Pile side load transmission prediction method for cast-in-place pile in IGM stratum

Abstract

The invention discloses a pile side load transmission prediction method for a cast-in-place pile in an IGM stratum, and belongs to the technical field of pile foundation bearing characteristic research. The method comprises the following steps: predicting lateral and vertical load transfer behaviors of the cast-in-place pile under different IGM stratum mechanical properties, pile body geometry and material properties and aperture roughness; a hole wall two-dimensional profile curve is drawn, reconstruction based on a similar right triangle rough body is conducted on the hole wall curve according to the characteristic value of the curve, the height distribution of the hole wall curve is made to accord with the Gaussian distribution law, and therefore the pile IGM contact face characteristic formed in the actual drilling process is simulated; the method comprises the following steps: performing mechanical modeling on a single triangular rough body to obtain local shear stress, summarizing a stress deformation rule, and popularizing a calculation method to a large number of similar triangular rough bodies on a macroscopic contact surface in combination with statistical parameters. And an effective way is provided for quantitative prediction of the cast-in-place pile side load transmission behavior considering the hole wall roughness.

Description

Technical Field

[0001] The present invention belongs to the technical field of pile foundation bearing characteristics research, and specifically relates to a method for predicting pile side load transfer of a bored pile in an IGM stratum by detecting the roughness of a hole wall and estimating the pile side load transfer behavior of the bored pile in the IGM stratum. Background Art

[0002] In bridge construction, bored piles are a common form of bridge foundation. During construction, they often need to penetrate hard clay layers or medium- to strong-weathered rock layers, such as shale and mudstone, until they reach a solid bearing layer. These strata have strong cohesiveness and can be regarded as a transitional material between soil and rock from a mechanical point of view. They can be defined as IGM (intermediate geomaterials). According to the stratum characteristics corresponding to the buried depth of the pile, IGM can be subdivided into three categories: (1) argillaceous geomaterials, including overconsolidated hard clay, clayey shale and mudstone; (2) limestone or calcareous geomaterials, including limestone, sandstone with calcareous cementation and soft sandstone; (3) dense granular geomaterials, such as partially or fully weathered granite and dense sand. They have physical and mechanical properties such as low strength, large porosity, poor cementation, significant influence of structural surface cutting and weathering, or contain a large amount of expansive clay minerals.

[0003] Bored piles are generally more than 50 meters long. This feature means that when subjected to vertical loads, the side resistance of the pile is exerted before the end resistance, which means that the exertion of the side resistance of the pile has a significant impact on the settlement of the pile top. Therefore, understanding and controlling the exertion of the side resistance of the pile is the key to ensuring the quality and safety of the project. When mechanical drilling is carried out in soft rock and hard soil layers, the rotary drilling of the tool causes the hole wall to become rough. This rough hole wall will form an undulating contact surface with the poured concrete. When subjected to vertical loads, these undulating contact surfaces will try to expand radially, but this expansion will be constrained by the strata outside the hole wall. The strength of this constraint depends on the stiffness of the soft rock and hard soil itself. The greater the stiffness, the stronger the constraint, thereby limiting the circumferential expansion of the contact surface. Therefore, the roughness of the hole wall and the material properties of the soft rock and hard soil are two key factors affecting the exertion of the side resistance of the pile. The roughness of the hole wall determines the contact area and friction coefficient with the concrete, while the material properties of the soft rock and hard soil determine its stiffness and its ability to constrain circumferential expansion. In order to optimize the performance of bored piles, it is necessary to comprehensively consider the roughness of the hole wall and the material properties of soft rock and hard soil, and reasonably design the construction parameters to ensure that the pile side resistance can be fully utilized, thereby effectively controlling the pile top settlement.

[0004] The current Technical Specification for Building Pile Foundation (JGJ 94-2008) provides a set of estimation methods based on the mechanical indicators of geotechnical materials for the design of the ultimate bearing capacity of single piles. In the absence of on-site static penetration data, this method can estimate the ultimate lateral resistance of each layer according to the soil properties, and then sum up the standard values ​​of the ultimate bearing capacity in the strata at different depths. This method is widely used in engineering practice because it is simple and easy to use, and the physical meaning of each parameter is clear. However, this method has some limitations in theory. It mainly estimates the lateral resistance based on the limit state, but the standard value of the ultimate lateral resistance cannot fully reflect the mechanism of the lateral resistance of the surrounding rock before failure or yielding. In addition, the standard method does not consider the influence of the relative displacement of the pile-rock interface caused by the compression of the pile body and the settlement of the stratum on the pile side on the degree of lateral resistance. Therefore, when the relative displacement of the pile-rock interface is small, the standard method may overestimate the pile lateral resistance, thereby affecting the accuracy and safety of the pile foundation design.

[0005] On the other hand, the roughness of the hole wall, as a crucial factor in the calculation of pile side resistance, has not received sufficient attention in the current engineering specifications. In fact, this roughness will form an uneven contact surface between the pile body and the concrete. When subjected to vertical loads, these contact surfaces will undergo circumferential expansion. This expansion process will be constrained by the strata outside the hole wall, which will then generate normal stress and have a direct impact on the performance of pile side resistance. The Federal Highway Administration (FHWA)'s bridge pile foundation design specifications clearly state that the roughness of the hole wall of bored piles can significantly increase the pile side resistance and the degree of increase is positively correlated with the roughness, but there is no relevant research or specification in China.

[0006] In recent years, some domestic scholars have conducted preliminary discussions on the correlation between hole-forming time and hole wall roughness. For example, based on the field hole-forming measured data, the non-monotonic correlation between hole-forming time and hole wall roughness was summarized. Generally speaking, the drill bit stays too long at the beginning of drilling, resulting in a large roughness, but the roughness will decrease slightly with the unloading process; as time goes on, the shrinkage phenomenon is obvious, and the roughness increases slightly. In addition, through a large number of field investigations, it was found that the more the hole wall collapses, the greater the roughness, which leads to an increase in the amount of slag discharge and the time for mud hole cleaning, which leads to a conclusion that the roughness is positively correlated with the hole cleaning time.

[0007] Although the current specifications provide effective guidance for the design of the ultimate bearing capacity of single bored piles, there are still many areas that need to be further explored and improved in practical applications. In particular, the current specifications have not yet fully reflected the actual impact of factors such as hole wall roughness on the pile side resistance. Summary of the invention

[0008] The purpose of the present invention is to provide a method for predicting the pile side load transfer of bored piles in IGM formations, which obtains the two-dimensional rough morphology and roughness parameters of the hole wall through an existing measuring device for detecting the actual hole diameter size along the depth after drilling, and uses the rough body of a right triangle to simplify the geometric shape of the hole wall, which is convenient for mechanical analysis and model building; then, a statistical method is used to reconstruct the irregular undulating contact surface of the hole wall; finally, the side resistance of the pile side unit is estimated through relevant theoretical calculations, thereby realizing the prediction of the pile side load transfer behavior, and further solving at least one technical problem involved in the background technology.

[0009] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0010] The present invention provides a method for predicting pile side load transfer for a bored pile in an IGM stratum, comprising the following steps:

[0011] Step 1: After the cast-in-place pile construction in the IGM formation is completed and the hole is mechanically formed, the two-dimensional contour of the hole wall is scanned using a boremeter;

[0012] Step 2: Reconstruct the broken line profile of the two-dimensional profile of the hole wall to determine the maximum height h of the roughness max , minimum height h min and mean inclination;

[0013] Step 3: Using the average inclination angle and the relative height values ​​of each point on the roughness two-dimensional profile, the average inclination angle is used to construct a Gaussian distribution with a height range falling within the interval [h min ,h max ] similar right triangles;

[0014] Step 4: obtain the basic mechanical parameters of the IGM formation through experiments, including Poisson's ratio, cohesion, internal friction angle, basic friction angle, residual friction angle and elastic modulus, and estimate the critical failure load corresponding to the spring stiffness and the maximum height of the roughness according to the basic mechanical parameters, and further estimate the critical displacement and critical normal displacement corresponding to the maximum height of the roughness;

[0015] Step 5, calculate the relationship between displacement and shear area ratio;

[0016] Step six, calculate the nonlinear relationship between displacement and shear stress through shear area ratio.

[0017] Optionally, in step 1, a two-dimensional profile of the hole wall is scanned using a porosimeter, specifically including:

[0018] A reference section was set at each position where the depth increased by 10 mm, and the aperture measurement values ​​at 8 different directions of the hole wall at every 45° in the clockwise direction were recorded;

[0019] The arithmetic mean of the eight recorded aperture measurement values ​​is taken as the average aperture value at that depth. If an average value exceeds 30% of the range value, the average value is excluded, and the arithmetic mean of the remaining average values ​​is recalculated. The above process is repeated until the range of all average values ​​does not exceed 30% of the range value.

[0020] Optionally, in step 2, the broken line profile of the two-dimensional profile of the hole wall is reconstructed to determine the maximum height h of the roughness max , minimum height h min and average inclination, including:

[0021] Connect the average apertures of all reference sections with a broken line, and then draw a horizontal line intersecting the broken line every 50 mm. Then use the broken line to connect all the intersections in sequence to form a large number of right triangles (replace the right triangles with right triangles). Read the absolute aperture of each intersection, and subtract the minimum aperture to obtain the relative aperture of each intersection. At the same time, determine the intersection of the maximum aperture and the minimum aperture, and take the horizontal distance between the maximum intersection and the minimum intersection as the maximum height h of the rough body. max ; The horizontal distance between the minimum intersection point and the second smallest intersection point is the minimum height h of the rough body min ;

[0022] Calculate the inclination angle θ of all right triangles through geometric relationships i , with an inclination angle θ i The mathematical mean of is the average inclination angle θ, which is expressed as follows:

[0023]

[0024] Among them, h i is the relative height of the right triangle.

[0025] Optionally, in step 3, the average inclination angle is used to construct a Gaussian distribution with a height range falling within the interval [h min ,h max ], specifically:

[0026] Since the relative height h i It obeys the Gaussian distribution in statistics, so the probability density function f(h) of the rough body height distribution is expressed as follows:

[0027]

[0028] Where h is the height of the roughness; μ and s are the mean and standard deviation of the roughness height distribution, respectively, which are expressed by the following formulas:

[0029]

[0030]

[0031] Optionally, in step 4, the spring stiffness K and the critical failure load q c , critical displacement x c and the critical normal displacement y c They are expressed by the following formulas:

[0032]

[0033]

[0034]

[0035] y c =x c tanθ

[0036] Where ν is Poisson's ratio, c is cohesion, φ is the internal friction angle, φ b is the basic friction angle and φ b =30°,σ n0 is the initial normal stress.

[0037] Optionally, in step 5, calculate the displacement x and shear area ratio a s The relationship between them is expressed as follows:

[0038]

[0039] Among them, h N is the maximum roughness height, h1 is the minimum roughness height, and the integral upper limit h c is a function of shear displacement and is expressed as follows:

[0040]

[0041] Where y is the lateral expansion of the pile.

[0042] Optional, integral term Approximation using Gauss-Legendre quadrature method.

[0043] Optionally, in step 6, by cutting area ratio a s The nonlinear relationship between the calculated displacement x and the shear stress τ is expressed as follows:

[0044] τ=(1-a s )(σ0+Ky)tan(φ+θ)+a s (σ0+Ky c )tanφ r

[0045] Among them, φ r is the residual friction angle.

[0046] Compared with the prior art, the present invention has the following beneficial effects:

[0047] (1) It can predict the side load transfer behavior of cast-in-place piles under different IGM stratum mechanical properties, pile geometry and material properties, and hole roughness, providing a certain theoretical reference for the preliminary design of pile foundations and the optimization of pile length and diameter;

[0048] (2) According to the "3σ criterion" of Gaussian distribution, the two key parameters of the mean and standard deviation of a large number of random variables are approximately reconstructed within the known roughness height range, which can avoid a large number of complex statistical operations and quickly solve the shear area ratio, greatly simplifying the difficulty of data processing;

[0049] (3) The concept of shear envelope of triangular roughness is introduced, and the results show that there is a monotonically increasing parabolic relationship between the critical shear displacement and the height of the roughness. This monotonicity ensures that we can link the real-time shear displacement with the height range of the shear roughness through the unique mapping relationship between the roughness height and the cumulative probability, and establish the corresponding functional relationship.

[0050] (4) Introducing the shear area ratio a s The concept of , which essentially describes the weight distribution of the unsheared and sheared areas. Through this weight distribution, we can quantify the different contributions of the local shear stress of the rough body that has experienced the climbing stage and the rough body that has experienced shearing to the total shear stress. s It provides us with a quantitative tool to analyze the changing trend of shear stress during the shearing process in order to determine the limiting shear stress. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] 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:

[0052] Figure 1 A rough two-dimensional topography of the hole wall provided by the present invention;

[0053] Figure 2 A quantitative diagram of the hole wall roughness parameters provided by the present invention;

[0054] Figure 3 A rough two-dimensional topography of the hole wall after reconstruction of the similar triangular rough bodies provided by the present invention;

[0055] Figure 4A schematic diagram of a constant normal stiffness model provided by the present invention;

[0056] Figure 5 A process diagram of the local roughness from climbing to shearing during the sliding process provided by the present invention;

[0057] Figure 6 A graph showing the relationship between the critical shear displacement and the height of the roughness provided by the present invention;

[0058] Figure 7 The roughness height h provided by the present invention is i Graph of evolution as cumulative probability increases;

[0059] Figure 8 The shear displacement x and shear area ratio a provided by the present invention are s The relationship diagram between

[0060] Fig. 9 A relationship diagram between shear displacement x and shear stress τ provided by the present invention. DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. 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.

[0062] The embodiment of the present invention provides a method for predicting pile side load transfer for a bored pile in an IGM stratum, comprising the following steps:

[0063] Step 1: After the cast-in-place pile construction in the IGM formation is completed and the hole is mechanically formed, the two-dimensional contour of the hole wall is scanned using a boremeter;

[0064] Step 2: Reconstruct the broken line profile of the two-dimensional profile of the hole wall to determine the maximum height h of the roughness max , minimum height h min and mean inclination;

[0065] Step 3: Using the average inclination angle and the relative height values ​​of each point on the roughness two-dimensional profile, the average inclination angle is used to construct a Gaussian distribution with a height range falling within the interval [h min ,h max ] similar right triangles;

[0066] Step 4: obtain the basic mechanical parameters of the IGM formation through experiments, including Poisson's ratio, cohesion, internal friction angle, basic friction angle, residual friction angle and elastic modulus, and estimate the critical failure load corresponding to the spring stiffness and the maximum height of the roughness according to the basic mechanical parameters, and further estimate the critical displacement and critical normal displacement corresponding to the maximum height of the roughness;

[0067] Step 5, calculate the relationship between displacement and shear area ratio;

[0068] Step six, calculate the nonlinear relationship between displacement and shear stress through shear area ratio.

[0069] In step 1, the two-dimensional profile of the hole wall is scanned using a boremeter, which specifically includes:

[0070] A reference section was set at each position where the depth increased by 10 mm, and the aperture measurement values ​​at 8 different directions of the hole wall at every 45° in the clockwise direction were recorded;

[0071] The arithmetic mean of the eight recorded aperture measurement values ​​is taken as the average aperture value at that depth. If an average value exceeds 30% of the range value, the average value is excluded, and the arithmetic mean of the remaining average values ​​is recalculated. The above process is repeated until the range of all average values ​​does not exceed 30% of the range value.

[0072] Combination Figure 1 As shown in the figure, by connecting the average aperture values ​​of all reference sections within the buried depth range, an approximate two-dimensional graph of hole wall roughness can be drawn. To further analyze the graph, first, select the point with the largest aperture value as the reference point o, set the relative profile height of the point to zero, and draw a vertical auxiliary line through the point; then, divide the entire two-dimensional contact surface into n-1 sections from top to bottom at intervals of 50 mm, so that the curve and the dividing line have n intersections, and then combine Figure 2 As shown, starting from the reference point o, connecting these n intersection points generates n right triangles. From any right triangle, two parameters can be obtained, which are recorded as the inclination angle θ of the right triangle. i and relative height h i (unit:

[0073] mm).

[0074] Among them, we measured the relative height h through the data measured by the aperture meter i Then, assuming that the relative height of the reference point is 0, the absolute aperture value of all cross sections is subtracted from the absolute aperture value of the reference point to obtain the relative height h of each point on the two-dimensional contour. i , and the relative height variation interval h can be determined i ∈[h min ,hmax ]. At this time, the inclination angle θ i It can be calculated by the following formula:

[0075]

[0076] Then, the average inclination angle θ of the two-dimensional contact surface can be obtained by the mathematical average, that is:

[0077]

[0078] In step 2, the polyline profile of the two-dimensional profile of the hole wall is reconstructed to determine the maximum height h of the roughness max , minimum height h min and average inclination, including:

[0079] Connect the average apertures of all reference sections with a broken line, and then draw a horizontal line intersecting the broken line every 50 mm. Then use the broken line to connect all the intersections in sequence to form a large number of right triangles. Read the absolute aperture of each intersection, and subtract the minimum aperture to obtain the relative aperture of each intersection. At the same time, determine the intersection of the maximum aperture and the minimum aperture. The horizontal distance between the maximum intersection and the minimum intersection is taken as the maximum height h of the rough body. max ; The horizontal distance between the minimum intersection point and the second smallest intersection point is the minimum height h of the rough body min .

[0080] In step 3, the average inclination angle is used to construct a Gaussian distribution with a height range falling within the interval [h min ,h max ], specifically:

[0081] Using the average inclination angle θ obtained above and the relative height h of each point on the two-dimensional profile i , the pile IGM contact surface can be reconstructed by a series of similar right-angled triangle rough bodies. The purpose is to simplify the two-dimensional form of the contact surface to make it easier to carry out mathematical and physical modeling. Specifically, a large number of right-angled triangles are constructed using the average inclination angle θ so that their height range falls within the interval [h min ,h max ] among.

[0082] Figure 3 The two-dimensional contact surface reconstructed by similar right-angled triangle rough bodies is shown (as shown by the dotted line in the figure), and the result has a good correlation with the solid line. By assuming that the relative height of the rough bodies meets certain statistical laws, the friction force on the reconstructed two-dimensional contact surface can be solved through mathematical and mechanical modeling.

[0083] Reconstruction of interface roughness based on statistics. The height of the roughness can be regarded as a variable randomly distributed in nature, and the relative height hi It can be considered to obey the Gaussian distribution in statistics. It should be noted that the height of the rough body is quantified as the relative height, which is equivalent. Therefore, the probability density function f(h) of the rough body height distribution can be expressed as:

[0084]

[0085] Where h is the height of the roughness; μ and s are the mean and standard deviation of the roughness height distribution, respectively. It must be noted that the roughness height cannot be negative. According to the "3σ criterion" of Gaussian distribution, about 99.73% of all cases fall within three standard deviations of the mean. Therefore, the standard deviation s can be calculated by the interval [h min ,h max ] reverse calculation, that is:

[0086]

[0087] The mean is:

[0088]

[0089] The shear mechanism of local roughness includes two stages: sliding along the slope of the inclination angle θ and sliding after the roughness is sheared. The shear strengths provided by these two stages are different, and the difference lies in the different sliding friction coefficients. The shear strengths in the climbing stage and after shearing can be expressed as:

[0090]

[0091] Determination of normal constraint stress. From the above formula, it can be seen that the exertion of local shear force is closely related to the normal constraint σ, so it is necessary to quantify it to improve the estimation method of the present invention. Specifically, the constant normal stiffness model can be used for implementation. The constant normal stiffness model refers to the lateral constraint force caused by the IGM formation on the pile body expansion is proportional to the pile body expansion amount y, and its proportionality coefficient is defined as the shear stiffness K. In the mechanical model, the lateral constraint can be represented by a horizontally placed spring, such as Figure 4 shown.

[0092] Then, the normal constraint stress can be expressed as:

[0093] σ=σ0+Ky (7)

[0094] Among them, σ0 is the initial normal constraint stress, and its magnitude is determined by the degree of stress release during the excavation process. In addition, the lateral expansion phenomenon of the contact surface can be approximately equivalent to the cylinder expansion model in elastic mechanics. According to the cylinder expansion solution, the relationship between the normal stress increment of the contact surface and the lateral expansion can be further obtained:

[0095]

[0096] In the formula, E is the elastic modulus of the IGM formation; ν is the Poisson's ratio of the rock mass; and r is the pile diameter. Combining formula (8) and the relationship between the normal stiffness K, stress increment, and expansion under the condition of constant normal stiffness constraint, the normal stiffness expression can be obtained as follows:

[0097]

[0098] At this point, the unit friction resistance that the local roughness can provide can be obtained by combining equations (6), (7) and (9):

[0099]

[0100] In the formula, y is the lateral expansion of the pile body, which can be written as follows according to the geometric relationship:

[0101] y=xtanφ (11)

[0102] Where x is the settlement of the pile.

[0103] Determine the critical shear displacement. During the sliding process of climbing, the actual contact area of ​​the rough body becomes smaller and smaller, and the surface shear stress becomes larger and larger. When it exceeds the shear strength of the IGM material, it will be sheared and a triangular slider (shaded part) will be formed. Figure 5 According to the static equilibrium condition and the result of Sokolovsky solution, the critical displacement x can be obtained. c for:

[0104]

[0105] in, c is the cohesion, φ b is the basic friction angle and φ b =30°,σ n0 is the initial normal stress.

[0106] Since a large number of similar triangular rough bodies have different heights, they will present different shearing states under a certain known shear displacement. In other words, whether any rough body is sheared under a certain shear displacement can be judged by the above formula (12).

[0107] When the above formula (12) is plotted as a graph (such as Figure 6As shown in the figure, it can be clearly seen that the stress increases parabolically with the increase of the roughness height, indicating that the failure of a single roughness occurs sequentially. Specifically, due to the short contact length, the maximum stress is generated on the contact surface of the lowest roughness. When the critical shear displacement is reached, the local shear stress on the lowest roughness exceeds its shear strength, causing it to shear first. The shear displacement continues to increase and causes the second lowest roughness to shear, and so on until the highest roughness is sheared. The above height-dependent sequential shearing process is called the shearing envelope of the triangular roughness, and its mathematical form is formula (12). By deforming formula (12), it can also be obtained that when the interface produces a relative displacement x, the height h of the cth roughness c (Note: At this time, all rough bodies are arranged from low to high, and all rough bodies from the 1st to the cth will be cut off) can be expressed as:

[0108]

[0109] According to the shearing envelope of the above triangular roughness, the total interface contact area A can be divided into two parts: the projection area A of the sheared roughness s and the projection area AA of the rough body that has not been cut off s , then the shear area ratio a s It can be defined as:

[0110]

[0111] According to formula (10), the shear area ratio a is introduced s It can serve as a concept of weight distribution. Formula (10) can be rewritten as:

[0112] τ=(1-a s )(σ0+Ky)tan(φ+θ)+a s (σ0+Ky c )tanφ r (15)

[0113] In the above formula, φ r is the residual friction angle; a s is a proportional factor between 0 and 1, which is used to determine how to distribute the sum of the uncut area and the cut area to achieve the cut area ratio a s Calculate the nonlinear relationship between displacement x and shear stress τ.

[0114] Specifically:

[0115] when a s =0, indicating that all rough bodies are experiencing the climbing stage.

[0116] when a s=1, indicating that all rough bodies are experiencing shearing.

[0117] When 0 s <1, the shear stress is the weighted sum of the shear stress of the roughness experiencing the climbing section and the roughness experiencing the shearing section, where a s is the weight of the shear area ratio, which has a dynamic evolution relationship with the shear displacement, namely, formula (14).

[0118] Formula (13) gives the relationship between shear displacement and the number of shear roughness c, which can be used to further calculate the shear displacement and shear area ratio a s The relationship is as follows.

[0119] In statistics, the inverse cumulative distribution function (ICDF) gives the value of a variable associated with a specific cumulative probability. For example, if we define a specific roughness height h i The cumulative probability p is:

[0120] p=Φ(h i ) (16)

[0121] The roughness height h can then be determined as follows i for:

[0122] h i =Φ -1 (p) (17)

[0123] Since the distribution of roughness height is assumed to be Gaussian, the value of the roughness height h less than a certain roughness height can be obtained by integrating formula (3): i The cumulative distribution probability (CDF) of occurrence is as follows:

[0124]

[0125] Figure 7 Shows the roughness height h i Evolution law with increasing cumulative probability, where the given mean is μ = 5.5 mm and the standard deviation is s = 1.5 mm. According to Riemann summation, by dividing the area of ​​region A into N blocks with width B and height h i The area is defined by the curve h i =Φ -1 (p) and the horizontal axis and the straight lines p = 0 and p = 1, the total area A of all rough bodies is obtained:

[0126]

[0127] The total area enclosed by the left side of the bar B in the figure represents the total area A of the sheared rough body under any cumulative probability. s , which can be written as: ​

[0128]

[0129] According to the definition of formula (14), combining formulas (19) and (20), we can get:

[0130]

[0131] By integrating by parts and simplifying we get:

[0132]

[0133] Note that equation (22) has no exact solution, but the Gauss-Legendre integration method can be used to estimate a s The numerical solution of h is obtained by using formula (13) c The value of is used to determine the upper limit of the integral. Substituting equation (22) into equation (15) yields the dynamic process of the shear stress τ developing with the shear displacement x, i.e., the load transfer behavior.

[0134] The following is a further detailed description of the method for predicting the side load transfer of a cast-in-place pile taking into account the roughness of the hole wall in an IGM formation according to a specific embodiment 1.

[0135] Example 1

[0136] A concrete cast-in-place test pile at a construction site passes through a 3m thick medium plastic clay filling layer and a 17m thick mudstone layer from top to bottom. The length of the test pile is L = 20m, and the pile diameter is r = 0.61m. The initial normal stress σ when the pile is formed n0 =400kPa.

[0137] After drilling is completed, the basic geometric parameters h of the IGM interface after drilling are measured by the on-site boremeter min =1mm,h max =4.6mm, and the average inclination angle of the contact surface is estimated to be θ≈20° using formula (23).

[0138]

[0139] The Gaussian distribution parameters can be determined by equations (24) and (25), where the standard deviation s = 0.6 mm and the mean μ = 2.8 mm.

[0140]

[0141]

[0142] The basic mechanical parameters of mudstone were obtained through indoor tests (the 3m thick medium plastic clay filling layer was approximately treated as mudstone), including Poisson's ratio ν = 0.24, cohesion c = 693 kPa, internal friction angle φ = 31.4°, basic friction angle φb =30°, residual friction angle φ r =24°, elastic modulus E = 232 MPa. The spring stiffness K = 600 kPa / mm is estimated using formula (26).

[0143]

[0144] ③ Use formula (27) to estimate the highest roughness (h max ) corresponds to the critical failure load q c =7904kPa.

[0145]

[0146] Using formula (28) to estimate the highest roughness (h max ) corresponds to the critical displacement x max =8mm; critical normal displacement y max =x max tanq=2.912mm.

[0147]

[0148] Use formula (29) to program and calculate displacement x and shear area ratio a s The relationship between Figure 8 curve.

[0149]

[0150] The upper limit of integration h in the above formula c is a function of shear displacement and can be calculated by formula (30):

[0151]

[0152] Using formula (31) to calculate the relationship between displacement x and shear stress τ, we can obtain Fig. 9 curve.

[0153] τ=(1-a s )(σ0+Ky)tan(φ+θ)+a s (σ0+Ky c )tanφ r (31)

[0154] It can be seen from the figure that the maximum shear stress τ = 1886 kPa, and the corresponding pile top settlement (shear displacement) occurs when x = 6.2 mm. Fig. 9 The curve shown is a theoretical prediction of the pile side load transfer process.

[0155] 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.

[0156] 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.

[0157] The embodiments of the present invention are described above, but the present invention is not limited to the above-mentioned specific implementation modes. The above-mentioned specific implementation modes 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 purpose of the present invention and the claims, all of which are protected by the present invention.

Claims

1. A method for predicting pile side load transfer for bored piles in IGM strata, characterized in that: The steps include: Step 1: After the cast-in-place pile construction in the IGM formation is completed and the hole is mechanically formed, the two-dimensional contour of the hole wall is scanned using a boremeter; Step 2: Reconstruct the broken line profile of the two-dimensional profile of the hole wall to determine the maximum height h of the roughness max , minimum height h min and mean inclination; Step 3: Using the average inclination angle and the relative height values ​​of each point on the roughness two-dimensional profile, the average inclination angle is used to construct a Gaussian distribution with a height range falling within the interval [h min ,h max ] similar right triangles; Step 4: obtain the basic mechanical parameters of the IGM formation through experiments, including Poisson's ratio, cohesion, internal friction angle, basic friction angle, residual friction angle and elastic modulus, and estimate the critical failure load corresponding to the spring stiffness and the maximum height of the roughness according to the basic mechanical parameters, and further estimate the critical displacement and critical normal displacement corresponding to the maximum height of the roughness; Step 5, calculate the relationship between displacement and shear area ratio; Step six, calculate the nonlinear relationship between displacement and shear stress through shear area ratio.

2. The method for predicting pile side load transfer for bored piles in IGM strata according to claim 1, characterized in that: In step 1, the two-dimensional profile of the hole wall is scanned using a boremeter, which specifically includes: A reference section was set at each position where the depth increased by 10 mm, and the aperture measurement values ​​at 8 different directions of the hole wall at every 45° in the clockwise direction were recorded; The arithmetic mean of the eight recorded aperture measurement values ​​is taken as the average aperture value at that depth. If an average value exceeds 30% of the range value, the average value is excluded, and the arithmetic mean of the remaining average values ​​is recalculated. The above process is repeated until the range of all average values ​​does not exceed 30% of the range value.

3. The method for predicting pile side load transfer for cast-in-place piles in IGM strata according to claim 2, characterized in that: In step 2, the polyline profile of the two-dimensional profile of the hole wall is reconstructed to determine the maximum height h of the roughness max , minimum height h min and average inclination, including: Connect the average apertures of all reference sections with a broken line, and then draw a horizontal line intersecting the broken line every 50 mm. Then use the broken line to connect all the intersections in sequence to form a large number of right triangles. Read the absolute aperture of each intersection, and subtract the minimum aperture to obtain the relative aperture of each intersection. At the same time, determine the intersection of the maximum aperture and the minimum aperture. Take the horizontal distance between the maximum intersection and the minimum intersection as the maximum height h of the rough body. max ; The horizontal distance between the minimum intersection point and the second smallest intersection point is the minimum height h of the rough body min ; Calculate the inclination angle θ of all right triangles through geometric relationships i , with an inclination angle θ i The mathematical mean of is the average inclination angle θ, which is expressed as follows: Among them, h i is the relative height of the roughness.

4. The method for predicting pile side load transfer for bored piles in IGM strata according to claim 3, characterized in that: In step 3, the average inclination angle is used to construct a Gaussian distribution with a height range falling within the interval [h min ,h max ], specifically: Since the relative height h i It obeys the Gaussian distribution in statistics, so the probability density function f(h) of the rough body height distribution is expressed as follows: Where h is the height of the roughness; μ and s are the mean and standard deviation of the roughness height distribution, respectively, which are expressed by the following formulas:

5. The method for predicting pile side load transfer for bored piles in IGM strata according to claim 4, characterized in that: In step 4, the spring stiffness K and the critical failure load q c、 Critical displacement x c and the critical normal displacement y c They are expressed by the following formulas: y c =x c tanθ Where ν is Poisson's ratio, c is cohesion, φ is the internal friction angle, φ b is the basic friction angle and φ b =30°,σ n0 is the initial normal stress.

6. The method for predicting pile side load transfer for bored piles in IGM strata according to claim 5, characterized in that: In step 5, calculate the displacement x and shear area ratio a s The relationship between them is expressed as follows: Among them, h N is the maximum roughness height, h1 is the minimum roughness height, and the integral upper limit h c is a function of shear displacement and is expressed as follows: Where y is the lateral expansion of the pile.

7. The method for predicting pile side load transfer for bored piles in IGM strata according to claim 6, characterized in that: Integral Item Approximation using Gauss-Legendre quadrature method.

8. The method for predicting pile side load transfer for bored piles in IGM strata according to claim 7, characterized in that: In step 6, the shear area ratio a s The nonlinear relationship between the calculated displacement x and the shear stress τ is expressed as follows: τ=(1-a s )(σ0+Ky)tan(φ+θ)+a s (σ0+Ky c )tanφ r Among them, φ r is the residual friction angle.

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