Load settlement calculation method and system for side resistance enhanced consolidation expanding disc pile

Abstract

The application discloses a side resistance enhanced consolidated expanding disc pile load settlement calculation method and system. The method obtains the parameters of the pile body, the branch disc, the consolidation body and the layered foundation; the elastic modulus, the shear modulus, the cohesion and the internal friction angle of the consolidation area are reconstructed by using the consolidation amplification coefficient, and the interface friction angle of the consolidation area is determined according to the upper limit of the soil internal friction angle and the lower limit of the natural interface friction angle; the nonlinear load transfer models of the ordinary section side resistance, the consolidation transition section side resistance, the disc body peripheral side resistance, the disc body ring end resistance and the pile end resistance are respectively established, wherein the disc body peripheral side resistance is calculated by the equivalent circumference determined by the pile diameter and the disc diameter; the pile end displacement is taken as the initial boundary condition, the displacement coordination iterative calculation is carried out from the pile end to the pile top based on the load transfer models of the pile sections, and the pile top load-settlement curve can be obtained by changing the pile end displacement. The application can consider multiple branch discs, local consolidation enhancement and disc body side resistance contribution in the same solving framework.

Description

Technical Field

[0001] This invention belongs to the field of pile foundation calculation technology in geotechnical engineering, specifically relating to a method and system for calculating the load settlement of side-resistance reinforced consolidated expanded piles. Background Technology

[0002] Consolidated expanded-soil piles form a cement-soil consolidated body at a predetermined depth within the pile shaft, and an outwardly expanding bearing disc is formed within the consolidated body, allowing the pile side resistance, disc end resistance, and pile end resistance to jointly bear the vertical load. The consolidated body alters the stiffness and shear strength of the surrounding soil, and the outer surface of the disc forms a lateral contact surface different from that of ordinary piles. Therefore, its load transfer process differs from that of equal-diameter piles and ordinary expanded-soil piles.

[0003] Existing methods for calculating the settlement of piles with expanded bearing plates typically employ equivalent piles, layered summation methods, or load transfer methods. CN110210145A discloses a method for calculating the settlement of a single grouting pile after expanding the bearing plate, which treats the pile body as two piles of equal diameter and uses the Mindlin solution to calculate the additional stress; CN110188499A further considers the load-sharing of the soil under the pile cap. The calculation objects and stress equivalence methods of the above methods are different from those of consolidated expanded bearing plate piles, which involve local reinforcement, contact with the outer periphery of the bearing plate, and segmental nonlinear load transfer.

[0004] CN111680353A discloses a method for calculating the bearing capacity and settlement of a single-disc pile with expansion joint, using a hyperbolic relationship to describe the resistance of the pile side, the disk end, and the pile end; CN115573399A discloses a method for predicting the bearing capacity of a single-disc pile with expansion joint. The aforementioned schemes provide a basis for calculating the resistance of the support disk, but they do not provide rules for reconstructing soil parameters within the consolidated body, nor do they incorporate the lateral resistance of the disk perimeter as an independent resistance component into the multi-disc segmental displacement coordination solution.

[0005] JP2006152799A discloses calculations for pile foundations with multiple enlarged diameter sections, taking into account the circumferential friction of the cylindrical portions of each enlarged diameter section; CN119026208A discloses load and settlement boundary transfer between multiple disk units. Therefore, the arrangement of multiple disks, circumferential friction of the enlarged diameter sections, or segment-by-segment transfer are not sufficient to solve the problems addressed by this invention. For partially consolidated enlarged disk piles, it is still necessary to determine how parameters are converted between the ordinary zone, the consolidated transition zone, and the disk zone, and how the converted parameters jointly control the disk side resistance, disk end resistance, and inter-segment displacement coordination.

[0006] Furthermore, while construction-based consolidated expanded-disk piles or grout-supported piles can demonstrate that grouting consolidation improves the properties of the surrounding soil, this alone cannot determine the values ​​of various mechanical parameters in the load transfer model within the consolidated zone, nor can it resolve the physical distortion caused by the amplified interface friction angle exceeding the internal friction angle of the consolidated soil. For piles with multiple supports, it is also necessary to maintain continuity of axial force and displacement between the ordinary sections, consolidated transition sections, and disc sections. Therefore, it is essential to establish a unified calculation method corresponding to the aforementioned structural and stress characteristics. Summary of the Invention

[0007] The purpose of this invention is to provide a method and system for calculating the load settlement of a side-resistance enhanced consolidated expanded-disk pile, which characterizes the local reinforcement of the consolidated body, the lateral resistance of the disk periphery, the annular end resistance of the disk, and the displacement coordination relationship between any number of disks within the same load transfer framework.

[0008] To achieve the above objectives, the first aspect of the present invention provides a method for calculating the load settlement of a side-resistance reinforced consolidated expanded-disk pile, comprising: S1. Obtain parameters of pile body, disk body, consolidated body and layered foundation. Using soil layer interface, consolidated body boundary and disk body boundary as segmentation control points, divide the pile body into calculation micro-segments of ordinary segment, consolidated transition segment and disk body segment; S2. Reconstruct the soil parameters of the consolidated transition section and the consolidation zone of the disk section based on the natural soil parameters and the consolidation amplification factor, and determine the interface friction angle of the consolidation zone with the internal friction angle after consolidation as the upper limit and the friction angle of the natural interface as the lower limit. S3. Establish a nonlinear load transfer model for the side resistance of the ordinary section, the side resistance of the consolidated transition section, the side resistance of the outer perimeter of the disk, the annular end resistance of the disk, and the pile end resistance; wherein, the side resistance of the outer perimeter of the disk is calculated based on the equivalent calculated perimeter determined by the pile diameter and the disk diameter, and the side resistance of the outer perimeter of the disk and the annular end resistance of the disk are determined by the relative displacement of the same pile and soil at the midpoint of the disk section and superimposed as the resistance of the disk section; S4. Given the pile tip displacement and determine the pile tip axial force, use these two as the initial boundary conditions. Based on the load transfer model of each pile segment, perform displacement coordination iterative calculation segment by segment from the pile tip to the pile top. After the current calculation micro-segment converges, use its top axial force and top displacement as the bottom boundary conditions of the adjacent upper calculation micro-segment until the pile top load and pile top settlement are obtained. S5. Change the pile end displacement and repeat step S4 to generate a load-settlement curve based on the obtained pile top load-pile top settlement data points.

[0009] As a further preferred embodiment, in step S1, for the j-th disk, the depth of the disk center is... Disc height and solidified body height Determine the disk range and consolidation zone .

[0010] As a further preferred embodiment, in step S1, the disk body interval is subtracted from the consolidation interval to obtain the consolidation transition interval located above and below the disk body; all disk body intervals, consolidation transition intervals, soil interfaces and pile end positions are merged and sorted to form candidate micro-segments based on the intervals between adjacent segment control points.

[0011] As a further preferred embodiment, in step S1, when the consolidation intervals corresponding to different disks overlap, the overlapping intervals are subjected to union processing, and the type of candidate micro-segment is determined according to the rule that disk segments take precedence over consolidation transition segments, and consolidation transition segments take precedence over ordinary segments; the candidate micro-segments with lengths greater than the preset discrete length are further divided equally to obtain the calculated micro-segments.

[0012] As a further preferred embodiment, in step S2, the elastic modulus after consolidation... shear modulus Cohesion and internal friction angle Determined according to the following formula: , , , ;in, , , and The calculations are as follows: the natural elastic modulus, natural shear modulus, natural cohesion, and natural internal friction angle of the soil layer containing the micro-segment. , , and The consolidation amplification factors are, in order, the elastic modulus, the shear modulus, the cohesion, and the tangent of the internal friction angle.

[0013] As a further preferred embodiment, in step S2, the interface friction angle of the consolidation zone is... according to It is confirmed that, among them, The friction angle at the natural pile-soil interface. The consolidation amplification factor is the tangent of the internal friction angle. The internal friction angle after consolidation; the coefficient of earth pressure at rest in the consolidated zone is calculated according to... The actual horizontal lateral earth pressure coefficient k after pile formation is determined by the static earth pressure coefficient of the consolidated zone. The ratio is used to correct the limiting side resistance of the consolidated region.

[0014] As a further preferred embodiment, in step S3, the total side resistance of the ordinary section... Total side resistance of the consolidation transition section According to and Sure, , Where d is the diameter of a typical pile, To calculate the length of the micro-segment, s represents the relative displacement between the pile and the soil at the midpoint of the micro-segment. and These represent the interfacial shear stresses between the ordinary section and the consolidation transition section, respectively. , , and The parameters are for the corresponding hyperbolic load transfer.

[0015] As a further preferred embodiment, in step S3, the peripheral resistance of the disk body... according to Sure, , ;in, To calculate the equivalent perimeter of the disk, D is the disk diameter, and Li is the disk height. This is the coefficient of performance for the side resistance of the disk. Shear stress on the side of the disk; annular end resistance of the disk according to Confirm the effective pressure-bearing area of ​​the disc. R and r are the radius of the disc and the radius of the ordinary pile, respectively. These are the initial compliance parameters at the disk end. For the ultimate resistance at the end of the plate The reciprocal of.

[0016] As a further preferred option, in step S3, the resistance of the ordinary segment micro-segment is taken as... The resistance of the consolidation transition section micro-segment is taken Micro-segment resistance of the disk body and The sum of, among which, For the outer side resistance of the disk body, For the annular end resistance of the disc; for the pile end resistance according to It is confirmed that, among them, For pile end displacement, These are the initial compliance parameters for the pile tip. ultimate resistance at the pile tip The reciprocal of.

[0017] As a further preferred embodiment, in step S4, for the i-th calculated micro-segment, its bottom displacement is... Calculate the axial force at the bottom , with bottom displacement and bottom axial force Estimate the midpoint displacement of segment i; determine the segment resistance based on the midpoint displacement and the segment type; according to... Update the top axial force of micro-segment i and according to , Calculate the length Li of the micro-segment, the elastic modulus Ep of the pile body, and the effective compressive area Ai of the micro-segment to correct the midpoint displacement.

[0018] As a further preferred embodiment, in step S4, when the absolute value of the difference between two adjacent midpoint displacement iteration values ​​is less than the preset displacement tolerance, the current calculated micro-segment is determined to be converged; the effective pressure-bearing area of ​​the ordinary segment and the consolidation transition segment... Effective pressure-bearing area of ​​the disc section After the current computational micro-segment converges, according to Determine the top displacement, where, , , and Let represent the bottom displacement, bottom axial force, top displacement, and top axial force of the i-th calculated micro-segment, respectively; Li is the length of the calculated micro-segment; and Ep is the elastic modulus of the pile; and let , To maintain the continuity of displacement and axial force between adjacent calculated micro-segments.

[0019] According to another aspect of the present invention, a system for calculating the load-settlement of a side-resistance enhanced consolidated expanded-disk pile is also provided, comprising: The segmented unit is used to obtain parameters of consolidated expanded piles, disk body, consolidated body and layered foundation, and divides the consolidated expanded piles into ordinary segment, consolidated transition segment and disk body segment; The parameter reconstruction unit is used to determine the soil parameters in the consolidated zone based on the natural soil parameters and the consolidation amplification factor, and to determine the interface friction angle in the consolidated zone according to the upper limit of the internal friction angle after consolidation and the lower limit of the friction angle of the natural interface. The resistance model building unit is used to establish a nonlinear load transfer model for the side resistance of the ordinary section, the side resistance of the consolidation transition section, the side resistance of the outer perimeter of the disk, the annular end resistance of the disk, and the pile end resistance. The iterative solution unit is used to perform displacement coordination iterative calculation segment by segment from the pile tip to the pile top, based on the load transfer model of each pile segment, with the pile tip axial force and pile tip displacement as the initial boundary conditions, and outputs the pile top load and pile top settlement. The curve generation unit is used to change the pile end displacement, call the iterative solution unit to obtain multiple pile top load-pile top settlement data points, and generate a load-settlement curve.

[0020] According to a third aspect of the present invention, a computer-readable storage medium is also provided, on which a computer program is stored, which, when executed by a processor, implements the method for calculating the load settlement of the side-resistance enhanced consolidated expanded pile.

[0021] Compared with the prior art, the present invention has at least the following beneficial effects: (1) The consolidation boundary, disk boundary and soil interface jointly control the dispersion, which can avoid replacing the local reinforcement parameters with the average parameters of the whole pile, and can handle the situation where multiple consolidation zones are adjacent or overlapping.

[0022] (2) The friction angle of the interface in the consolidated zone is constrained by both the upper limit of the friction angle of the soil after consolidation and the lower limit of the friction angle of the natural interface, thus avoiding the simple proportional enlargement that would cause the shear strength of the interface to exceed the shear strength of the soil itself or fall below the level before reinforcement.

[0023] (3) The outer side resistance and the annular end resistance are taken into account for the disc section. The equivalent perimeter is determined by the ordinary pile diameter and the disc diameter, which can reflect the influence of the gradually changing shape of the disc and the effective contact perimeter on the load sharing.

[0024] (4) The bottom-up micro-segment iteration transmits axial force and displacement between segments, which can solve single or multi-disc consolidated expanded piles in a unified manner and output complete load-settlement curves instead of just giving a single ultimate bearing capacity value. Attached Figure Description

[0025] Figure 1 A schematic diagram of the structure, zoning, and vertical resistance composition of the consolidated expanded pile; Figure 2 A schematic diagram illustrating the hyperbolic load transfer relationship and the meaning of its parameters; Figure 3 A schematic diagram showing the division of the disk body region, the consolidation transition region, and the calculation micro-segments; Figure 4 A schematic diagram illustrating the local iteration of micro-segments and the transfer of boundaries between segments; Figure 5 A schematic diagram showing the comparison between calculated and experimental values ​​of the load-settlement curve; Figure 6 A flowchart illustrating the overall process for calculating the load-settlement of side-resistance reinforced consolidated expanded-disk piles; Figure 7 A schematic diagram for calculating the equivalent perimeter and annular effective bearing area of ​​the disc; Figure 8 This is a block diagram of the load settlement calculation system for side-resistance enhanced consolidated expanded piles.

[0026] Figure reference numerals: 11-segmented element; 12-parameter reconstruction element; 13-resistance model construction element; 14-iterative solution element; 15-curve generation element. Detailed Implementation

[0027] The present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments are used to illustrate the cooperation relationship between the various technical features and are not intended to limit the scope of protection.

[0028] Example 1: Segmented Load Transfer Model like Figure 1 As shown, a consolidated expanded-disk pile includes a pile body, one or more discs arranged along the pile body, and a consolidated body surrounding the discs and extending along the pile axis. The portion of the pile body not within the consolidated body is the ordinary section; the portion within the consolidated body and located on the upper and lower sides of the discs is the consolidated transition section; and the portion corresponding to the axial height of the discs is the disc section. The pile top load is borne jointly by the side resistance of the ordinary section, the side resistance of the consolidated transition section, the side resistance of the outer perimeter of the discs, the annular end resistance of the discs, and the pile end resistance.

[0029] This embodiment makes the following calculation assumptions: the pile material is treated as a linear elastic body within the calculated load range; the natural parameters within the same soil layer are taken as the layered exploration parameters; the consolidation parameters are only assigned to the calculation micro-segments within the consolidation body range; the load transfer relationship between the pile side, the pile end, and the pile tip adopts a hyperbolic form; the axial force in each calculation micro-segment varies linearly along the axial direction.

[0030] like Figure 2 As shown, the following hyperbolic relationship is adopted for the interfacial shear stress τ and relative displacement s, and the concentrated end resistance P and relative displacement s: (1) (2) In equation (1), τ is the interfacial shear stress exerted by the ordinary section, the consolidated transition section, or the side of the disk under the current relative displacement, in kPa; s is the pile-soil relative displacement at the corresponding interface, in meters; and a is the initial compliance parameter of the side resistance, in m / kPa. ρ is the initial shear stiffness; b is the side drag limit parameter, in units of 1 / kPa. The ultimate side friction resistance. In equation (2), P is the annular end resistance of the disk or the pile end resistance, kN; f is the initial compliance parameter of the end resistance, in m / kN. ρ is the initial compressive stiffness; g is the end resistance limit parameter, in units of 1 / kN. This represents the resistance at the extreme end.

[0031] Step S1: Calculate the interval partition Let the pile length be L, and establish a depth coordinate z along the pile top downwards. For the j-th disk, input the center depth of the disk. Disc height and solidified body height The disk body range is The solidified body interval is After subtracting the disk section from the consolidated section, we obtain two consolidation transition sections: the upper and lower sections.

[0032] like Figure 3As shown, the interfaces of each soil layer, the endpoints of each disk section, the endpoints of each consolidated section, the pile top, and the pile tip are merged into a control point sequence. When different consolidated section intervals overlap, the union is first calculated, and then the intervals are marked according to the rule of prioritizing disk segments, followed by consolidated transition segments, and then ordinary segments. Intervals with a length greater than the preset discrete length ΔLmax are further divided equally. The disk segment is kept as an independently calculated micro-segment to avoid the disk annular end resistance being counted repeatedly.

[0033] Step S2: Reconstruction of consolidation zone parameters For ordinary sections, the natural elastic modulus of the soil layer is used. Natural shear modulus Natural cohesive force , natural internal friction angle Friction angle between natural pile and soil interface For the consolidation transition section and the disk section, the parameters after consolidation are reconstructed using the following formula:

[0034] (3)

[0035] In equation (3), , and These are the elastic modulus, shear modulus, and cohesion of the consolidated soil, respectively, with units of MPa, MPa, and kPa. , , These represent the elastic modulus, shear modulus, and cohesion of the natural soil at the same location, respectively, with units of MPa, MPa, and kPa; αE, and The consolidation amplification factors are, in order, the elastic modulus, the shear modulus, and the cohesion, all of which are dimensionless.

[0036] The internal friction angle of the consolidated soil is amplified according to the tangent of the friction angle: (4)

[0037] In equation (4), The internal friction angle of the consolidated soil is expressed in degrees (°). αφ is the internal friction angle of natural soil at the same location, in °; αφ is the consolidation amplification factor of the tangent of the internal friction angle, which is dimensionless; tan and arctan are the tangent and arctangent functions, respectively.

[0038] The friction angle at the interface of the consolidated zone should neither exceed the internal friction angle of the consolidated soil itself nor be lower than the friction angle at the natural interface. Therefore, we take: (5) In equation (5), The friction angle of the pile-soil interface in the consolidated zone is expressed in degrees (°). The friction angle of the natural pile-soil interface at the same location is expressed in degrees (°). The consolidation amplification factor is given by equation (4); The internal friction angle of the consolidated soil is denoted by ; min and max represent the smaller and larger values, respectively. This formula first uses... right Apply upper limit constraints, and then... Apply a lower bound constraint.

[0039] Step S3: Calculate the resistance of various micro-segments Calculate the total side resistance of the micro segment in the ordinary section. for: (6) In equation (6), d is the diameter of a common pile, in meters; Li is the length of the i-th calculated micro-segment, in meters; The shear stress at the pile-soil interface of this micro-segment is given in kPa. The total side resistance provided for this microsegment is kN.

[0040] The shear stress at the interface of the ordinary section is: (7) In equation (7), The initial compliance parameter for the side resistance of the ordinary section is given in m / kPa. The side resistance limit parameter for the ordinary section is 1 / kPa; s is the relative displacement between the pile and soil at the midpoint of the calculated micro-segment, in meters. and These correspond to the initial shear stiffness and the ultimate side friction, respectively.

[0041] Based on the elastic shear deformation relationship, the shear stress at the interface of the ordinary segment also satisfies: (8) In equation (8), Gs is the average shear modulus of the soil layer in the ordinary section, in MPa; denoted as the radius affected by shear deformation (m); d is the pile diameter (m); ln is the natural logarithm function.

[0042] From the condition of consistent initial slopes in equations (7) and (8), we obtain: (9) In equation (9), These are the initial compliance parameters for the side resistance of the ordinary section, in m / kPa; d, rm, and These represent the ordinary pile diameter, the radius of influence of shear deformation, and the weighted average shear modulus, respectively, with units of m, m, and MPa; ln is the natural logarithm function. The radius of influence of shear deformation can be taken as... Where L is the pile length in meters; vs is the weighted average Poisson's ratio of the soil within the pile length range; and ρm is the average modulus ratio coefficient.

[0043] The weighted average shear modulus, weighted average Poisson's ratio, and average modulus ratio coefficient within the pile length range are determined by the following formula:

[0044] (10)

[0045] In equation (10), Let be the thickness of the i-th soil layer within the pile length, in meters. , and Let be the natural shear modulus, Poisson's ratio, and elastic modulus of the i-th soil layer, respectively. ; ρm is the weighted average shear modulus, MPa; vs is the weighted average Poisson's ratio; ρm is the average modulus ratio coefficient; n is the number of soil layers traversed by the pile; L is the pile length, m; Gmax is the maximum natural shear modulus of each soil layer within the pile length range, MPa.

[0046] The side drag limiting parameters for the ordinary section are: (11)

[0047] In equation (11), The ultimate side friction resistance of the ordinary section is expressed in kPa. The lateral resistance failure ratio is a dimensionless quantity. Depth at the midpoint of the micro-segment The effective vertical self-weight stress at the location is kPa; k is the actual horizontal lateral earth pressure coefficient after pile formation. The coefficient of earth pressure at rest for natural soil; denoted as the natural interface friction angle, in °. k / k0 is the correction ratio for the impact of pile compaction.

[0048] The total lateral resistance and interfacial shear stress of the consolidation transition section are: (12)

[0049] In equation (12), The total side resistance of the consolidation transition section is kN; The shear stress at the interface of the consolidated zone is given in kPa. and These are the initial compliance parameter and the limiting parameter of the side resistance in the consolidated region, respectively; the meanings of d, Li, and s are the same as those mentioned above.

[0050] The side resistance parameters of the consolidated region are: (13) (14)

[0051] In equation (13), Where is the radius of a typical pile body, in meters; Gc is the shear modulus after consolidation, in MPa. Let the radius be m, representing the influence radius of shear deformation. In equation (14), The ultimate side friction resistance of the consolidated zone is given in kPa. This is the coefficient of earth pressure at rest in the consolidated zone; The friction angle of the consolidation zone interface is determined by equation (5); the other symbols are the same as those in equation (11).

[0052] The peripheral resistance of the disk segment is: (15)

[0053] In equation (15), The resistance of the outer side of the disk body is kN; The equivalent perimeter of the disk is calculated in meters; Li takes the height hbr of the disk segment in meters. is the disk side resistance utilization coefficient, which is a dimensionless quantity; The shear stress on the side of the disk is given in kPa, and its hyperbolic parameters are taken from the consolidation zone where the disk is located. and .

[0054] like Figure 7 As shown, considering the gradient surfaces on the top and bottom of the disk and the effective contact area on the outer perimeter, the equivalent calculated perimeter of the disk is: (16) In equation (16), D is the diameter of the disk, m; d is the diameter of the ordinary pile, m; and π is the ratio of π to π.

[0055] The pile end resistance is expressed by the following formula: (17) In equation (17), The pile end resistance under the current pile end displacement, in kN; The displacement at the pile end is in meters (m). and These are the initial compliance parameters and ultimate limit parameters of the pile tip, respectively.

[0056] Elastic relationships at the initial stage of pile tip and the resulting determination for: (18) (19) In equations (18) and (19), The shear modulus of the soil in the bearing stratum at the pile tip, in MPa; d is the Poisson's ratio of the soil in the bearing stratum at the pile tip; d is the pile diameter, in meters. The current pile end resistance is given in kN. Let the pile end displacement be m; let the initial loading stage be... This makes the initial slope of equation (17) consistent with that of equation (18).

[0057] The ultimate resistance at the pile tip is: (20) In equation (20), The ultimate resistance at the pile tip is kN. The soil cohesion at the pile tip is expressed in kPa. and These are the dimensionless bearing capacity coefficients of the pile tip bearing layer; The average effective lateral pressure stress at the pile tip is expressed in kPa. The bearing area of ​​the circular pile tip is in m².

[0058] The average effective lateral compressive stress and bearing capacity coefficient at the pile tip are:

[0059] (twenty one)

[0060] In equation (21), The internal friction angle of the bearing stratum at the pile tip, in °; depth of pile tip The effective vertical self-weight stress at the point is kPa; e is the natural constant; the other symbols are the same as in equation (20).

[0061] The ultimate limit parameters of the pile tip are: (twenty two) In equation (22), The unit is 1 / kN, and the meanings of the other symbols are the same as those in equations (20) and (21).

[0062] The annular end resistance at the bottom of the disk is: (twenty three) In equation (23), The annular end resistance of the disk is kN; s is the relative displacement of the midpoint of the disk segment, m. and These are the initial compliance parameters and the limiting parameters of the disk end resistance, respectively.

[0063] The initial compliance parameters of the disk end resistance are: (twenty four) In equation (24), The initial compliance parameter for the disk end resistance is m / kN; Poisson's ratio of the consolidated soil at the bottom of the pan; The shear modulus of the consolidated soil at the bottom of the pan, in MPa; Let be the radius of the disk, in meters. The radius of a typical pile is in meters (m).

[0064] The ultimate resistance of the disk is: (25) In equation (25), The ultimate resistance of the disk body is kN; The cohesion of the consolidated soil at the bottom of the pan, kPa; and The dimensionless bearing capacity coefficient is determined based on the internal friction angle of the consolidated soil at the bottom of the plate. The average effective lateral compressive stress at the bottom of the pan is expressed in kPa. The effective bearing area of ​​the disc ring is in m².

[0065] The average effective lateral compressive stress and bearing capacity coefficient at the bottom of the plate are:

[0066] (26)

[0067] In equation (26), The internal friction angle of the bearing stratum at the pile tip, in °; depth of pile tip The effective vertical self-weight stress at the location, kPa; , and The meaning is the same as that of equation (25).

[0068] The limiting parameters of the disk body terminal resistance are: (27) In equation (27), The unit is 1 / kN, and the meanings of the other symbols are the same as those in equations (25) and (26).

[0069] Step S4: Bottom-up displacement coordination iteration Figure 6 The overall solution process is shown, from automatic segmentation and boundary initialization to state recursion and upward movement. Figure 4 The diagram illustrates the midpoint displacement iteration within a single computational micro-segment and the boundary transfer relationship between this micro-segment and its adjacent micro-segments.

[0070] Given the pile end displacement sb, calculate the pile end resistance Pb using equation (17), and use it as the bottom axial force of the lowest calculation segment. For the i-th calculation segment, the bottom displacement is known. and bottom axial force The initial value of the midpoint displacement is: (28) In equation (28), Let be the initial value of the midpoint displacement of the i-th calculated micro-segment, m; Li be the length of the micro-segment, m; Ep be the elastic modulus of the pile, kPa; Ai be the effective compressive area of ​​the micro-segment, m²; and take for the ordinary segment and the consolidation transition segment. Disk body segment .

[0071] In the k-th local iteration, the micro-segment resistance is determined based on the micro-segment type: (29) In equation (29), Let N be the resistance of the i-th micro-segment in the k-th iteration; , , and These are the side resistance of the ordinary section, the side resistance of the consolidation transition section, the side resistance of the outer perimeter of the disk, and the annular end resistance of the disk, respectively, in kN.

[0072] Update the top axial force based on the static equilibrium of the micro-segment: (30) In equation (30), Let be the top axial force of the i-th micro-segment in the k-th iteration, in kN; The value is the axial force at the bottom of the micro-segment, in kN.

[0073] Correct the midpoint displacement based on the linear variation condition of axial force within the micro-segment: (31) In equation (31), Let m be the corrected midpoint displacement; the meanings of the other symbols are the same as in equations (28) and (30). When The local iteration of the current micro-segment ends when the number of iterations reaches the upper limit kmax. The displacement tolerance can be determined based on the calculation accuracy. to .

[0074] After the current micro-segment converges, its top displacement is: (32) In equation (32), Let m be the displacement of the top of the i-th micro-segment. Let... , The current top state of the micro-segment is transferred to the adjacent upper micro-segment. The calculation is performed segment by segment up to the pile top, yielding the pile top settlement *st* and pile top load *Pt*. This transfer relationship ensures that all disks and their consolidated zones work collaboratively within the same axial force-displacement chain.

[0075] Step S5: Load-settlement curve generation Multiple samples are taken in an increasing sequence within the preset pile end displacement range. Value, for each Repeat step S4. The values ​​obtained from each solution... and Composition of data points By connecting the piles in ascending order of top load, a load-settlement curve is obtained. Based on the settlement limit, ultimate load criterion, or test termination condition used in the design, the corresponding bearing capacity and settlement value can be extracted from the curve.

[0076] Example 2: Calculation Case Taking a consolidated expanded-disk pile with a length of 30.0m, a standard pile diameter of 1.6m, a disc diameter of 2.4m, and two discs as an example. The elastic modulus of the pile body is taken as... Side drag ratio Take 0.8 as the horizontal side pressure correction ratio. Take 1.1, disk height Take 1.3m as the height of the solidified body. The diameter is set to 2.0m, and the side resistance utilization factor ηb is set to 0.7. The consolidation parameter amplification factor is determined based on indoor mix proportioning tests, in-situ tests, or inversion from similar projects.

[0077] The soil layer input should include at least the top and bottom depths, effective unit weight, elastic modulus, Poisson's ratio, cohesion, and internal friction angle; the pile-soil interface friction angle can be determined by interfacial shear tests. The program first generates segmented control points and labels the segment types, then calculates the internal friction angle for each segment. , , , , , , and For disk segments, the program calculates simultaneously within the same micro-segment. and This avoids only calculating the resistance at the bottom of the disk and neglecting the resistance on the outer side of the disk.

[0078] like Figure 5 As shown, the static load test curve can be used as the target curve for inversion within the allowable range of each amplification factor, and the calculated curve can be compared with the test data in the same figure. When the inverted parameters are used for design calculations under the same site, the same construction technology, and similar soil conditions, the source and scope of application of the parameters should be traceable.

[0079] Example 3: Computing System like Figure 8 As shown, segmentation unit 11 reads geometric and stratigraphic data and outputs a sequence of micro-segments with type labels; parameter reconstruction unit 12 calculates consolidation zone parameters and interface friction angle; resistance model construction unit 13 establishes a side resistance or end resistance model for each micro-segment; iterative solution unit 14 solves in the reverse order of the micro-segment sequence, i.e. from the pile tip to the pile top; curve generation unit 15 changes the pile tip displacement and summarizes the pile top output.

[0080] The aforementioned unit can be implemented by a processor executing a program stored in memory, or it can be deployed in pile foundation design software, engineering calculation servers, or field test analysis terminals. Input data, parameters of each micro-segment, local iteration processes, and final curves can all be saved for verification of the calculation basis.

[0081] Those skilled in the art can adjust the micro-segment length, convergence tolerance, parameter calibration method, or curve point selection method without departing from the concept of the present invention; as long as the partition parameter reconstruction, disk periphery side resistance and annular end resistance combination, and bottom-up inter-segment displacement coordination relationship described in the present invention are still used, they should all fall within the protection scope of the present invention.

Claims

1. A method for calculating the load-settlement of a side-resistance reinforced consolidated expanded-disk pile, characterized in that, include: S1. Obtain parameters of pile body, disk body, consolidated body and layered foundation. Using soil layer interface, consolidated body boundary and disk body boundary as segmentation control points, divide the pile body into calculation micro-segments of ordinary segment, consolidated transition segment and disk body segment; S2. Reconstruct the soil parameters of the consolidated transition section and the consolidation zone of the disk section based on the natural soil parameters and the consolidation amplification factor, and determine the interface friction angle of the consolidation zone with the internal friction angle after consolidation as the upper limit and the friction angle of the natural interface as the lower limit. S3. Establish a nonlinear load transfer model for the side resistance of the ordinary section, the side resistance of the consolidated transition section, the side resistance of the outer perimeter of the disk, the annular end resistance of the disk, and the pile end resistance; wherein, the side resistance of the outer perimeter of the disk is calculated based on the equivalent calculated perimeter determined by the pile diameter and the disk diameter, and the side resistance of the outer perimeter of the disk and the annular end resistance of the disk are determined by the relative displacement of the same pile and soil at the midpoint of the disk section and superimposed as the resistance of the disk section; S4. Given the pile tip displacement and determine the pile tip axial force, use these two as the initial boundary conditions. Based on the load transfer model of each pile segment, perform displacement coordination iterative calculation segment by segment from the pile tip to the pile top. After the current calculation micro-segment converges, use its top axial force and top displacement as the bottom boundary conditions of the adjacent upper calculation micro-segment until the pile top load and pile top settlement are obtained. S5. Change the pile end displacement and repeat step S4 to generate a load-settlement curve based on the obtained pile top load-pile top settlement data points. In step S1, for the j-th disk, the depth of the disk center is... Disc height and solidified body height Determine the disk range and consolidation zone ; In step S1, the disk body interval is subtracted from the consolidation interval to obtain the consolidation transition interval located above and below the disk body; all disk body intervals, consolidation transition intervals, soil interfaces and pile end positions are merged and sorted to form candidate micro-segments based on the intervals between adjacent segment control points. In step S1, when the consolidation intervals corresponding to different disks overlap, the overlapping intervals are subjected to union processing, and the type of candidate micro-segment is determined according to the rule that disk segments take precedence over consolidation transition segments, and consolidation transition segments take precedence over ordinary segments; candidate micro-segments with lengths greater than the preset discrete length are further divided equally to obtain the calculated micro-segments; In step S2, the elastic modulus after consolidation shear modulus Cohesion and internal friction angle Determined according to the following formula: , , , ;in, , , and The calculations are as follows: the natural elastic modulus, natural shear modulus, natural cohesion, and natural internal friction angle of the soil layer containing the micro-segment. , , and The consolidation amplification factors are, in order, elastic modulus, shear modulus, cohesion, and the tangent of the internal friction angle; In step S2, the interface friction angle of the consolidation zone according to It is confirmed that, among them, The friction angle at the natural pile-soil interface. The consolidation amplification factor is the tangent of the internal friction angle. The internal friction angle after consolidation; the coefficient of earth pressure at rest in the consolidated zone is calculated according to... The actual horizontal lateral earth pressure coefficient k after pile formation is determined by the static earth pressure coefficient of the consolidated zone. The ratio is used to correct the limiting side resistance of the consolidated region.

2. The method for calculating the load-settlement of side-resistance enhanced consolidated expanded-disk piles according to claim 1, characterized in that, In step S3, the total side resistance of the ordinary section Total side resistance of the consolidation transition section According to and Sure, , Where d is the diameter of a typical pile, To calculate the length of the micro-segment, s represents the relative displacement between the pile and the soil at the midpoint of the micro-segment. and These represent the interfacial shear stresses between the ordinary section and the consolidation transition section, respectively. , , and The parameters are for the corresponding hyperbolic load transfer.

3. The method for calculating the load-settlement of side-resistance enhanced consolidated expanded-disk piles according to claim 2, characterized in that, In step S3, the peripheral resistance of the disk body according to Sure, , ;in, The equivalent perimeter of the disk is calculated, where D is the disk diameter and Li is the length of the calculated micro-segment. This is the coefficient of performance for the side resistance of the disk. Shear stress on the side of the disk; annular end resistance of the disk according to Confirm the effective pressure-bearing area of ​​the disc. R and r are the radius of the disc and the radius of the ordinary pile, respectively. These are the initial compliance parameters at the disk end. For the ultimate resistance at the end of the plate The reciprocal of.

4. A system for calculating the load-settlement of laterally resisted reinforced consolidated expanded piles, used to implement the method for calculating the load-settlement of laterally resisted reinforced consolidated expanded piles as described in any one of claims 1-3, characterized in that, include: The segmented unit is used to obtain parameters of consolidated expanded piles, disk body, consolidated body and layered foundation, and divides the consolidated expanded piles into ordinary segment, consolidated transition segment and disk body segment; The parameter reconstruction unit is used to determine the soil parameters in the consolidated zone based on the natural soil parameters and the consolidation amplification factor, and to determine the interface friction angle in the consolidated zone according to the upper limit of the internal friction angle after consolidation and the lower limit of the friction angle of the natural interface. The resistance model building unit is used to establish a nonlinear load transfer model for the side resistance of the ordinary section, the side resistance of the consolidation transition section, the side resistance of the outer perimeter of the disk, the annular end resistance of the disk, and the pile end resistance. The iterative solution unit is used to perform displacement coordination iterative calculation segment by segment from the pile tip to the pile top, based on the load transfer model of each pile segment, with the pile tip axial force and pile tip displacement as the initial boundary conditions, and outputs the pile top load and pile top settlement. The curve generation unit is used to change the pile end displacement, call the iterative solution unit to obtain multiple pile top load-pile top settlement data points, and generate a load-settlement curve.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for calculating the load settlement of the side-resistance enhanced consolidated expanded pile as described in any one of claims 1-3.

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