A horizontal bearing design method suitable for root foundation

Abstract

The invention discloses a horizontal bearing design method suitable for root foundation, which belongs to the technical field of civil engineering. The method comprises: obtaining soil body related parameters, constructing soil unit stress-strain curve; defining variables and scaling factors related to root foundation design parameters; establishing functional relationships between root foundation design parameters and variables and between root foundation design parameters and scaling factors, respectively, and solving variable values ​​and scaling factor values ​​based on the established functional relationships; constructing P'‑y' Curve and M'‑ i 'Curve; based on the construction P'‑y' Curve and M'-θ The invention has the beneficial effects of improving the accuracy of estimating the horizontal bearing capacity of the root foundation and being applicable to the design of different parameters of the root foundation in actual engineering.

Description

Technical Field

[0001] The invention belongs to the technical field of civil engineering, and in particular relates to a horizontal bearing design method suitable for a root foundation. Background Art

[0002] Root foundations (root piles) are widely used in bridge engineering because they can improve the overall bearing capacity of the foundation. Root piles are mainly used to bear horizontal loads in engineering applications. The existing horizontal bearing design method for root foundations is to simplify the role of the root key and pile axis in the root pile foundation and consider their bearing capacity contribution to establish a simplified theoretical analysis model of the root pile foundation under horizontal loads.

[0003] In a root foundation, due to the existence of the root key, its bearing characteristics are different from those of ordinary piles. The influence of the root key on the pile shaft makes the horizontal soil reaction provided by the pile shaft part higher than the horizontal soil reaction provided by the pile shaft of the equal-section pile with the same pile diameter. However, the current method often ignores the mutual coupling between the root key and the pile shaft, and directly uses the horizontal soil reaction of the equal-section pile to calculate the soil reaction contribution of the pile shaft part in the root pile, resulting in insufficient accuracy in the estimation of the horizontal bearing capacity.

[0004] Therefore, it is necessary to study the influence of the mutual coupling between the pile axis and the root key in the root pile on the horizontal bearing capacity of the root pile, and to establish the corresponding relationship between the horizontal bearing capacity of the root pile and the specific design parameters of the root pile. Summary of the invention

[0005] The purpose of an embodiment of the present invention is to provide a horizontal bearing design method suitable for root-type foundations, which studies the influence of the mutual coupling between the pile shaft and the root key in the root pile on the horizontal bearing capacity of the root pile, and establishes the corresponding relationship between the horizontal bearing capacity of the root pile and the specific design parameters of the root pile, thereby improving the accuracy of estimating the horizontal bearing capacity of the root foundation, thereby solving at least one technical problem involved in the background technology.

[0006] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0007] An embodiment of the present invention provides a horizontal load design method applicable to a root foundation, comprising the following steps:

[0008] Step S1, obtaining soil related parameters and constructing soil unit stress-strain curve;

[0009] Step S2, defining variables and scaling factors related to the root foundation design parameters, wherein the root foundation design parameters include the pile shaft diameter D , vertical spacing of root keys , root key length , root key width and the number of single-layer root bond arrangements ; The variables include the influence coefficient of the root key on the pile axis Influence coefficient of pile axis on root key And the ultimate resistance moment coefficient ;

[0010] Step S3, respectively establish the functional relationship between the root-based design parameters and the variables and the functional relationship between the root-based design parameters and the scaling coefficients, and respectively solve the variable values ​​and the scaling coefficient values ​​based on the established functional relationships. The functional relationship between the root-based design parameters and the variables is expressed by the following formula:

[0011] (1);

[0012] (2);

[0013] (3);

[0014] In the formula, is the depth of the pile segment;

[0015] Step S4, solving the limit horizontal reaction force and the limit resistance moment according to the variable value and soil related parameters;

[0016] Step S5: construct a soil stress-strain curve according to the ultimate horizontal reaction force, the ultimate resistance moment, the scaling factor value, the soil body related parameters and the soil unit stress-strain curve. Curve and curve;

[0017] Step S6, based on the constructed Curve and Curve, use finite element difference method to calculate the horizontal bearing capacity of root foundation;

[0018] Step S7, judging whether the root foundation meets the horizontal bearing design requirements based on the calculated horizontal bearing capacity of the root foundation.

[0019] Optionally, in step S1, the soil-related parameters include undrained soil shear strength Initial shear stiffness and plastic failure strain .

[0020] Optionally, in step S3, the functional relationship between the root-based design parameter and the scaling factor is expressed by the following formula:

[0021] (4);

[0022] (5);

[0023] (6);

[0024] (7);

[0025] In the formula, is the scaling factor of elastic shear strain; is the scaling factor for plastic shear strain.

[0026] Optionally, in step S4, the limit horizontal reaction force is solved by the following formula: and ultimate resistance moment :

[0027] (8);

[0028] (9);

[0029] In the formula, and They are the ultimate soil reaction per unit length of the pile with uniform cross-section and the additional horizontal resistance of the root bond per unit thickness without considering the coupling effect between the root bond and the pile shaft. is the root bond cross-sectional area, ;

[0030] in:

[0031] (10);

[0032] (11);

[0033] In the formula, is the pile-soil roughness coefficient.

[0034] Optionally, step S5 specifically includes:

[0035] Step S51, the total horizontal reaction force per unit length of the pile segment is solved by the following formula: and total root bond resistance moment Soil element stress The corresponding relationship between them:

[0036] (12);

[0037] (13);

[0038] In the formula, is the shear stress on the soil element stress-strain curve; and for Curve and The soil resistance on the curve is exerted;

[0039] Step S52, solve the horizontal displacement by the following formula: and pile segment angle Soil element strain The corresponding relationship between them:

[0040] (14);

[0041] (15);

[0042] In the formula, is the elastic shear strain The scaling factor of is the plastic shear strain The scaling factor is , and the elastic shear strain and plastic shear strain Calculated by the following formula:

[0043] (16);

[0044] (17);

[0045] Step S53: The total horizontal reaction force per unit length of the pile segment is obtained based on the soil unit stress-strain relationship. With horizontal displacement The corresponding relationship between them is constructed Curve, root bond total resistance moment Angle with pile segment The corresponding relationship between them is constructed curve.

[0046] Alternatively, the soil element stress-strain relationship is expressed as follows:

[0047] (18).

[0048] The beneficial effects of the embodiments of the present invention are:

[0049] 1. Compared with the existing horizontal bearing analysis method for root foundation which does not consider the mutual coupling between the root key and the pile shaft, the horizontal bearing analysis method of the present invention can consider the mutual coupling between the root key and the pile shaft, thereby improving the accuracy of estimating the horizontal bearing capacity of the root foundation;

[0050] 2. The present invention can construct different and accurate Curve and Curve, which can be applied to the design of different parameters of root foundation in actual engineering;

[0051] 3. The method of the present invention is based on the MSD design concept and is constructed by the stress-strain response of soil elements. Curve and Curve, this construction method requires fewer parameters to be determined and is easy to obtain, which is simpler and more efficient in actual engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0053] Figure 1 A schematic diagram of a pile finite element model provided by the present invention;

[0054] Figure 2 A schematic diagram of the pile finite element model area provided by the present invention;

[0055] Figure 3 The influence coefficient of the root key on the pile shaft provided by the present invention is Design parameters of root foundation The relationship curve diagram of

[0056] Figure 4 The influence coefficient of the root key on the pile shaft provided by the present invention is Design parameters of root foundation The relationship curve diagram;

[0057] Figure 5 The influence coefficient of the root key on the pile shaft provided by the present invention is Design parameters of root foundation The relationship curve diagram;

[0058] Figure 6 The influence coefficient of the pile shaft on the root key provided by the present invention Design parameters of root foundation The relationship curve diagram;

[0059] Figure 7 The influence coefficient of the pile shaft on the root key provided by the present invention Design parameters of root foundation The relationship curve diagram;

[0060] Figure 8 The influence coefficient of the pile shaft on the root key provided by the present invention Design parameters of root foundation The relationship curve diagram;

[0061] Fig. 9 The ultimate resistance moment coefficient provided by the present invention is Design parameters of root foundation The relationship curve diagram;

[0062] Fig.10 The ultimate resistance moment coefficient provided by the present invention is Design parameters of root foundation The relationship curve diagram;

[0063] Fig.11 The ultimate resistance moment coefficient provided by the present invention is Design parameters of root foundation The relationship curve diagram;

[0064] Fig.12 The scaling factor provided by the present invention Design parameters of root foundation The relationship curve diagram of

[0065] Fig.13 The scaling factor provided by the present invention Design parameters of root foundation The relationship curve diagram of

[0066] Fig.14 The scaling factor provided by the present invention Design parameters of root foundation The relationship curve diagram of

[0067] Fig.15 The scaling factor provided by the present invention Design parameters of root foundation The relationship curve diagram of

[0068] Fig.16 The scaling factor provided by the present invention Design parameters of root foundation The relationship curve diagram of

[0069] Fig.17 It is a schematic diagram of the horizontal load calculation principle of the present invention;

[0070] Fig.18 This is the undrained shear strength distribution diagram of a bridge pile test site;

[0071] Fig.19 The present invention provides a comparison chart of the load-displacement curve calculated based on the method of the present invention and the existing method and the measured data. DETAILED DESCRIPTION

[0072] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0073] The terms "first", "second", etc. in the specification and claims of the present invention are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention can be implemented in an order other than those illustrated or described herein, and the objects distinguished by "first", "second", etc. are generally of the same type, and the number of objects is not limited. For example, the first object can be one or more. In addition, "and / or" in the specification and claims represents at least one of the connected objects, and the character " / " generally indicates that the objects associated with each other are in an "or" relationship.

[0074] An embodiment of the present invention provides a horizontal load design method applicable to a root foundation, comprising the following steps:

[0075] Step S1, obtaining soil related parameters and constructing soil unit stress-strain curve;

[0076] Step S2, defining variables and scaling factors related to the radical foundation design parameters;

[0077] Step S3, respectively establishing a functional relationship between the radical basis design parameter and the variable and a functional relationship between the radical basis design parameter and the scaling factor, and respectively solving the variable value and the scaling factor value based on the established functional relationship;

[0078] Step S4, solving the limit horizontal reaction force and the limit resistance moment according to the variable value and soil related parameters;

[0079] Step S5: construct a soil stress-strain curve according to the ultimate horizontal reaction force, the ultimate resistance moment, the scaling factor value, the soil body related parameters and the soil unit stress-strain curve. Curve and curve;

[0080] Step S6, based on the constructed Curve and Curve, use finite element difference method to calculate the horizontal bearing capacity of root foundation;

[0081] Step S7, judging whether the root foundation meets the horizontal bearing design requirements based on the calculated horizontal bearing capacity of the root foundation.

[0082] In step S1, the soil-related parameters are obtained by measuring the soil, including the undrained shear strength of the soil Initial shear stiffness and plastic failure strain .

[0083] In step S2, the root foundation design parameters include the pile shaft diameter D , vertical spacing of root keys , root key length , root key width and the number of single-layer root bond arrangements ; The variables include the influence coefficient of the root key on the pile axis Influence coefficient of pile axis on root key And the ultimate resistance moment coefficient ; The scaling system includes elastic shear strain The scaling factor and and plastic shear strain The scaling factor and .

[0084] In step S3, the functional relationship between the root-based design parameters and the variables and the functional relationship between the root-based design parameters and the scaling coefficients are obtained by the following method:

[0085] (1) Four sets of root key parameter conditions were designed. The diameter of the test pile in each condition was 5 m, the pile length was 47 m, and the loading height was 12 m. The parameter settings of each condition are shown in Table 1.

[0086] Table 1 Parameter settings for each working condition

[0087]

[0088] (2) Combination Figure 1 and Figure 2 As shown in the figure, a finite element model of the parameter condition is established, and the horizontal loading analysis and calculation are performed for each parameter condition, and then the coefficients under each parameter condition are calculated. value;

[0089] The soil and pile bodies of each parameter working condition were modeled using PLAXIS finite element software. The soil size was 82m×82m×50m, and the pile body size of each working condition was as described above. The soil body model adopted the NGI-ADP model, and the pile body adopted the linear elastic model. The material parameters of the soil and pile bodies are shown in Table 2. The loading method of horizontal loading in each working condition adopted step-by-step loading, with each level of load being 1000kN, the first level of load being 1000kN, and a total of 10 levels of load.

[0090] Table 2 Soil and pile material parameters

[0091]

[0092] (3) Draw the relationship curve between the variables and the radical basis design parameters using the finite element calculation results, as shown in the attached figure. Figure 3-Figure 11 As shown, the least square method is used for fitting. After fitting, the functional relationship between the root-based design parameters and the variables is obtained, which is expressed by the following formula:

[0093] (1) ;

[0094] (2);

[0095] (3);

[0096] In the formula, is the pile segment depth.

[0097] (4) Draw the relationship curve between scaling factor and radical foundation design parameters based on the finite element calculation results, as shown in the attached figure. Figure 12-16 As shown, the least square method is used for fitting. After fitting, the functional relationship between the root-based design parameters and the scaling coefficient is expressed as follows:

[0098] (4);

[0099] (5);

[0100] (6);

[0101] (7);

[0102] In the formula, is the scaling factor of elastic shear strain; is the scaling factor for plastic shear strain.

[0103] In step S4, the limit horizontal reaction force is solved by the following formula: and ultimate resistance moment :

[0104] (8);

[0105] (9);

[0106] In the formula, and They are the ultimate soil reaction per unit length of the pile with uniform cross-section and the additional horizontal resistance of the root bond per unit thickness without considering the coupling effect between the root bond and the pile shaft. is the root bond cross-sectional area, ;

[0107] in:

[0108] (10);

[0109] (11);

[0110] In the formula, is the pile-soil roughness coefficient.

[0111] Step S5 specifically includes:

[0112] Step S51, the total horizontal reaction force per unit length of the pile segment is solved by the following formula: and total root bond resistance moment Soil element stress The corresponding relationship between them:

[0113] (12);

[0114] (13);

[0115] In the formula, is the shear stress on the soil element stress-strain curve; and for Curve and The soil resistance on the curve is exerted;

[0116] Step S52, solve the horizontal displacement by the following formula: and pile segment angle Soil element strain The corresponding relationship between them:

[0117] (14);

[0118] (15);

[0119] In the formula, is the elastic shear strain The scaling factor of is the plastic shear strain The scaling factor is , and the elastic shear strain and plastic shear strain Calculated by the following formula:

[0120] (16);

[0121] (17);

[0122] The stress-strain relationship of soil element is expressed by the following formula:

[0123] (18).

[0124] Step S53: The total horizontal reaction force per unit length of the pile segment is obtained based on the soil unit stress-strain relationship. With horizontal displacement The corresponding relationship between them is constructed Curve, root bond total resistance moment Angle with pile segment The corresponding relationship between them is constructed ' curve.

[0125] It should be further explained that ' The curve represents the corresponding relationship between the lateral displacement of the pile and the total horizontal reaction per unit pile length; The curve represents the corresponding relationship between the rotational displacement of the pile and the resistance moment per unit pile length, and the interaction force between the pile body and the soil can be expressed by a set of nonlinear Spring and rotational spring nonlinearity concentrated in the keyed pile segment The spring is represented as Fig.17 As shown, by constructing Curve and The curve can reflect the corresponding relationship between the spring deformation and the elastic force.

[0126] Engineering verification: This paper proposes a horizontal load-bearing design method suitable for root foundations, and takes two groups of root foundation horizontal load tests carried out in a highway bridge construction project as the research object.

[0127] First, the influence coefficient of the root key on the pile axis is obtained based on the root foundation design parameters of the field test pile and the engineering geological parameters. Influence coefficient of pile axis on root key Ultimate resistance moment coefficient and four scaling factors .

[0128] Then, the horizontal bearing capacity of the root foundation horizontal load test of the above-mentioned highway bridge was calculated by using the method provided by the present invention and the current horizontal bearing design method, and compared with the load-displacement curve under the on-site test piles to verify the correctness, effectiveness and rationality of the method provided by the present invention.

[0129] (1) On-site pile test root foundation design parameters and engineering geological parameters;

[0130] Root bond arrangement of the test piles: The dimensions of the two groups of test piles are the same, with a pile diameter of 5m, a pile length of 47m, a buried depth of 34.6m, root bond dimensions of 1.6m×0.8m×0.8m (root bond length×width×height), 13 root bond layers, 5 single-layer root bonds, and a root bond layer spacing of 2m. The root foundation structure density is 2500kg / m 3 , engineering geological parameters soil strength distribution according to Fig.18 As shown in Table 3, the linear fitting results of the intensity in each depth range are obtained.

[0131] Table 3 Engineering geological parameters

[0132]

[0133] (2) Calculate specific coefficient values ​​based on the radical foundation design parameters;

[0134] The design parameters of the field test pile root foundation are input into formula (1) to formula (7) to obtain the calculation results of the coefficients, as shown in Table 4.

[0135] Table 4 Coefficient calculation results

[0136]

[0137] (3) Load-displacement curves of the test piles based on the method of the present invention and the existing method;

[0138] Attached Fig.19 The pile head horizontal load-displacement curve predicted by the analysis method proposed in the present invention is compared with the current calculation method and the measured results. The comparison results show that based on the analysis method proposed in the present invention, the calculated load-displacement curve results are in good consistency with the measured results. Compared with the calculation results of the current BNWF model, it can be found that when the coupling between the root key and the pile shaft is ignored, the maximum error of the load-displacement curve increases from 7.6% to 24.6% compared with the measured results. In the convergence stage of the load-displacement curve close to reaching the ultimate bearing capacity, the load-displacement curve calculated by the current BNWF model still has an upward trend, and the calculation results of the analysis method proposed by the present invention are more consistent with the measured trend. This is precisely because the mutual influence between the root key and the pile shaft is ignored in the current method, which makes the estimation of the ultimate bearing capacity inaccurate. The calculation results of the horizontal bearing capacity obtained based on the method of the present invention are more accurate, which verifies the correctness and effectiveness of the method of the present invention.

[0139] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.

[0140] In addition, it should be noted that the scope of the methods and systems in the embodiments of the present invention is not limited to performing functions in the order shown or discussed, and may also include performing functions in a substantially simultaneous manner or in reverse order according to the functions involved. For example, the described methods may be performed in an order different from that described, and various steps may be added, omitted, or combined. In addition, features described with reference to certain examples may be combined in other examples.

[0141] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A horizontal bearing design method suitable for root foundation, characterized in that: The steps include: Step S1, obtaining soil related parameters and constructing soil unit stress-strain curve; Step S2, defining variables and scaling factors related to the root foundation design parameters, wherein the root foundation design parameters include the pile shaft diameter D , vertical spacing of root keys hr , root key length l , root key width b and the number of single-layer root bond arrangements m ; The variables include the influence coefficient of the root key on the pile axis α , the influence coefficient of pile axis on root key β And the ultimate resistance moment coefficient η ; Step S3, respectively establish the functional relationship between the root-based design parameters and the variables and the functional relationship between the root-based design parameters and the scaling coefficients, and respectively solve the variable values ​​and the scaling coefficient values ​​based on the established functional relationships. The functional relationship between the root-based design parameters and the variables is expressed by the following formula: （1） （2） （3） In the formula, z is the depth of the pile segment; Step S4, solving the limit horizontal reaction force and the limit resistance moment according to the variable value and soil related parameters; Step S5, constructing a soil element stress-strain curve according to the ultimate horizontal reaction force, the ultimate resistance moment, the scaling factor value, the soil body related parameters and the soil element stress-strain curve P'-y' Curve and M'-θ' The curve, where P'-y' The curve represents the total horizontal reaction force per unit length of the pile segment. P' With horizontal displacement y' The corresponding relationship between them; M'-θ' The curve represents the total resistance moment of the root bond M' Angle with pile segment θ' The corresponding relationship between them; Step S6, based on the constructed P'-y' Curve and M'-θ' Curve, use finite element difference method to calculate the horizontal bearing capacity of root foundation; Step S7, judging whether the root foundation meets the horizontal bearing design requirements based on the calculated horizontal bearing capacity of the root foundation.

2. The horizontal load design method applicable to root foundation according to claim 1 is characterized in that: In step S1, the soil related parameters include soil undrained shear strength s u , initial shear stiffness G max and plastic failure strain .

3. The horizontal load design method applicable to root foundation according to claim 2 is characterized in that: In step S3, the functional relationship between the root-based design parameter and the scaling factor is expressed as follows: （4） （5） （6） （7） In the formula, ξpe , ξθe is the scaling factor of elastic shear strain; ξpp , ξθp is the scaling factor for plastic shear strain.

4. The horizontal load design method applicable to root foundation according to claim 3 is characterized in that: In step S4, the limit horizontal reaction force is solved by the following formula: P' u and ultimate resistance moment M' u : （8） （9） In the formula, P pu and P ru They are the ultimate soil reaction per unit length of the pile with uniform cross-section and the additional horizontal resistance of the root bond per unit thickness without considering the coupling effect between the root bond and the pile shaft. A 0 is the root bond cross-sectional area, A 0 = l × b ; in: （10） （11） In the formula, a is the pile-soil roughness coefficient.

5. The horizontal load design method applicable to root foundation according to claim 4 is characterized in that: Step S5 specifically includes: Step S51, the total horizontal reaction force per unit length of the pile segment is solved by the following formula: P' and total root bond resistance moment M' Soil element stress τ The corresponding relationship between them: （12） （13） In the formula, τ / s u is the shear stress on the soil element stress-strain curve; P' / P' u and M' / M' u for P'-y' Curve and M'-θ' The soil resistance on the curve is exerted; Step S52, solve the horizontal displacement by the following formula: y' and pile segment angle θ' Soil element strain The corresponding relationship between them: （14） （15） In the formula, ξ p e , ξ θ e is the elastic shear strain The scaling factor of ξ p p , ξ θ p is the plastic shear strain The scaling factor is , and the elastic shear strain and plastic shear strain Calculated by the following formula: （16） （17） Step S53: The total horizontal reaction force per unit length of the pile segment is obtained based on the soil unit stress-strain relationship. P' With horizontal displacement y' The corresponding relationship between them is constructed P'-y' Curve, root bond total resistance moment M' Angle with pile segment θ' The corresponding relationship between them is constructed M'-θ' curve.

6. The horizontal load design method applicable to root foundation according to claim 5 is characterized in that: The stress-strain relationship of soil element is expressed by the following formula: （18）。

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