CN114969889A - Method for calculating stress of overhanging raft plate of piled raft foundation - Google Patents
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- 238000004364 calculation method Methods 0.000 claims abstract description 43
- 239000002689 soil Substances 0.000 claims description 148
- 238000007906 compression Methods 0.000 claims description 62
- 230000006835 compression Effects 0.000 claims description 61
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- 238000005452 bending Methods 0.000 claims description 13
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- 229920001971 elastomer Polymers 0.000 claims description 4
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Abstract
The invention provides a method for calculating stress of an overhanging raft plate of a piled raft foundation. The calculation method comprises the following steps: (1) simplifying a calculation model; (2) calculating the top uniform load coefficient of the overhanging raft according to the calculation model; (3) calculating the uniformly distributed load coefficient at the bottom of the overhanging raft according to the calculation model; (4) calculating equivalent uniform load of the overhanging raft; (5) and (5) calculating the stress of the outward-picking raft. The stress of the overhanging raft is calculated by establishing a pile raft foundation overhanging raft internal force simplified calculation model, so that the calculation process is simplified, the stress state of the overhanging raft can be calculated within the foundation settlement allowable range, and whether the reinforcing bars of the overhanging raft can meet the stress requirement is judged.
Description
Technical Field
The invention relates to the field of geotechnical engineering, in particular to a pile-raft foundation overhanging raft plate stress calculation method based on a foundation compression theory.
Background
The piled raft foundation has excellent integrity and uneven settlement resistance, and is widely used in high-rise buildings. When stake raft foundation design, often make the raft choose certain length outside the outside pile foundation, the setting of choosing the board through outside has increased the area of raft to the anti uneven settlement ability of reinforcing. After a certain length is chosen outside, because this section chooses structure upper portion earthing outside, receives the effect of soil pressure, and the lower part supports on the soil body, and the pile foundation takes place to subside the back, and raft bottom atress will change, so need consider its atress condition in the design process of choosing the board outside, judge according to its atress condition and choose the raft arrangement of reinforcement outward and whether satisfy the atress requirement to prevent that the raft from taking place to destroy, thereby guarantee the stability of whole stake raft foundation. However, the settlement of the building pile foundation is a slow dynamic process, the soil body at the lower part of the overhanging raft is compressed in the settlement process of the pile foundation, the compression process is also a dynamic process, and the stress of the overhanging raft is also a dynamic process along with the compression of the soil body, so that the calculation and solving of the stress condition of the overhanging raft are complex, a finite element model can be established for calculation at present, and the process is complex; how to simplify the calculation, the internal force of the exterior raft is calculated by using the settlement calculation result of the building or the maximum settlement allowable value of the building specified by the specification, so as to judge whether the reinforcement of the exterior raft meets the stress requirement or not, so as to prevent the raft from being damaged, which is a problem to be solved.
Disclosure of Invention
The invention aims to provide a simplified stress calculation method of an overhanging raft of a piled raft foundation based on a foundation soil compression theory, aiming at the problem of stress calculation of an overhanging raft of the existing piled raft foundation.
In order to achieve the technical purpose, the invention provides a method for calculating the stress of an overhanging raft plate of a piled raft foundation, which is characterized by comprising the following steps of:
(1) simplifying the calculation model: assuming that the outer cantilever raft is a linear elastomer, the raft is rigidly connected with the pile foundation and the outer wall of the building, the geological conditions are horizontally layered, and n layers of soil exist above bedrock below the raft; the structure is simplified into a cantilever structure, the top load of the overhanging raft is simplified into uniform wiring load, the load is the vertical dead weight stress of a soil body, and the bottom load of the overhanging raft is simplified into a group of springs; the settlement of the building foundation is equivalent to the sum of the compression of soil bodies on each layer below the raft;
(2) calculating the evenly distributed load coefficients at the top of the overhanging raft according to the calculation model in the step (1); the uniform load applied to the top surface of the raft is the vertical dead weight stress of the filled soil on the raft, and the uniform load coefficient applied to the top surface of the raft is the vertical dead weight stress sigma of the filled soil on the raft z The calculation formula is as follows:
σ z ＝γh ①
in the formula: gamma is the filling weight above the overhanging raft plate; h is the filling thickness above the overhanging raft plate;
(3) calculating the uniformly distributed load coefficients at the bottom of the overhanging raft according to the calculation model in the step (1);
assuming that the sum S of the force f received at the bottom of the outward-picking raft and the soil body compression amount of each layer below the raft has a linear relation, simplifying the soil body at the bottom of the outward-picking raft into a group of springs, obtaining the linear elastic coefficient k of the group of springs as the uniformly distributed load coefficient at the bottom of the outward-picking raft, and establishing the relation between the force f received at the bottom of the raft and the sum S of the soil body compression amount of each layer below the raft according to the hooke law:
f＝ks ②
according to the soil consolidation settlement theory, the sum of the compression amount of each layer of soil below the raft is S, and the method comprises the following steps:
in the formula: s. the i The compression amount of the i-th layer of soil body below the overhanging raft plate is determined; namely, it is
H i The thickness of the i-th layer of soil body below the overhanging raft plate;
e 1i the pore ratio of the ith layer of soil body below the overhanging raft plate before compression is adopted;
e 2i the porosity ratio of the compressed i-th layer of soil body below the overhanging raft plate is obtained;
substituting the formula III into the formula II to obtain the relation between the force f borne by the bottom of the outward-picking raft and the thickness of the ith layer of soil body below the outward-picking raft and the pore ratio before and after the ith layer of soil body is compressed:
in the formula: h i The thickness of the i-th layer of soil body below the overhanging raft plate;
e 1i the pore ratio of the ith layer of soil body below the overhanging raft plate before compression is adopted;
e 2i the porosity ratio of the compressed i-th layer of soil body below the overhanging raft plate is obtained;
when the gaps of the soil bodies of all layers below the raft plate completely disappear, that is, e 2i When the sum of the compression amount of each layer of soil body under the raft plate is 0, the sum of the compression amount of each layer of soil body under the raft plate is maximum, namely S is S max And substituting the formula (c) to obtain:
when the sum of the compression amount of each layer of soil body under the overhanging raft is maximum, namely S is equal to S max The force on the bottom of the overhanging raft is the largest, i.e. f ═ f max (ii) a Maximum force f applied max Taking the ultimate bearing capacity P of each soil layer below the raft at the moment u The minimum value of (a) is obtained:
f＝ks max ＝p u ⑥
substituting the formula (v) into the formula (v):
ultimate bearing capacity p of each soil layer below known overhanging raft u The minimum value is the pore ratio e before the ith layer of soil below the outward cantilever raft is compressed 1i Thickness H of the i-th layer soil below the overhanging raft i Determining the load coefficients k uniformly distributed on the bottom of the outward raft by the soil body according to a formula;
(4) calculating equivalent uniform load of the overhanging raft;
use vertical downwards for just, choose raft equivalent equipartition load outward for choosing raft top equipartition load outward and choose raft bottom equipartition load stack outward, have promptly:
substituting the formulas (i) and (b) into the formula (viii) to obtain the formula:
calculating the equivalent uniformly distributed load of the outward-picking raft plate according to the formula ninthly;
(5) calculating the stress of the outward-projecting raft;
obtaining a calculation formula of bending moment M and shear force value V of the overhanging raft plate by structural mechanics:
bringing formula ninthly into formula (R),
The formula is given as follows:
in the above formula: m is the bending moment of the overhanging raft plate; v is the shearing force of the overhanging raft plate;
s is the sum of the compressed amount of each layer of soil body below the overhanging raft plate;
p u the minimum value of the ultimate bearing capacity in each soil layer below the overhanging raft;
gamma is the filling weight above the overhanging raft, and h is the filling thickness above the overhanging raft;
l is the length of the outer overhang of the raft plate; h i The thickness of the i-th layer of soil body below the overhanging raft plate;
e 1i the pore ratio of the ith layer of soil body below the overhanging raft plate before compression is adopted;
according to the above formula
And the simplified calculation of the sum of the internal force of the overhanging structure of the raft and the compression amount of each layer of soil body below the raft is established.
The further technical scheme of the invention is as follows: in the step (3), after the foundation is settled, the load borne by the bottom of the overhanging raft is the force of the soil body on the bottom of the overhanging raft, and the soil body compression is a dynamic process along with the settlement of the foundation; the settlement of the foundation is assumed to be equal to the sum of the compressed amounts of all layers of soil bodies below the raft; the sum of the soil body compression quantities of all layers below the raft is set as s, and the force f borne by the bottom of the outward-picking raft and the sum of the soil body compression quantities of all layers below the raft are in the following relation:
when the foundation does not settle, the soil bodies of all layers below the raft plates do not compress, i.e. s is equal to 0, and the force borne by the bottom of the outward-picking raft plate is zero, i.e. f is equal to 0;
when the foundation settlement is maximum, all the soil bodies below the raft plate have no pore, and the sum of the compression amounts is maximum, namely s is s max The force on the bottom of the overhanging raft is the largest, i.e. f ═ f max ；
According to the relation, the linear relation between the force f borne by the bottom of the outward-picking raft and the sum s of the compression amounts of all layers of soil bodies below the raft can be assumed, the soil bodies at the bottom of the outward-picking raft are simplified into a group of springs, the linear elastic coefficient k of the group of springs is the uniformly distributed load coefficient at the bottom of the outward-picking raft, and the relation between the force f borne by the bottom of the raft and the sum s of the compression amounts of all layers of soil bodies below the raft is established according to the hooke's law.
The further technical scheme of the invention is as follows: in the step (3), after the foundation settlement reaches the maximum value, the rock-soil mass does not have compressibility any more until being damaged, so that a certain layer of soil mass below the raft plate can be assumed to reach the ultimate bearing capacity P at the moment u ，P u Taking the minimum value of ultimate bearing capacity in each layer of rock-soil, namely P u ＝min(P u1 ，P u2 ，…，P un )。
The invention assumes that the outer cantilever raft is a linear elastomer, the raft is rigidly connected with the pile foundation and the outer wall of the building, the geological conditions are horizontally layered, and n layers of soil are arranged above bedrocks below the raft. The structure can be simplified into a cantilever structure, the solution can be carried out by utilizing structural mechanics, and because the top of the overhanging raft is under the action of the soil pressure of the covered soil body, the top load of the overhanging raft is simplified into uniform wiring load, and the load is the vertical dead weight stress of the soil body; the bottom load of the overhanging raft varies with the variation of the settlement of the building, and the larger the settlement is, the larger the load is, so that the bottom load of the overhanging raft is simplified into a group of springs, and the elastic coefficient of the springs is the load coefficient; the settlement of the foundation is equivalent to the sum of the compression of the soil bodies on each layer below the raft.
The stress of the overhanging raft is calculated by establishing the pile raft foundation overhanging raft internal force simplified calculation model, so that the calculation process is simplified, and the stress state of the overhanging raft can be calculated within the foundation settlement allowable range, so that whether the reinforcing bars of the overhanging raft can meet the stress requirement is judged.
Drawings
Fig. 1 is a schematic structural view of an overhanging raft plate in the invention;
FIG. 2 is a simplified model for calculating the internal force of the overhanging raft in the present invention;
fig. 3 is a schematic diagram of calculation of internal force of the overhanging raft in the example;
fig. 4 shows the position relationship and coordinate directions of the outer raft and the outer contour of the building in the embodiment.
In the figure: 1-building outer wall, 2-raft, 3-raft overhanging area, 4-pile.
Detailed Description
The present invention will be further described with reference to the following examples. The technical solutions presented in the following examples are specific solutions of the examples of the present invention, and are not intended to limit the scope of the claimed invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a method for calculating stress of an overhanging raft plate of a piled raft foundation, which is characterized by comprising the following steps of:
(1) simplifying the calculation model: assuming that the outer cantilever raft is a linear elastomer, the raft is rigidly connected with the pile foundation and the outer wall of the building, the geological conditions are horizontally layered, and n layers of soil exist above bedrock below the raft; the structure can be simplified into a cantilever structure, and can be solved by using structural mechanics. Because the top of the overhanging raft is under the action of soil pressure of the soil body to be covered, the top load of the overhanging raft is simplified into uniform wiring load, and the load is the vertical self-weight stress of the soil body; the bottom load of the overhanging raft changes along with the change of the settlement amount, and the larger the settlement amount is, the larger the load is, so that the bottom load of the overhanging raft is simplified into a group of springs, and the elastic coefficient is the load coefficient; the settlement of the foundation is equivalent to the sum of the compression of the soil bodies of all layers below the raft; the structural schematic diagram is shown in fig. 1, and the simplified model for computing the internal force of the outer raft is shown in fig. 2;
(2) calculating the evenly distributed load coefficients at the top of the overhanging raft according to the calculation model in the step (1);
when the pile-raft foundation is constructed, firstly the foundation pit is excavated to the bottom surface of raft plate, after the construction of raft plate is completed, the foundation pit is backfilled, so that the uniformly-distributed load borne by top surface of raft plate is the vertical dead-weight stress of the filling soil covered on the raft plate, and the uniformly-distributed load coefficient borne by top surface of raft plate is the vertical dead-weight stress sigma of the filling soil covered on the raft plate z The calculation formula is as follows:
σ z ＝γh ①
in the formula: gamma is the filling weight above the overhanging raft, and h is the filling thickness above the overhanging raft;
(3) calculating the uniformly distributed load coefficients at the bottom of the overhanging raft according to the calculation model in the step (1);
after the foundation is settled, the load borne by the bottom of the raft is the force of the soil body on the bottom of the raft. As the soil body compression is a dynamic process along with the settlement of the foundation, the settlement of the foundation is equivalent to the sum of the compression of the soil bodies of all layers below the raft. The sum of the compression amount of soil bodies of the layers below the raft is set as s, and the force f borne by the bottom of the raft and the sum of the compression amount of the soil bodies of the layers below the raft are in the following relation:
when the foundation does not settle, the soil bodies of all layers below the raft plates do not compress, i.e. s is equal to 0, and the force borne by the bottom of the outward-picking raft plate is zero, i.e. f is equal to 0;
when the foundation settlement is maximum, all the soil bodies below the raft plate have no pore, and the sum of the compression amounts is maximum, namely s is s max The force applied to the bottom of the overhanging raft is the greatest, i.e. f ═ f max ；
According to the relation, the linear relation between the force f borne by the bottom of the outward-picking raft and the sum s of the compression amounts of the soil bodies on the following layers of the raft can be assumed, the soil bodies on the bottom of the outward-picking raft are simplified into a group of springs, the linear elastic coefficient k of the group of springs is the uniformly distributed load coefficient on the bottom of the outward-picking raft, and the relation between the force f borne by the bottom of the raft and the sum s of the compression amounts of the soil bodies on the following layers of the raft is established according to the hooke's law:
f＝ks②
according to the soil consolidation settlement theory, the sum of the compression amount of the soil of each layer below the raft is S, and the method comprises the following steps:
in the formula: s i The compression amount of the i-th layer of soil body below the overhanging raft plate is determined; namely, it is
H i The thickness of the i-th layer of soil body below the overhanging raft plate;
e 1i the pore ratio of the ith layer of soil body below the overhanging raft plate before compression is adopted;
e 2i the porosity ratio of the compressed i-th layer of soil body below the overhanging raft plate is obtained;
substituting the formula III into the formula II to obtain the relation between the force f borne by the bottom of the outward-picking raft and the thickness of the ith layer of soil body below the outward-picking raft and the pore ratio before and after the ith layer of soil body is compressed:
in the formula: h i The thickness of the i-th layer of soil body below the overhanging raft plate;
e 1i the pore ratio of the i-th layer of soil mass below the overhanging raft plate before compression is adopted;
e 2i the porosity ratio of the compressed i-th layer of soil body below the overhanging raft plate is obtained;
when the gaps of the soil body of each layer below the raft completely disappear, i.e. e 2i When it is equal to 0, the sum of the compression of soil body in each layer under the raft plate reaches maximum value, i.e. S is equal to S max And substituting the formula (c) to obtain:
when the sum of the compression amount of each layer of soil body below the raft reaches the maximum value, the rock-soil body has no compressibility until being damaged, so that the situation that the rock-soil body is compressed at the moment can be assumedThe limit bearing capacity P of a certain layer of soil body below the raft plate u ，P u Taking the minimum value of ultimate bearing capacity in each layer of rock-soil, namely P u ＝min(P u1 ，P u2 ，…，P un ) (ii) a When the sum of the compression amount of each layer of soil body below the overhanging raft is maximum, i.e. s is equal to s max The force applied to the bottom of the overhanging raft is the greatest, i.e. f ═ f max (ii) a Thus obtaining:
f＝ks max ＝p u ⑥
substituting the formula (v) into the formula (v):
the ultimate bearing capacity p of each soil layer below the known overhanging raft u The minimum value is the pore ratio e before the ith layer of soil below the outward cantilever raft is compressed 1i Thickness H of the i-th layer soil below the overhanging raft i Determining the load coefficients k of the soil body uniformly distributed at the bottom of the overhanging raft plates according to a formula;
(4) computing equivalent uniform load of overhanging raft
Use vertical downwards for just, choose raft equivalent equipartition load outward for choosing raft top equipartition load outward and choose raft bottom equipartition load stack outward, have promptly:
substituting the formulas (i) and (b) into the formula (viii) to obtain the formula:
calculating the equivalent uniformly distributed load of the outward-picking raft plate according to the formula ninthly;
(5) and (3) calculating the stress of the overhanging raft:
obtaining a calculation formula of bending moment M and a shear force value V of the overhanging raft by structural mechanics:
bringing formula ninthly into formula (R),
The formula is given as follows:
in the above formula: m is the bending moment of the overhanging raft plate; v is the shearing force of the overhanging raft plate;
s is the sum of the compression amount of each layer of soil body below the overhanging raft;
p u the minimum value of the ultimate bearing capacity of each soil layer below the overhanging raft plate;
gamma is the filling weight above the overhanging raft, and h is the filling thickness above the overhanging raft;
l is the length of the outer overhang of the raft plate; h i The thickness of the i-th layer of soil body below the overhanging raft plate; e.g. of the type 1i The pore ratio of the ith layer of soil body below the overhanging raft plate before compression is adopted;
according to the above formula
And the simplified calculation of the sum of the internal force of the overhanging structure of the raft and the compression of each layer of soil body below the raft is established.
The calculation method of the present invention is further illustrated by the following specific examples:
the embodiment takes a certain S-type house as an example, and the floor area of the building is 387m 2 99.90m of the height of the above-ground part building and 11474.88m of the total building area 2 Adopting a piled raft foundation; the raft plate is 1400mm thick, the overhang length of the raft plate is 2.0m, and the raft plate is made of C35 concrete (f) t ＝1.57N/mm 2 ) In the two-layer basement, the depth of the foundation pit is 7.4m, the pile diameter d is 1000-2000 mm, and the pile length is 24.5-25.8 m. The position relation and the coordinate direction of the outer cantilever rafts and the outer outline of the building are shown in figure 4. The raft reinforcement carries out bending moment calculation according to the multi-pile rectangular plate strip, and the result is as follows:
the maximum value of the bottom bending moment in the x direction is 51730.50(kN m), and the reinforcement area is calculated (considering rho) min ):118268.18mm 2 Steel bar for reinforcing
25@250 double layer +
18@ 250; actual matching area of 131047.8mm 2 . The reinforcement is pulled through during reinforcement, namely the reinforcement of the overhanging part is the same as the reinforcement of the raft plate.
The maximum value of the bottom bending moment in the y direction is 39405.76(kN m), and the reinforcement area is calculated (considering rho) min ):90090.91mm 2 Steel bar for reinforcing
25@250 double layer
18@250, actual area 131047.8mm 2 . The reinforcement is pulled through when in reinforcement arrangement, namely the reinforcement of the overhanging part is the same as the reinforcement of the raft plate.
The upper part of the raft is filled with silt (gamma is 19.9 KN/m) 3 ) Two layers of soil are arranged in the range above the bed rock below the raft, and the parameters take the following values: silt (pore ratio e before compression) 11 0.68, thickness H 1 10m, ultimate bearing capacity P u1 260Kpa), secondary red clay (pore ratio before compression e) 12 0.84, thickness H 1 15m, ultimate bearing capacity P u1 ＝320Kpa)。
To the stratum condition of below the raft foundation raft of above-mentioned building within range place, for effective judgement after subsiding and taking place, the atress situation of choosing the raft outward, whether its supporting bar can satisfy the requirement, prevent to choose the raft outward and take place to destroy, guarantee that the basis is stable, need to choose the structure internal force that receives outward to this raft and calculate.
The maximum settlement of the high-rise building pile foundation with the shear wall structure with a simple body shape is not more than 20cm according to the standard requirement, and the allowable maximum settlement is calculated by 20cm below; the pile length is 24.5-25.8 m, and the pile length is 25 m; the filling thickness above the top surface of the raft is the foundation pit depth (7.4m) minus the thickness of the raft (1.4m), namely 6m, the calculation is simplified into a model of a cantilever plate, and the calculation diagram is shown in figure 3:
the calculation process is as follows: taking the plate strip with unit width for calculation:
let l be 2m, gamma be 19.9KN/m 3 ，h＝6m，p u ＝min(P u1 ，P u2 )＝260Kpa，s＝0.2m，
e 11 ＝0.68，e 12 ＝0.84，H 1 ＝10m，H 2 15 m. Substituting the following two formulae:
calculating to obtain: m229.25 knm, V229.25 KN.
According to the calculation result, under the condition that the settlement reaches 20cm, the maximum bending moment borne by the outward-picking raft is 229.25KN m, the maximum shearing force is 229.25KN, the bending moment value is far smaller than the bottom bending moment 51730.50(kN m) of the raft calculated by the multi-pile rectangular slab band, and the shearing force value is far smaller than the shearing force 1305.61kN of the outward-picking raft (beta is determined according to foundation specification 8.2.9 strips) hs Beta is as follows hs ＝(800/h 0 ) 1/4 ＝(800/1350.00) 1/4 0.88; shear resistance calculation of 0.7 beta hs f t b w h 0 0.7 × 0.88 × 1570.00 × 1.0 × 1.35 ═ 1305.61 kN). The calculation result shows that the reinforcement bars obtained by calculating the bending moment at the bottom of the raft plate obtained by calculating the multi-pile rectangular plate strip can meet the stress requirement of the overhanging raft plate; when the pile foundation takes place the biggest settlement, the power that the raft receives of choosing outward is far less than the power that raft itself received under the external load effect, and raft itself can not take place to destroy in advance in choosing outward (2 m).
The above description is only one embodiment of the present invention, and the description is specific and detailed, but not construed as limiting the scope of the present invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the appended claims.
Claims (3)
1. A method for calculating the stress of an overhanging raft plate of a piled raft foundation is characterized by comprising the following steps:
(1) simplifying the calculation model: assuming that the outer cantilever raft is a linear elastomer, the raft is rigidly connected with the pile foundation and the outer wall of the building, the geological conditions are horizontally layered, and n layers of soil exist above bedrock below the raft; the structure is simplified into a cantilever structure, the top load of the overhanging raft is simplified into uniform wiring load, the load is the vertical dead weight stress of a soil body, and the bottom load of the overhanging raft is simplified into a group of springs; the settlement of the building foundation is equivalent to the sum of the compression of soil bodies on each layer below the raft;
(2) calculating the evenly distributed load coefficients at the top of the overhanging raft according to the calculation model in the step (1); the uniformly distributed load on the top surface of the raft is the vertical dead weight stress of the filled soil on the raft, and the uniformly distributed load coefficient on the top surface of the raft is the vertical dead weight stress sigma of the filled soil on the raft z The calculation formula is as follows:
σ z ＝γh ①
in the formula: gamma is the filling weight above the overhanging raft plate; h is the filling thickness above the overhanging raft plate;
(3) calculating the uniformly distributed load coefficients at the bottom of the overhanging raft according to the calculation model in the step (1);
assuming that the sum S of the force f received at the bottom of the outward-picking raft and the soil body compression amount of each layer below the raft has a linear relation, simplifying the soil body at the bottom of the outward-picking raft into a group of springs, obtaining the linear elastic coefficient k of the group of springs as the uniformly distributed load coefficient at the bottom of the outward-picking raft, and establishing the relation between the force f received at the bottom of the raft and the sum S of the soil body compression amount of each layer below the raft according to the hooke law:
f＝ks ②
according to the soil consolidation settlement theory, the sum of the compression amount of each layer of soil below the raft is S, and the method comprises the following steps:
in the formula: s i The compression amount of the i-th layer of soil body below the overhanging raft plate is determined; namely, it is
H i The thickness of the i-th layer of soil body below the overhanging raft plate;
e 1i the pore ratio of the ith layer of soil body below the overhanging raft plate before compression is adopted;
e 2i the porosity ratio of the compressed i-th layer of soil body below the overhanging raft plate is obtained;
substituting the formula III into the formula II to obtain the relation between the force f borne by the bottom of the outward-picking raft and the thickness of the ith layer of soil body below the outward-picking raft and the pore ratio before and after the ith layer of soil body is compressed:
in the formula: h i The thickness of the i-th layer soil body below the overhanging raft plate is measured;
e 1i the pore ratio of the ith layer of soil body below the overhanging raft plate before compression is adopted;
e 2i is arranged under the outward-projecting raft boardThe porosity of the compressed i-th layer of soil body;
when the gaps of the soil bodies of all layers below the raft plate completely disappear, that is, e 2i When the sum of the compression amount of each layer of soil body under the raft plate is 0, the sum of the compression amount of each layer of soil body under the raft plate is maximum, namely S is S max And substituting the formula (c) to obtain:
when the sum of the soil compression of each layer under the overhanging raft is maximum, namely S is S max The force on the bottom of the overhanging raft is the largest, i.e. f ═ f max (ii) a Maximum force f applied max Taking the ultimate bearing capacity P of each soil layer below the raft at the moment u The minimum value of (a) is obtained:
f＝ks max ＝p u ⑥
substituting the formula (v) into the formula (v):
ultimate bearing capacity p of each soil layer below known overhanging raft u The minimum value of the intermediate value is the pore ratio e before the compression of the ith layer of soil below the outer cantilever raft 1i Thickness H of the i-th layer soil below the overhanging raft i Determining the load coefficients k uniformly distributed on the bottom of the outward raft by the soil body according to a formula;
(4) calculating equivalent uniform load of the overhanging raft;
use vertical downwards for just, choose raft equivalent equipartition load outward for choosing raft top equipartition load outward and choose raft bottom equipartition load stack outward, have promptly:
substituting the formulas (i) and (b) into the formula (viii) to obtain the formula:
calculating the equivalent uniformly distributed load of the outward-picking raft plate according to the formula ninthly;
(5) calculating the stress of the outward-picking raft plate;
obtaining a calculation formula of bending moment M and a shear force value V of the overhanging raft by structural mechanics:
bringing formula ninthly into formula (R),
The formula is obtained:
in the above formula: m is the bending moment of the overhanging raft plate; v is the shearing force of the overhanging raft plate;
s is the sum of the compressed amount of each layer of soil body below the overhanging raft plate;
p u the minimum value of the ultimate bearing capacity in each soil layer below the overhanging raft;
gamma is the filling weight above the overhanging raft, and h is the filling thickness above the overhanging raft;
l is the length of the outer overhang of the raft plate; h i The thickness of the i-th layer of soil body below the overhanging raft plate;
e 1i before the ith layer of soil mass below the overhanging raft is compressedThe porosity ratio of (a);
according to the above formula
And the simplified calculation of the sum of the internal force of the overhanging structure of the raft and the compression amount of each layer of soil body below the raft is established.
2. The method for calculating the stress of the overhanging raft plate of the piled raft foundation according to claim 1, wherein the method comprises the following steps: in the step (3), after the foundation is settled, the load borne by the bottom of the overhanging raft is the force of soil body on the bottom of the overhanging raft, and soil body compression is a dynamic process along with the settlement of the foundation; assuming that the settlement of the foundation is equal to the sum of the compression of each layer of soil body below the raft; the sum of the soil body compression quantities of all layers below the raft is set as s, and the force f borne by the bottom of the outward-projecting raft and the sum of the soil body compression quantities of all layers below the raft have the following relations:
when the foundation does not settle, the soil bodies of all layers below the raft plates do not compress, i.e. s is equal to 0, and the force borne by the bottom of the outward-picking raft plate is zero, i.e. f is equal to 0;
when the foundation settlement is maximum, all the soil bodies below the raft plate have no pore, and the sum of the compression amounts is maximum, namely s is s max The force on the bottom of the overhanging raft is the largest, i.e. f ═ f max ；
According to the relation, the linear relation between the force f borne by the bottom of the outward-picking raft and the sum s of the compression amounts of all layers of soil bodies below the raft can be assumed, the soil bodies at the bottom of the outward-picking raft are simplified into a group of springs, the linear elastic coefficient k of the group of springs is the uniformly distributed load coefficient at the bottom of the outward-picking raft, and the relation between the force f borne by the bottom of the raft and the sum s of the compression amounts of all layers of soil bodies below the raft is established according to the hooke's law.
3. The method for calculating the stress of the overhanging raft plate of the piled raft foundation according to claim 1, wherein the method comprises the following steps: in the step (3), after the foundation settlement reaches the maximum value, the rock-soil mass does not have compressibility any more until being damaged, so that a certain layer of soil mass below the raft plate can be assumed to reach the ultimate bearing capacity P at the moment u ，P u Taking the minimum value of ultimate bearing capacity in each layer of rock-soil, namely P u ＝min(P u1 ，P u2 ，…，P un )。
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| JP2013209839A (en) * | 2012-03-30 | 2013-10-10 | Fujita Corp | Method for analyzing settlement of piled raft foundation |
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