaction replacement treatment according to the Pan family shining maximum principle;
and 5, solving a linear programming model of the ultimate bearing capacity of the pile group of the silt soft soil foundation by using an interior point algorithm to obtain the ultimate bearing capacity of the pile group of the silt soft soil foundation.
Step 6, calculating the main stress and the maximum shear stress of the soil body of the silt soft soil foundation;
and 7, calculating the point safety coefficient of the soil body of the sludge soft soil foundation, and drawing a point safety coefficient isoline.
Wherein, the basic parameters of the silt soft soil foundation subjected to the stone crushing and dynamic compaction replacement treatment in the step 1 comprise: the method comprises the following steps of arranging a tamping replacement gravel pile group pile scheme, replacing depth and replacing range of gravel piles, volume weight and shearing resistance parameters of in-situ foundation soil after dynamic tamping replacement, and foundation underground water level information. The method comprises the following specific steps:
the gravel pile group pile arrangement scheme is as follows: the grouped piles are arranged in a 3.0m multiplied by 3.0m square, each gravel pile can be tamped for 3-8 times by adopting 3000 kN.m tamping energy, and can be tamped for 30-31 times by adopting 6000 kN.m tamping energy, and the filling amount of each tamping point is 70-89 m3；
Replacement depth of gravel pile: the depth of substitution is 10.0 m;
gravel pile replacement range: the substitution range is a region where "length × width × depth" is 3.0 × 10.0 m;
volume weight and shear parameters of the gravel pile: the volume weight of the gravel pile is 25kN/m3The cohesive force is 10.00kPa, and the internal friction angle is 40.00 degrees;
carrying out dynamic compaction replacement on original foundation soil, and then carrying out volume weight and shearing resistance parameters: the volume weight of the plain filling soil is 18.00kN/m3The cohesive force is 16.00kPa, the internal friction angle is 5.00 degrees, and the volume weight of the sludge is 19.00kN/m3The cohesive force is 5.00kPa, the internal friction angle is 0.00 DEG, and the volume weight of the medium sand layer is 20.00kN/m3The cohesive force was set at 0.00kPa and the internal friction angle was set at 30.00 ℃.
And (3) ground underground water level information: the ground water level of the foundation is-0.5 m below the earth surface;
the section of the silt soft soil foundation after the stone breaking and dynamic compaction replacement treatment is shown in figure 4.
The step 2 specifically comprises the following steps: constructing a stress field of a foundation, using three-node finite unit discrete gravel dynamic compaction to replace the treated coastal sludge soft soil foundation, setting an overall coordinate system (x, y), wherein the x axis is horizontally right, the y axis is vertically upward, and under the overall coordinate system, any finite unit e in a foundation soil body is provided with three nodes which are a first node 1, a second node 2 and a third node 3; the ith node of the e-th finite element has an effective positive stress in the x-direction
Figure GDA0003056818490000081
Effective positive stress in the y-direction
Figure GDA0003056818490000082
And shear stress
Figure GDA0003056818490000083
Wherein i is 1,2, 3; meanwhile, each node has pore water pressure action, and the ith node of the e finite element has pore water pressure action
Figure GDA0003056818490000084
Wherein i is 1,2, 3.
Specifically, the finite element mesh of the silt soft soil foundation after the dynamic compaction replacement treatment of the broken stones by using the finite element discrete embodiment is shown in fig. 5, and the finite element N obtained by the total dispersion ise805 pieces of,Node Nz2415 common edges N between limited unitsd1169 pieces.
The step 3 of calculating the pore water pressure of the finite element node is specifically as follows: supposing that the underground water in the base is a static water level, the seepage field in the foundation is a stable seepage field, and the pore water pressure of the node of the finite unit is calculated according to the following formula:
Figure GDA0003056818490000091
in the formula:
Figure GDA0003056818490000092
the ith node of the e-th finite element is acted upon by the pore water pressure, gammawIs the volume weight of the water and is,
Figure GDA0003056818490000093
is the vertical coordinate of the ith node of the e-th cell, HwIs the ground water level of the foundation, i is 1,2,3, e is (1, …, N)e)，NeIs the number of limited units in a silt soft soil foundation.
Specifically, coordinate information and groundwater level information H of the finite element grid obtained according to the step threew-0.5m, pore water pressure of each node in the foundation is calculated based on formula (1); FIG. 6 is a pore water pressure contour line of a finite element node of the silt soft soil foundation of example 1.
The step 4 specifically comprises the following steps: constructing stress fields and objective functions of finite elements according to the Pan family shining maximum value principle, specifically: firstly, establishing a pile group ultimate bearing capacity objective function; establishing a balance equation constraint condition of the limited foundation soil unit; establishing stress continuous constraint conditions of the common edges of the limited units of the foundation soil body; establishing yield constraint conditions of limited foundation soil units; establishing static force boundary constraint conditions of the limited foundation soil units; and sixthly, establishing a linear programming model of the limit bearing capacity of the pile group of the coastal sludge soft soil foundation after the broken stone dynamic compaction replacement treatment.
The method further comprises the following steps:
establishing a pile group ultimate bearing capacity objective function: according to the panhomer shining maximum principle, the maximum value of the uniformly distributed load acting on the surface of the foundation pile needs to be solved, so that the objective function is as follows:
Maximize:Pd (2)
in the formula: maximize means "max"; pdEvenly distributed loads acting on the surface of foundation pile groups;
establishing a balance equation constraint condition of the limited foundation soil body unit:
Aeσe＝Bepe+Ce (3)
in the formula: e ═ 1, …, Ne)，NeIs the number of finite elements in the foundation;
Figure GDA0003056818490000094
Figure GDA0003056818490000101
Figure GDA0003056818490000102
Figure GDA0003056818490000103
are 6 shape function coefficients of a triangle finite element e, respectively;
Figure GDA0003056818490000104
effective positive stress along the x direction of a first node 1, a second node 2 and a third node 3 which are respectively a finite element e;
Figure GDA0003056818490000105
a first node 1, a second node 2 and a third node which are finite elements e respectively3 effective positive stress in the y-direction;
Figure GDA0003056818490000106
shear stress of a first node 1, a second node 2 and a third node 3 of the finite element e respectively;
Figure GDA0003056818490000107
the pore water pressure of the first node 1, the second node 2 and the third node 3 of the finite element e respectively;
Aeis the area of finite element e; gamma rayeIs the volume weight of finite element e;
establishing stress continuous constraint conditions of the common edges of the limited units of the foundation soil body;
Figure GDA0003056818490000108
in the formula: d ═ 1, …, Nd)，NdIs the number of common edges of the finite element in the foundation;
Figure GDA0003056818490000109
Figure GDA00030568184900001010
Figure GDA00030568184900001015
θdis the inclination angle of the common edge of the limited unit, and is positive anticlockwise;
Figure GDA00030568184900001011
effective positive stress along the x direction of a first node 1, a second node 2, a third node 3 and a fourth node 4 which are respectively a finite element common edge d 5;
Figure GDA00030568184900001012
effective positive stress along the y direction of a first node 1, a second node 2, a third node 3 and a fourth node 4 which are respectively a finite element common edge d 5;
Figure GDA00030568184900001013
the shear stress of the first node 1, the second node 2, the third node 3 and the fourth node 4 which are the common edge d 5 of the finite element respectively;
establishing yield constraint conditions of the limited foundation soil units:
Anσn＝Bn (5)
in the formula: n ═ 1, …, Nz)，NzIs the number of finite element nodes in the foundation;
Figure GDA00030568184900001014
Figure GDA0003056818490000111
Figure GDA0003056818490000112
Ck＝2sin(2kπ/p)；
Figure GDA0003056818490000113
k is (1, …, p), and p is the number of the edges of the regular polygon linearized under the molar coulomb yield condition of the foundation soil material;
Figure GDA0003056818490000114
is the effective positive stress of the nth node in the x direction;
Figure GDA0003056818490000115
is the effective positive stress of the nth node in the y direction;
Figure GDA0003056818490000116
is the shear stress of the nth node;
Figure GDA0003056818490000117
is the internal friction angle of the nth node; c. CnIs the cohesion of the nth node;
establishing a static force boundary constraint condition of the limited unit of the foundation soil body:
the static boundary conditions on the boundary without the external load action on the surface of the foundation are as follows:
Figure GDA0003056818490000118
in the formula: b ═ 1, …, Nb)，NbIs the number of finite elements on the foundation boundary without external load;
Figure GDA0003056818490000119
Figure GDA00030568184900001110
Figure GDA00030568184900001111
respectively effective positive stress along the x direction of two nodes close to the boundary in the finite element b on the boundary;
Figure GDA00030568184900001112
respectively effective positive stress along the y direction of two nodes close to the boundary in the finite element b on the boundary;
Figure GDA00030568184900001113
respectively the shear stress of two nodes close to the boundary in the limited unit b on the boundary;
θbis an edgeThe inclination angle of the connection line of the two nodes of the boundary of the limited unit b on the boundary is positive anticlockwise;
uniformly distributing load action P on the surface of foundation pile groupdThe static boundary conditions on the boundary of (1) are as follows:
Figure GDA00030568184900001114
in the formula: s ═ 1, …, Ns)，NsThe number of limited units with uniformly distributed load action on the boundary of the foundation;
Figure GDA00030568184900001115
Figure GDA0003056818490000121
Figure GDA0003056818490000122
respectively effective positive stress along the x direction of two nodes close to the boundary in the finite element s on the boundary;
Figure GDA0003056818490000123
respectively effective positive stress along the y direction of two nodes close to the boundary in the finite element s on the boundary;
Figure GDA0003056818490000124
respectively the shear stress of two nodes close to the boundary in the finite element s on the boundary;
θsthe inclination angle of a connecting line of two nodes of the boundary, which is close to the finite element s on the boundary, is positive anticlockwise; pdIs the uniform load acting on the surface of the foundation pile group.
Establishing a linear programming model of the limit bearing capacity of the pile group of the coastal sludge soft soil foundation after the broken stone dynamic compaction replacement treatment:
Figure GDA0003056818490000125
the step 5 specifically comprises the following steps: (1) with stress σ of finite elementeAs decision variable, limit load PdFor the objective function, the constraints include: the method comprises the following steps of (1) balancing equation constraint conditions of limited foundation units, stress continuous constraint conditions of common edges of the limited foundation units and speed boundary conditions of the limited foundation units;
(2) taking an initial penalty factor of a linear programming model for solving the limit bearing capacity of the pile group of the silt soft soil foundation, and defining an allowable error;
(3) taking an initial point in a feasible region;
(4) constructing a penalty function of the linear programming model, and solving an extreme point of the penalty function by using an unconstrained optimization method from an initial point;
(5) and (4) performing loop iteration calculation, and if the iteration error is smaller than the defined allowable error, terminating the iteration and obtaining the optimal solution of the ultimate bearing capacity of the foundation.
The calculation result is:
example 1 calculation results of pile group ultimate bearing capacity of silt soft soil foundation subjected to stone crushing, dynamic compaction and replacement treatment are shown in table 1. After the foundation is treated by dynamic compaction replacement, the limit bearing capacity of the pile group of the silt soft soil foundation is 480.00 kPa.
Table 1 calculation result of limit bearing capacity of pile group of silt soft soil foundation by dynamic compaction replacement treatment of crushed stone
Working conditions Ultimate bearing capacity Pd(kPa)
Dynamic compaction replacement 480.00
The step 6 specifically comprises the following steps: (1) the principal stress of the nodes of finite elements in the foundation soil is calculated according to the following formula:
Figure GDA0003056818490000131
in the formula: n ═ 1, …, Nz)，NzIs the number of finite element nodes in the foundation;
Figure GDA0003056818490000132
is the effective positive stress of the nth node in the x direction;
Figure GDA0003056818490000133
is the effective positive stress of the nth node in the y direction;
Figure GDA0003056818490000134
is the shear stress of the nth node;
Figure GDA0003056818490000135
is the first principal stress of the nth node,
Figure GDA0003056818490000136
is the second principal stress of the nth node.
(2) The maximum node shear stress of the limited units in the foundation soil body is calculated according to the following formula:
Figure GDA0003056818490000137
in the formula: n ═ 1, …, Nz)，NzIs the number of finite element nodes in the foundation;
Figure GDA0003056818490000138
is the first principal stress of the nth node,
Figure GDA0003056818490000139
is the second principal stress of the nth node,
Figure GDA00030568184900001310
is the maximum shear stress at the nth node.
(3) And drawing a main stress contour line and a maximum shear stress contour line of the foundation soil body.
The calculation result is: the first principal stress contour when the foundation reaches the limit state is shown in figure 7, the second principal stress contour is shown in figure 8, and the maximum tangent contour is shown in figure 9, which reflects the stress field of the foundation soil body under the limit state.
The step 7 specifically comprises the following steps: (1) the point safety factors of the nodes of the limited units in the foundation soil body are calculated according to the following formula:
Figure GDA00030568184900001311
in the formula: n ═ 1, …, Nz)，NzIs the number of finite element nodes in the foundation;
Figure GDA00030568184900001312
is the effective positive stress of the nth node in the x direction;
Figure GDA00030568184900001313
is the effective positive stress of the nth node in the y direction;
Figure GDA00030568184900001314
is the shear stress of the nth node;
Figure GDA00030568184900001315
is the internal friction angle of the nth node; c. CnIs the cohesion of the nth node.
(2) And drawing a point safety factor contour map according to the point safety factors of the limited unit nodes in the foundation soil body.
The calculation result is: the point safety factor contour line for the coastal silt soft soil foundation is shown in fig. 10, which shows the safety degree of each point in the foundation.
Reference throughout this specification to multiple illustrative embodiments means that a particular method described in connection with the embodiments is included in at least one embodiment described generally throughout this application. The appearances of the same phrase in various places in the specification are not necessarily all referring to the same embodiment. Further, while a method is described in connection with any one embodiment, it is to be understood that it is within the scope of the invention to implement such a method in connection with other embodiments.

Claims (7)

1. The method for calculating the limit bearing capacity of the sludge soft soil foundation pile group through dynamic compaction replacement of broken stones is characterized by comprising the following steps of: the method comprises the following steps:
step 1, drawing up basic parameters of a sludge soft soil foundation subjected to stone crushing and dynamic compaction replacement treatment;
2, using a limited unit discrete gravel dynamic compaction to replace the treated sludge soft soil foundation;
the step 2 specifically comprises the following steps: constructing a stress field of a foundation, using three-node finite unit discrete gravel dynamic compaction to replace the treated sludge soft soil foundation, setting an overall coordinate system (x, y), wherein the x axis is horizontally right, the y axis is vertically upward, and under the overall coordinate system, any e-th finite unit in a foundation soil body is provided with three nodes which are a first node (1), a second node (2) and a third node (3); the ith node of the e-th finite element has an effective positive stress in the x-direction
Figure FDA0003063159060000011
Effective positive stress in the y-direction
Figure FDA0003063159060000012
And shear stress
Figure FDA0003063159060000013
Wherein i is 1,2, 3; at the same time, each node also has pore water pressure action, i node of e limited unitActing on pore water pressure
Figure FDA0003063159060000014
Wherein i is 1,2, 3;
step 3, calculating the pore water pressure of the finite element node;
step 4, establishing a linear programming model of the ultimate bearing capacity of the pile group of the silt soft soil foundation after the stone breaking dynamic compaction replacement treatment according to the Pan family shining maximum principle;
the step 4 is specifically as follows: constructing stress fields and objective functions of finite elements according to the Pan family shining maximum value principle, specifically: firstly, establishing a pile group ultimate bearing capacity objective function; establishing a balance equation constraint condition of the limited foundation soil unit; establishing stress continuous constraint conditions of the common edges of the limited units of the foundation soil body; establishing yield constraint conditions of limited foundation soil units; establishing static force boundary constraint conditions of the limited foundation soil units; establishing a linear programming model of the ultimate bearing capacity of the sludge soft soil foundation pile groups after the broken stone dynamic compaction replacement treatment;
the step 4 is specifically as follows:
establishing a pile group ultimate bearing capacity objective function: according to the panhomer shining maximum principle, the maximum value of the uniformly distributed load acting on the surface of the foundation pile needs to be solved, so that the objective function is as follows:
Maximize:Pd (2)
in the formula: maximize means "max"; pdEvenly distributed loads acting on the surface of foundation pile groups;
establishing a balance equation constraint condition of the limited foundation soil body unit:
Ae σe＝Bepe+Ce (3)
in the formula: e ═ 1, …, Ne)，NeIs the number of finite elements in the foundation;
Figure FDA0003063159060000021
Figure FDA0003063159060000022
Figure FDA0003063159060000023
Figure FDA0003063159060000024
are the 6 shape function coefficients of the e-th finite element of the triangle respectively;
Figure FDA00030631590600000211
effective positive stress of a first node (1), a second node (2) and a third node (3) of the e-th finite element respectively along the x direction;
Figure FDA0003063159060000025
effective positive stress of a first node (1), a second node (2) and a third node (3) of the e-th finite element respectively along the y direction;
Figure FDA0003063159060000026
the shear stress of a first node (1), a second node (2) and a third node (3) of the e-th finite element respectively;
Figure FDA0003063159060000027
the pore water pressure of a first node (1), a second node (2) and a third node (3) of the e-th finite unit respectively;
Aeis the area of the e-th finite element; gamma rayeIs the volume weight of the e-th finite element;
establishing stress continuous constraint conditions of the common edges of the limited units of the foundation soil body;
Figure FDA0003063159060000028
in the formula: d ═ 1, …, Nd)，NdIs the number of common edges of the finite element in the foundation;
Figure FDA0003063159060000029
Figure FDA00030631590600000210
Figure FDA0003063159060000031
θdis the inclination angle of the common edge of the limited unit, and is positive anticlockwise;
Figure FDA0003063159060000032
effective positive stress of a first node (1), a second node (2), a third node (3) and a fourth node (4) which are respectively a common edge d (5) of the finite element along the x direction;
Figure FDA0003063159060000033
effective positive stress of a first node (1), a second node (2), a third node (3) and a fourth node (4) which are respectively a common edge d (5) of the finite element along the y direction;
Figure FDA0003063159060000034
the shear stress of a first node (1), a second node (2), a third node (3) and a fourth node (4) which are respectively a common edge d (5) of the finite element;
establishing yield constraint conditions of the limited foundation soil units:
Anσn＝Bn (5)
in the formula：n＝(1,…,Nz)，NzIs the number of finite element nodes in the foundation;
Figure FDA0003063159060000035
Figure FDA0003063159060000036
Figure FDA0003063159060000037
Ck＝2sin(2kπ/p)；
Figure FDA0003063159060000038
k is (1, …, p), and p is the number of the edges of the foundation soil material molar coulomb yield condition linearized regular polygon;
Figure FDA0003063159060000039
is the effective positive stress of the nth node in the x direction;
Figure FDA00030631590600000310
is the effective positive stress of the nth node in the y direction;
Figure FDA00030631590600000311
is the shear stress of the nth node;
Figure FDA00030631590600000312
is the internal friction angle of the nth node; c. CnIs the cohesion of the nth node;
establishing a static force boundary constraint condition of the limited unit of the foundation soil body:
the static boundary conditions on the boundary without the external load action on the surface of the foundation are as follows:
Figure FDA00030631590600000313
in the formula: b ═ 1, …, Nb)，NbIs the number of finite elements on the foundation boundary without external load;
Figure FDA00030631590600000314
Figure FDA0003063159060000041
Figure FDA0003063159060000042
respectively effective positive stress along the x direction of two nodes close to the boundary in the finite element b on the boundary;
Figure FDA0003063159060000043
respectively effective positive stress along the y direction of two nodes close to the boundary in the finite element b on the boundary;
Figure FDA0003063159060000044
respectively the shear stress of two nodes close to the boundary in the limited unit b on the boundary;
θbthe inclination angle of a connecting line of two nodes of the limited unit b close to the boundary on the boundary is positive anticlockwise;
uniformly distributing load action P on the surface of foundation pile groupdThe static boundary conditions on the boundary of (1) are as follows:
Figure FDA0003063159060000045
in the formula: s ═ 1, …, Ns)，NsThe number of limited units with uniformly distributed load action on the boundary of the foundation;
Figure FDA0003063159060000046
Figure FDA0003063159060000047
Figure FDA0003063159060000048
respectively effective positive stress along the x direction of two nodes close to the boundary in the finite element s on the boundary;
Figure FDA0003063159060000049
respectively effective positive stress along the y direction of two nodes close to the boundary in the finite element s on the boundary;
Figure FDA00030631590600000410
respectively the shear stress of two nodes close to the boundary in the finite element s on the boundary;
θsthe inclination angle of a connecting line of two nodes of the boundary, which is close to the finite element s on the boundary, is positive anticlockwise; pdEvenly distributed loads acting on the surface of foundation pile groups;
establishing a linear programming model of the ultimate bearing capacity of the sludge soft soil foundation pile groups after the broken stone dynamic compaction replacement treatment:
Figure FDA00030631590600000411
and 5, solving a linear programming model of the ultimate bearing capacity of the pile group of the silt soft soil foundation by using an interior point algorithm to obtain the ultimate bearing capacity of the pile group of the silt soft soil foundation.
2. The method for calculating the limit bearing capacity of the pile group of the silt soft soil foundation by the dynamic compaction replacement of the crushed stones according to claim 1, is characterized in that: step 6, calculating the main stress and the maximum shear stress of the soil body of the silt soft soil foundation; and 7, calculating the point safety coefficient of the soil body of the sludge soft soil foundation, and drawing a point safety coefficient isoline.
3. The method for calculating the limit bearing capacity of the pile group of the silt soft soil foundation by the dynamic compaction replacement of the crushed stones according to claim 1, is characterized in that: the basic parameters of the silt soft soil foundation subjected to the broken stone dynamic compaction replacement treatment in the step 1 comprise: the method comprises the following steps of arranging a tamping replacement gravel pile group pile scheme, replacing depth and replacing range of gravel piles, volume weight and shearing resistance parameters of in-situ foundation soil after dynamic tamping replacement, and foundation underground water level information.
4. The method for calculating the limit bearing capacity of the pile group of the silt soft soil foundation by the dynamic compaction replacement of the crushed stones according to claim 1, is characterized in that: the step 3 of calculating the pore water pressure of the finite element node is specifically as follows: supposing that the underground water in the base is a static water level, the seepage field in the foundation is a stable seepage field, and the pore water pressure of the node of the finite unit is calculated according to the following formula:
Figure FDA0003063159060000051
in the formula:
Figure FDA0003063159060000052
the ith node of the e-th finite element is acted upon by the pore water pressure, gammawIs the volume weight of the water and is,
Figure FDA0003063159060000053
is the vertical coordinate of the ith node of the e-th finite element, HwGround water of foundationBit, i ═ 1,2,3, e ═ 1, …, Ne)，NeIs the number of limited units in a silt soft soil foundation.
5. The method for calculating the limit bearing capacity of the pile group of the silt soft soil foundation by the dynamic compaction replacement of the crushed stones according to claim 1, is characterized in that: the step 5 specifically comprises the following steps: (1) with stress σ of finite elementeAs decision variable, limit load PdFor the objective function, the constraints include: the method comprises the following steps of (1) balancing equation constraint conditions of limited foundation units, stress continuous constraint conditions of common edges of the limited foundation units and speed boundary conditions of the limited foundation units;
(2) taking an initial penalty factor of a linear programming model for solving the limit bearing capacity of the pile group of the silt soft soil foundation, and defining an allowable error;
(3) taking an initial point in a feasible region;
(4) constructing a penalty function of the linear programming model, and solving an extreme point of the penalty function by using an unconstrained optimization method from an initial point;
(5) and (4) performing loop iteration calculation, and if the iteration error is smaller than the defined allowable error, terminating the iteration and obtaining the optimal solution of the ultimate bearing capacity of the foundation.
6. The method for calculating the limit bearing capacity of the pile group of the silt soft soil foundation by the dynamic compaction replacement of the crushed stones according to claim 2 is characterized in that: the step 6 specifically comprises the following steps: (1) the principal stress of the nodes of finite elements in the foundation soil is calculated according to the following formula:
Figure FDA0003063159060000061
in the formula: n ═ 1, …, Nz)，NzIs the number of finite element nodes in the foundation;
Figure FDA0003063159060000062
is the effective positive stress of the nth node in the x direction;
Figure FDA0003063159060000063
is the effective positive stress of the nth node in the y direction;
Figure FDA0003063159060000064
is the shear stress of the nth node;
Figure FDA0003063159060000065
is the first principal stress of the nth node,
Figure FDA0003063159060000066
is the second principal stress of the nth node;
(2) the maximum node shear stress of the limited units in the foundation soil body is calculated according to the following formula:
Figure FDA0003063159060000067
in the formula: n ═ 1, …, Nz)，NzIs the number of finite element nodes in the foundation;
Figure FDA0003063159060000068
is the first principal stress of the nth node,
Figure FDA0003063159060000069
is the second principal stress of the nth node,
Figure FDA00030631590600000610
is the maximum shear stress of the nth node;
(3) and drawing a main stress contour line and a maximum shear stress contour line of the foundation soil body.
7. The method for calculating the limit bearing capacity of the pile group of the silt soft soil foundation by the dynamic compaction replacement of the crushed stones according to claim 2 is characterized in that: the step 7 specifically comprises the following steps: (1) the point safety factors of the nodes of the limited units in the foundation soil body are calculated according to the following formula:
Figure FDA00030631590600000611
in the formula: n ═ 1, …, Nz)，NzIs the number of finite element nodes in the foundation;
Figure FDA00030631590600000612
is the effective positive stress of the nth node in the x direction;
Figure FDA00030631590600000613
is the effective positive stress of the nth node in the y direction;
Figure FDA00030631590600000614
is the shear stress of the nth node;
Figure FDA00030631590600000615
is the internal friction angle of the nth node; c. CnIs the cohesion of the nth node;
(2) and drawing a point safety factor contour map according to the point safety factors of the limited unit nodes in the foundation soil body.
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