CN110210145B - Single pile settlement calculation method for grouting filling pile after squeezing and expanding support plate - Google Patents
Single pile settlement calculation method for grouting filling pile after squeezing and expanding support plate Download PDFInfo
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Abstract
The invention discloses a method for calculating the single pile settlement of a grouting filling pile after extruding and expanding a supporting plate, which belongs to the technical field of building pile foundations and adopts the following scheme: the pile foundation settlement calculation method of the grouting filling pile after the support plate is squeezed and expanded does not consider the bearing platform bottom foundation soil load sharing effect, and the single pile settlement calculation method of the grouting filling pile after the support plate is squeezed and expanded is as follows: respectively establishing a coordinate system for two equal section piles, respectively calculating additional stress in foundation soil on the pile body axis below the pile end plane according to Mindlin solution considering the influence of the pile diameter, then superposing the additional stress generated by calculation points, calculating the settlement of the pile foundation by adopting a unidirectional compression layering sum method, and calculating the compression of the pile body at the section part from the pile top to the disc top; the invention is suitable for the field of calculation of settlement of building pile foundations.
Description
Technical Field
The invention discloses a single pile settlement calculation method for grouting bored concrete piles after extruding and expanding a supporting plate, and belongs to the technical field of building pile foundations.
Background
Pile foundations are one of the important forms of building foundations, and for high-rise buildings and bridges, the vast majority of pile foundations are adopted. In the later 50 s of the 20 th century, india starts to adopt multi-section reaming piles in expansive soil, and in the early 1978, two-section and three-section reaming short piles with the diameter of an enlarged head of 480m and the length of 5m are subjected to experimental study on a 300mm small-diameter pile body by the Beijing city building engineering institute. Then about 2000, the application popularization and mechanism research of the extruded and expanded support disc pile are carried out in many places in China. The extruding and expanding support plate concrete filling pile is formed by extruding and expanding soil at different positions of the lower part of a pile body by using special extruding and expanding equipment, so that the compression amount of the soil is reduced, and then a reinforcement cage is hung and filled with concrete to form the extruding and expanding support plate filling pile. When the grouting pipe is pre-buried at the pile bottom and grouting is carried out at the pile bottom after pile forming, the grouting filling pile after the extruding and expanding supporting disc is formed. Because the supporting disks are arranged at different positions of the pile body, the end bearing force is used for replacing part of friction force, so that the bearing force of a single pile is greatly improved, and the settlement is obviously reduced. And further, obvious economic and social benefits are obtained in the aspects of increasing the safety of pile foundations, reducing the construction cost and shortening the construction period. At present, the extruding and expanding support disc pile is applied and popularized in the domestic partial area, and some engineering data are accumulated, but the whole technology is still in the technology development and research application stage.
The pile foundation design for bearing vertical load comprises two parts, namely, the bearing capacity of the pile is determined, and the settlement of the pile is determined. The mandatory regulations of foundation design of building (GB 50007-2011) prescribe that the design grade is A-grade and B-grade buildings are designed according to foundation deformation. At present, the bearing capacity transfer mechanism of the grouting filling pile after the branch plate is squeezed and expanded is more studied, but the sedimentation study is less, and the grouting filling pile after the branch plate is squeezed and expanded is not formally listed in the current industry specification of building pile foundation technical specification (JGJ 94-2008) and the current national specification of building foundation basic design specification (GB 50007-2011). At present, no theory exists for settlement calculation when the grouting filling pile bears vertical load after the branch plate is extruded and expanded.
The invention provides a single pile, single row pile or pile foundation single pile settlement calculation method formed by grouting and filling piles after extruding and expanding a supporting disc, which is unified with the thought of Guan Zhuangji settlement calculation in the existing industry standard building pile foundation technical Specification (JGJ 94-2008), and is beneficial to providing a calculation method for solving the settlement problem of grouting and filling piles after bearing vertical load extruding and expanding the supporting disc.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a single pile settlement calculation method for a single pile, a single row pile or a sparse pile foundation with a pile center distance of more than 6 times of pile diameter formed by grouting filling piles after extruding and expanding a supporting disc.
In order to solve the problems, the invention adopts the following scheme:
the single pile settlement calculation method of the grouting filling pile after the support plate is squeezed and expanded comprises the following steps of:
simplifying the grouting filling pile after extruding and expanding the supporting disc into an upper equal-diameter pile and a lower equal-diameter pile, and equivalently simplifying the variable-section pile body into two equal-section pile bodies; the stress equivalent of the foundation pile is simplified to be that the pile top bears the uniformly distributed side resistance to the disc top section of the upper disc, and the disc top section of the upper disc bears the uniformly distributed side resistance and the uniformly distributed end resistance to the pile end;
the settlement amount of the grouting filling pile single pile after the branch plate is extruded and expanded is calculated as follows: and respectively establishing a coordinate system for two equal-section piles, respectively calculating the additional stress in foundation soil on the pile body axis below the pile end plane according to Mindlin solution considering the influence of the pile diameter, then superposing the additional stress generated by calculation points, calculating the settlement of the pile foundation by adopting a unidirectional compression layering sum method, and calculating the compression of the pile body at the section part of the pile top to the disc top.
Further, the post-extrusion expansion support disc grouting filling pile is divided into two equal-diameter piles from the pile top to the disc top section of the upper disc and from the disc top section of the upper disc to the pile end at the disc top section of the upper disc, a coordinate system is respectively established, and Mindlin solutions considering the influence of the pile diameter are respectively applied to solve stress influence coefficients;
a. calculating an equal cross-section pile according to the actual cross-section area and the length of the pile at the section part of the pile top to the upper disc top, and only considering side resistance; the section from the top of the upper disc to the pile end is simplified into a large-diameter equal-section pile with the maximum projection area of the supporting disc as the equivalent section area of the pile body, and the length from the top of the upper disc to the pile end is equivalent pile length;
b. the origin of coordinates of the section part of the pile top to the upper disc top is the pile top of the original grouting filling pile after the extruding and expanding support disc, the ordinate z=l is taken as a settlement initial calculation point, l is the pile length of the grouting filling pile after the extruding and expanding support disc, and stress influence coefficients generated by different depths of the foundation of the section of side resistance on the pile body axis below the pile end are calculated;
c. the origin of coordinates from the top section of the upper disc to the pile end part is the plane where the top section of the upper disc is located, and the ordinate z=l is adopted 2 Calculate the point for the onset of sedimentation, where l 2 For the length from the top of the upper disc to the pile end,respectively calculating stress influence coefficients generated by different depths of the foundation on the pile body axis below the pile end of the section of simplified side resistance and end resistance;
d. the pile top to upper disc top section and the pile end two parts of foundation pile side resistance distribution from the upper disc top section to the pile end are simplified into a mode of uniform distribution along the pile body, and the pile end resistance is simplified into a mode of uniform distribution in the maximum projection area of the supporting disc;
e. pile end equivalent end resistance, pile top to upper disc top section pile side resistance and pile top section to pile end pile side resistance are stress influence coefficients Ip and I at half thickness of ith layer soil on pile body axis below pile end plane sr1 And I sr2 Respectively calculating according to a formula (2-1) and a formula (2-2), or checking an annex F (Mindlin) stress relief influence coefficient considering the influence of pile diameter) of an existing industry standard (building pile foundation technical Specification) (JGJ 94-2008), and directly determining I p 、I sr1 And I sr2 ；
Wherein:
calculating the I from the top section of the upper disc to the pile end according to the formula (2-1) p When r=d/2, l=l 2 Substituting the formula for replacement, wherein r is the radius of the foundation pile of the calculated section, and the unit is m; d is the pile diameter from the top section of the upper disc to the pile end section, and the unit is m; z is the distance from the sedimentation calculation point to the top section of the upper disc, and the unit is m;
calculating the I of the section of the pile top and the upper disc top according to the formula (2-2) sr1 When r=d/2, l=l 1 Substituting the formula for replacement, wherein r is the radius of the foundation pile of the calculated section, and the unit is m; d is the pile diameter of the section of the pile top to the upper disc top, and the unit is m; z is the distance from the settlement calculation point to the pile top, and the unit is m;
calculating the I from the top section of the upper disc to the pile end according to the formula (2-2) sr2 At the time, r=D/2，l＝l 2 Substituting the formula for replacement, wherein r is the radius of the foundation pile of the calculated section, and the unit is m; d is the pile diameter from the top section of the upper disc to the pile end section, and the unit is m; z is the distance from the sedimentation calculation point to the top section of the upper disc, and the unit is m;
poisson's ratio μ is 0.35;
f. when the positive stress superposition result under the calculation point is a negative value, the value should be taken according to zero.
Further, the final sedimentation calculation depth Z of the pile foundation of the grouting filling pile after the branch plate is squeezed and expanded n Determined by stress ratio, i.e. Z n Additional stress sigma induced by the pile z Dead weight stress sigma with earth c The following formula requirements should be met:
σ z ≤0.2σ c 。 (3-1)
further, the final settlement s of the pile foundation without load sharing of the foundation soil at the bottom of the bearing platform is calculated according to the following formula:
wherein,,
n- -calculating the number of layers of the soil layer in the sedimentation calculation depth range; the layering number should be combined with the soil layer property, and the layering thickness should not exceed 0.3 times of the calculated depth;
the final settlement of the grouting filling pile on the pile body axis below the pile end plane after the s-squeezing and expanding supporting disc is in mm;
s e pile head to upper discCalculating the compression amount of the pile body in mm by the top length section;
σ z1i -the length section from the pile top to the upper disc top, wherein the side resistance is uniformly distributed to generate additional stress at the position of half thickness of the ith layer of soil on the pile body axis below the pile end plane, and the unit is kPa;
σ z2i -the length section from the top of the upper disc to the pile end, wherein the pile end equivalent end resistance and the uniformly distributed side resistance generate the sum of additional stress at the position of one half thickness of the ith layer of soil on the pile body axis below the pile end plane, and the unit is kPa;
calculating the soil layer thickness of Deltazi-ith, wherein the unit is m;
E si calculating the compression modulus of the soil layer, wherein the unit is MPa, and the compression modulus from the self-weight pressure of the soil to the self-weight pressure of the soil plus the pressurizing force is adopted;
q is the additional load of the pile top under the quasi-permanent combined action of the load effect of the grouting filling pile after extruding and expanding the supporting disc, and the unit is kN;
Q 1 under the quasi-permanent combined action of load effect, the sum of axial forces born by pile top and pile body of upper disk top section is given as kN, and the unit is equal to the sum of side resistances of pile top and upper disk top length section in value, and can be calculated according to Q t ＝πd∑q sj l j Calculation, where q sj For the soil side resistance of the j th layer around the pile, l j The thickness of the j-th soil layer around the pile is the thickness of the j-th soil layer around the pile, and d is the diameter of a part of the pile on the top surface section of the upper disc;
Q 2 under the quasi-permanent combined action of load effect, the axial force of pile body at the top section of upper disk is calculated according to Q 2 ＝Q-Q t Calculating a unit kN;
l 1 -the section length from the pile top to the top of the upper disc is m;
l 2 -the length from the top section of the upper disc to the pile end is m;
A ps pile body section area from pile top to upper disc top section length section, the unit is m 2 ；
The ratio of the resistance of the alpha-pile end, namely the ratio of the equivalent total end resistance of the chassis and the pile end to the axial force of the pile body at the section of the top of the upper disc, is approximately the ratio of the equivalent total end resistance born by the chassis and the pile end to the difference of the single pile bearing capacity minus the total side resistance of the pile side of the part above the top of the upper disc;
I p，i 、I sr1，i 、I sr2，i mindlin stress influence coefficient considering pile diameter influence, I p，i The stress influence coefficient is the stress influence coefficient of the equivalent end resistance of the chassis and the pile end at the position of one half of the thickness of the i-th layer of soil below the pile end plane; i sr1，i The stress influence coefficient is the stress influence coefficient of the pile top to the pile side resistance of the section of the upper disc top at the position of one half thickness of the ith layer of soil below the pile end plane; i sr2，i The stress influence coefficient is the stress influence coefficient of the resistance from the top section of the upper disc to the pile side of the pile end at the position of one half thickness of the ith layer of soil below the pile end plane;
E c the elastic modulus of pile body concrete is expressed as MPa;
ξ e pile body compression coefficient, according to local settlement observation data and experience determination, taking psi when no local experience exists D ＝1.0；
Psi-pile foundation settlement correction coefficient, according to local settlement observation data and experience determination, taking psi when no local experience exists D ＝1.0。
Compared with the prior art, the invention has the following beneficial effects:
1. the top section of the upper disc of the grouting filling pile after the support disc is extruded and expanded is divided into two parts, and the two parts are simplified into an upper equal-diameter pile and a lower equal-diameter pile which are connected, so that the variable-section pile body is changed into two equal-section pile bodies, and the complex problem is simplified.
2. The coordinate system is respectively established by the sections of the pile top and the upper disc top, the Mindlin solution formula considering the influence of the pile diameter is respectively applied to the upper and lower equal-diameter piles to calculate the additional stress generated in the foundation on the pile body axis below the pile end plane, the additional stress generated by the calculation points is overlapped, and then the settlement of the pile foundation is calculated by adopting the unidirectional compression layering sum method, so that the continuity of Guan Zhuangji settlement calculation ideas is ensured with the current industry specification of building pile foundation technical specification (JGJ 94-2008).
3. After the grouting filling pile is simplified into an upper pile and a lower pile which are connected with each other and have equal diameters after the branch disc is extruded and expanded, a Mindlin solution formula considering the influence of the pile diameter is applied, and the grouting filling pile is easy to accept by engineering technicians and is convenient to popularize and apply practically.
Drawings
The method for calculating the single pile settlement of the grouting filling pile after the branch plate is squeezed and expanded is further described below with reference to the accompanying drawings.
FIG. 1 is a schematic diagram showing stress decomposition of single pile side resistance and end resistance of a grouting filling pile after squeezing and expanding a supporting disc.
Fig. 2 is data of single pile settlement calculation of grouting bored concrete piles after squeezing and expanding a supporting disc according to an embodiment of the present invention.
In the figure: d is the diameter of the section of the pile top to the disc top of the upper disc; d is the equivalent diameter from the top section of the upper disc to the pile end; l is the pile length of the grouting filling pile after extruding and expanding the supporting disc; l (L) 1 The pile length is the pile length of the section of the pile top to the upper disc top; l (L) 2 Pile length from the top section of the upper disc to the pile end; q is the additional load of the pile top of the grouting filling pile after the branch plate is squeezed and expanded under the quasi-permanent combined action of the load effect; q (Q) 1 In order to ensure that the sum of axial forces born by the pile body at the upper part of the section of the top surface of the upper disc under the quasi-permanent combined action of the load effect, Q 2 The pile shaft axial force is applied to the top section of the upper disc under the quasi-permanent combined action of the load effect.
Detailed Description
The invention is further described with reference to fig. 1-2, in particular to a single pile settlement calculation method and data of grouting filling piles after squeezing and expanding supporting plates when foundation soil at the bottom of a bearing platform does not share load.
The single pile settlement calculation method of the grouting filling pile after the support plate is squeezed and expanded comprises the following steps of:
simplifying the grouting filling pile after extruding and expanding the supporting disc into an upper equal-diameter pile and a lower equal-diameter pile, and equivalently simplifying the variable-section pile body into two equal-section pile bodies; the stress equivalent of the foundation pile is simplified to be that the pile top bears the uniformly distributed side resistance to the disc top section of the upper disc, and the disc top section of the upper disc bears the uniformly distributed side resistance and the uniformly distributed end resistance to the pile end;
the settlement amount of the grouting filling pile single pile after the branch plate is extruded and expanded is calculated as follows: and respectively establishing a coordinate system for two equal-section piles, respectively calculating the additional stress in foundation soil on the pile body axis below the pile end plane according to Mindlin solution considering the influence of the pile diameter, then superposing the additional stress generated by calculation points, calculating the settlement of the pile foundation by adopting a unidirectional compression layering sum method, and calculating the compression of the pile body at the section part of the pile top to the disc top.
Further, the post-extrusion expansion support disc grouting filling pile is divided into two equal-diameter piles from the pile top to the disc top section of the upper disc and from the disc top section of the upper disc to the pile end at the disc top section of the upper disc, a coordinate system is respectively established, and Mindlin solutions considering the influence of the pile diameter are respectively applied to solve stress influence coefficients;
a. calculating an equal cross-section pile according to the actual cross-section area and the length of the pile at the section part of the pile top to the upper disc top, and only considering side resistance; the section from the top of the upper disc to the pile end is simplified into a large-diameter equal-section pile with the maximum projection area of the supporting disc as the equivalent section area of the pile body, and the length from the top of the upper disc to the pile end is equivalent pile length;
b. the origin of coordinates of the section part of the pile top to the upper disc top is the pile top of the original grouting filling pile after the extruding and expanding support disc, the ordinate z=l is taken as a settlement initial calculation point, l is the pile length of the grouting filling pile after the extruding and expanding support disc, and stress influence coefficients generated by different depths of the foundation of the section of side resistance on the pile body axis below the pile end are calculated;
c. the origin of coordinates from the top section of the upper disc to the pile end part is the plane where the top section of the upper disc is located, and the ordinate z=l is adopted 2 Calculate the point for the onset of sedimentation, where l 2 For the length from the top of the upper disc to the pile end, respectively calculating stress influence coefficients generated by different depths of the foundation on the pile body axis below the pile end by the simplified side resistance and end resistance of the section;
d. the pile top to upper disc top section and the pile end two parts of foundation pile side resistance distribution from the upper disc top section to the pile end are simplified into a mode of uniform distribution along the pile body, and the pile end resistance is simplified into a mode of uniform distribution in the maximum projection area of the supporting disc;
e. pile end equivalent end resistance, pile top to upper disc top section pile side resistance and upper disc top section to upper disc top sectionStress influence coefficient Ip, I of pile end pile side resistance at half thickness of ith layer soil on pile body axis below pile end plane sr1 And I sr2 Respectively calculating according to a formula (2-1) and a formula (2-2), or checking an annex F (Mindlin) stress relief influence coefficient considering the influence of pile diameter) of an existing industry standard (building pile foundation technical Specification) (JGJ 94-2008), and directly determining I p 、I sr1 And I sr2 ；
Wherein:
calculating the I from the top section of the upper disc to the pile end according to the formula (2-1) p When r=d/2, l=l 2 Substituting the formula for replacement, wherein r is the radius of the foundation pile of the calculated section, and the unit is m; d is the pile diameter from the top section of the upper disc to the pile end section, and the unit is m; z is the distance from the sedimentation calculation point to the top section of the upper disc, and the unit is m;
calculating the I of the section of the pile top and the upper disc top according to the formula (2-2) sr1 When r=d/2, l=l 1 Substituting the formula for replacement, wherein r is the radius of the foundation pile of the calculated section, and the unit is m; d is the pile diameter of the section of the pile top to the upper disc top, and the unit is m; z is the distance from the settlement calculation point to the pile top, and the unit is m;
calculating the I from the top section of the upper disc to the pile end according to the formula (2-2) sr2 When r=d/2, l=l 2 Substituting the formula for replacement, wherein r is the radius of the foundation pile of the calculated section, and the unit is m; d is the pile diameter from the top section of the upper disc to the pile end section, and the unit is m; z is the distance from the sedimentation calculation point to the top section of the upper disc, and the unit is m;
poisson's ratio μ is 0.35;
f. when the positive stress superposition result under the calculation point is a negative value, the value should be taken according to zero.
Further, the final sedimentation calculation depth Z of the pile foundation of the grouting filling pile after the branch plate is squeezed and expanded n Determined by stress ratio, i.e. Z n Additional stress sigma induced by the pile z Dead weight stress sigma with earth c The following formula requirements should be met:
σ z ≤0.2σ c 。 (3-1)
further, the final settlement s of the pile foundation without load sharing of the foundation soil at the bottom of the bearing platform is calculated according to the following formula:
wherein,,
n- -calculating the number of layers of the soil layer in the sedimentation calculation depth range; the layering number should be combined with the soil layer property, and the layering thickness should not exceed 0.3 times of the calculated depth;
the final settlement of the grouting filling pile on the pile body axis below the pile end plane after the s-squeezing and expanding supporting disc is in mm;
s e -calculating the compression amount of the pile body in mm from the pile top to the upper disc top;
σ z1i -the length section from the pile top to the upper disc top, wherein the side resistance is uniformly distributed to generate additional stress at the position of half thickness of the ith layer of soil on the pile body axis below the pile end plane, and the unit is kPa;
σ z2i the length section from the top of the upper disc to the pile end, the equivalent end resistance of the pile end and the uniformly distributed side resistance generate the sum of additional stress at the position of half thickness of the ith layer of soil on the pile shaft axis below the pile end plane,the unit is kPa;
calculating the soil layer thickness of Deltazi-ith, wherein the unit is m;
E si calculating the compression modulus of the soil layer, wherein the unit is MPa, and the compression modulus from the self-weight pressure of the soil to the self-weight pressure of the soil plus the pressurizing force is adopted;
q is the additional load of the pile top under the quasi-permanent combined action of the load effect of the grouting filling pile after extruding and expanding the supporting disc, and the unit is kN;
Q 1 under the quasi-permanent combined action of load effect, the sum of axial forces born by pile top and pile body of upper disk top section is given as kN, and the unit is equal to the sum of side resistances of pile top and upper disk top length section in value, and can be calculated according to Q t ＝πd∑q sj l j Calculation, where q sj For the soil side resistance of the j th layer around the pile, l j The thickness of the j-th soil layer around the pile is the thickness of the j-th soil layer around the pile, and d is the diameter of a part of the pile on the top surface section of the upper disc;
Q 2 under the quasi-permanent combined action of load effect, the axial force of pile body at the top section of upper disk is calculated according to Q 2 ＝Q-Q t Calculating a unit kN;
l 1 -the section length from the pile top to the top of the upper disc is m;
l 2 -the length from the top section of the upper disc to the pile end is m;
A ps pile body section area from pile top to upper disc top section length section, the unit is m 2 ；
The ratio of the resistance of the alpha-pile end, namely the ratio of the equivalent total end resistance of the chassis and the pile end to the axial force of the pile body at the section of the top of the upper disc, is approximately the ratio of the equivalent total end resistance born by the chassis and the pile end to the difference of the single pile bearing capacity minus the total side resistance of the pile side of the part above the top of the upper disc;
I p，i 、I sr1，i 、I sr2，i mindlin stress influence coefficient considering pile diameter influence, I p，i The stress influence coefficient is the stress influence coefficient of the equivalent end resistance of the chassis and the pile end at the position of one half of the thickness of the i-th layer of soil below the pile end plane; i sr1 I is the bisection of the ith layer of soil with pile top to upper disc top section pile side resistance below the pile end planeA stress influencing coefficient at a thickness; i sr2 I is the stress influence coefficient of the resistance from the top section of the upper disc to the pile side of the pile end at the position of one half of the thickness of the ith layer of soil below the pile end plane;
E c the elastic modulus of pile body concrete is expressed as MPa;
ξ e pile body compression coefficient, which is determined based on local settlement observation data and experience, and is obtained without local experience ψD ＝1.0；
Psi-pile foundation settlement correction coefficient, according to local settlement observation data and experience determination, taking when no local experience exists ψD ＝1.0。
The construction foundation adopts a 34-layer shear wall structure, grouting pile after a drilling extrusion and expansion support plate, the length of the construction foundation is 63.6m, the width of the construction foundation is 18.6m, the burial depth is 7m, and grouting pile after a drilling extrusion and expansion support plate is adopted. The pile diameter is 800mm, the effective pile length is 24m, the pile spacing is 5m, and the piles are arranged in full. Two bearing disks are arranged, the upper disk is positioned at the 16.8m position (elevation at the maximum diameter position) below the pile top, the elevation of the section of the disk top is 16.0m below the pile top, the lower disk is positioned at the 22.8m position (elevation at the maximum diameter position) below the pile top, the disk heights are 1.6m, and the diameters of the upper disk and the lower disk are 1.8m. The ground stratum condition and related material indexes are shown in table 1, and the ground water level is 7m below the ground. Under the quasi-permanent combined action of the load effect, the pile top load is 4015kN. Concrete adopts C40 and E c ＝3.25×10 4 MPa。
Table 1 shows the site formation parameters, specifically as follows:
and (3) single pile settlement calculation of the grouting filling pile after extruding and expanding the supporting disc, wherein the distance-diameter ratio s/d=5/0.8=6.25 is larger than 6, and a single pile settlement calculation formula is adopted. Dividing the grouting filling pile after extruding and expanding the supporting disc into an upper part and a lower part at the top section of the upper disc, respectively calculating additional stress, and then superposing and calculating the settlement of the grouting filling pile after extruding and expanding the supporting disc.
1. Calculating pile end resistance ratio alpha;
quasi-permanent combined action at load effectUnder the condition that pile top load is Q=4015kN, Q is taken out sj ＝20kPa，l 1 ＝16m，d＝0.8m。
Q 1 ＝πd∑qsjl j ＝3.14×0.8×20×16＝804kN
Q 2 ＝Q-Q 1 ＝3211kN
Q p ＝A p2 q p ＝3.14×1.8 2 /4×800＝2035kN
α＝Q p /Q 2 ＝2035/3211＝0.63
2. Additional stresses on the shaft axis below the pile end plane in the section of the top-to-top disc
The section part of the pile top to the upper disc top is calculated according to the actual section of the pile, only the side resistance is considered, the side resistance distribution of the foundation pile is simplified into a mode of uniformly distributing along the pile body, and q is taken sj =20 kPa. Establishing a coordinate system, taking the pile top of the grouting filling pile after the original extruding and expanding support disc from a coordinate origin, namely, at the elevation of the bottom surface of the bearing platform at the position 7m below the ground, l 1 =16m, d=0.8m, z 1 =l=24m as the starting calculation point, where l 1 /d＝16/0.8＝20，n＝ρ/l 1 =0 (ρ is the horizontal distance of the pile axis calculated for the adjacent pile values, and ρ=0 is taken for a single pile irrespective of the influence of the adjacent pile), when m=z 1 /l 1 Taking I as the starting point (corresponding to 31m below ground) =24/16=1.5 sr1 =0.367; when m=z 1 /l 1 =24/16=1.6, take I sr1 =0.298; when m=1.5-1.6, I sr1 Calculating according to interpolation; when m is more than 1.6, take I sr1 =0.298. Checking annex F (Mindlin stress relief influence coefficient considering pile diameter influence) of current industry standard building pile foundation technical Specification (JGJ 94-2008), and calculating vertical stress influence coefficients I generated for different depths below a pile end downwards sr1 See fig. 2.
Calculation of sigma from formula z1 ：
3. Additional stress generated on pile shaft axis from top section of upper disc to pile end part below pile end plane
When the pile side resistance and the equivalent end resistance from the top section of the upper disc to the pile end generate settlement at the pile end plane settlement calculation point, the part from the top section of the upper disc to the pile end is simplified into a large-diameter equal-section pile with the maximum supporting disc projection area as the equivalent section area of the pile body, and the length from the top section of the upper disc to the pile end is equivalent pile length. From this, l 2 =8m, d=1.8m. The pile side resistance distribution of the grouting filling pile foundation after the support disc is squeezed and expanded is simplified into a uniform distribution mode along the pile body, and the pile end resistance is simplified into a uniform distribution mode in the projection area of the maximum support disc.
The origin of coordinates is the plane in which the top section of the upper disc lies, i.e. the origin of reference at 23m below the ground. In z 2 ＝l 2 =8m is the starting calculation point (corresponding to 31m below ground). At this time l 2 D=8/1.8=4.4 < 10, taking l 2 Corresponding table of/d=10, n=ρ/l 2 =0 (ρ is the horizontal distance of the pile axis calculated for the adjacent pile values, and ρ=0 is taken for a single pile irrespective of the influence of the adjacent pile), when m=z 2 /l 2 For a starting point, 8/8=1.0, find annex F (Mindlin solution stress influence coefficient considering pile diameter influence) of current industry standard building pile foundation technical Specification (JGJ 94-2008), and calculate downward vertical stress influence coefficient I for pile side resistance and equivalent end resistance at different depths below the pile end sr2 And I p See fig. 2.
From the formula, σ is calculated separately zp Sum sigma zsr2 Then calculate sigma z2 ：
σ z2 ＝σ zp +σ zsr2 ＝31.61I p +18.56I sr2 ；
4. Grouting filling pile after determining extruding and expanding support discCalculated depth Z of final sedimentation of (a) n . Can be determined by stress ratio method, i.e. Z n Additional stress sigma induced by the pile z Dead weight stress sigma with earth c The following formula requirements should be met:
σ z ＝σ z1 +σ z2
σ z ≤0.2σ c ； (3-1)
as can be seen from FIG. 2, Z is below the pile end n When=27.2m (34.2 m below ground), σ z Corresponding dead weight stress of 0.2σ = 51.038kPa c = 76.288kPa, satisfying the formula (3-1).
5. Calculating pile body compression amount by using section length from pile top to upper disc top
E c ＝3.25×10 4 MPa，ξ e ＝1，A ps1 ＝3.14×0.8 2 /4＝0.5024m 2 ，l 1 ＝16m，Q＝4015kN
Then
6. And when the foundation soil at the bottom of the bearing platform does not share the load, determining the final settlement s of the grouting filling pile after extruding and expanding the supporting disc, and calculating the final settlement s by the following method.
As can be seen from FIG. 2, in the calculated depth of settlement, the pile side resistance and equivalent end resistance of the grouting bored concrete pile after squeezing and expanding the supporting disc are 42.23mm due to the additional stress generated in the foundation on the pile body axis below the pile end plane, and the section length of the pile top to the upper disc top calculates the compression amount s of the pile body e Taking psi=1 for 3.93mm, it is known that the final settlement s of the grouting filling pile single pile after squeezing and expanding the supporting disc is 46.16mm.
In summary, the principles and embodiments of the present invention have been described in detail with reference to specific embodiments thereof, the description of which is only for the purpose of aiding in the understanding of the method of the present invention and the core idea of its design; also, variations in implementation and application scope are possible in light of the concepts of the present invention to those of ordinary skill in the art. The description is not to be taken as limiting the invention.
Claims (2)
1. The method for calculating the single pile settlement of the grouting filling pile after the squeezing and expanding of the supporting plate is characterized in that the grouting filling pile after the squeezing and expanding of the supporting plate is a single pile, a single row of piles or a sparse pile foundation with the center distance being more than 6 times of the pile diameter, the pile foundation settlement of the filling pile does not consider the bearing platform bottom foundation soil load sharing effect, and the single pile settlement calculation method of the grouting filling pile after the squeezing and expanding of the supporting plate is as follows:
simplifying the grouting filling pile after extruding and expanding the supporting disc into an upper equal-diameter pile and a lower equal-diameter pile, and equivalently simplifying the variable-section pile body into two equal-section pile bodies; the stress equivalent of the foundation pile is simplified to be that the pile top bears the uniformly distributed side resistance to the disc top section of the upper disc, and the disc top section of the upper disc bears the uniformly distributed side resistance and the uniformly distributed end resistance to the pile end;
the settlement amount of the grouting filling pile single pile after the branch plate is extruded and expanded is calculated as follows: respectively establishing a coordinate system for two equal-section piles, respectively calculating additional stress in foundation soil on the pile body axis below a pile end plane according to Mindlin solution considering the influence of the pile diameter, then superposing the additional stress generated by calculation points, calculating the settlement of the pile foundation by adopting a unidirectional compression layering summation method, and calculating the compression of the pile body at the section part of the pile top to the disc top;
the post-extrusion-expansion grouting filling pile is divided into two equal-diameter piles from a pile top to an upper disc top section and from the upper disc top section to a pile end at the upper disc top section, a coordinate system is respectively established, and stress influence coefficients are respectively solved by applying Mindlin solution considering the influence of the pile diameter;
a. calculating an equal cross-section pile according to the actual cross-section area and the length of the pile at the section part of the pile top to the upper disc top, and only considering side resistance; the section from the top of the upper disc to the pile end is simplified into a large-diameter equal-section pile with the maximum projection area of the supporting disc as the equivalent section area of the pile body, and the length from the top of the upper disc to the pile end is equivalent pile length;
b. the origin of coordinates of the section part of the pile top to the upper disc top is the pile top of the original grouting filling pile after the extruding and expanding support disc, the ordinate z=l is taken as a settlement initial calculation point, l is the pile length of the grouting filling pile after the extruding and expanding support disc, and stress influence coefficients generated by different depths of the foundation of the section of side resistance on the pile body axis below the pile end are calculated;
c. the origin of coordinates from the top section of the upper disc to the pile end part is the plane where the top section of the upper disc is located, and the ordinate z=l is adopted 2 Calculate the point for the onset of sedimentation, where l 2 For the length from the top of the upper disc to the pile end, respectively calculating stress influence coefficients generated by different depths of the foundation on the pile body axis below the pile end by the simplified side resistance and end resistance of the section;
d. the pile top to upper disc top section and the pile end two parts of foundation pile side resistance distribution from the upper disc top section to the pile end are simplified into a mode of uniform distribution along the pile body, and the pile end resistance is simplified into a mode of uniform distribution in the maximum projection area of the supporting disc;
e. pile end equivalent end resistance, pile top to upper disc top section pile side resistance and pile top section to pile end pile side resistance are stress influence coefficients Ip and I at half thickness of ith layer soil on pile body axis below pile end plane sr1 And I sr2 Respectively calculating according to a formula (2-1) and a formula (2-2), or checking an annex F (Mindlin) stress relief influence coefficient considering the influence of pile diameter) of an existing industry standard (building pile foundation technical Specification) (JGJ 94-2008), and directly determining I p 、I sr1 And I sr2 ；
Wherein:
calculating the I from the top section of the upper disc to the pile end according to the formula (2-1) p When r=d/2, l=l 2 Substituting the formula for replacement, wherein r is the radius of the foundation pile of the calculated section, and the unit is m; d is the pile diameter from the top section of the upper disc to the pile end section, and the unit is m; z is the sedimentation calculationThe unit of the distance from the point to the top section of the upper disc is m;
calculating the I of the section of the pile top and the upper disc top according to the formula (2-2) sr1 When r=d/2, l=l 1 Substituting the formula for replacement, wherein r is the radius of the foundation pile of the calculated section, and the unit is m; d is the pile diameter of the section of the pile top to the upper disc top, and the unit is m; z is the distance from the settlement calculation point to the pile top, and the unit is m;
calculating the I from the top section of the upper disc to the pile end according to the formula (2-2) sr2 When r=d/2, l=l 2 Substituting the formula for replacement, wherein r is the radius of the foundation pile of the calculated section, and the unit is m; d is the pile diameter from the top section of the upper disc to the pile end section, and the unit is m; z is the distance from the sedimentation calculation point to the top section of the upper disc, and the unit is m;
poisson's ratio μ is 0.35;
f. when the positive stress superposition result under the calculation point is a negative value, the value should be taken according to zero;
final sedimentation calculation depth Z of pile foundation of grouting filling pile after squeezing and expanding support disc n Determined by stress ratio, i.e. Z n Additional stress sigma induced by the pile z Dead weight stress sigma with earth c The following formula requirements should be met:
σ z ≤0.2σ c (3-1)。
2. the method for calculating single pile settlement of grouting bored concrete pile after extruding and expanding a supporting plate according to claim 1, wherein the final settlement s of the pile foundation without load sharing of foundation soil at the bottom of a bearing platform is calculated according to the following formula:
wherein,,
n- -calculating the number of layers of the soil layer in the sedimentation calculation depth range; the layering number should be combined with the soil layer property, and the layering thickness should not exceed 0.3 times of the calculated depth;
the final settlement of the grouting filling pile on the pile body axis below the pile end plane after the s-squeezing and expanding supporting disc is in mm;
s e -calculating the compression amount of the pile body in mm from the pile top to the upper disc top;
σ z1i -the length section from the pile top to the upper disc top, wherein the side resistance is uniformly distributed to generate additional stress at the position of half thickness of the ith layer of soil on the pile body axis below the pile end plane, and the unit is kPa;
σ z2i -the length section from the top of the upper disc to the pile end, wherein the pile end equivalent end resistance and the uniformly distributed side resistance generate the sum of additional stress at the position of one half thickness of the ith layer of soil on the pile body axis below the pile end plane, and the unit is kPa;
calculating the soil layer thickness of Deltazi-ith, wherein the unit is m;
E si calculating the compression modulus of the soil layer, wherein the unit is MPa, and the compression modulus from the self-weight pressure of the soil to the self-weight pressure of the soil plus the pressurizing force is adopted;
q is the additional load of the pile top under the quasi-permanent combined action of the load effect of the grouting filling pile after extruding and expanding the supporting disc, and the unit is kN;
Q 1 under the quasi-permanent combined action of load effect, the sum of axial forces born by pile top and pile body of upper disk top section is given as kN, and the unit is equal to the sum of side resistances of pile top and upper disk top length section in value, and can be calculated according to Q 1 ＝πd∑q sj l j Calculation, where q sj For the soil side resistance of the j th layer around the pile, l j The thickness of the j-th soil layer around the pile is the thickness of the j-th soil layer around the pile, and d is the diameter of a part of the pile on the top surface section of the upper disc;
Q 2 -under the quasi-permanent combined action of load effect, upper discPile body axial force at top section according to Q 2 ＝ Q-Q 1 Calculating a unit kN;
l 1 -the section length from the pile top to the top of the upper disc is m;
l 2 -the length from the top section of the upper disc to the pile end is m;
A ps pile body section area from pile top to upper disc top section length section, the unit is m 2 ；
The ratio of the resistance of the alpha-pile end, namely the ratio of the equivalent total end resistance of the chassis and the pile end to the axial force of the pile body at the section of the top of the upper disc, is approximately the ratio of the equivalent total end resistance born by the chassis and the pile end to the difference of the single pile bearing capacity minus the total side resistance of the pile side of the part above the top of the upper disc;
I p，i 、I sr1，i 、I sr2，i mindlin stress influence coefficient considering pile diameter influence, I p，i The stress influence coefficient is the stress influence coefficient of the equivalent end resistance of the chassis and the pile end at the position of one half of the thickness of the i-th layer of soil below the pile end plane; i sr1，i The stress influence coefficient is the stress influence coefficient of the pile top to the pile side resistance of the section of the upper disc top at the position of one half thickness of the ith layer of soil below the pile end plane; i sr2，i The stress influence coefficient is the stress influence coefficient of the resistance from the top section of the upper disc to the pile side of the pile end at the position of one half thickness of the ith layer of soil below the pile end plane;
E c the elastic modulus of pile body concrete is expressed as MPa;
ξ e pile body compression coefficient, according to local settlement observation data and experience determination, taking psi when no local experience exists D ＝1.0；
Psi-pile foundation settlement correction coefficient, according to local settlement observation data and experience determination, taking psi when no local experience exists D ＝1.0。
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