A pile side load transfer prediction method for cast-in-place piles in IGM strata

Abstract

The application discloses a pile side load transfer prediction method for a cast-in-place pile in an IGM stratum, and belongs to the technical field of pile foundation bearing characteristic researches. The method comprises the following steps: predicting the lateral and vertical load transfer behaviors of the cast-in-place pile under different IGM stratum mechanical properties, pile body geometrical and material properties, and hole diameter roughness; drawing a two-dimensional profile curve of a hole wall; and then, according to characteristic values of the curve, reconstructing the hole wall curve based on similar right-angled triangle rough bodies, so that the height distribution of the hole wall curve conforms to a Gaussian distribution law, and the pile IGM contact surface characteristics formed in an actual drilling process are simulated. Local shear stress is obtained by performing mechanical modeling on a single triangle rough body, and a stress deformation law is summarized, and then, the calculation method is generalized to a large number of similar triangle rough bodies on a macroscopic contact surface in combination with statistical parameters, so that an effective way is provided for quantitatively predicting the cast-in-place pile lateral load transfer behaviors considering the hole wall roughness.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of pile foundation bearing property research, and particularly relates to a pile side load transfer prediction method for a cast-in-place pile in an IGM stratum, which predicts the pile side load transfer behavior of the cast-in-place pile in the IGM stratum through hole wall roughness detection. BACKGROUND

[0002] In bridge construction, as a common form of bridge foundation, bored piles often need to pass through hard clay layers or medium-strong weathered rock layers, such as shale and mudstone, and even penetrate into solid bearing layers during the construction process. These strata have strong cohesion and can be regarded as a kind of transitional material between soil and rock from the mechanical point of view, which can be defined as IGM (intermediate geomaterials). According to the stratum characteristics corresponding to the pile embedding depth, IGM can be subdivided into three categories: (1) argillaceous rock-soil materials, including over-consolidated hard clay, clay shale and mudstone; (2) limestone or calcareous rock-soil materials, including limestone, calcareous cemented sandstone and soft sandstone; (3) dense granular rock-soil materials, such as partially weathered or fully weathered granite and dense sand. They have physical and mechanical properties such as low strength, high porosity, poor cementation, significant influence of structural plane cutting and weathering, and a large amount of swelling clay minerals.

[0003] The general length of a bored pile can exceed 50 meters, which means that the pile side resistance will develop before the end resistance when subjected to vertical load, which means that the degree of development of the pile side resistance has a significant impact on the settlement of the pile top. Therefore, understanding and controlling the development of the pile side resistance is the key to ensuring the quality and safety of the project. When mechanical hole forming is performed in soft rock and hard soil layers, the rotary excavation of the cutter will cause the hole wall to become rough. The rough hole wall and the poured concrete form an undulating contact surface. When subjected to vertical load, these undulating contact surfaces will attempt to expand radially, but this expansion will be constrained by the stratum 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 amount of 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 that affect the development of the pile side resistance. 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 constraint ability to circumferential expansion. In order to optimize the performance of the bored pile, the roughness of the hole wall and the material properties of the soft rock and hard soil need to be considered comprehensively, and the construction parameters need to be designed reasonably to ensure that the pile side resistance can be fully developed, thereby effectively controlling the settlement of the pile top.

[0004] The current Technical Code for Building Pile Foundations (JGJ 94-2008) provides a set of estimation methods for the ultimate bearing capacity of single pile based on the mechanical indexes of rock-soil materials. This method can estimate the ultimate side resistance of each layer according to the stratification of soil properties in the absence of in-situ static sounding data, and then sum the standard values of the ultimate bearing capacity in different depths of the stratum. This method is widely used in engineering practice because it is simple and easy to implement, and the physical meaning of each parameter is clear. However, this method has some limitations in theory. It is mainly based on the ultimate state to estimate the side resistance, but the standard value of the ultimate side resistance cannot fully reflect the side resistance mechanism before the failure or yielding of the surrounding rock. In addition, the standard method does not consider the influence of the relative displacement of the pile-soil interface caused by the compression of the pile body and the settlement of the stratum on the degree of side resistance development. Therefore, when the relative displacement of the pile-soil interface is small, the standard method may overestimate the side resistance of the pile, 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 been fully considered in the current engineering specifications. In fact, this roughness forms an uneven contact surface between the pile body and the concrete, which can expand circumferentially when subjected to vertical loads. This expansion process is constrained by the stratum outside the hole wall, thereby directly affecting the development of the side resistance. The Federal Highway Administration (FHWA) bridge pile foundation design specification clearly states that the roughness of the hole wall of a cast-in-place pile can significantly increase the side resistance of the pile, and the degree of increase is positively related to the roughness. There is no related research or specification provisions in China.

[0006] In recent years, some domestic scholars have preliminarily explored the correlation between the hole forming time and the roughness of the hole wall. For example, based on in-situ hole forming data, the non-monotonic correlation between the hole forming time and the roughness of the hole wall is summarized. Generally, the drill bit stays for too long at the beginning of drilling, resulting in a larger roughness, but the roughness decreases slightly during the unloading process. With further development of time, the hole shrinking phenomenon is obvious, and the roughness increases slightly. In addition, through a large number of field investigations, it is found that the more the hole wall collapses, the greater the roughness, which leads to an increase in the amount of discharged material and the time of mud hole cleaning. Therefore, it is concluded that the roughness is positively correlated with the hole cleaning time.

[0007] Although the current specification provides effective guidance for the design of the ultimate bearing capacity of a single pile of a cast-in-place pile, there are still many aspects that need to be further explored and improved in actual application. In particular, in terms of considering factors such as hole wall roughness, the current specification has not fully reflected its actual influence on the side resistance of the pile. SUMMARY

[0008] The purpose of the present application is to provide a pile side load transfer prediction method for cast-in-place piles in IGM strata, which obtains the two-dimensional rough morphology and roughness parameters of the hole wall through the existing detection device for measuring the actual hole diameter size after the hole is formed, simplifies the geometry of the hole wall by using the right-angled triangle rough body, facilitates mechanical analysis and model establishment, then reconstructs the irregular undulating contact surface of the hole wall by using statistical methods, and finally estimates the pile side unit side resistance through relevant theoretical calculations, so as to realize the prediction of the pile side load transfer behavior, and thus at least one technical problem involved in the background art can be solved.

[0009] In order to solve the above technical problems, the present application is implemented as follows:

[0010] The present application provides a pile side load transfer prediction method for cast-in-place piles in IGM strata, comprising the following steps:

[0011] Step one: after the cast-in-place pile construction in the IGM strata is completed and the mechanical hole is formed, the two-dimensional profile of the hole wall is scanned by using a hole diameter instrument;

[0012] Step two: the broken line profile of the two-dimensional profile of the hole wall is reconstructed to determine the maximum height h max , the minimum height h min and the average inclination of the rough body;

[0013] Step three: by using the average inclination and the relative height value of each point on the two-dimensional profile of the roughness, a similar right-angled triangle with a height range falling within the interval [h min , h max ] is constructed by using the average inclination, which conforms to the Gaussian distribution;

[0014] Step four: the basic mechanical parameters of the IGM strata are obtained through experiments, including Poisson's ratio, cohesive force, internal friction angle, basic friction angle, residual friction angle and elastic modulus, and the spring stiffness and the critical failure load corresponding to the maximum height of the rough body are estimated according to the basic mechanical parameters, and the critical displacement and the critical normal displacement corresponding to the maximum height of the rough body are further estimated;

[0015] Step five: the relationship between the displacement and the shear area ratio is calculated;

[0016] Step six: the nonlinear relationship between the displacement and the shear stress is calculated through the shear area ratio.

[0017] Optionally, in step one, the two-dimensional profile of the hole wall is scanned by using a hole diameter instrument, which specifically comprises:

[0018] A reference section is set at a position where the depth is increased by 10 millimeters, and the hole diameter measurement values of the hole wall in 8 different directions every 45° in the clockwise direction are recorded;

[0019] Take the arithmetic mean of the eight recorded aperture measurements as the average aperture at that depth. If any average exceeds 30% of the range, exclude that average and recalculate the arithmetic mean of the remaining averages. Repeat the above process until the range of all averages does not exceed 30% of the range.

[0020] Optionally, in step two, the polygonal profile of the two-dimensional contour of the hole wall is reconstructed to determine the maximum height h of the rough body. max Minimum height h min and mean dip angle, specifically including:

[0021] Connect the average apertures of all reference sections with a broken line. Then, draw a horizontal line intersecting this broken line every 50 mm. Connect all intersection points with the broken line to form a large number of right triangles (replace the right triangles with right triangles). Read the absolute aperture of each intersection point and subtract the minimum aperture to obtain the relative aperture at each intersection point. Determine the intersection point of the maximum and minimum apertures. Take the horizontal distance between the maximum and minimum intersection points as the maximum height h of the roughness body. max The horizontal distance between the smallest and second smallest intersection points is the minimum height h of the roughness body. min ;

[0022] Calculate the inclination angle θ of all right triangles using geometric relationships. i With an inclination angle θ i The mathematical average value of θ is taken as the average tilt angle θ, and is expressed by the following formula:

[0023]

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

[0025] Optionally, in step three, an average tilt angle is used to construct a structure that follows a Gaussian distribution and whose height range falls within the interval [h]. min h max Similar right triangles include:

[0026] Due to the relative height value h i Since the roughness follows a Gaussian distribution in statistics, the probability density function f(h) of the roughness height distribution is expressed by the following equation:

[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, expressed by the following formulas:

[0029]

[0030]

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

[0032]

[0033]

[0034]

[0035] y c = x c tan θ

[0036] wherein v is the Poisson's ratio, c is the 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 five, the relationship between the displacement x and the shear area ratio a s is calculated and represented by the following formula:

[0038]

[0039] wherein h N is the maximum rough body height, h1 is the minimum rough body height, and the upper limit of the integral h c is a function of the shear displacement and is represented by the following formula:

[0040]

[0041] wherein y is the lateral expansion of the pile body.

[0042] Optionally, the integral term is approximated by using the Gauss-Legendre integral method.

[0043] Optionally, in step six, the nonlinear relationship between the displacement x and the shear stress τ is calculated by the shear area ratio a s and represented by the following formula:

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

[0045] wherein φ r is the residual friction angle.

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

[0047] (1) The pile side load transfer behavior under different IGM stratum mechanical properties, pile body geometry and material properties, and hole diameter roughness can be predicted, thereby providing certain theoretical reference for preliminary design of pile foundation and optimization of pile length and pile diameter;

[0048] (2) According to the "3σ criterion" of Gaussian distribution, the two key parameters of mean value and standard deviation of a large number of random variables are approximately reconstructed within the known rough body height interval, the solution of the shear area ratio can be quickly performed by avoiding a large number of complex statistical operations, and the data processing difficulty is greatly simplified;

[0049] (3) The shear envelope line concept of the triangular rough body is introduced, and the results show that there is a monotonic increasing parabolic relationship between the critical shear displacement and the rough body height. The monotonicity ensures that we can associate the real-time shear displacement with the height interval of the shear rough body through the unique mapping relationship between the roughness height and the cumulative probability, and establish the corresponding function relationship.

[0050] (4) The concept of shear area ratio a s is introduced, which essentially describes the weight distribution of the uncut and cut parts. Through the weight distribution, we can quantify the different contributions of the rough body experiencing the climbing stage and the rough body experiencing the shear to the total shear stress on the local shear stress. The shear area ratio a s provides a quantitative tool for analyzing the change trend of the shear stress in the shear process so as to determine the ultimate shear stress. BRIEF DESCRIPTION OF DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0052] Figure 1 A two-dimensional hole wall roughness map is provided for the present application;

[0053] Figure 2 A quantification map of the hole wall roughness parameters is provided for the present application;

[0054] Figure 3 A two-dimensional hole wall roughness map after reconstruction of similar triangular rough bodies is provided for the present application;

[0055] Figure 4The schematic diagram of the normal stiffness model provided by the present application is shown in the following figure:

[0056] Figure 5 The process diagram of the local rough body climbing to shearing in the sliding process provided by the present application is shown in the following figure:

[0057] Figure 6 The diagram of the relationship between the critical shearing displacement and the rough body height provided by the present application is shown in the following figure:

[0058] Figure 7 The rough body height h provided by the present application is shown in the following figure: i The evolution law diagram with the increase of the cumulative probability is shown in the following figure:

[0059] Figure 8 The diagram of the relationship between the shearing displacement x and the shearing area ratio a provided by the present application is shown in the following figure: s

[0060] Figure 9 The diagram of the relationship between the shearing displacement x and the shearing stress τ provided by the present application is shown in the following figure. DETAILED DESCRIPTION

[0061] The technical solutions in the embodiments of the present application will be clearly and completely described below. Obviously, the described embodiments are some of the embodiments of the present application, but not all the embodiments of the present application. Based on the embodiments in the present application, all the other embodiments obtained by those skilled in the art without creative work fall within the protection scope of the present application.

[0062] The pile side load transfer prediction method for the cast-in-place pile in the IGM stratum provided by the embodiments of the present application comprises the following steps:

[0063] Step one, after the construction of the cast-in-place pile in the IGM stratum is completed and the mechanical hole is formed, the hole diameter instrument is used to scan the two-dimensional profile of the hole wall;

[0064] Step two, the broken line profile of the two-dimensional profile of the hole wall is reconstructed to determine the maximum height h max , the minimum height h min and the average inclination angle of the rough body;

[0065] Step three, the average inclination angle and the relative height value of each point on the roughness two-dimensional profile are used to construct the similar right triangle which obeys the Gaussian distribution and the height range falls in the interval [h min , h max ] by using the average inclination angle;

[0066] ​Step four, the basic mechanical parameters of IGM stratum are obtained by test, including Poisson's ratio, cohesive force, internal friction angle, basic friction angle, residual friction angle and elastic modulus, and the spring stiffness and the critical failure load corresponding to the maximum height of the rough body are estimated according to the basic mechanical parameters, and the critical displacement and the critical normal displacement corresponding to the maximum height of the rough body are further estimated;

[0067] Step five, the relationship between displacement and shear area ratio is calculated;

[0068] Step six, the nonlinear relationship between displacement and shear stress is calculated by shear area ratio.

[0069] In step one, the two-dimensional profile of the hole wall is scanned by the aperture instrument, specifically including:

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

[0071] The arithmetic mean of the recorded 8 aperture measurement values is taken as the average value of the aperture at this depth, if a certain average value exceeds 30% of the range value, the average value is excluded, and the arithmetic mean of the remaining average values is recalculated, and the above process is repeated until the range of all average values does not exceed 30% of the range value.

[0072] Combining Figure 1 As shown in the figure, by connecting the aperture average values of all reference sections in the embedding depth range, an approximate two-dimensional roughness profile of the hole wall can be drawn. Further analyzing the graph, first, select the point with the largest aperture value as the reference point o, and set the relative profile height of the point as zero, draw a vertical auxiliary line through the point; then, divide the entire two-dimensional contact surface into n-1 sections by 50 mm from top to bottom, so that the curve and the division line produce n intersection points, and then combine Figure 2 As shown in the figure, connect the n intersection points from the reference point o to produce n right triangles, from any one right triangle, two parameters can be obtained, denoted as the inclination angle θ i and the relative height h i (unit:

[0073] mm).

[0074] Among them, the absolute value of the relative height h i is measured by the aperture instrument, then assuming that the relative height of the reference point is 0, the absolute aperture value of all sections is subtracted from the absolute aperture value of the reference point, then the relative height h i of each point on the two-dimensional profile can be obtained, and the variation interval h i of the relative height can be determined. h min , hmax At this time, the inclination θ i can be calculated by the following formula:

[0075]

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

[0077]

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

[0079] Connect all the average pore diameters of the reference sections with a polyline, then make a horizontal line every 50 mm to intersect with the polyline, and then connect all the intersection points in turn with a polyline to form a large number of right-angled triangles. Read out the absolute pore diameter of each intersection point, and at the same time subtract the minimum pore diameter to obtain the relative pore diameter of each intersection point. At the same time, determine the intersection points at the maximum and minimum pore diameters, and take the horizontal distance between the maximum intersection point and the minimum intersection point as the maximum height h max of the rough body; the horizontal distance between the minimum intersection point and the second minimum intersection point is the minimum height h min of the rough body.

[0080] In step three, the average inclination is used to construct similar right-angled triangles that conform to the Gaussian distribution and have a height range falling within the interval [h min , h max ]. Specifically, it includes:

[0081] Using the average inclination θ obtained in the previous step and the relative height h i of each point on the two-dimensional profile, the 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 model mathematically and physically. Specifically, a large number of right-angled triangles are constructed using the average inclination θ, so that their height range falls within the interval [h min , h max ].

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

[0083] Statistical-based interface rough body reconstruction. The height of the rough body can be regarded as a random variable distributed in nature, and the relative height hi It can be considered to be subject to Gaussian distribution in statistics, it should be noted that the rough body height is quantified as relative height here, which is equivalent, so the probability density function f(h) of the rough body height distribution can be expressed as:

[0084]

[0085] Where h is the rough body height; 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 rule”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 ], that is:

[0086]

[0087] The mean is:

[0088]

[0089] The shear mechanism of local rough body includes two stages, sliding along the inclination θ and sliding after the rough body is sheared. The shear strength provided by the two stages is different, and the difference lies in the difference of the sliding friction coefficient. The shear strength of the climbing stage and after shearing can be expressed as:

[0090]

[0091] The determination of the normal constraint stress, it can be seen from the above formula that the exertion of local shear force is closely related to the normal constraint σ, so it is necessary to quantify it to perfect the prediction method of the present application. Specifically, the normal stiffness model can be cited for implementation. The normal stiffness model refers to the fact that the lateral constraint force of the IGM stratum caused by the expansion of the pile body is proportional to the expansion amount y of the pile body, and the proportional coefficient is defined as the shear stiffness K. In the mechanical model, this lateral constraint can be represented by a horizontally placed spring, as shown in Figure 4 .

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

[0093] σ=σ0+Ky (7)

[0094] Where σ0 is the initial normal constraint stress, which is determined by the degree of stress release during excavation. In addition, the lateral expansion phenomenon of the contact surface can be approximately equivalent to the cylindrical expansion model in elasticity. According to the cylindrical expansion solution, the relationship between the normal stress increment of the contact surface and the lateral expansion amount can be further obtained:

[0095]

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

[0097]

[0098] Therefore, the unit frictional resistance provided by the locally rough body can be obtained by combining equations (6), (7), and (9):

[0099]

[0100] In the formula, y represents the lateral expansion of the pile body, which can be written as follows based on geometric relationships:

[0101] y=xtanφ (11)

[0102] In the formula, x represents the settlement of the pile.

[0103] Determine the critical shear displacement. During the sliding process of climbing the slope, the actual contact area of ​​the rough body decreases, while the surface shear stress increases. Once it exceeds the shear strength of the IGM material, it will be sheared, and a new triangular slider (shaded area) will form. Figure 5 As shown. Based on the static equilibrium conditions and the results of the Sokolovsky solution, the critical displacement x can be obtained. c for:

[0104]

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

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

[0107] When the above equation (12) is plotted as a graph (e.g.) Figure 6As can be clearly seen from the plot (Fig. 5), the contact area increases parabolically with the increase of the asperity height, indicating that the failure of individual asperities occurs sequentially. Specifically, the maximum stress occurs at the contact surface of the lowest asperity due to its short contact length. When the critical shear displacement is reached, the local shear stress on the lowest asperity exceeds its shear strength, resulting in its first shear-off. The shear displacement continues to increase and causes the second-lowest asperity to shear-off, and so on until the highest asperity is sheared off. The above sequential shear-off process related to the height is referred to as the shear-off envelope of the triangular asperities, whose mathematical form is given by equation (12). By rearranging equation (12), the height h c (Notes: At this time, all asperities are arranged from low to high, and the first to the cth asperities are sheared off) can be expressed as:

[0108]

[0109] According to the shear-off envelope of the triangular asperities, the total interface contact area A can be divided into two parts: the projected area of the sheared-off asperities A s and the projected area of the un-sheared-off asperities A-A s , then the shear area ratio a s can be defined as:

[0110]

[0111] According to equation (10), the introduction of the shear area ratio a s can play a concept of assigning weights. Equation (10) can be rewritten as:

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

[0113] In the above equation, φ r is the residual friction angle; a s is a proportional factor between 0 and 1, which determines how to distribute the sum of the un-sheared-off area and the sheared-off area, so as to achieve the nonlinear relationship between the displacement x and the shear stress τ through the shear area ratio a s .

[0114] Specifically:

[0115] When a s = 0, it means that all asperities are experiencing the ramp-up segment.

[0116] When a s= 1, indicating that all asperities are experiencing shearing.

[0117] When 0 < a < 1, the shear stress is the weighted sum of the shear stress of asperities experiencing the ramp-up segment and asperities experiencing shearing, where a is the weight of the shearing fraction area ratio, which has a dynamic evolution relationship with the shear displacement, i.e., equation (14). s <1, the shear stress is the weighted sum of the shear stress of asperities experiencing the ramp-up segment and asperities experiencing shearing, where a is the weight of the shearing fraction area ratio, which has a dynamic evolution relationship with the shear displacement, i.e., equation (14). s is the weight of the shearing fraction area ratio, which has a dynamic evolution relationship with the shear displacement, i.e., equation (14).

[0118] Equation (13) gives the relationship between the shear displacement and the number of shearing asperities c, which can be used to further obtain the relationship between the shear displacement and the shearing area ratio a s , as follows.

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

[0120] p = Φ(h i ) (16)

[0121] Then the roughness height h i can be determined as follows:

[0122] h i = Φ -1 (p) (17)

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

[0124]

[0125] Figure 7 The evolution of the roughness height h i with increasing cumulative probability is shown, where the mean is given as 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 rectangles of width B and height h i = Φ -1 (p) and the horizontal axis, as well as the straight lines p = 0 and p = 1, the total area A of all asperities is obtained:

[0126]

[0127] The total area enclosed by the left side of the block B shown in the figure represents the total area A s of shearing asperities at any cumulative probability, which can be written as:

[0128]

[0129] According to the definition of formula (14), formula (19) and (20) can be obtained:

[0130]

[0131] By integral and simplification, we get:

[0132]

[0133] Note that formula (22) has no exact solution, and the numerical solution of a s can be estimated by Gauss-Legendre integral method, and the numerical value of h c must be calculated by formula (13) to determine the upper limit of integration. Then, formula (22) is substituted into formula (15) to obtain the dynamic process of shear stress τ with shear displacement x, i.e. load transfer behavior.

[0134] The application of the pile side load transfer prediction method considering hole wall roughness in IGM stratum is further described in detail through specific embodiment 1.

[0135] Embodiment 1

[0136] A concrete bored pile test at a construction site penetrates a 3m thick medium plastic clay filler layer and a 17m thick mudstone layer from top to bottom. The test pile has a length of L = 20m and a diameter of r = 0.61m. The initial normal stress σ n0 = 400kPa when the pile is formed.

[0137] After the hole is drilled, the basic geometric parameters h min = 1mm, h max = 4.6mm of the IGM interface after hole formation are measured by a field diameter instrument, and the average inclination angle θ ≈ 20° of the contact surface is estimated using formula (23).

[0138]

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

[0140]

[0141]

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

[0143]

[0144] ③ Estimate the highest roughness (h) using formula (27) max The corresponding critical failure load q c =7904 kPa.

[0145]

[0146] The highest roughness (h) is estimated using equation (28). max The corresponding critical displacement x max =8mm; Critical normal displacement y max =x max tanq = 2.912 mm.

[0147]

[0148] Using equation (29), programmatically calculate the displacement x and the shear area ratio a. s The relationship between them, to obtain such Figure 8 The curve.

[0149]

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

[0151]

[0152] Using equation (31) to calculate the relationship between displacement x and shear stress τ, we obtain the following: Figure 9 The curve.

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

[0154] The figure shows that the maximum shear stress τ = 1886 kPa, which corresponds to the pile top settlement (shear displacement) occurring when x = 6.2 mm. Figure 9 The curve shown represents the theoretical prediction of the load transfer process on the pile side.

[0155] It should be noted that, as used in this place, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element preceded by "comprises a" does not, without more constraints, foreclose the existence of additional identical elements in the process, method, article, or apparatus that comprises the recited element.

[0156] Further, it is noted that the scope of the methods and systems of the embodiments of the present application are not limited to the exact sequence of acts described, but that the methods and systems can include additional, fewer, or different acts, depending on the application of the method and system. Further, features described in relation to certain examples can be combined in other examples.

[0157] The above describes the embodiments of the present application, but the present application is not limited to the above-described specific embodiments, and the above-described specific embodiments are merely illustrative, not restrictive. Those skilled in the art can make many forms under the inspiration of the present application without departing from the purpose of the present application and the scope protected by the claims, which are all within the protection of the present application.

Claims

1. A method for predicting pile side load transfer of a cast-in-place pile in an IGM stratum, characterized by, The method comprises the following steps: Step one, after the completion of the construction of the cast-in-place pile in the IGM stratum and the mechanical hole forming, the hole diameter instrument is used to scan the two-dimensional profile of the hole wall; Step two, reconstruct the broken line profile of the two-dimensional profile of the hole wall to determine the maximum height of the rough body , minimum height and average inclination angle; Step three, using the average inclination angle and the relative height value of each point on the two-dimensional profile of roughness, the average inclination angle is used to construct a similar right triangle subject to Gaussian distribution and the height range falls within the interval [ , ]; the broken line type profile of the two-dimensional profile of the hole wall is reconstructed to determine the maximum height , the minimum height and the average inclination angle ， Specifically includes: All the average pore diameter of reference section is connected with broken line, then every 50mm is made a horizontal line intersecting with the broken line, then the all intersection points are connected with broken line to form a large number of right triangle, the absolute pore diameter of each intersection point is read out, at the same time the relative pore diameter of every intersection point is obtained by subtracting the minimum pore diameter, at the same time the intersection points of the maximum pore diameter and the minimum pore diameter are determined, the horizontal distance between the maximum intersection point and the minimum intersection point is taken as the maximum height of the rough body ; the horizontal distance between the minimum intersection point and the second minimum intersection point is taken as the minimum height of the rough body ; The dip angles of all right-angled triangles are calculated by geometric relations with the mathematical mean of the dip angles as the average dip angle is expressed by the following equation: wherein, hi the relative height of the asperities; Step four, the basic mechanical parameters of the IGM stratum are obtained through tests, including Poisson's ratio, cohesive force, internal friction angle, basic friction angle, residual friction angle, and elastic modulus, and the critical failure load corresponding to the lateral stiffness and the maximum height of the rough body is estimated according to the basic mechanical parameters, and the critical displacement and the critical normal displacement corresponding to the maximum height of the rough body are further estimated; the lateral constraint force of the IGM stratum caused by the expansion of the pile body is proportional to the expansion amount of the pile body, and the proportional coefficient is defined as the normal stiffness K ; the normal stiffness 、 The critical failure load 、 The critical displacement and the critical normal displacement are respectively represented by the following formula: wherein E is the elastic modulus of the IGM formation, r is the pile diameter, is the Poisson's ratio, is the cohesion, is the internal friction angle, is the basic friction angle and , is the initial normal stress; Step five, calculate the relationship between the displacement and the shear area ratio; calculate the displacement x and the shear area ratio a s, which is expressed by the following equation: wherein is the maximum asperity height, is the minimum asperity height, the upper limit of integration is a function of the shear displacement, expressed by the following equation: wherein, is the lateral expansion of the pile shaft, and , is the settlement of the pile shaft; wherein and are the mean and standard deviation of the roughness height distribution, respectively; Step six, the nonlinear relationship between displacement and shear stress is calculated by the shear area ratio; the nonlinear relationship between displacement and shear stress is calculated by the shear area ratio displacement and shear stress is expressed by the following equation: wherein is the residual friction angle.

2. The method for predicting the pile side load transfer of a cast-in-place pile in an IGM stratum according to claim 1, wherein In step one, the two-dimensional profile of the hole wall is scanned by the hole diameter instrument, which specifically comprises: A reference section is set at every position where the depth is increased by 10 millimeters, and the hole diameter measurement values of the hole wall in 8 different directions every 45º in the clockwise direction are recorded; The arithmetic mean of the recorded 8 hole diameter measurement values is taken as the average value of the hole diameter at the depth, if a certain average value exceeds 30% of the range value, the average value is excluded, and the arithmetic mean of the remaining average values is recalculated, and 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 the pile side load transfer of a cast-in-place pile in an IGM stratum according to claim 1, wherein In step three, similar right-angled triangles obeying Gaussian distribution and having height range falling in interval [ , ] are constructed with average inclination, specifically including: Due to the relative height values h i Subject to the Gaussian distribution in statistics, then, the probability density function of the roughness height distribution is expressed by the following equation: wherein is the roughness height; and are the mean and standard deviation of the roughness height distribution, respectively, expressed by the following equations: 。 4. The method for predicting the pile side load transfer of a cast-in-place pile in an IGM stratum according to claim 3, characterized in that, Integral term Approximated using Gauss-Legendre integration.

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