CN113987645A - Simplified internal force calculation method for straight-inclined combined pile foundation in mountain slope - Google Patents

Simplified internal force calculation method for straight-inclined combined pile foundation in mountain slope Download PDF

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CN113987645A
CN113987645A CN202111269617.XA CN202111269617A CN113987645A CN 113987645 A CN113987645 A CN 113987645A CN 202111269617 A CN202111269617 A CN 202111269617A CN 113987645 A CN113987645 A CN 113987645A
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foundation
force
bending moment
displacement
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CN113987645B (en
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彭雄志
王刚巧
石少华
冯瑨
王约斌
范帅
田萌
骆富强
刁晓俊
曾应祝
陈旖平
邓晨雨
苏平玉
刘帆
李坤
张易林
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Nuclear Industry Southwest Survey & Design Institute Co ltd
Southwest Jiaotong University
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Abstract

The invention discloses a simplified internal force calculation method for a slope straight-inclined combined pile foundation in a mountainous area, which adopts a reliable and simple and feasible stress calculation method for the slope straight-inclined combined pile foundation, thereby saving investment and engineering quantity; aiming at a bearing platform, a pile foundation, a landslide body and bedrock on a slope, the method fully considers the factors such as the basic bearing characteristic and the stress mode of the bearing platform, the pile foundation, the landslide body and the bedrock, simplifies the complex three-dimensional geological problem into the plane strain problem, establishes a simplified calculation analysis model of the straight-inclined combined pile foundation, deduces the calculation formulas of the deformation of the pile top and the internal force of the pile body, and provides support for the design and calculation of the internal force of the slope straight-inclined combined pile foundation.

Description

Simplified internal force calculation method for straight-inclined combined pile foundation in mountain slope
Technical Field
The invention belongs to the technical field of civil engineering, and particularly relates to a simplified internal force calculation method for a straight-inclined combined pile foundation in a mountain slope.
Background
The western mountainous areas of China are steep and severe in terrain, uneven in terrain and densely distributed in mountain forest and valley, and in order to meet the line extension requirements, line projects such as expressways and railways cannot avoid building bridge structures on mountainous area slopes, so that the bridge pile foundation is built on the mountainous area slopes under different conditions.
Due to complexity of external environment and stress, the bridge foundation on the slope has a bearing mechanism which is different from that of a conventional pile foundation on the flat ground, and the stress deformation characteristic and the influence of environmental conditions are more complicated than those of the conventional pile foundation. On one hand, the upper load of the bridge acts on the foundation, so that the stress in the slope rock-soil body becomes complicated, and the structural stability is influenced; on the other hand, different from the flat ground condition, because of the existence of the slope face, the foundation soil body around the foundation pile is not a completely symmetrical system, and the bearing performance of the foundation pile is different from that of the flat ground pile foundation to show specificity.
The current specification and calculation theory mainly aims at flat bridge pile foundations, has less regulation on the bridge pile foundations under the condition of a slope, and does not provide a related special calculation theory formula. For the bridge pile group foundation under the condition of the mountain slope, the pile foundation not only needs to bear the horizontal and vertical combined load action from the upper structure of the bridge, but also needs to bear the slope body gliding force action of the pile side rock-soil body, and the corresponding pile group effect needs to be considered. Particularly, for a bridge foundation form of 'vertical piles and inclined piles', a pile foundation bearing mechanism is more special, and a theoretical formula for specially calculating stress deformation is not provided for the foundation form by the current relevant specifications, so that the research is further deeply discussed.
Disclosure of Invention
Aiming at the defects in the prior art, the simplified internal force calculation method for the straight-inclined combined pile foundation in the mountain slope provided by the invention solves the problem that the stress calculation method for the straight-inclined combined pile foundation on the slope is complex.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: a simplified internal force calculation method for a straight-inclined combined pile foundation in a mountain slope comprises the following steps:
s1, collecting the distance from the front row of foundation piles to the slope surface, the depth of thrust action of the rear landslide of the foundation piles and the length data of the foundation piles, and establishing a straight-inclined combined pile foundation calculation analysis model;
s2, calculating landslide thrust according to the established calculation analysis model, and further obtaining post-pile landslide thrust on each foundation pile on the rear side of the foundation;
s3, establishing a thrust distribution function equation of the pile rear landslide according to the pile rear landslide thrust;
s4, calculating a horizontal displacement and a corner generated by the pile top of the foundation pile according to the slope straight-inclined combined pile foundation calculation analysis model;
s5, obtaining a stiffness value of the pile top according to the horizontal displacement and the corner generated by the foundation pile, further calculating a pile top reaction value of the pile foundation, and establishing a typical equation of a displacement method according to the pile top reaction value of the pile foundation;
s6, combining a pile back landslide thrust distribution function equation, a foundation pile tangent plane deformation condition equation and a foundation pile tangent plane bending moment and shear force equation to obtain a bending moment on the pile top and a shear force on the pile top;
s7, substituting the bending moment on the pile top and the shearing force on the pile top into a typical equation of displacement method to obtain the horizontal displacement a of the pile group foundation bearing platform0Vertical displacement of pile group foundation bearing platform b0And pile group foundation bearing platform corner beta0And further obtaining the axial force, the shearing force and the bending moment of any pile top through a displacement method, and using the axial force, the shearing force and the bending moment as a simplified internal force calculation result of the slope straight-inclined combined pile foundation in the mountainous area.
Further: in step S1, the assumed conditions when the straight-inclined combined pile foundation calculation model is established are specifically:
(1) establishing a horizontal line at the intersection point of the sliding surface and the pile foundation central shaft, and simplifying the sliding surface into a plane;
(2) neglecting the interaction between the soil body above the sliding surface and the foundation pile, and neglecting the interaction between the soil body and the foundation pile in the front side range of the foundation according to the influence of the steep slope effect;
(3) setting the acting depth of the pushing force of the pile back landslide as l1And the landslide thrust within the width range of the bearing platform is uniformly shared through foundation piles according to the soil arch effect, and the distribution form is distributed according to a parabola form;
(4) according to the depth of influence of steep slope effect, pile row is arranged to the slope surface from the bottom surface of the bearing platform to the intersection point O of the central line of the pile foundation and the sliding surfaceDistance b1Should not be less than 4d, where d is the diameter of the pile, if b1Less than 4d, the reference plane at the O point should be lowered so as to satisfy b1Greater than 4 d;
(5) the rock-socketed position of the inclined pile is taken as a horizontal line, the inclined rock-socketed surface is simplified into a plane, and the inclined pile and the vertical pile are taken as the same level.
The beneficial effects of the above further scheme are: when the pile foundation is under the action of landslide thrust, a horizontal soil arch is formed around the pile, and the soil pressure or landslide thrust after the arch is transmitted to the pile and the surrounding soil body. Considering that the soil arch effect can occur at the position of the rear row of piles to block the sliding body from sliding downwards, the blocking effect is generated, the soil body behind the front row of piles is in a stable interval, and therefore the thrust of the sliding body behind the piles is only born by the last row of piles, and the front row of piles have no landslide thrust.
Further: in step S2, the expression of the landslide thrust E is specifically:
E＝Exib
in the formula, ExiThe thrust of the ith block of sliding body horizontal landslide is the unit width, and b is the width of the basic bearing platform;
pile rear landslide thrust E on each foundation pile at rear side of foundation1The expression (c) is specifically:
E1＝E/k
in the formula, k is the number of pile rows.
The beneficial effects of the above further scheme are: the pile back landslide thrust E on each foundation pile at the rear side of the foundation can be obtained by calculating the pile back landslide thrust E1。
Further: the step S3 specifically includes: obtaining an undetermined coefficient a, an undetermined coefficient b and a undetermined coefficient c of a distribution function of the thrust of the landslide after the pile according to the thrust of the landslide after the pile, and further establishing a thrust distribution function equation of the landslide after the pile;
the expressions of the undetermined coefficient a, the undetermined coefficient b and the undetermined coefficient c of the distribution function are specifically as follows:
Figure BDA0003327668220000041
in the formula I0For the height of the pile foundation in the soil body of the thrust section lcThe height from the resultant force action point of the rock-soil body of the thrust section to the potential slip surface;
the expression of the pile rear landslide thrust distribution function equation q (z) is specifically as follows:
q(z)＝az2+bz+c
wherein z is the pile length.
The beneficial effects of the above further scheme are: the post-landslide thrust of the inclined pile is increased and then reduced from the pile top along the pile body direction, the overall distribution form is similar to parabolic distribution, and therefore a post-pile landslide thrust distribution function equation q (z) is established.
Further: in step S4, the method for calculating the horizontal displacement and the rotation angle generated by the pile top of the foundation pile specifically includes:
when the horizontal force H applied to the pile top of the foundation pile is 1, the pile top of the foundation pile generates horizontal displacement deltaHHAnd the angle of rotation deltaMHThe expression (c) is specifically:
Figure BDA0003327668220000042
Figure BDA0003327668220000043
in the formula, EI is the bending rigidity of the foundation pile,
Figure BDA0003327668220000044
and
Figure BDA0003327668220000045
respectively, the base pile sliding surface z ═ l0When unit horizontal force is acted, the section of the sliding surface of the foundation pile generates a corner and horizontal displacement;
Figure BDA0003327668220000046
and
Figure BDA0003327668220000047
respectively, the base pile sliding surface z ═ l0When a unit bending moment is acted, the section of the sliding surface of the foundation pile generates a corner and horizontal displacement;
when the bending moment M applied to the pile top of the foundation pile is equal to 1, the horizontal displacement delta generated by the pile top of the foundation pileHMAnd the angle of rotation deltaMMThe expression (c) is specifically:
Figure BDA0003327668220000051
Figure BDA0003327668220000052
the beneficial effects of the above further scheme are: and the rigidity value of the pile top can be obtained according to the horizontal displacement and the corner generated by the foundation pile.
Further: in the step S5, the stiffness value of the pile top includes an axial force ρ generated by the pile top1Horizontal force ρ2First bending moment rho3And a second bending moment ρ4；
Wherein, when the pile top of the foundation pile only generates axial unit displacement, the axial force rho generated by the pile top1The expression (c) is specifically:
Figure BDA0003327668220000053
where xi is the coefficient of the pile side frictional resistance distribution, C0Is the vertical resistance coefficient of the foundation, A0The pressed area of the pile bottom plane foundation is shown, A is the section area of the pile, and h is the distance from the sliding surface of the foundation pile to the rock-socketed surface;
when the pile top of the foundation pile only undergoes the axial unit displacement of the vertical pile, the generated horizontal force rho2And the first bending moment rho3The expression (c) is specifically:
Figure BDA0003327668220000054
Figure BDA0003327668220000055
when only unit corner occurs on the pile top of the foundation pile, the second bending moment rho generated by the pile top4The expression (c) is specifically:
Figure BDA0003327668220000056
the beneficial effects of the above further scheme are: the pile top reaction force value of the pile foundation can obtain a displacement method typical equation.
Further: in the step S5, the pile top reaction value of the foundation pile includes the sum of the pile top vertical reaction, the sum of the pile top horizontal reaction and the sum of the pile top bending moment;
the method for calculating the pile top reaction force value of the foundation pile specifically comprises the following steps:
when the slope straight-inclined combined pile foundation bearing platform generates horizontal unit displacement, the sum gamma of the pile top vertical counter forces of all the foundation pilesbaSum of horizontal counter-forces of pile top gammaaaAnd the sum of pile top bending moment gammaβaThe expression (c) is specifically:
Figure BDA0003327668220000061
Figure BDA0003327668220000062
Figure BDA0003327668220000063
in the formula, alphaiIs the angle of inclination, x, of the foundation pileiThe horizontal length from the pile top position of the ith row of foundation piles to the center of the bearing platform;
when the bottom plate of the bearing platform of the slope straight-inclined combined pile foundation generates vertical unit displacement, all the combined piles are arrangedSum gamma of vertical counter-forces of pile top of foundation pilebbSum of horizontal counter-forces of pile top gammaabAnd the sum of the bending moment and the counter force of the pile topβbThe expression (c) is specifically:
Figure BDA0003327668220000064
γab＝γba
Figure BDA0003327668220000065
when the unit corner is generated around the central O point on the bottom plate of the bearing platform of the slope straight-inclined combined pile foundation, the sum gamma of the vertical counter forces of the pile tops of all the foundation piles isbβSum of horizontal counter-forces of pile top gammaaβSum of pile top bending moment gammaββThe expression (c) is specifically:
γbβ＝γβb
γaβ＝γβa
Figure BDA0003327668220000071
in step S5, the expression of the typical equation of the displacement method is specifically:
Figure BDA0003327668220000072
in the formula, a0For horizontal displacement of pile group foundation cap, b0For vertical displacement of pile group foundation bearing platform, beta0For pile group foundation bearing platform corner, MqBending moment on pile top, QqIs the shear force on the pile top, H is the horizontal force on the pile top, M is the bending moment on the pile top, N is the vertical force, aiThe transverse displacement generated by the pile top of the ith row pile is shown, wherein i is 1,2, …, n is the row pile number.
The beneficial effects of the above further scheme are: typical equation of displacement methodCan calculate the horizontal displacement a of the pile group foundation bearing platform0Vertical displacement of pile group foundation bearing platform b0And pile group foundation bearing platform corner beta0。
Further: in step S6, the expression of the tangent plane deformation conditional equation of the foundation pile is specifically:
Figure BDA0003327668220000073
bending moment on tangent plane of foundation pile
Figure BDA0003327668220000075
And shear force
Figure BDA0003327668220000076
The expression of the equation of (a) is specifically:
Figure BDA0003327668220000074
in the formula, MqBending moment on pile top, QqIs the shear force on the pile top.
The beneficial effects of the above further scheme are: bending moment M on tangent plane of foundation pile10And shear force Q10A displacement method typical equation can be solved.
Further: axial force P of any pile topiShear force QiAnd bending moment MiThe expression (c) is specifically:
Figure BDA0003327668220000081
in the formula, aiFor transverse displacement of the pile top of the ith row of piles, biFor axial displacement, beta, produced at the top of the ith row of pilesiThe corner is generated for the top of the ith row of piles.
The beneficial effects of the above further scheme are: the axial force P of any pile top is obtained through calculationiShear force QiWith bending moment MiAnd obtaining an internal force design index so as to calculate the internal force of the foundation pile, and then carrying out reinforcement design on the foundation pile, wherein the specific calculation method is the same as that of the existing single pile foundation design. And checking the design parameters of the straight-inclined combined pile foundation according to the calculated deflection of the bearing platform and the deflection of the pile foundation and whether the deflection of the pile foundation meets the requirement of a standard allowable value, thereby completing the foundation design.
The invention has the beneficial effects that:
(1) the invention provides a reliable and simple and feasible stress calculation method for a straight-inclined combined pile foundation on a slope, so that the investment and the engineering amount are saved, the possibility of engineering risk occurrence is prevented, and the method has an engineering application value.
(2) The invention establishes a general calculation analysis model, can fully consider the basic bearing characteristics, stress mode and other factors of a bearing platform, a pile foundation, a landslide body and bedrock on a slope, simplifies the complex three-dimensional geological problem into a plane strain problem, establishes a straight-inclined combined pile foundation simplified calculation analysis model, deduces a calculation formula of pile top deformation and pile body internal force, and provides support for the design calculation of the internal force of the slope straight-inclined combined pile foundation.
(3) The invention establishes a calculation analysis model of the straight-inclined combined pile foundation on the slope based on an elastic theory method, and further deduces a calculation method of the internal force of the straight-inclined combined pile foundation. Aiming at the defects of the stress calculation method of the straight-inclined combined pile foundation on the related standard slope, the method can simply and conveniently obtain the stress state of the straight-inclined combined pile foundation and the deflection (including horizontal displacement, vertical displacement and corner) of the bearing platform. The design precision can be improved in the design of the slope straight-inclined combined pile foundation, the design is closer to the actual value, the material waste is reduced, and the construction cost of the pile foundation is reduced.
Drawings
FIG. 1 is a flow chart of a simplified internal force calculation method for a straight-inclined combined pile foundation in a mountain slope;
FIG. 2 is a diagram showing the results of the distribution pattern of the soil pressure test of the inclined piles;
FIG. 3 is a diagram of a generalized computational analysis model;
FIG. 4 is a distribution function calculation diagram;
FIG. 5 is a model diagram of a calculation of deflection of a foundation pile at a sliding surface by a unit horizontal force;
FIG. 6 is a model diagram of a calculation of deflection of a foundation pile at a sliding surface by a unit bending moment;
FIG. 7 shows bending moment M on the pile topqAnd shear force Q on pile topqAnd (5) calculating a schematic diagram.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate the understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
As shown in fig. 1, in an embodiment of the present invention, a simplified internal force calculation method for a mountain slope straight-inclined combined pile foundation includes the following steps:
s1, collecting the distance from the front row of foundation piles to the slope surface, the depth of thrust action of the rear landslide of the foundation piles and the length data of the foundation piles, and establishing a straight-inclined combined pile foundation calculation analysis model;
s2, calculating landslide thrust according to the established calculation analysis model, and further obtaining post-pile landslide thrust on each foundation pile on the rear side of the foundation;
s3, establishing a thrust distribution function equation of the pile rear landslide according to the pile rear landslide thrust;
s4, calculating a horizontal displacement and a corner generated by the pile top of the foundation pile according to the slope straight-inclined combined pile foundation calculation analysis model;
s5, obtaining a stiffness value of the pile top according to the horizontal displacement and the corner generated by the foundation pile, further calculating a pile top reaction value of the pile foundation, and establishing a typical equation of a displacement method according to the pile top reaction value of the pile foundation;
s6, combining a pile back landslide thrust distribution function equation, a foundation pile tangent plane deformation condition equation and a foundation pile tangent plane bending moment and shear force equation to obtain a bending moment on the pile top and a shear force on the pile top;
s7, substituting the bending moment on the pile top and the shearing force on the pile top into a typical equation of displacement method to obtain the horizontal displacement a of the pile group foundation bearing platform0Vertical displacement of pile group foundation bearing platform b0And pile group foundation bearing platform corner beta0And further obtaining the axial force, the shearing force and the bending moment of any pile top through a displacement method, and using the axial force, the shearing force and the bending moment as a simplified internal force calculation result of the slope straight-inclined combined pile foundation in the mountainous area.
In step S1, the assumed conditions when the straight-inclined combined pile foundation calculation model is established are specifically:
establishing a horizontal line at the intersection point of the sliding surface and the pile foundation central shaft, and simplifying the sliding surface into a plane;
neglecting the interaction between the soil body above the sliding surface and the foundation pile, and neglecting the interaction between the soil body and the foundation pile in the front side range of the foundation according to the influence of the steep slope effect;
as shown in fig. 2 and 3, the depth of action of the pile back landslide thrust is set to l1And the landslide thrust within the width range of the bearing platform is uniformly shared through foundation piles according to the soil arch effect, and the distribution form is distributed according to a parabola form;
according to the depth influenced by the steep slope effect, the distance b from the front row of piles to the slope surface at the O point plane1Should not be less than 4d, where d is the diameter of the pile, if b1Less than 4d, the reference plane at the O point should be lowered so as to satisfy b1Greater than 4 d. The distance by which the reference plane is lowered is d1The upper soil pressure of the pile foundation is q2The soil pressure of the lower part of the pile foundation is q3The upper soil pressure and the lower soil pressure of the pile foundation are determined according to b in the actual engineering1And 4d, whether to affect the calculations of the present invention.
The rock-socketed position of the inclined pile is taken as a horizontal line, the inclined rock-socketed surface is simplified into a plane, and the inclined pile and the vertical pile are taken as the same level.
In step S2, the expression of the landslide thrust E is specifically:
E＝Exib
in the formula, ExiThe thrust of the ith block of sliding body horizontal landslide is the unit width, and b is the width of the basic bearing platform;
after foundationPile back landslide thrust E on each side foundation pile1The expression (c) is specifically:
E1＝E/k
in the formula, k is the number of pile rows.
As shown in fig. 4, the step S3 specifically includes: obtaining an undetermined coefficient a, an undetermined coefficient b and a undetermined coefficient c of a distribution function of the thrust of the landslide after the pile according to the thrust of the landslide after the pile, and further establishing a thrust distribution function equation of the landslide after the pile;
the expressions of the undetermined coefficient a, the undetermined coefficient b and the undetermined coefficient c of the distribution function are specifically as follows:
Figure BDA0003327668220000111
in the formula I0For the height of the pile foundation in the soil body of the thrust section lcThe height from the resultant force action point of the rock-soil body of the thrust section to the potential slip surface;
lcgenerally about l0(0.4-0.5) times of the total weight of the composition, which can be obtained under static equilibrium conditions: the resultant force q (z) of the post pile soil pressure should be equal to the post pile soil thrust.
The expression of the pile rear landslide thrust distribution function equation q (z) is specifically as follows:
q(z)＝az2+bz+c
wherein z is the pile length.
In step S4, the method for calculating the horizontal displacement and the rotation angle generated by the pile top of the foundation pile specifically includes:
when the horizontal force H applied to the pile top of the foundation pile is 1, the pile top of the foundation pile generates horizontal displacement deltaHHAnd the angle of rotation deltaMHThe expression (c) is specifically:
Figure BDA0003327668220000121
Figure BDA0003327668220000122
in the formula, EI is the bending rigidity of the foundation pile,
Figure BDA0003327668220000123
and
Figure BDA0003327668220000124
respectively, the base pile sliding surface z ═ l0When unit horizontal force is acted, the section of the sliding surface of the foundation pile generates a corner and horizontal displacement;
Figure BDA0003327668220000125
and
Figure BDA0003327668220000126
respectively, the base pile sliding surface z ═ l0When a unit bending moment is acted, the section of the sliding surface of the foundation pile generates a corner and horizontal displacement;
when the bending moment M applied to the pile top of the foundation pile is equal to 1, the horizontal displacement delta generated by the pile top of the foundation pileHMAnd the angle of rotation deltaMMThe expression (c) is specifically:
Figure BDA0003327668220000127
Figure BDA0003327668220000128
Figure BDA0003327668220000129
and
Figure BDA00033276682200001210
the road bridge and culvert foundation design standard can be obtained by table lookup calculation;
Figure BDA00033276682200001211
Figure BDA00033276682200001212
Figure BDA00033276682200001213
in the formula, alpha is the deformation coefficient of the pile body; a. the1、A2、B1、B2、C1、C2、D1And D2All the coefficients are dimensionless coefficients, and the coefficients can be obtained by looking up a coefficient table in 'highway bridge foundation and foundation design specifications'.
As shown in fig. 5 and 6, in the step S5, the stiffness value of the pile top includes an axial force ρ generated by the pile top1Horizontal force ρ2First bending moment rho3And a second bending moment ρ4；
Wherein, when the pile top of the foundation pile only generates axial unit displacement, the axial force rho generated by the pile top1The expression (c) is specifically:
Figure BDA0003327668220000131
where xi is the coefficient of the pile side frictional resistance distribution, C0Is the vertical resistance coefficient of the foundation, A0The pressed area of the pile bottom plane foundation is shown, A is the section area of the pile, and h is the distance from the sliding surface of the foundation pile to the rock-socketed surface;
when the pile top of the foundation pile only undergoes the axial unit displacement of the vertical pile, the generated horizontal force rho2And the first bending moment rho3The expression (c) is specifically:
Figure BDA0003327668220000132
Figure BDA0003327668220000133
when radicalWhen the pile top only generates a unit corner, a second bending moment rho generated by the pile top4The expression (c) is specifically:
Figure BDA0003327668220000134
in the step S5, the pile top reaction value of the foundation pile includes the sum of the pile top vertical reaction, the sum of the pile top horizontal reaction and the sum of the pile top bending moment;
the method for calculating the pile top reaction force value of the foundation pile specifically comprises the following steps:
when the slope straight-inclined combined pile foundation bearing platform generates horizontal unit displacement, the sum gamma of the pile top vertical counter forces of all the foundation pilesbaSum of horizontal counter-forces of pile top gammaaaAnd the sum of pile top bending moment gammaβaThe expression (c) is specifically:
Figure BDA0003327668220000135
Figure BDA0003327668220000136
Figure BDA0003327668220000137
in the formula, alphaiIs the angle of inclination, x, of the foundation pileiThe horizontal length from the pile top position of the ith row of foundation piles to the center of the bearing platform;
when the bottom plate of the bearing platform of the slope straight-inclined combined pile foundation generates vertical unit displacement, the sum gamma of the vertical counter forces of the pile tops of all the foundation piles isbbSum of horizontal counter-forces of pile top gammaabAnd the sum of the bending moment and the counter force of the pile topβbThe expression (c) is specifically:
Figure BDA0003327668220000141
γab＝γba
Figure BDA0003327668220000142
when the unit corner is generated around the central O point on the bottom plate of the bearing platform of the slope straight-inclined combined pile foundation, the sum gamma of the vertical counter forces of the pile tops of all the foundation piles isbβSum of horizontal counter-forces of pile top gammaaβSum of pile top bending moment gammaββThe expression (c) is specifically:
γbβ＝γβb
γaβ＝γβa
Figure BDA0003327668220000143
in step S5, the expression of the typical equation of the displacement method is specifically:
Figure BDA0003327668220000144
in the formula, a0For horizontal displacement of pile group foundation cap, b0For vertical displacement of pile group foundation bearing platform, beta0For pile group foundation bearing platform corner, MqBending moment on pile top, QqIs the shear force on the pile top, H is the horizontal force on the pile top, M is the bending moment on the pile top, N is the vertical force, aiThe transverse displacement generated by the pile top of the ith row pile is shown, wherein i is 1,2, …, n is the row pile number.
In step S6, the expression of the tangent plane deformation conditional equation of the foundation pile is specifically:
Figure BDA0003327668220000151
bending moment on the tangent plane of the foundation pile, as shown in fig. 7
Figure BDA0003327668220000154
And shear force
Figure BDA0003327668220000155
The expression of the equation of (a) is specifically:
Figure BDA0003327668220000152
in the formula, MqBending moment on pile top, QqIs the shear force on the pile top.
In step S7, the axial force P of any pile top is obtainediShear force QiAnd bending moment MiThe expression (c) is specifically:
Figure BDA0003327668220000153
in the formula, aiFor transverse displacement of the pile top of the ith row of piles, biFor axial displacement, beta, produced at the top of the ith row of pilesiThe corner is generated for the top of the ith row of piles.
The axial force P of any pile top is obtained through calculationiShear force QiWith bending moment MiAnd obtaining an internal force design index so as to calculate the internal force of the foundation pile, and then carrying out reinforcement design on the foundation pile, wherein the specific calculation method is the same as that of the existing single pile foundation design. And checking the design parameters of the straight-inclined combined pile foundation according to the calculated deflection of the bearing platform and the deflection of the pile foundation and whether the deflection of the pile foundation meets the requirement of a standard allowable value, thereby completing the foundation design.
In the second embodiment of the invention, the engineering background of a super bridge on a certain highway in the southwest area is used, and for convenience of calculation, the external force in the transverse bridge direction is not calculated, and the problem of plane strain is considered. External loading: n-70367 kN, H-58536 kN, M-59308 kN · M;
and dividing the most dangerous sliding surface according to slope numerical simulation software, and finding the position where the sliding surface passes through the pile length of 19 m. Get l0Is 19m, l119.7 meters. Calculating to obtain landslide thrust E on each foundation pile1The value is 3558kN, and further the obtained post-pile soil pressure distribution function is as follows:
q(z)＝-5.32907E-15z2+1013687E-13z-374.5263158
looking up 'design specifications of foundations and foundations of roads, bridges and culverts' to obtain a pile body deformation coefficient alpha;
Figure BDA0003327668220000161
wherein α z is 0.291 × 50 and 14.55, which is greater than 4, and belongs to the flexible pile.
According to the slope straight-inclined combined pile foundation calculation analysis model, calculating to obtain the horizontal displacement and the corner generated by the foundation pile: deltaHH＝5.59725E-5，δMH＝301249E-6，δMM＝2.49525E-7；
Respectively substituting the horizontal displacement and the rotation angle generated by the foundation pile into the axial force rho generated by the pile top1Expression of (1), horizontal force ρ2Expression of (1), first bending moment ρ3Expression (c) and second bending moment ρ4Can obtain:
ρ1＝7688142.6kN/m，ρ2＝59389.1kN/m，ρ3＝743753.1kN/rad，ρ4＝13321928.2kN·m/rad。
and calculating the counter force of each pile top as follows: gamma rayba＝4881472.353kN/m，γaa＝1665163.2kN/m，γβa＝32257525.9kN，γbb＝40656333.7kN/m，γbβ＝7569167.901kN/rad，γββ＝2191025725kN·m/rad。
The simultaneous formula is calculated to obtain: ml0＝9711.4kN·m，Ql0＝-1408.6kN，Mq＝84351.7kN·m，Qq＝-2149.4kN。
Finally, the method is obtained by a typical equation of a displacement method: a is0＝13.3mm，b0＝0.66mm，β0＝3.6E-5rad。
The implementation process of the method comprises the following steps: establishing a general computational analysis model based on the assumed conditions, and calculating according to the general computational analysis modelThrust E of pile-out backward landslide and thrust E of pile backward landslide on each foundation pile at rear side of foundation1Establishing a thrust distribution function equation q (z) of the pile rear landslide, and establishing a thrust E of the pile rear landslide according to the thrust E of the pile rear landslide and the thrust E of the pile rear landslide on each foundation pile at the rear side of the foundation1And calculating an undetermined coefficient a, an undetermined coefficient b and an undetermined coefficient c of a post-pile landslide thrust distribution function equation q (z), and perfecting the distribution function equation q (z). Obtaining a dimensionless coefficient A by table look-up calculation of' road bridge and culvert foundation and foundation design specifications1、A2、B1、B2、C1、C2、D1And D2Calculating to obtain the horizontal displacement and the corner generated by the foundation pile, calculating the pile top reaction value of the pile foundation according to the horizontal displacement and the corner generated by the foundation pile, and establishing a typical equation of a displacement method; by combining the section deformation condition equation of the foundation pile and the bending moment M on the section of the foundation pilel0And shear force Ql0To obtain bending moment M on the pile topqAnd shear force Q on pile topqBending moment M on pile topqAnd shear force Q on pile topqSubstituting into a displacement normal equation to obtain the horizontal displacement a of the pile group foundation bearing platform0Vertical displacement of pile group foundation bearing platform b0And pile group foundation bearing platform corner beta0And further obtaining the axial force, the shearing force and the bending moment of any pile top by a displacement method, and completing the simplified internal force calculation of the slope straight-inclined combined pile foundation in the mountainous area.
The invention has the beneficial effects that: the invention provides a reliable and simple and feasible stress calculation method for a straight-inclined combined pile foundation on a slope, so that the investment and the engineering amount are saved, the possibility of engineering risk occurrence is prevented, and the method has an engineering application value.
The invention establishes a general calculation analysis model, can fully consider the basic bearing characteristics, stress mode and other factors of a bearing platform, a pile foundation, a landslide body and bedrock on a slope, simplifies the complex three-dimensional geological problem into a plane strain problem, establishes a straight-inclined combined pile foundation simplified calculation analysis model, deduces a calculation formula of pile top deformation and pile body internal force, and provides support for the design calculation of the internal force of the slope straight-inclined combined pile foundation.
The invention establishes a calculation analysis model of the straight-inclined combined pile foundation on the slope based on an elastic theory method, and further deduces a calculation method of the internal force of the straight-inclined combined pile foundation. Aiming at the defects of the stress calculation method of the straight-inclined combined pile foundation on the related standard slope, the method can simply and conveniently obtain the stress state of the straight-inclined combined pile foundation and the deflection (including horizontal displacement, vertical displacement and corner) of the bearing platform. The design precision can be improved in the design of the slope straight-inclined combined pile foundation, the design is closer to the actual value, the material waste is reduced, and the construction cost of the pile foundation is reduced.
In the description of the present invention, it is to be understood that the terms "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial", and the like, indicate orientations and positional relationships based on the orientations and positional relationships shown in the drawings, and are used merely for convenience in describing the present invention and for simplicity in description, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or an implicit indication of the number of technical features. Thus, features defined as "first", "second", "third" may explicitly or implicitly include one or more of the features.

Claims (9)

1. A simplified internal force calculation method for a straight-inclined combined pile foundation in a mountain slope is characterized by comprising the following steps:
s1, collecting the distance from the front row of foundation piles to the slope surface, the depth of thrust action of the rear landslide of the foundation piles and the length data of the foundation piles, and establishing a straight-inclined combined pile foundation calculation analysis model;
s2, calculating landslide thrust according to the established calculation analysis model, and further obtaining post-pile landslide thrust on each foundation pile on the rear side of the foundation;
s3, establishing a thrust distribution function equation of the pile rear landslide according to the pile rear landslide thrust;
s4, calculating the horizontal displacement and the corner generated by the pile top of the foundation pile according to the straight-inclined combined pile foundation calculation analysis model;
s5, obtaining a stiffness value of the pile top according to the horizontal displacement and the corner generated by the pile top of the foundation pile, further calculating a pile top reaction value of the pile foundation, and establishing a typical equation of a displacement method according to the pile top reaction value of the pile foundation;
s6, combining a pile back landslide thrust distribution function equation, a foundation pile tangent plane deformation condition equation and a foundation pile tangent plane bending moment and shear force equation to obtain a bending moment on the pile top and a shear force on the pile top;
s7, substituting the bending moment on the pile top and the shearing force on the pile top into a typical equation of displacement method to obtain the horizontal displacement a of the pile group foundation bearing platform0Vertical displacement of pile group foundation bearing platform b0And pile group foundation bearing platform corner beta0And further obtaining the axial force, the shearing force and the bending moment of any pile top through a displacement method, and using the axial force, the shearing force and the bending moment as a simplified internal force calculation result of the slope straight-inclined combined pile foundation in the mountainous area.
2. The method for calculating internal force of a simplified straight-inclined combined pile foundation in a mountain slope according to claim 1, wherein in step S1, the assumed conditions when the straight-inclined combined pile foundation calculation model is established are specifically:
(1) establishing a horizontal line at the intersection point of the sliding surface and the pile foundation central shaft, and simplifying the sliding surface into a plane;
(2) neglecting the interaction between the soil body above the sliding surface and the foundation pile, and neglecting the interaction between the soil body and the foundation pile in the front side range of the foundation according to the influence of the steep slope effect;
(3) setting the acting depth of the pushing force of the pile back landslide as l1And the landslide thrust within the width range of the bearing platform is uniformly shared through foundation piles according to the soil arch effect, and the distribution form is distributed according to a parabola form;
(4) according to the depth influenced by the steep slope effect, the distance b from the bottom surface of the bearing platform to the slope surface from the front row pile at the plane of the intersection point O of the center line of the pile foundation and the sliding surface1Should not be less than 4d, where d is the diameter of the pile, if b1Less than 4d, the reference plane at the O point should be lowered so as to satisfy b1Greater than 4 d;
(5) the rock-socketed position of the inclined pile is taken as a horizontal line, the inclined rock-socketed surface is simplified into a plane, and the inclined pile and the vertical pile are taken as the same level.
3. The simplified internal force calculation method for the mountain slope straight-inclined combined pile foundation according to claim 2, wherein in step S2, the expression of the landslide thrust E is specifically:
E＝Exib
in the formula, ExiThe thrust of the ith block of sliding body horizontal landslide is the unit width, and b is the width of the basic bearing platform;
pile rear landslide thrust E on each foundation pile at rear side of foundation1The expression (c) is specifically:
E1＝E/k
in the formula, k is the number of pile rows.
4. The method for calculating the simplified internal force of the mountain slope straight-inclined combined pile foundation according to claim 3, wherein the step S3 is specifically as follows: obtaining an undetermined coefficient a, an undetermined coefficient b and a undetermined coefficient c of a distribution function of the thrust of the landslide after the pile according to the thrust of the landslide after the pile, and further establishing a landslide thrust distribution function equation;
the expressions of the undetermined coefficient a, the undetermined coefficient b and the undetermined coefficient c of the distribution function are specifically as follows:
Figure FDA0003327668210000021
in the formula I0For the height of the pile foundation in the soil body of the thrust section lcThe height from the resultant force action point of the rock-soil body of the thrust section to the potential slip surface;
the expression of the pile rear landslide thrust distribution function equation q (z) is specifically as follows:
q(z)＝az2+bz+c
wherein z is the pile length.
5. The simplified internal force calculation method for the mountain slope straight-inclined combined pile foundation according to claim 4, wherein in step S4, the method for calculating the horizontal displacement and the rotation angle generated by the pile top of the foundation pile is specifically as follows:
when the horizontal force H applied to the pile top of the foundation pile is 1, the pile top of the foundation pile generates horizontal displacement deltaHHAnd the angle of rotation deltaMHThe expression (c) is specifically:
Figure FDA0003327668210000031
Figure FDA0003327668210000032
in the formula, EI is the bending rigidity of the foundation pile,
Figure FDA0003327668210000033
and
Figure FDA0003327668210000034
respectively, the base pile sliding surface z ═ l0When unit horizontal force is acted, the section of the sliding surface of the foundation pile generates a corner and horizontal displacement;
Figure FDA0003327668210000035
and
Figure FDA0003327668210000036
respectively, the base pile sliding surface z ═ l0When a unit bending moment is acted, the section of the sliding surface of the foundation pile generates a corner and horizontal displacement;
when the bending moment M applied to the pile top of the foundation pile is equal to 1, the horizontal displacement delta generated by the pile top of the foundation pileHMAnd the angle of rotation deltaMMThe expression (c) is specifically:
Figure FDA0003327668210000037
Figure FDA0003327668210000038
6. the simplified internal force calculation method for the mountain slope straight-inclined combined pile foundation according to claim 5, wherein in step S5, the stiffness value of the pile top comprises an axial force ρ generated by the pile top1Horizontal force ρ2First bending moment rho3And a second bending moment ρ4；
Wherein, when the pile top of the foundation pile only generates axial unit displacement, the axial force rho generated by the pile top1The expression (c) is specifically:
Figure FDA0003327668210000041
where xi is the coefficient of the pile side frictional resistance distribution, C0Is the vertical resistance coefficient of the foundation, A0The pressed area of the pile bottom plane foundation is shown, A is the section area of the pile, and h is the distance from the sliding surface of the foundation pile to the rock-socketed surface;
when the pile top of the foundation pile only undergoes the axial unit displacement of the vertical pile, the generated horizontal force rho2And the first bending moment rho3The expression (c) is specifically:
Figure FDA0003327668210000042
Figure FDA0003327668210000043
when only unit corner occurs on the pile top of the foundation pile, the second bending moment rho generated by the pile top4The expression (c) is specifically:
Figure FDA0003327668210000044
7. the simplified internal force calculation method for the straight-inclined combined pile foundation in the mountainous area slope according to claim 6, wherein in step S5, the pile top reaction force value of the foundation pile comprises a sum of a vertical pile top reaction force, a sum of a horizontal pile top reaction force and a sum of a bending moment of the pile top;
the method for calculating the pile top reaction force value of the foundation pile specifically comprises the following steps:
when the slope straight-inclined combined pile foundation bearing platform generates horizontal unit displacement, the sum gamma of the pile top vertical counter forces of all the foundation pilesbaSum of horizontal counter-forces of pile top gammaaaAnd the sum of pile top bending moment gammaβaThe expression (c) is specifically:
Figure FDA0003327668210000045
Figure FDA0003327668210000046
Figure FDA0003327668210000047
in the formula, alphaiIs the angle of inclination, x, of the foundation pileiThe horizontal length from the pile top position of the ith row of foundation piles to the center of the bearing platform;
when the bottom plate of the bearing platform of the slope straight-inclined combined pile foundation generates vertical unit displacement, the sum gamma of the vertical counter forces of the pile tops of all the foundation piles isbbSum of horizontal counter-forces of pile top gammaabAnd the sum of the bending moment and the counter force of the pile topβbThe expression (c) is specifically:
Figure FDA0003327668210000051
γab＝γba
Figure FDA0003327668210000052
when the unit corner is generated around the central O point on the bottom plate of the bearing platform of the slope straight-inclined combined pile foundation, the sum gamma of the vertical counter forces of the pile tops of all the foundation piles isbβSum of horizontal counter-forces of pile top gammaaβSum of pile top bending moment gammaββThe expression (c) is specifically:
γbβ＝γβb
γaβ＝γβa
Figure FDA0003327668210000053
in step S5, the expression of the typical equation of the displacement method is specifically:
Figure FDA0003327668210000054
in the formula, a0For horizontal displacement of pile group foundation cap, b0For vertical displacement of pile group foundation bearing platform, beta0For pile group foundation bearing platform corner, MqBending moment on pile top, QqIs the shear force on the pile top, H is the horizontal force on the pile top, M is the bending moment on the pile top, N is the vertical force, aiThe transverse displacement generated by the pile top of the ith row pile is shown, wherein i is 1,2, …, n is the row pile number.
8. The method for calculating simplified internal force of a mountain slope straight-inclined combined pile foundation according to claim 7, wherein in step S6, the expression of the conditional equation of tangent plane deformation of the foundation pile is specifically as follows:
Figure FDA0003327668210000061
bending moment on tangent plane of foundation pile
Figure FDA0003327668210000062
And shear force
Figure FDA0003327668210000063
The expression of the equation of (a) is specifically:
Figure FDA0003327668210000064
in the formula, MqBending moment on pile top, QqIs the shear force on the pile top.
9. The method for calculating simplified internal force of a straight-inclined combined pile foundation in a mountain slope according to claim 8, wherein in step S7, the axial force P of any pile topiShear force QiAnd bending moment MiThe expression (c) is specifically:
Figure FDA0003327668210000065
in the formula, aiFor transverse displacement of the pile top of the ith row of piles, biFor axial displacement, beta, produced at the top of the ith row of pilesiThe corner is generated for the top of the ith row of piles.
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