Anchoring axial resistance calculation method based on interface friction, internal friction and end resistance

Abstract

The application discloses an anchor chain axial resistance calculation method based on interface friction, internal friction and end resistance, and belongs to the field of ocean engineering anchoring system. The method divides the anchor chain axial resistance into three parts of interface friction, internal friction and end resistance, and separately calculates and analyzes each part based on the configuration of the anchor chain. In the interface friction part, the chain-sand interface shear area is divided into two parts, including a side interface friction area A b‑s and an interface friction component A e‑s of the chain ring end face, and the latter is subjected to reduction analysis; in the internal friction part, sand particle friction is assumed to occur on the side face of the chain ring; and the end resistance adopts a cross-shaped projection area multiplied by the Terzaghi bearing capacity formula. The application directly provides a calculation method of the axial resistance of a unit chain ring, based on three-component resistances of interface friction, internal friction and end resistance, and can directly provide a calculation method of the resistance of the anchor chain based on the configuration of the anchor chain, without the need of test testing, and is convenient and fast.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of offshore engineering mooring system, and particularly relates to a method for calculating axial resistance of anchor chain based on interface friction, internal friction and end resistance. BACKGROUND

[0002] Deep embedded anchors are often used in the mooring system of tension or semi-tension mooring system, and part of the anchor chain is buried below the mud surface. The stress analysis of the embedded section of the anchor chain has an important influence on the design of the mooring foundation, and the axial resistance of the embedded section significantly affects the load transfer mechanism of the mooring line.

[0003] Since the anchor chain is a special-shaped structure, the soil resistance acting on the anchor chain is very complex, and therefore the equivalent diameter is generally used for calculating the axial resistance of the mooring line. Degenkamp & Dutta (1989) carried out a series of model tests in saturated clay, proposed a formula for calculating the axial resistance of the anchor chain in clay, and recommended the tangential equivalent width parameter E t = 8.

[0004] However, there is no systematic study on the mechanism of the axial resistance of the anchor chain in sand, and there is also a lack of recommended value of the equivalent diameter of the anchor chain in the sand seabed, and there is no calculation theory and method for analyzing the axial resistance of the anchor chain. SUMMARY

[0005] The application adopts the following technical solutions:

[0006] In view of the defects in the above background art, the application provides a method for calculating the axial resistance of the anchor chain based on interface friction, internal friction and end resistance.

[0007] The application adopts the following technical solutions:

[0008] The application assumes that a chain ring and half of the chain rings connected to the left and right of the chain ring are a unit chain ring, and regards the unit chain ring as a three-dimensional hollow rectangular box.

[0009] 1. Expression of three-part soil resistance

[0010] When the three-dimensional hollow rectangular box moves in the soil along its axis, the soil resistance includes three parts. The axial resistance f e，c of the unit chain ring can be decomposed into three parts, i.e. the shear resistance f sand of the sand, the shear resistance f interface of the chain-sand interface and the internal passive resistance f tip :

[0011] f e,c = f sand + f interface + f tip (1)

[0012] It is worth noting that the shear behavior of sand is very complex, related to confining stress, initial soil density, particle size distribution, sand fabric, etc. The present application aims to provide a practical calculation method, therefore the most basic expression is adopted as follows:

[0013]

[0014] In the formula, A sand is the sand shear area of the unit link during the test; σ is the confining pressure applied on the anchor chain; is the peak value of the internal friction angle of sand. A sand The determination will be described in the next part.

[0015] Similarly, the most basic expression is adopted to express the chain-sand interface shear resistance, specifically:

[0016] f interface = A interface ·σ·tan(δ) (3)

[0017] In the formula, A interface is the sand shear area of the unit link during the test; σ is the confining pressure applied on the anchor chain; δ is the peak value of the internal friction angle of sand.

[0018] For internal passive resistance, it can be expressed as:

[0019] f tip = A end ·P u (4)

[0020] In the formula, A end represents the contact area in front of the link; P u is the ultimate bearing capacity.

[0021] 2. Expression of A sand , A interface and A end

[0022] After the calculation method is proposed, the focus is on the calculation of each soil resistance. For friction resistance, i.e. sand shear resistance and chain-sand interface shear resistance, the determination of the contact surface is the key to the calculation of friction resistance. For internal passive resistance, the contact area and the ultimate bearing capacity need to be determined.

[0023] Before calculation, the characteristic size of the anchor chain should be obtained. Among the typical sizes of a single link, the most important one is the nominal chain diameter d b , i.e. the diameter of the link. For a link, W b is defined as the link width, and L b ​defined as the length of the link, perpendicular to the width of the link. The three parameters above can determine the size of the link. From the link configuration, the link can be generally divided into two straight rods and two ring rods. The ring rod is a semicircle with a radius of r b , and the straight rod has a length of L s-b . The link also has an inner width of W i . The above parameters (r b , L s-b , W i ) can be derived from the three basic parameters d b , L b , and W b . The above description is intended to more accurately describe the configuration of the link.

[0024] Next, the link surface is divided: the link side plane A s-p is the plane tangent to the surface of the straight rod and the ring rod. The straight rod surface A b-s is defined as the semicylindrical surface on the outside of the straight rod. The link end surface A e-s refers to the outer surface of the ring rod. Then A sand , A interface , and A end are calculated.

[0025] (1) The sand shear area A sand

[0026] Based on the assumption that the sand particles inside the link move with the anchor chain, sand particle friction occurs on the side surface of the link. Due to the intersection of adjacent links, there will be an overlapping area A o-a in the connecting side plane, thereby reducing the sand shear area. Considering the overlapping effect, the sand shear area of the unit link is:

[0027] A sand = 4(A s-p -A o-a ) (5)

[0028] where the overlapping area A o-a is the area of two cross-sectional circles: A o-a = 2π·(d b / 2) 2 ;

[0029] (2) The sand-steel interface shear area A interface

[0030] The chain-sand interface shear area includes the side interface friction area A b-s and the interface friction component A e-s of the link end surface. However, if A e-s is directly used, the friction area will be overestimated, because the end surface is not along the loading direction. The present application proposes an equivalent area A end-equto calculate the interfacial friction component of the chain ring end face. Thus, the interfacial friction area can be calculated as:

[0031] A interface = 4(A b-s + A end-equ ) (6)

[0032] Since A e-s is the annular surface of the chain ring, this area can mobilize passive resistance and interfacial shear friction. A end-equ value is calculated based on the assumption that the end friction force can be equivalent. The end friction force is:

[0033]

[0034] where τ is the friction force; the equivalent area A end-equ is d b · R, and R is equal to W i / 2;

[0035] (3) The contact area A end of the chain ring front face

[0036] To calculate the passive resistance inside the anchor chain, the end area A end needs to be calculated. The end area A end is the projected area of the chain ring end face A e-s in the direction along the long axis of the anchor chain, similar to a cross.

[0037] The passive resistance of a component is calculated using the bearing capacity of the foundation. It is worth noting that the bearing capacity of the foundation is mainly used for strip foundations. The bearing capacity is as follows:

[0038]

[0039] where, for sandy soil, c is equal to 0, N c and N q , N γ are bearing capacity coefficients; γ is the unit weight of the soil; B is the foundation width;

[0040] q is set to

[0041]

[0042] The end bearing capacity coefficient is as follows:

[0043]

[0044]

[0045] The present application has the following advantages:

[0046] The application directly gives a calculation method of the axial resistance of the anchor chain, and based on the three-component resistance of the interface friction, the internal friction and the end resistance, the calculation method of the resistance of the anchor chain can be directly given based on the configuration of the anchor chain. In the method of the application, in the interface friction part, the chain sand interface shear area is divided into two parts: the side interface friction area A b-s and the interface friction component A e-s of the chain ring end face, and the latter is analyzed by reduction; in the internal friction part, it is assumed that the sand particle friction occurs on the side surface of the chain ring; and the end resistance adopts the cross-shaped projection area multiplied by the Terzaghi bearing capacity formula. The method of the application does not need to be tested and is convenient and fast. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 The proposed anchor chain unit axial resistance calculation model, wherein 1(a) is a schematic diagram of representing the unit chain ring as a three-dimensional hollow rectangular box; 1(b) represents the axial resistance of the anchor chain unit;

[0048] Figure 2 Anchor chain characteristic size, 2(a) is the main size of the anchor chain, and 2(b) is the surface division of the anchor chain;

[0049] Figure 3 Division of the area for calculating the axial resistance;

[0050] Figure 4 Calculation method of the interface friction of the end of the anchor chain;

[0051] Figure 5 End area A end Calculation method. DETAILED DESCRIPTION

[0052] The technical solutions of the application will be further described below in combination with the embodiments and the drawings:

[0053] The application proposes an anchor chain axial resistance calculation method based on interface friction, internal friction and end resistance. It is assumed that a chain ring and half of the chain rings connected to the left and right of the chain ring are a unit chain ring, and the unit chain ring is regarded as a three-dimensional hollow rectangular box.

[0054] 1. Expression of the three-part soil resistance

[0055] The application first proposes a calculation model for dividing the axial resistance of the anchor chain into three parts. As shown in Figure 1 (a), it is assumed that the unit chain ring is a three-dimensional hollow rectangular box. When the hollow rectangular box moves in the soil along its axis, the soil resistance includes three parts. As shown in Figure 1 (b), the axial resistance f e，c of the unit chain ring can be divided into three parts, that is, the sand soil shear resistance f sand , the chain sand interface shear resistance f interfaceand internal passive resistance f tip :

[0056] f e,c = f sand + f interface + f tip (1)

[0057] It is worth noting that the shear behavior of sand is very complex, related to confining stress, initial soil density, particle size distribution, sand fabric, etc. The present application aims to provide a practical calculation method, therefore the most basic expression is adopted as follows:

[0058]

[0059] In the formula, A sand is the sand shear area of the unit chain ring during the test; σ is the confining pressure applied on the anchor chain; is the peak value of the internal friction angle of sand. A sand The determination of A

[0060] Similarly, the most basic expression of the sand-steel interface shear force is adopted, and the interface shear force is also very complex. The chain-sand interface shear interface can be expressed as:

[0061] f interface = A interface ·σ·tan(δ) (3)

[0062] In the formula, A interface is the sand-steel interface shear area of the unit chain ring during the test, σ is the confining pressure applied on the anchor chain, and δ is the peak value of the internal friction angle of sand.

[0063] For the internal passive resistance, it can be expressed as:

[0064] f tip = A end ·P u (4)

[0065] In the formula, A end represents the contact area in front of the unit chain ring; P u is the ultimate bearing capacity.

[0066] 2. Expression of A sand , A interface and A end

[0067] After the calculation method is proposed, the focus is on the calculation of each soil resistance. For the friction resistance, i.e. sand shear resistance and sand-steel interface shear resistance, the determination of the contact surface is the key to the calculation of the friction resistance. For the internal passive resistance, the contact area and the ultimate bearing capacity need to be determined.

[0068] ​Prior to the calculation, the characteristic dimensions of the chain should be introduced. Figure 2 (a) shows the typical dimensions of a single link. The most important dimension is the nominal chain diameter d b , i.e. the link diameter. For a link, W b is defined as the link width, L b as the link length, perpendicular to the link width. The three above parameters determine the size of the chain. From the link configuration, the link can be divided into two straight rods and two looped rods. The looped rods are half circles with a radius r b , the straight rods have a length of L s-b . The link also has an inner width W i . The above parameters (r b , L s-b , W i ) can be derived from the three basic parameters d b , L b and W b . The above description aims to more accurately describe the configuration of the link.

[0069] Figure 2 (b) shows the division of the chain surface. Red is the link side plane A s-p , which is the plane tangent to the surface of the straight rod and the looped rod. The straight rod surface A b-s is defined as the half-cylinder surface of the straight rod. The link end surface A e-s refers to the surface of the looped rod.

[0070] The following calculations of A sand , A interface and A end will adopt the above definitions.

[0071] (1) The sand shear area A sand of a unit link

[0072] Based on the assumption that the sand particles inside the link move with the chain, sand particle friction occurs on the side surface of the link. Figure 3 The area division of the link element is shown to calculate the sand particle friction resistance. Due to the intersection of adjacent links, there will be an overlapping area A o-a inside the connecting side plane, thus reducing the sand shear area. Considering the overlapping effect, the sand area of a unit is:

[0073] A sand = 4(A s-p -A o-a ) (5)

[0074] where the overlapping area A o-a is the area of two cross-sectional circles: A o-a = 2π·(d b / 2) 2 ;

[0075] (2) Sand-steel interface shear area A interface

[0076] As Figure 3 shown, the chain sand interface shear area includes side interface friction area A b-s and interface friction component of the chain ring end face A e-s . However, if A e-s is used directly, the friction area will be overestimated because the end face is not along the loading direction. The present invention proposes an equivalent area A end-equ to calculate the interface friction component of the chain ring end face. Therefore, the interface friction area can be calculated as:

[0077] A interface = 4(A b-s + A end-equ ) (6)

[0078] Since A e-s is the annular surface of the chain ring, this area can mobilize passive resistance and interface shear friction. The calculation of A end-equ value is based on the assumption that the end friction force can be equivalent. The method of calculating the end friction force is shown in Figure 4 . Then the total resistance of the end can be calculated:

[0079]

[0080] where τ is the friction force; the equivalent area A end-equ is d b • R, R equals W i / 2;

[0081] (3) Chain ring front contact area A end

[0082] To calculate the passive resistance of the anchor chain, the end area A end needs to be calculated. The end area A end is the projected area of the chain ring end face A e-s in the direction along the long axis of the anchor chain, similar to the cross shown in Figure 5 .

[0083] The passive resistance of a component is calculated using the bearing capacity of the foundation. It is worth noting that the bearing capacity of the foundation is mainly used for strip foundations. The bearing capacity is as follows:

[0084]

[0085] where, for sandy soil, c equals 0, N c and N γ , N γ are bearing capacity coefficients; γ is the unit weight of the soil; B is the foundation width;

[0086] q is set to

[0087]

[0088] According to Terzaghi et al. (1996), the end-bearing factor of safety is as follows:

[0089]

[0090]

Claims

1. A method for calculating the axial resistance of an anchor chain based on interfacial friction, internal friction, and end resistance, characterized in that, First, assume that a link and half of the links connected to its left and right constitute a unit link, and consider a unit link as a three-dimensional hollow rectangular box; the axial resistance f of the unit link. e，c It can be decomposed into three parts, namely, the shear resistance f of the sand. sand Chain sand interface shear resistance f interface and internal passive resistance f tip : f e,c =f sand +f interface +f tip (1) The expression for the shear resistance of sand is as follows: In the formula, A sand σ is the shear area of ​​the sand in the unit chain link during the test; σ is the confining pressure applied to the anchor chain; This represents the peak value of the internal friction angle of the sandy soil. The shear resistance of the chain sand interface is expressed as: f interface =A interface ·σ·tan(δ) (3) In the formula, A interface It is the area of ​​the sand-steel interface shear region of the unit chain link during the test, and δ is the peak value of the internal friction angle of the sand. Internal passive resistance is represented as: f tip =A end ·P u (4) In the formula, A end P represents the contact area in front of the unit chain link; u It is the ultimate bearing capacity.

2. The method for calculating the axial resistance of an anchor chain based on interfacial friction, internal friction, and end resistance according to claim 1, characterized in that, Calculate A sand A interface And A end The specific method is as follows: First, the characteristic dimensions of the anchor chain need to be obtained: the nominal chain diameter of a single link is d. b For a chain link, W b Defined as the link width, L b Defined as the link length, perpendicular to the chain width; based on d b W b L b These three basic parameters determine the size of the chain; in terms of the chain link configuration, the chain links consist of two straight links and two circular links; the circular links have a radius of r. b A semicircle, with a straight rod of length L. s-b The internal width of the chain link is W. i ; where parameter r b L s-b W i It can be derived from three basic parameters; Then, the surface of the chain link is divided: chain link side plane A s-p This represents a plane tangent to both the surfaces of the straight bar and the ring bar; surface A of the straight bar. b-s Defined as the semi-cylindrical surface on the outer side of the straight rod; chain link end face A e-s Refers to the outer surface of the ring rod; (1)A sand Calculation Based on the assumption that sand grains within the chain links move with the anchor chain, sand grain friction occurs on the side of the chain links; due to the intersection of adjacent chain links, an overlapping region A will appear in the connecting side plane. o-a This reduces the shear area of ​​the sand; considering the overlap effect, the shear area of ​​the sand in the unit chain link is: A sand =4(A s-p -A o-a ) (5) The overlapping region A o-a Let A be the area of ​​the two cross-section circles. o-a =2π·(d b / 2) 2 ; (2)A interface Calculation A interface =4(A b-s +A end-equ ) (6) In the formula, A b-s The side interface friction region, i.e., the straight rod surface obtained after dividing the chain link surface, A end-equ Equivalent area; Equivalent area A end-equ The calculation is based on the assumption that the end friction force can be equivalent, and the end friction force is: Where τ is the frictional force; the equivalent area A end-equ For d b ·R, R equals W i / 2; (3)A end Calculation Contact area A in front of the unit chain link end It is the chain link end face A e-s The projected area along the long axis of the anchor chain.

3. The method for calculating the axial resistance of an anchor chain based on interfacial friction, internal friction, and end resistance according to claim 1, characterized in that, The ultimate bearing capacity P u The calculation method is as follows: The ultimate bearing capacity P is obtained based on the calculation formula of foundation bearing capacity. u The calculation formula is as follows: For sandy soil, c equals 0; N c and N q N γ γ is the bearing capacity coefficient; B is the soil unit weight; and B is the foundation width. q is set to The end bearing capacity coefficients are as follows:

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