Calculation method of free penetration depth of open steel pipe piles into mud

Abstract

The invention relates to a method for calculating the free penetration depth of an open steel pipe pile into the mud. The method comprises the following steps: calculating the deadweight of the steel pipe pile; calculating the buoyancy exerted on the pile end at the mud surface before the pile foundation is immersed in the mud; assuming the penetration depth h of the steel pipe pile into the mud and the soil layer where the pile end is located under the action of its deadweight; calculating the pile side friction resistance and pile end resistance per unit area of ​​the steel pipe pile under static load; calculating the velocity v of the steel pipe pile at the penetration depth h into the mud; calculating the free penetration depth of the steel pipe pile into the mud; obtaining the deadweight of the hammer according to hammer type parameters; judging whether the steel pipe pile will continue to sink under the action of the hammer weight after completing self-sinking; and calculating the penetration depth of the steel pipe pile under the combined action of the pile weight and the hammer weight.

Description

Technical Field

[0001] The invention relates to an analysis of the free penetration depth of a steel pipe pile in marine engineering, in particular to a calculation method for determining the free penetration depth of an offshore large-diameter open steel pipe pile. Background Art

[0002] Steel pipe pile foundations are a primary foundation type for marine engineering structures and offshore platforms. After being hoisted and erected, steel pipe pile foundations in marine engineering projects penetrate the soil to a certain depth under their own weight. At this point, the steel pipe piles are cantilever structures. After the pile driver is placed, the pile's stability under the hammer's weight—that is, its free-standing stability—must be verified. If the pile foundation's free-standing depth is too small, resulting in a long pile length above the mud surface, the excessive slenderness ratio can cause the pile foundation to buckle and fail, significantly impacting the safety of the steel pipe pile construction.

[0003] Furthermore, with the increasing scale of marine engineering projects, the bearing capacity requirements for steel pipe pile foundations have also increased. In particular, in offshore wind farm construction, as turbine capacity and water depth increase, the diameter of steel pipe pile foundations has reached 10 meters, and the weight of the pile hammers has reached 700 tons. The increased weight of the steel pipe piles and hammers can lead to pile slippage during the free entry phase, which can damage construction machinery and even cause casualties. Therefore, accurately determining the free entry depth of steel pipe pile foundations is crucial for ensuring safe and smooth installation. Summary of the Invention

[0004] The present invention provides a method for accurately calculating the penetration depth of a large-diameter open-end steel pipe pile into the soil under its own weight, as well as the penetration depth of a pipe pile into the soil under the combined action of its own weight and a hammer weight. The technical solution is as follows:

[0005] A method for calculating the free penetration depth of an open steel pipe pile into the mud comprises the following steps:

[0006] 1) Calculate the deadweight W of the steel pipe pile based on the design parameters of the steel pipe pile p ;

[0007] 2) Calculate the buoyancy F on the pile end at the mud surface before the pile foundation enters the mud using formula (1): b ;

[0008]

[0009] Where: ρ w h is the seawater density at the site; w is the seawater depth at the site; g is the acceleration of gravity; A(h0) is the cross-sectional area of ​​the pile foundation at a depth of h0 from the sea level;

[0010] 3) Assume that the steel pipe pile is buried to a depth of h under its own weight, and the pile tip is located in the i-th layer of soil from top to bottom;

[0011] 4) Calculate the pile side friction and pile end resistance per unit area of ​​the steel pipe pile under static load, and determine the average pile side friction f and pile end resistance q per unit area of ​​each soil layer;

[0012] For a steel pipe pile section in clay soil, the lateral friction resistance per unit area is calculated using formula (2):

[0013] f s =αs u (2)

[0014] Where: α is a dimensionless coefficient, α≤1; s u is the undrained shear strength of the soil at the calculation point;

[0015] Calculate α using formula (3):

[0016]

[0017] Where: η is the undrained shear strength of the soil at the calculation point s u The ratio of the effective overburden pressure P0′ to the

[0018] Calculate η using formula (4):

[0019]

[0020] When the pile tip is located in a clay layer, the pile tip resistance per unit area q u Calculated by formula (5):

[0021] q u =9s u (5)

[0022] For a steel pipe pile section in non-cohesive soil, the lateral friction resistance per unit area is calculated using formula (6):

[0023] f s =KP0′tanδ (6)

[0024] Where: K is the lateral earth pressure coefficient; δ is the friction angle between the pile sidewall and the soil;

[0025] When the pile tip is located in a non-cohesive soil layer, the pile tip resistance per unit area q u Calculated by formula (7):

[0026] q u =N q P tip ′ (7)

[0027] Where: Nq is the bearing capacity coefficient; P tip ′ is the effective overburden pressure at the pile tip;

[0028] The average unit lateral friction of each calculated soil layer in the layered soil is determined by formula (8):

[0029]

[0030] Where: f is the average unit lateral friction resistance of the calculated soil layer; f top is the unit lateral friction resistance at the top of the soil layer; f bot To calculate the unit lateral friction resistance at the bottom of the soil layer;

[0031] The average unit pile tip resistance of each soil layer in the layered soil is determined by formula (9):

[0032]

[0033] Where: q is the average unit pile tip resistance of the calculated soil layer; q top is the unit pile tip resistance at the top of the calculated soil layer; q bot To calculate the unit pile tip resistance at the bottom of the soil layer;

[0034] 5) Calculate the velocity v of the steel pipe pile when it penetrates the mud to a depth h;

[0035] According to Newton's second law, the control equation (10) is obtained:

[0036]

[0037] Where: m is the mass of the steel pipe pile; F s is the soil resistance during the sinking process of the steel pipe pile;

[0038] The soil resistance F of the steel pipe pile is calculated by formula (11): s ;

[0039]

[0040] Where: A s is the annular area at the bottom of the steel pipe pile; N1 is the end resistance reduction coefficient; N2 is the resistance coefficient; N3 is the side resistance reduction coefficient; ρ is the density of the soil at the pile end; C a is the sum of the inner and outer perimeters of the steel pipe pile; f i is the average unit lateral friction resistance of the steel pipe pile in the i-th layer of soil; h i is the length of the steel pipe pile in the i-th soil layer;

[0041] After simplifying formula (10), we get formula (12):

[0042]

[0043] Where: A1, A2 and A3 are constants;

[0044] A1, A2, and A3 are expressed by equations (13), (14), and (15), respectively:

[0045]

[0046]

[0047]

[0048] By solving equation (12), we can obtain equation (16) for calculating the velocity v of the steel pipe pile when the depth of the pile is h:

[0049]

[0050] Where: C i is the constant of the pile end when it is in the i-th layer of soil;

[0051] When the pile end is located in the i-th soil layer, C can be calculated by formula (17): i :

[0052]

[0053] Where: v i,top is the speed when the pile tip sinks to the top of the i-th soil layer; h i,top is the top depth of the i-th soil layer;

[0054] 6) Calculate the free penetration depth of steel pipe piles;

[0055] Determine the depth calculation step δh1 based on the calculation accuracy. If the velocity v calculated by formula (16) is not 0, assign h+δh1 to h and return to step 4) to recalculate until the calculated velocity v=0. At this time, the assumed mud penetration depth h is the self-sinking depth h of the steel pipe pile. p ;

[0056] 7) Obtain the hammer's deadweight W based on the hammer's shape parameters h ;

[0057] 8) Determine whether the steel pipe pile will continue to sink under the action of the hammer weight after it has completed self-sinking:

[0058] Through step 6), the free penetration depth h of the steel pipe pile under its own weight is obtained. p , calculate the moment when the steel pipe pile is self-sinking and the pressure hammer is at depth h by formula (18) p The resultant force F a :

[0059] F a=W h +W p -F b -F s (18)

[0060] If F a ≤0, it means that the steel pipe pile will not continue to sink under the action of the hammer weight; if F a >0, it means that the steel pipe pile will continue to sink after the hammer;

[0061] 9) Assume that the depth of the steel pipe pile after hammering is h m When , the pile tip is in the jth layer of soil from top to bottom;

[0062] 10) Calculate the depth of the steel pipe pile into the mud after hammering using formula (16): h m Speed ​​v m ;

[0063] At this time, A1, A2 and A3 are calculated by equations (19), (20) and (21) respectively:

[0064]

[0065]

[0066]

[0067] Where: m total is the total weight of the steel pipe pile and pile hammer;

[0068] Then calculate C using formula (17) i , and then substitute into formula (16), we get v m ;

[0069] 11) Calculate the final depth of the steel pipe pile after it has completed its self-weight sinking and hammering;

[0070] If the velocity v after hammering is calculated by formula (17) m When it is not 0, h m +δh1 is assigned to h m , return to step 9) and recalculate until the calculated speed v after the hammer is m =0, the assumed mud penetration depth h m That is, the depth h of the steel pipe pile into the mud under the combined action of the pile weight and hammer weight total .

[0071] Furthermore, the depth calculation step size δh1 = 0.01 m.

[0072] The advantages and positive effects of the present invention are:

[0073] 1) The influence of inertia force during the sinking process of steel pipe piles under the action of their own weight and hammer weight is taken into account, so as to more accurately predict the penetration resistance of steel pipe piles during the self-sinking process. The velocity change of steel pipe piles during the self-sinking process can be obtained, providing a strong basis for the calculation of the free penetration velocity of steel pipe piles in the mud;

[0074] 2) The introduction of pile tip resistance fully considers that the velocity of the steel pipe pile will not increase indefinitely, and takes into account the fact that the resistance of the steel pipe pile degenerates into a static load when the velocity is zero. This makes the calculation result of the depth of the steel pipe pile into the mud more reliable.

[0075] 3) The reduction of the pile end resistance and pile side resistance during the sinking process of the steel pipe pile is comprehensively considered, providing a more convenient method for the subsequent study of the reduction coefficient;

[0076] 4) This method is in line with engineering practice, the method is simple and clear, easy to operate, and the parameters involved are easy to determine and reliable, which makes the calculation results more accurate and reasonable.

[0077] In summary, the present invention can calculate the free penetration depth of steel pipe piles in complex soil layers, and comprehensively consider the influence of inertial force during the sinking process of steel pipe piles. It can calculate the speed change during the sinking process of steel pipe piles, and consider the possible reduction of the resistance on the side and end of the steel pipe piles, so that the calculation results are more accurate and reasonable. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 This is a flow chart of the method of the present invention for calculating the depth of a steel pipe pile into the mud under its own weight;

[0079] Figure 2 The present invention is a flowchart of the method for calculating the free penetration depth of a steel pipe pile under the combined action of a pile hammer. DETAILED DESCRIPTION

[0080] To further understand the content, features and effects of the present invention, the following examples are given and described in detail with reference to the accompanying drawings:

[0081] The calculation method for the free penetration depth of large-diameter open-end steel pipe piles and the penetration depth of the piles under the combined action of their own weight and hammer weight is as follows:

[0082] 1) Calculate the deadweight W of the steel pipe pile based on the design parameters of the steel pipe pile p ;

[0083] 2) Calculate the buoyancy F on the pile end at the mud surface before the pile foundation enters the mud using formula (1): b ;

[0084]

[0085] Where: ρw h is the seawater density at the site; w is the seawater depth at the site; g is the acceleration of gravity; A(h0) is the cross-sectional area of ​​the pile foundation at a depth of h0 from the sea level.

[0086] 3) Assume that the depth of the steel pipe pile embedded in the soil under its own weight is h, and the pile end is located in the i-th layer of soil from top to bottom.

[0087] 4) Calculate the pile side friction and pile end resistance per unit area of ​​the steel pipe pile under static load, and determine the average pile side friction f and pile end resistance q per unit area of ​​each soil layer;

[0088] For a steel pipe pile section in clay soil, the lateral friction resistance per unit area is calculated using formula (2):

[0089] f s =αs u (2)

[0090] Where: α is a dimensionless coefficient, α≤1; s u is the undrained shear strength of the soil at the calculation point.

[0091] Calculate α using formula (3):

[0092]

[0093] Where: η is the undrained shear strength of the soil at the calculation point s u The ratio of the effective overlying soil pressure P0′.

[0094] Calculate η using formula (4):

[0095]

[0096] When the pile tip is located in a clay layer, the pile tip resistance per unit area q u Calculated by formula (5):

[0097] q u =9s u (5)

[0098] For a steel pipe pile section in non-cohesive soil, the lateral friction resistance per unit area is calculated using formula (6):

[0099] f s =KP0′tanδ (6)

[0100] Where: K is the lateral earth pressure coefficient; δ is the friction angle between the pile sidewall and the soil.

[0101] f in non-cohesive soils sIt will not increase infinitely with the increase of overburden pressure. According to the American Petroleum Institute (API) recommendation, the maximum value that can be obtained is shown in Table 1.

[0102] When the pile tip is located in a non-cohesive soil layer, the pile tip resistance per unit area q u Calculated by formula (7):

[0103] q u =N q P tip ′ (7)

[0104] Where: N q is the bearing capacity coefficient, which is determined according to Table 1; P tip ′ is the effective overburden pressure at the pile end.

[0105] The average unit lateral friction of each calculated soil layer in the layered soil is determined by formula (8):

[0106]

[0107] Where: f is the average unit lateral friction resistance of the calculated soil layer; f top is the unit lateral friction resistance at the top of the soil layer; f bot To calculate the unit lateral friction at the bottom of the soil layer.

[0108] The average unit pile tip resistance of each calculated soil layer in the layered soil is determined by formula (9):

[0109]

[0110] Where: q is the average unit pile tip resistance of the calculated soil layer; q top is the unit pile tip resistance at the top of the calculated soil layer; q bot To calculate the unit pile tip resistance at the bottom of the soil layer.

[0111] Table 1 Design parameters of non-cohesive soil

[0112]

[0113]

[0114] 5) Calculate the velocity v of the steel pipe pile when it penetrates the mud to a depth h;

[0115] According to Newton's second law, the control equation (10) is obtained:

[0116]

[0117] Where: m is the mass of the steel pipe pile; F s is the soil resistance during the sinking process of the steel pipe pile.

[0118] The soil resistance F of the steel pipe pile is calculated by formula (11): s ;

[0119]

[0120] Where: N1 is the end resistance reduction coefficient; N2 is the resistance coefficient; N3 is the side resistance reduction coefficient; ρ is the density of the soil at the pile end; C a is the sum of the inner and outer perimeters of the steel pipe pile; f i is the average unit lateral friction resistance of the steel pipe pile in the i-th layer of soil; h i is the length of the steel pipe pile in the i-th soil layer.

[0121] After simplifying formula (10), we get formula (12):

[0122]

[0123] Where: A1, A2 and A3 are constants.

[0124] A1, A2, and A3 are expressed by equations (13), (14), and (15), respectively:

[0125]

[0126]

[0127]

[0128] By solving equation (12), we can obtain equation (16) for calculating the velocity v of the steel pipe pile when the depth of the pile is h:

[0129]

[0130] Where: C i is the constant when the pile end is in the i-th layer of soil.

[0131] When the pile end is located in the i-th soil layer, C can be calculated by formula (17): i :

[0132]

[0133] Where: v i,top is the speed when the pile tip sinks to the top of the i-th soil layer; h i,top is the top depth of the i-th soil layer.

[0134] 6) Calculate the free penetration depth of steel pipe piles;

[0135] If the velocity v calculated by formula (16) is not 0, it is necessary to return to step 4) and recalculate until the calculated velocity v = 0. At this time, the assumed mud penetration depth h is the self-sinking depth h of the steel pipe pile. p .

[0136] 7) Obtain the hammer's deadweight W based on the hammer's shape parameters h ;

[0137] 8) Determine whether the steel pipe pile will continue to sink under the action of the hammer weight after it has completed self-sinking;

[0138] Through step 8), the free penetration depth h of the steel pipe pile under its own weight is obtained. p , calculate the moment when the steel pipe pile is self-sinking and the pressure hammer is at depth h by formula (18) p The resultant force F a :

[0139] F a =W h +W p -F b -F s (18)

[0140] If F a ≤0, it means that the steel pipe pile will not continue to sink under the action of the hammer weight. a >0, it means that the steel pipe pile will continue to sink after being hammered.

[0141] 9) Assume that the depth of the steel pipe pile after hammering is h m When , the pile tip is in the jth layer of soil from top to bottom;

[0142] 10) Calculate the depth of the steel pipe pile into the mud after hammering using formula (16): h m Speed ​​v m ;

[0143] At this time, A1, A2 and A3 are calculated by equations (19), (20) and (21) respectively:

[0144]

[0145]

[0146]

[0147] Where: m total It is the total weight of steel pipe pile and pile hammer.

[0148] Then calculate C using formula (17) i , and then substitute into formula (16), we get v m .

[0149] 11) Calculate the final depth of the steel pipe pile after it has completed its self-weight sinking and hammering;

[0150] If the velocity v calculated by formula (17) m If it is not 0, it is necessary to return to step 9) and recalculate until the calculated velocity v = 0. At this time, the assumed mud penetration depth h m That is, the depth h of the steel pipe pile into the mud under the combined action of the pile weight and hammer weight total .

[0151] The flowchart of the above calculation process is shown in Figure 1 and Figure 2 .

[0152] Here is a project example

[0153] An offshore wind turbine foundation on the southeast coast uses open-end steel pipe piles with a diameter of 7-8.4m and a wall thickness of 70-90mm. The piles are 101.725m long, with a designed penetration depth of 45.6m and a net pile weight of 1598t. Specific parameters are shown in Table 2. The seawater depth at the pile foundation is 36.4m, and soil parameters are shown in Table 3. The selected pile hammer is an MHU 3500S with a hammer weight of 576.9t.

[0154] Table 2 Structural dimension parameters of steel pipe piles

[0155]

[0156] Table 3 Soil parameters at pile foundation

[0157]

[0158] The detailed calculation process is as follows:

[0159] 1) Calculate the deadweight W of the pile p

[0160] According to the pile weight given in Table 2, the pile deadweight W is calculated. p It is 15676.38kN.

[0161] 2) Calculate the buoyancy F on the pile end at the mud surface before the pile foundation enters the mud using formula (1): b ;

[0162] According to the pile foundation structure size parameters, the buoyancy F of the pile foundation when entering the mud is calculated. b It is 722.98kN.

[0163] 3) Assumed mud penetration depth

[0164] Assuming that the depth of the steel pipe pile in the mud under its own weight is 14m, the pile end of the steel pipe pile is located in the third layer of soil.

[0165] 4) Determine the average unit area pile side friction resistance f and pile tip resistance q of each soil layer

[0166] The average unit area side friction resistance and pile tip resistance of each soil layer were calculated based on the soil parameters in Table 3. The specific calculation results are shown in Table 4.

[0167] 5) Calculate the velocity v of the steel pipe pile when it penetrates the mud to a depth h

[0168] The intermediate coefficient C of the first two soil layers is obtained by calculation i , we can get the sinking speed of the steel pipe pile between soil layers. The specific results are shown in the table. The speed v of the steel pipe pile when the depth of the pile is 14m is calculated by formula (16) to be 10.18m / s.

[0169] 6) Calculate the free penetration depth of steel pipe piles

[0170] Table 4 shows that when the pile's burial depth is 15 m, its velocity is greater than 0, indicating that the assumed burial depth is too small and a larger burial depth is required. After multiple iterations, the velocity of the steel pipe pile is 0 when the burial depth is 21.654 m, indicating that the burial depth of the steel pipe pile under its own weight is 21.654 m.

[0171] Table 4 Calculation results at corresponding depths of soil layers

[0172]

[0173] 7) Calculate the hammer weight of the pile hammer

[0174] Get the hammer weight W of the pile hammer according to the provided pile hammer parameters h It is 5658.41kN.

[0175] 8) Determine whether the steel pipe pile continues to sink after the hammer is added;

[0176] The calculated external force F on the steel pipe pile after hammering is a =-12779.32kN, so the steel pipe pile will not continue to sink after the hammer is added. The final depth of the steel pipe pile in the mud under the combined action of its own weight and the weight of the hammer is h total It is 21.654m, which is consistent with the free mud penetration depth of 21.85m measured in the piling records.

[0177] Although the preferred embodiments of the present invention have been described above in conjunction with the appended tables, the present invention is not limited to the above-mentioned specific embodiments. The above-mentioned specific embodiments are merely illustrative and not 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, which all fall within the scope of protection of the present invention.

Claims

1. A method for calculating the free penetration depth of an open steel pipe pile, comprising the following steps: 1) Calculate the deadweight W of the steel pipe pile based on the design parameters of the steel pipe pile p ; 2) Calculate the buoyancy F on the pile end at the mud surface before the pile foundation enters the mud using formula (1): b ; Where: ρ w h is the seawater density at the site; w is the seawater depth at the site; g is the acceleration of gravity; A(h0) is the cross-sectional area of ​​the pile foundation at a depth of h0 from the sea level; 3) Assume that the steel pipe pile is buried to a depth of h under its own weight, and the pile tip is located in the i-th layer of soil from top to bottom; 4) Calculate the pile side friction and pile end resistance per unit area of ​​the steel pipe pile under static load, and determine the average pile side friction f and pile end resistance q per unit area of ​​each soil layer; For a steel pipe pile section in clay soil, the lateral friction resistance per unit area is calculated using formula (2): f s =αs u (2) Where: α is a dimensionless coefficient, α≤1; s u is the undrained shear strength of the soil at the calculation point; Calculate α using formula (3): Where: η is the undrained shear strength of the soil at the calculation point s u The ratio of the effective overburden pressure P0′ to the Calculate η using formula (4): When the pile tip is located in a clay layer, the pile tip resistance per unit area q u Calculated by formula (5): q u =9s u (5) For a steel pipe pile section in non-cohesive soil, the lateral friction resistance per unit area is calculated using formula (6): f s =KP0′tanδ (6) Where: K is the lateral earth pressure coefficient; δ is the friction angle between the pile sidewall and the soil; When the pile tip is located in a non-cohesive soil layer, the pile tip resistance per unit area q u Calculated by formula (7): q u =N q P tip ′ (7) Where: N q is the bearing capacity coefficient; P tip ′ is the effective overburden pressure at the pile tip; The average unit lateral friction of each calculated soil layer in the layered soil is determined by formula (8): Where: f is the average unit lateral friction resistance of the calculated soil layer; f top is the unit lateral friction resistance at the top of the soil layer; f bot To calculate the unit lateral friction resistance at the bottom of the soil layer; The average unit pile tip resistance of each soil layer in the layered soil is determined by formula (9): Where: q is the average unit pile tip resistance of the calculated soil layer; q top is the unit pile tip resistance at the top of the calculated soil layer; q bot To calculate the unit pile tip resistance at the bottom of the soil layer; 5) Calculate the velocity v of the steel pipe pile when it penetrates the mud to a depth h; According to Newton's second law, the control equation (10) is obtained: Where: m is the mass of the steel pipe pile; F s is the soil resistance during the sinking process of the steel pipe pile; The soil resistance F of the steel pipe pile is calculated by formula (11): s ; Where: A s is the annular area at the bottom of the steel pipe pile; N1 is the end resistance reduction coefficient; N2 is the resistance coefficient; N3 is the side resistance reduction coefficient; ρ is the density of the soil at the pile end; C a is the sum of the inner and outer perimeters of the steel pipe pile; f i is the average unit lateral friction resistance of the steel pipe pile in the i-th layer of soil; h i is the length of the steel pipe pile in the i-th soil layer; After simplifying formula (10), we get formula (12): Where: A1, A2 and A3 are constants; A1, A2, and A3 are expressed by equations (13), (14), and (15), respectively: By solving equation (12), we can obtain equation (16) for calculating the velocity v of the steel pipe pile when the depth of the pile is h: Where: C i is the constant of the pile end when it is in the i-th layer of soil; When the pile end is located in the i-th soil layer, C can be calculated by formula (17): i : Where: v i,top is the speed when the pile tip sinks to the top of the i-th soil layer; h i,top is the top depth of the i-th soil layer; 6) Calculate the free penetration depth of steel pipe piles; Determine the depth calculation step δh1 based on the calculation accuracy. If the velocity v calculated by formula (16) is not 0, assign h+δh1 to h and return to step 4) to recalculate until the calculated velocity v=0. At this time, the assumed mud penetration depth h is the self-sinking depth h of the steel pipe pile. p ; 7) Obtain the hammer's deadweight W based on the hammer's shape parameters h ; 8) Determine whether the steel pipe pile will continue to sink under the action of the hammer weight after it has completed self-sinking: Through step 6), the free penetration depth h of the steel pipe pile under its own weight is obtained. p , calculate the moment when the steel pipe pile is self-sinking and the pressure hammer is at depth h by formula (18) p The resultant force F a : F a =W h +W p -F b -F s (18) If F a ≤0, it means that the steel pipe pile will not continue to sink under the action of the hammer weight; if F a >0, it means that the steel pipe pile will continue to sink after the hammer; 9) Assume that the depth of the steel pipe pile after hammering is h m When , the pile tip is in the jth layer of soil from top to bottom; 10) Calculate the depth of the steel pipe pile into the mud after hammering using formula (16): h m Speed ​​v m ; At this time, A1, A2 and A3 are calculated by equations (19), (20) and (21) respectively: Where: m total is the total weight of the steel pipe pile and pile hammer; Then calculate C using formula (17) i , and then substitute into formula (16), we get v m ; 11) Calculate the final depth of the steel pipe pile after it has completed its self-weight sinking and hammering; If the velocity v after hammering is calculated by formula (17) m When it is not 0, h m +δh1 is assigned to h m , return to step 9) and recalculate until the calculated speed v after the hammer is m =0, the assumed mud penetration depth h m That is, the depth h of the steel pipe pile into the mud under the combined action of the pile weight and hammer weight total .

2. The method for calculating the free penetration depth of open steel pipe piles according to claim 1 is characterized in that: The depth calculation step is δh1 = 0.01 m.

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