A calculation method for pile pullout coefficient

Abstract

The present invention relates to the field of geotechnical engineering design and is a method for calculating the pullout coefficient of foundation piles. The method comprises the following steps: first, based on the stress state of the soil on the side of the compression pile, a stress analysis is performed on the soil unit on the side of the pile to derive the horizontal stress of the soil unit on the side of the compression pile and the soil pressure coefficient on the side of the pile; second, based on the stress state of the soil on the side of the pullout pile, a stress analysis is performed on the soil unit on the side of the pile to derive the horizontal stress of the soil unit on the side of the pullout pile and the soil pressure coefficient on the side of the pullout pile; and finally, based on the soil pressure coefficients on the side of the compression and pullout piles, a calculation formula for the pullout coefficient of the foundation pile is derived. The present invention solves the problem of inaccurate evaluation based on experience during construction.

Description

Technical Field

[0001] The invention relates to the field of geotechnical engineering design and is a method for calculating the pull-out coefficient of a foundation pile. Background Art

[0002] The groundwater level in my country's coastal areas is relatively high, and underground buildings usually need to withstand huge buoyancy. As one of the main forms of pull-out foundations, pull-out piles are widely used in engineering.

[0003] The current design method for pullout piles mainly draws on the design method for compression piles. This method uses the compression lateral friction value of the pile multiplied by an empirical reduction factor as the pullout lateral friction value, and then estimates the bearing capacity of the pullout pile. This empirical reduction factor is the pullout coefficient of the foundation pile.

[0004] According to the Technical Specifications for Building Pile Foundations (JGJ 94-2008), the current formula for calculating the ultimate bearing capacity of pull-out piles is based on pull-out pile test data and uses an empirical formula that multiplies the ultimate compressive bearing capacity calculation model by the pull-out coefficient. The specific formula is as follows:

[0005] T uk =∑λ i q sik u i l i

[0006] where λ i is the pull-out coefficient, which can be obtained according to the table below.

[0007] Soil type λ sand 0.50～0.70 Clay soil, silt soil 0.70～0.80

[0008] The pullout coefficient in the specification is based on the results of pullout pile tests and is an empirical coefficient. It lacks a theoretical basis and cannot be calculated using a theoretical formula. Based on the current state of research both domestically and internationally, most studies on the pullout coefficient remain empirical, with little systematic and in-depth mechanistic research. There is no theoretical solution to the pullout coefficient of foundation piles. Summary of the Invention

[0009] In order to solve the problem of calculating the pull-out coefficient of pile foundation, starting from the stress mechanism of pull-out pile, the theoretical calculation formula of the pull-out coefficient of pile foundation is derived, which provides a theoretical basis for reasonably determining the pull-out bearing capacity of pile foundation.

[0010] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0011] First, according to the stress state of the soil on the side of the compression pile, a stress analysis is performed on the soil unit on the side of the pile, and the horizontal stress of the soil unit on the side of the compression pile and the pile side earth pressure coefficient are derived; secondly, according to the stress state of the soil on the side of the pull-out pile, a stress analysis is performed on the soil unit on the side of the pile, and the horizontal stress of the soil unit on the side of the pull-out pile and the pile side earth pressure coefficient are derived; then, based on the pile side earth pressure coefficients of the compression and pull-out piles, the calculation formula for the pile pull-out coefficient is derived.

[0012] Furthermore, according to the stress state of the soil on the side of the compression pile, a stress analysis is performed on the soil unit on the side of the pile, and the horizontal stress of the soil unit on the side of the compression pile and the soil pressure coefficient on the side of the pile are derived. Specifically, stress analysis is performed on the pile side wall and the soil unit on the side of the pile, and the two stress states in the soil on the side of the pile are calculated; the Mohr stress circle of the side wall of the compression pile and the soil on the side of the pile is drawn; the calculation formula for the horizontal stress of the soil unit on the side of the pile is derived, and the soil pressure coefficient on the side of the compression pile is obtained from this calculation formula.

[0013] Furthermore, according to the stress state of the soil on the side of the compression pile, a stress analysis is performed on the soil unit on the side of the pile, and the horizontal stress of the soil unit on the side of the compression pile and the soil pressure coefficient on the side of the pile are derived. The method is characterized in that it specifically includes: performing stress analysis on the pile side wall and the soil unit on the side of the pile, and calculating two stress states in the soil on the side of the pile; drawing the Mohr stress circle of the side wall of the compression pile and the soil on the side of the pile; and deriving a calculation formula for the horizontal stress of the soil unit on the side of the pile, and obtaining the soil pressure coefficient on the side of the compression pile from the calculation formula.

[0014] Furthermore, the pile pullout coefficient ξ can be expressed as

[0015]

[0016] Where: K ax , K px are the pile side earth pressure coefficients of the pull-out pile and the compression pile, is the internal friction angle of the soil, and δ is the friction angle between the pile and the soil.

[0017] The present invention has the following beneficial effects:

[0018] This invention derives a theoretical calculation formula for the pile pullout coefficient based on the load-bearing mechanism of pullout piles. This solution is theoretically reliable, scientifically sound, and features a simple formula, making it easy to apply in engineering projects. Compared to existing technologies, this solution avoids errors caused by empiricism and provides a theoretical basis for rationally determining the pullout bearing capacity of piles. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 The stress diagram of the soil unit at the ultimate state of the compression pile according to one embodiment of the present invention is shown;

[0020] Figure 2A diagram showing the center offset of a compression pile stress according to an embodiment of the present invention;

[0021] Figure 3 The earth pressure stress circle of the soil body on the side of the compression foundation pile according to one embodiment of the present invention;

[0022] Figure 4 The stress diagram of the soil unit in the ultimate state of the anti-uplift pile according to one embodiment of the present invention is shown;

[0023] Figure 5 This is the earth pressure stress circle of the soil on the side of the compression pile according to one embodiment of the present invention. DETAILED DESCRIPTION

[0024] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments. The advantages and features of the present invention will become clearer based on the following description and claims. The technical content and features of the present invention will be described in detail below by combining the enumerated embodiments with the accompanying drawings. It should be noted that the drawings are all in a very simplified form and are not in precise proportions, and are only used to conveniently and clearly assist in explaining the purpose of the embodiments of the present invention. For the convenience of description, the "upper" and "lower" described below are consistent with the upper and lower directions of the drawings, but this cannot be a limitation of the technical solution of the present invention.

[0025] Example 1

[0026] This embodiment discloses a theoretical calculation method for the pull-out coefficient of a pile foundation, which includes the following steps:

[0027] 1. According to the stress state of the soil on the side of the compression pile, stress analysis is performed on the soil unit on the side of the pile to derive the horizontal stress of the soil unit on the side of the compression pile and the soil pressure coefficient on the side of the pile.

[0028] For compression piles, due to the friction between the pile and the soil, the soil on the side of the pile will be in two stress states: the major and minor principal stresses of the soil on the relatively far side of the pile are vertical self-weight stress and horizontal stress respectively; due to the friction between the wall and the soil and the bonding force, the vertical self-weight stress and horizontal stress on the side of the pile are no longer major and minor principal stresses, and the principal stress axis will be offset to a certain extent outside the pile side. Obviously, there is a common line (i.e., the boundary line) between these two stress states, such as Figure 1 shown.

[0029] Take the pile side wall and pile side soil units for stress analysis. The two stress states in the pile side soil are calculated, and the stress on the boundary line is inconsistent ( Figure 2 ). Figure 2 In the equation, the undeflected Mohr circle is tangent to the envelope at T, and the intersection of the deflected and undeflected Mohr circles is X. For clay, since the cohesion is not zero, the τ axis can be shifted to the left to obtain a new coordinate system with the origin at (0,0), s′=s+l,σ′xx =σ xx +l. By applying the law of sines to triangle ABX, we get:

[0030]

[0031] Assume that the stress circle produces a small rotation 2dθ. When ds′→0, Common point X→T, then At this time, formula (1) becomes:

[0032]

[0033] but:

[0034] Where: θ—rotation angle of the principal stress direction;

[0035] —soil internal friction angle;

[0036] s′—the horizontal coordinate of the center of the adjusted Mohr circle.

[0037] Draw the Mohr stress circle of the compression pile side wall and the soil on the pile side ( Figure 3 ), where the principal stress direction of the soil stress circle 2 behind the wall is not deflected, and the horizontal coordinate of the center of the circle is s′2. Assuming that the deflection of the principal stress direction is a finite value θ, the soil stress circle 1 behind the wall is obtained, and the horizontal coordinate of the center of circle 1 is s′1. Obviously, the deflection angle of circle 2 is 0, and the deflection angle of circle 1 is θ. Integrating equation (3):

[0038]

[0039] have to:

[0040]

[0041] In the stress circle 1 after the principal stress direction is deflected ( Figure 3 ):

[0042] O′C=s′1cosδ

[0043]

[0044]

[0045] Where: δ—friction angle between pile and soil.

[0046] Also because

[0047]

[0048] And the principal stress direction in circle 2 does not deflect, that is:

[0049]

[0050] Therefore:

[0051]

[0052] The horizontal stress of the soil unit on the pile side is:

[0053]

[0054] Where:

[0055]

[0056] Among them, θ p is the principal stress deflection angle of the soil at the pile side,

[0057] 2. According to the stress state of the soil on the side of the anti-uplift pile, stress analysis is performed on the soil unit on the side of the pile to derive the horizontal stress of the soil unit on the side of the anti-uplift pile and the soil pressure coefficient on the side of the pile.

[0058] The stress state of the soil around the pile under the action of pull-out load is as follows: Figure 4 Similarly, the pile side wall and pile side soil units are analyzed, and the Mohr stress circle of the pile side wall and pile side soil is as follows: Figure 5 As shown. Among them, the active earth pressure stress circle 1 is the stress circle of the soil unit on the pile side, the horizontal coordinate of the circle center is s′1, and the principal stress direction has not deflected. The stress circle 2 of the soil on the pile side wall has a principal stress direction deflection angle of θ. Similarly,

[0059]

[0060] Depend on Figure 5 We can get:

[0061] O′H=s′2cosδ

[0062]

[0063]

[0064]

[0065] Since the principal stress direction in circle 1 does not deflect, then:

[0066]

[0067] We can get:

[0068]

[0069] Horizontal stress of soil element on pile side wall:

[0070]

[0071] Where:

[0072] Among them, θ a is the principal stress deflection angle of the soil at the pile side,

[0073] 3. The calculation formula for the pile pullout coefficient is derived based on the pile side soil pressure coefficient of the compression and pullout piles.

[0074] From the above formulas (9) and (12), it can be seen that the pile pullout coefficient ξ is:

[0075]

[0076] The above formula (13) is the theoretical solution of the pile pull-out coefficient.

[0077] Example 2

[0078] The pile pullout coefficient calculation method described in Example 1 is used to analyze the variation of the pile pullout coefficient with the soil internal friction angle and the pile-soil interface friction angle. The specific steps are as follows:

[0079] For the convenience of analysis, it is assumed that the pile compressive resistance coefficient K y , pull-out lateral resistance coefficient K b Determined by the following formula:

[0080] K y =K px tanδ (14)

[0081] K b =K ax tanδ (15)

[0082] assumed The above-mentioned derivation formula is used to calculate the pile pull-out coefficient, and the calculation results are shown in Table 1.

[0083] Table 1 Variation of pull-out coefficient ξ with soil internal friction angle and pile-soil interface friction angle

[0084]

[0085]

[0086] The pull-out coefficient ξ changes with the internal friction angle of soil The variation law of the pile-soil interface friction angle δ is shown in Table 1. Increase and decrease, also with Increase and decrease ξ=0.619~0.826; ξ=0.541~0.666; this range is basically consistent with the value range recommended by the following specifications and regulations.

[0087] Table 2 Recommended values ​​of pull-out coefficient (Technical Specification for Building Pile Foundations (JGJ 94-2008))

[0088] Soil type λ sand 0.50～0.70 Clay soil, silt soil 0.70～0.80

[0089] Table 3 Recommended values ​​of pull-out coefficient (Code for Geotechnical Engineering Investigation (DGJ 08-37-2012))

[0090] Soil type λ Sandy soil, sandy silt 0.60～0.70 Clay soil, clay silt 0.70～0.80

[0091] Table 4 Recommended values ​​of pull-out coefficient (Standard for Geotechnical Engineering Investigation of High-rise Buildings (JGJ / T 72-2017))

[0092]

[0093] It can be seen from Table 1 that the compressive side pressure coefficient increases with and The lateral pressure coefficient increases with the increase of Increased and increased significantly, with Increase slightly, when When When , the increase is not obvious and is approximately equal. In order to improve the bearing capacity of the pull-out pile, measures can be taken to increase the friction angle between the pile-soil interface and the soil. Soil, measures to improve the bearing capacity of pull-out piles should focus on increasing the friction angle at the pile-soil interface. This is the theoretical basis for improving the bearing capacity of pull-out bored piles in sandy soil layers by doing a good job of cleaning the hole with mud wall protection and using pile side wall post-grouting to increase the friction resistance at the pile-soil interface.

[0094] The above description is only a description of the preferred embodiments of the present invention and does not limit the scope of the present invention. Any changes and modifications made by ordinary technicians in the field of the present invention based on the above disclosure shall fall within the scope of protection of the claims.

Claims

1. A method for calculating the pull-out coefficient of a pile foundation, characterized in that: The following steps are involved: S1: Based on the stress state of the soil on the side of the compression pile, stress analysis is performed on the soil unit on the side of the pile to derive the horizontal stress of the soil unit on the side of the compression pile and the soil pressure coefficient on the side of the pile; specifically, the following are included: Take the pile side wall and pile side soil elements for stress analysis and calculate the two stress states in the pile side soil; Draw the Mohr stress circle of the compression pile side wall and the soil around the pile; The calculation formula of the horizontal stress of the soil unit on the pile side is derived, and the soil pressure coefficient on the pile side of the compression pile is obtained from this calculation formula; S2: Based on the stress state of the soil on the side of the anti-uplift pile, stress analysis is performed on the soil unit on the side of the pile to derive the horizontal stress of the soil unit on the side of the anti-uplift pile and the soil pressure coefficient on the side of the pile; specifically, the following are included: Take the foundation pile side wall and pile side soil unit for analysis, and calculate the stress state of the pile side wall and pile side soil; Draw the Mohr stress circle of the pile side wall and the soil around the pile; The calculation formula of the horizontal stress of the soil unit on the pile side wall is derived, and the soil pressure coefficient on the side of the pull-out pile is obtained from this calculation formula. S3: The calculation formula of the pile pullout coefficient ξ is derived based on the pile side earth pressure coefficient of the compression and pullout piles; The calculation formula of the pile side earth pressure coefficient of the compression pile is: where θ p is the principal stress deflection angle of the soil at the pile side, θ is the rotation angle about the principal stress direction; is the friction angle within the soil; δ is the friction angle between the pile and the soil; The calculation formula of the pile side earth pressure coefficient of the anti-uplift pile is: where θ a is the principal stress deflection angle of the soil at the pile side, θ is the rotation angle about the principal stress direction; is the internal friction angle of soil; δ is the friction angle between pile and soil.

2. The method for calculating the pull-out coefficient of pile foundation according to claim 1, characterized in that: The pile pullout coefficient ξ can be expressed as: Where: K ax , K px are the pile side earth pressure coefficients of the pull-out pile and the compression pile, is the internal friction angle of the soil, and δ is the friction angle between the pile and the soil.

Images