Methods for calculating the curvature and bending moment of sheet piles and methods for evaluating the stability of sheet piles

Abstract

This invention discloses a method for calculating the curvature and bending moment of sheet piles and a method for evaluating the stability of sheet piles, belonging to the field of deep foundation pit sheet pile support structures. The method includes establishing a functional relationship between the lateral displacement and curvature of the sheet pile; establishing a functional relationship between the lateral displacement and bending moment of the sheet pile; calculating the allowable bending moment and allowable curvature of the sheet pile, comparing them with their actual values; determining that the support structure is safe if any actual value is less than the corresponding design value; otherwise, determining that enhanced monitoring is needed or that the structure is in danger. This invention utilizes the aforementioned method for calculating the curvature and bending moment of sheet piles and the method for evaluating the stability of sheet piles to achieve accurate calculation of the curvature and bending moment of sheet piles, as well as a scientific and rapid assessment of the stability of the support structure.

Description

Technical Field

[0001] This invention relates to the field of deep foundation pit steel sheet pile support structure technology, and in particular to a method for calculating the curvature and bending moment of steel sheet piles and a method for evaluating the stability of steel sheet piles. Background Technology

[0002] Sheet piles are a commonly used support system in deep foundation pit engineering. During the support process, the deformation and stress state of the sheet piles are important indicators reflecting the stability and safety of the support structure. Therefore, accurately calculating the curvature and bending moment of the sheet piles, and simultaneously conducting a scientific and rapid evaluation of the stability of the support structure, is of great significance for ensuring the safety of foundation pit engineering.

[0003] In existing technologies, the safety evaluation and internal force monitoring of sheet pile supported structures mainly rely on two types of methods, both of which have significant limitations: First, indirect evaluation methods based on deformation. During the design and construction phases, structural safety is initially assessed by monitoring whether the pile displacement exceeds a preset warning value. However, in engineering practice, situations often arise where the sheet pile deformation far exceeds the maximum warning value, yet the structure remains stable; conversely, there is also a risk of structural damage due to localized stress concentration even when the deformation does not exceed the warning value. Relying solely on deformation data cannot accurately reflect the actual stress state of the pile, and the lack of effective correlation analysis between deformation and internal forces results in evaluation results that lack scientific rigor and accuracy, failing to meet the requirements for precise early warning.

[0004] Second, the strain gauge measurement method. This method involves attaching strain gauges to key sections of the sheet pile to directly measure the pile strain data, and then using material mechanics formulas to calculate the pile bending moment. This method has three main drawbacks: First, the observation points are limited to preset key sections, ignoring the potential for stress concentration or sudden changes in internal forces at non-key sections, resulting in incomplete monitoring coverage; second, the installation quality of the strain gauges directly affects the measurement accuracy, requiring extremely high operational precision; and third, in the complex construction environment of deep foundation pits—characterized by dampness, high vibration, and susceptibility to external impacts—strain gauges are prone to damage and failure, leading to data interruption or distortion, making long-term stable monitoring difficult.

[0005] Inclinometers, commonly used displacement monitoring devices in deep foundation pit engineering, can monitor the tilting deformation of the foundation pit retaining structure. They have advantages such as wide monitoring range, convenient operation, and strong adaptability to complex environments. However, in current technology, inclinometers are only used for displacement early warning, and a quantitative conversion relationship between displacement data and pile curvature and bending moment has not been established. This results in a limited application scenario for inclinometer data, and the data value has not been fully explored, failing to provide effective support for the internal force analysis and safety evaluation of sheet piles.

[0006] In summary, existing technologies suffer from problems such as limited evaluation dimensions, incomplete monitoring coverage, low data utilization, and insufficient accuracy in safety early warning, making it difficult to meet the needs of deep foundation pit engineering for precise analysis and timely early warning of the stress state of steel sheet pile structures. Summary of the Invention

[0007] The purpose of this invention is to provide a method for calculating the curvature and bending moment of sheet piles and a method for evaluating the stability of sheet piles, so as to achieve accurate calculation of the curvature and bending moment of the entire pile body, improve the scientificity and comprehensiveness of the safety evaluation of sheet pile support structures, and provide timely and scientific safety warnings.

[0008] To achieve the above objectives, the present invention provides a method for calculating the curvature and bending moment of a steel sheet pile, comprising the following steps:

[0009] S1: Observation points are arranged along the transverse and longitudinal directions of the steel sheet pile, and the inclinometer tube is fixed on the steel sheet pile. During the test, the inclinometer probe is inserted into the inclinometer tube and slides down along the depth direction to obtain displacement data and lateral displacement data at each elevation of all monitored piles.

[0010] S2: Determine the pile height-curvature data based on the elevation-displacement data of all monitored piles;

[0011] S3: Based on the elevation-curvature data of all monitored piles, plot the elevation-curvature curve.

[0012] S4: Determine the bending moment of the pile cross section based on the elevation-displacement data of all monitored piles.

[0013] Preferably, the transverse direction is perpendicular to the length of the pile body, and the longitudinal direction is parallel to the length of the pile body; the inclinometer tube is fixed on the sheet pile so that the deformation of the inclinometer tube is synchronized with that of the sheet pile, reflecting the deflection of the support structure.

[0014] Preferably, S2 includes the following steps:

[0015] S201: According to mechanics of materials, the curvature of the pile at a certain elevation is represented by the second derivative of the displacement function, and the curvature of the pile cross-section... The calculation expression is as follows:

[0016] ;

[0017] In the formula, express Curvature of the pile cross section at elevation displacement Indicates elevation;

[0018] S202: Second-order three-point derivative calculation;

[0019] Curvature of the pile cross section The calculation expression is discretized using second-order three-point differentiation, and the calculation expression is as follows:

[0020] ;

[0021] In the formula, Indicates the calculation step size. Indicates the calculation section number. , , They represent the first , , Lateral displacement of the cross section, Indicates the calculation interval , This represents the additional curvature caused by lateral displacement; the additional curvature is the truncation error term.

[0022] The calculation step size is defined as: the vertical distance between adjacent sections after the sheet pile is uniformly divided into calculation sections along the depth direction;

[0023] S203: Curvature rounding error correction;

[0024] The displacement readings of the inclinometer have rounding errors. Based on the worst-case scenario, the curvature is rounded off. ;

[0025] The expression for calculating the actual curvature after deducting rounding errors is as follows:

[0026] ;

[0027] In the formula, Indicates the actual curvature. Indicates the curvature of the pile cross section The curvature is calculated from the discretized expression after second-order three-point differentiation.

[0028] Preferably, in step S3, the elevation-displacement data obtained in step S1 and the elevation-curvature correspondence calculated in step S2 are combined to draw a pile height-curvature diagram to reflect the curvature distribution characteristics of the entire pile body.

[0029] Preferably, S4 includes the following steps:

[0030] S401: Based on mechanics of materials, the relationship between bending moment and displacement is realized, and the bending moment of the pile cross-section is calculated. The calculation expression is as follows:

[0031] ;

[0032] In the formula, express Bending moment at elevation, This indicates the bending stiffness of the sheet pile, where This represents the elastic modulus of the steel sheet pile. Represents the moment of inertia of the cross section;

[0033] S402: Based on mechanics of materials, this establishes a correlation between lateral pressure and bending moment, where lateral pressure... The calculation expression is as follows:

[0034] ;

[0035] In the formula, express Lateral pressure at elevation;

[0036] S403: Discretization calculation of bending moment:

[0037] Combined with the curvature of the pile cross section The expression for calculating the lateral pressure is obtained after discretization using the second-order three-point derivative. Substituting the calculation expression into the second-order three-point derivative formula, we obtain the bending moment calculation formula as follows:

[0038] ;

[0039] In the formula, Indicates elevation Bending moment at section, This represents the additional bending moment generated by lateral pressure.

[0040] The additional bending moment is the cutoff error term, and the cutoff error is related to the step size. Proportional;

[0041] S404: Moment rounding error correction;

[0042] Moment rounding error The actual bending moment calculation formula is as follows:

[0043] ;

[0044] In the formula, Indicates the actual bending moment. Indicates the bending moment in step S403. The bending moment is calculated using the formula.

[0045] Preferably, in S402, the lateral pressure includes active earth pressure outside the foundation pit, water pressure, and temporary additional loads during construction.

[0046] This invention also provides a method for evaluating the stability of steel sheet piles, comprising the following steps:

[0047] S01: Determine the allowable bending moment of the reduced pile wall design according to the principle of equal curvature;

[0048] S02: Calculate the design allowable curvature based on the reduced design allowable bending moment;

[0049] S03: Evaluate the stability of the sheet pile by comparing the actual curvature of the sheet pile body with the allowable curvature of the design and the actual bending moment with the allowable bending moment of the design.

[0050] Preferably, based on the inversion results of measured data from multiple projects, the stiffness of a single sheet pile is calculated by reducing the stiffness of the composite pile wall by 50%.

[0051] Preferably, in S02, the reduced allowable bending moment of the pile wall design Based on the principle of constant curvature, the calculation expression is as follows:

[0052] ;

[0053] In the formula, This represents the maximum design bending moment value of a single pile. This indicates the allowable bending moment value for the pile wall design after reduction. Indicates the stiffness of a single pile. Indicates the stiffness of the pile wall after reduction;

[0054] Calculate the allowable curvature of the sheet pile based on the design bending moment of a single sheet pile. The calculation expression is as follows:

[0055] .

[0056] Preferably, in S03, the stability evaluation of steel sheet piles is as follows:

[0057] Based on the calculated actual curvature of the pile body Compared to the allowable curvature of the pile body design Based on the calculated actual bending moment of the pile body Compared with the allowable bending moment of the pile wall design Determine whether the sheet pile support structure is safe:

[0058] when , At that time, the steel sheet pile support structure was assessed as safe;

[0059] when , At that time, the steel sheet pile support structure was assessed as unsafe, and a danger warning was issued;

[0060] when , Or when , At the same time, strengthen monitoring and reinforcement.

[0061] Therefore, the present invention employs the above-mentioned method for calculating the curvature and bending moment of sheet piles and the method for evaluating the stability of sheet piles, which has the following beneficial effects:

[0062] This invention, through methods for calculating the curvature and bending moment of sheet piles and for evaluating their stability, enables accurate calculation of the curvature and bending moment of the entire pile section, improving the scientific rigor and comprehensiveness of the safety evaluation of sheet pile support structures, and providing timely and scientific safety warnings.

[0063] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0064] Figure 1 This is a schematic diagram illustrating the calculation step length of the method for calculating the curvature and bending moment of sheet piles according to an embodiment of the present invention.

[0065] Figure 2 This is a monitoring layout diagram of the first layer of support for pier No. 6 according to an embodiment of the present invention;

[0066] Figure 3 This is an elevation-displacement curve diagram of pile 6NA185 according to an embodiment of the present invention;

[0067] Figure 4 The elevation-curvature diagram of pile 6NA185 is obtained by fitting a calculation step size of 0.5m in this embodiment of the invention.

[0068] Figure 5 The elevation-curvature diagram of pile 6NA185 is obtained by fitting a calculation step size of 1.5m in this embodiment of the invention. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages disclosed in the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments in this application without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0070] It should be noted that the terms “comprising” and “having”, and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such processes, methods, products, or devices.

[0071] Similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0072] In the description of this invention, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the product of this invention is usually placed when in use. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0073] In the description of this invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," and "connect" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0074] Example:

[0075] The present invention discloses a method for calculating the curvature and bending moment of a steel sheet pile. Based on the readings of an inclinometer on the entire section of the steel sheet pile, the curvature and bending moment of the corresponding cross-section are deduced from the displacement of the steel sheet pile. The method includes the following steps:

[0076] S1: Observation points are arranged along the transverse and longitudinal directions of the steel sheet pile, and the inclinometer tube is fixed on the steel sheet pile. During the test, the inclinometer probe is inserted into the inclinometer tube and slides down along the depth direction to obtain displacement data and lateral displacement data at each elevation of all monitored piles.

[0077] The horizontal direction is perpendicular to the length of the pile, and the longitudinal direction is parallel to the length of the pile. The inclinometer tube is fixed to the sheet pile to ensure that the deformation of the inclinometer tube is synchronized with that of the sheet pile, so as to truly reflect the deflection of the support structure.

[0078] S2: Determine the pile height-curvature data based on the elevation-displacement data of all monitored piles.

[0079] S201: According to mechanics of materials, the curvature of the pile at a certain elevation is represented by the second derivative of the displacement function, and the curvature of the pile cross-section... The calculation expression is as follows:

[0080] ;

[0081] In the formula, express Curvature of the pile cross section at elevation displacement Indicates elevation;

[0082] S202: Second-order three-point derivative calculation;

[0083] Curvature of the pile cross section The calculation expression is discretized using second-order three-point differentiation to eliminate the influence of the remainder term. The calculation expression is as follows:

[0084] ;

[0085] In the formula, Indicates the calculation step size. Indicates the calculation section number. , , They represent the first , , Lateral displacement of the cross section, Indicates the calculation interval , This represents the additional curvature caused by lateral displacement; the additional curvature is the truncation error term.

[0086] The calculation step size is defined as: the perpendicular distance between adjacent sections after the sheet pile is uniformly divided into calculation sections along the depth direction, such as... Figure 1 As shown; specifically, the step size and The step size is inversely proportional to the accuracy of the calculation; that is, the smaller the step size, the higher the calculation accuracy, but the more sensitive the calculation results will be, making it difficult to fit a smooth curve. At the same time, too small a step size will also consume a lot of computing power. Therefore, the step size should be determined based on actual engineering and repeated calculation experiments. The example details the differences in fitting results between the two step size values.

[0087] S203: Curvature rounding error correction;

[0088] The displacement readings of the inclinometer have rounding errors. Based on the worst-case scenario, the curvature is rounded off. ;

[0089] The actual curvature needs to be reduced by rounding error. The calculation expression is as follows:

[0090] ;

[0091] In the formula, Indicates the actual curvature. Indicates the curvature of the pile cross section The curvature is calculated from the discretized expression after second-order three-point differentiation.

[0092] S3: Based on the elevation-curvature data of all monitored piles, draw an elevation-curvature curve; combine the elevation-displacement data obtained in step S1 with the elevation-curvature correspondence calculated in step S2, draw a pile height-curvature diagram to intuitively reflect the curvature distribution characteristics of the entire pile body.

[0093] S4: Determine the bending moment of the pile cross section based on the elevation-displacement data of all monitored piles.

[0094] S401: Based on mechanics of materials, the relationship between bending moment and displacement is realized, and the bending moment of the pile cross-section is calculated. The calculation expression is as follows:

[0095] ;

[0096] In the formula, express Bending moment at elevation, This indicates the bending stiffness of the sheet pile, where This represents the elastic modulus of the steel sheet pile. Represents the moment of inertia of the cross section;

[0097] S402: Based on mechanics of materials, this establishes a correlation between lateral pressure and bending moment, where lateral pressure... The calculation expression is as follows:

[0098] ;

[0099] In the formula, express Lateral pressure at elevation;

[0100] Lateral pressure includes active earth pressure, water pressure, and temporary additional loads on the outside of the foundation pit. The values ​​should be determined in conjunction with the soil unit weight and internal friction angle in the survey report, and calculated in accordance with the "Technical Specification for Foundation Pit Support" (JGJ120-2012).

[0101] S403: Discretization calculation of bending moment:

[0102] Combined with the curvature of the pile cross section The expression for calculating the lateral pressure is obtained after discretization using the second-order three-point derivative. Substituting the calculation expression into the second-order three-point derivative formula, we obtain the bending moment calculation formula as follows:

[0103] ;

[0104] In the formula, Indicates elevation Bending moment at section, This represents the additional bending moment generated by lateral pressure.

[0105] The additional bending moment, also known as the cutoff error term, has a larger error at the location of concentrated force; the cutoff error is related to the step size. They are directly proportional; the smaller the step size, the smaller the error.

[0106] S404: Moment rounding error correction;

[0107] Moment rounding error The actual bending moment calculation formula is as follows:

[0108] ;

[0109] In the formula, Indicates the actual bending moment. Indicates the bending moment in step S403. The bending moment is calculated using the formula.

[0110] This invention discloses a method for evaluating the stability of sheet piles. It uses the principle of equal curvature to inversely deduce the design allowable bending moment of the pile wall, calculates the design allowable curvature based on the design bending moment of the sheet pile body, and evaluates the safety of the support structure by comparing the actual curvature with the design allowable curvature and the actual bending moment with the design allowable bending moment. This evaluation serves as a basis for on-site monitoring and early warning, and is embedded into the overall evaluation system of current Chinese standards. Specifically, it includes the following steps:

[0111] S01: Determine the allowable bending moment of the reduced pile wall design according to the principle of equal curvature;

[0112] The joints of sheet piles are controlled by friction. When subjected to bending, the overall stiffness is between that of a single pile and a rigid pile wall (a pile wall is made up of several single sheet piles spliced ​​together, both of which are sheet piles). Based on the inversion results of multi-project measured data, the stiffness of a single sheet pile is calculated by reducing the stiffness of a composite pile wall by 50%.

[0113] S02: Calculate the design allowable curvature based on the reduced design allowable bending moment;

[0114] Reduced allowable bending moment for pile wall design Based on the principle of constant curvature, the calculation expression is as follows:

[0115] ;

[0116] In the formula, This represents the maximum design bending moment value of a single pile. This indicates the allowable bending moment value for the pile wall design after reduction. Indicates the stiffness of a single pile. Indicates the stiffness of the pile wall after reduction;

[0117] Calculate the allowable curvature of the sheet pile based on the design bending moment of a single sheet pile. The calculation expression is as follows:

[0118] ;

[0119] S03: Evaluate the stability of the sheet pile by comparing the actual curvature of the sheet pile body with the allowable curvature of the design and the actual bending moment with the allowable bending moment of the design.

[0120] Based on the calculated actual curvature of the pile body Compared to the allowable curvature of the pile body design Based on the calculated actual bending moment of the pile body Compared with the allowable bending moment of the pile wall design Determine whether the sheet pile support structure is safe:

[0121] when , At that time, the steel sheet pile support structure was assessed as safe;

[0122] when , At that time, the steel sheet pile support structure was assessed as unsafe, and a danger warning was issued;

[0123] when , Or when , At the same time, strengthen monitoring and reinforcement.

[0124] This example illustrates a deep foundation pit steel sheet pile cofferdam project for pier No. 6 of a bridge in a certain city. The pier cap dimensions are 34.7m × 48.3m × 6.0m (longitudinal to bridge height). FSP type IV steel sheet piles are used, and the parameter data are shown in Table 1. Each pile is 12m long, and they are spliced ​​together to form a 24m long pile, which is driven in using a 90kW vibratory hammer. The cofferdam is equipped with four layers of steel supports, and the maximum head difference between the inside and outside of the cofferdam is about 10m.

[0125] Three observation points are set up on each side of the cofferdam along the transverse direction of the bridge, and one observation point is set up at the midpoint of each side along the longitudinal direction of the bridge, for a total of 8 observation points for a single cofferdam and 16 observation points for the entire project. Figure 2 As shown. Initial data was taken before pumping water out of the cofferdam; monitoring was conducted every 1-3 days before dismantling, with daily monitoring during the pumping phase to the lowest water level and every 3 days during the remaining phases, and more frequent monitoring in case of abnormalities. A high-precision inclinometer was used, with a reading accuracy of 0.1 mm, and a calculation step size of 1.5 m.

[0126] Table 1 Key parameters of FSP Type IV steel sheet piles

[0127]

[0128] In Table 1:

[0129] The This indicates the allowable stress in the pile design. Indicates the stiffness of the pile wall;

[0130] Based on the inclinometer readings of the sheet piles, the elevation-displacement curve of the piles was determined and plotted; taking pile 6NA185 as an example, the elevation-displacement curve diagram is as follows. Figure 3 As shown;

[0131] Based on the pile height-displacement curve, determine the corresponding curvature and bending moment of the pile body. Taking pile 6NA185 as an example, draw the elevation-curvature diagram.

[0132] In determining the corresponding curvature of the pile body, the smaller the step size, the higher the calculation accuracy. Since the step size of the inclinometer is 0.5m during the inclinometer measurement process, the initial step size is also 0.5m when calculating the curvature. The fitting result is as follows: Figure 4 As shown in the image, a step size that is too small will lead to sensitive calculation results, resulting in more noise in the fitted curve and making it difficult to provide reliable data support for subsequent stability evaluation. Therefore, after repeated verification, a step size of 1.5m was chosen, and the fitting result is as follows. Figure 5 As shown, the fitted curve is smooth and has prominent features, which meets the needs of engineering practice;

[0133] Based on the pile displacement and bending moment of the monitored piles, the extreme values ​​of displacement and bending moment for pier No. 6 under the corresponding working conditions were determined; the extreme values ​​of sheet pile displacement and bending moment for each working condition are summarized in Table 2.

[0134] Table 2 Monitoring Results of Steel Sheet Piles

[0135]

[0136] The corresponding operating condition includes the following steps:

[0137] 1) Drive steel sheet piles and close them;

[0138] 2) Drive in the uprights and install the first layer of horizontal supports (+5.50m);

[0139] 3) Install the second layer of horizontal supports (+3.40m), and pump water to +1.10m;

[0140] 4) Install the third layer of horizontal support (+1.60m), and pump water to -0.70m;

[0141] 5) Install the fourth layer of horizontal support (-0.20m), and pump water to -2.54m;

[0142] 6) Three layers of round timber with a diameter greater than 100mm are installed between every two sheet piles to replace the fourth layer of support;

[0143] 7) Remove the fourth layer of horizontal supports.

[0144] S4: Determine whether the sheet pile is safe based on the above parameters;

[0145] The sheet piles referred to are all the monitored sheet piles, and the determination includes the following steps:

[0146] S401: Based on the design value of the bending moment of a single pile, taking pile 6NA185 as an example, determine the allowable curvature.

[0147] Design allows for curvature ;

[0148] S402: Determine the design value of bending moment based on the sheet pile parameters;

[0149] Reduced pile wall stiffness ;

[0150] Design value of reduced pile wall bending moment ;

[0151] S403: Determine the stability of pile 6NA185 based on its displacement and curvature extreme values. The displacement and curvature extreme values ​​are shown in Table 3.

[0152] Table 3. Extreme values ​​of displacement and curvature of pile 6NA185;

[0153]

[0154]

[0155] In this embodiment, the monitoring period was three months, with a total of 51 inclination measurements conducted. Specifically for pile 6NA185, three large displacement events were predicted in a timely manner. By adjusting the preload of the steel support and slowing down the pumping speed, the displacements were all controlled within 300mm. The maximum measured bending moment was located in the support structure at an elevation of 1.7m under working condition 1, which was less than the design allowable bending moment for FSP IV type steel sheet piles, and the section strength met the requirements. The monitoring data showed a high degree of matching with the construction conditions, verifying the scientific validity and practicality of the method of this invention.

[0156] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for calculating the curvature and bending moment of a steel sheet pile, characterized in that, Includes the following steps: S1: Observation points are arranged along the transverse and longitudinal directions of the steel sheet pile, and the inclinometer tube is fixed on the steel sheet pile. During the test, the inclinometer probe is inserted into the inclinometer tube and slides down along the depth direction to obtain displacement data and lateral displacement data at each elevation of all monitored piles. S2: Determine the pile height-curvature data based on the elevation-displacement data of all monitored piles; S3: Based on the elevation-curvature data of all monitored piles, plot the elevation-curvature curve. S4: Determine the bending moment of the pile cross section based on the elevation-displacement data of all monitored piles; The transverse direction is perpendicular to the length of the pile, and the longitudinal direction is parallel to the length of the pile; the inclinometer tube is fixed to the sheet pile so that the deformation of the inclinometer tube is synchronized with that of the sheet pile, reflecting the deflection of the support structure. S2 includes the following steps: S201: According to mechanics of materials, the curvature of the pile at a certain elevation is represented by the second derivative of the displacement function, and the curvature of the pile cross-section... The calculation expression is as follows: ； In the formula, express Curvature of the pile cross section at elevation displacement Indicates elevation; S202: Second-order three-point derivative calculation; Curvature of the pile cross section The calculation expression is discretized using second-order three-point differentiation, and the calculation expression is as follows: ； In the formula, Indicates the calculation step size. Indicates the calculation section number, , , They represent the first , , Lateral displacement of the cross section Indicates the calculation interval , This represents the additional curvature caused by lateral displacement; the additional curvature is the truncation error term. The calculation step size is defined as: the vertical distance between adjacent sections after the sheet pile is uniformly divided into calculation sections along the depth direction; S203: Curvature rounding error correction; The displacement readings of the inclinometer have rounding errors. Based on the worst-case scenario, the curvature is rounded off. ; The expression for calculating the actual curvature after deducting rounding errors is as follows: ； In the formula, Indicates the actual curvature. Indicates the curvature of the pile cross section Curvature calculated from the expression after discretization by second-order three-point differentiation; In S3, the elevation-displacement data obtained in step S1 and the elevation-curvature correspondence calculated in step S2 are combined to draw a pile height-curvature diagram, reflecting the curvature distribution characteristics of the entire pile body.

2. The method for calculating the curvature and bending moment of sheet piles according to claim 1, characterized in that, S4 includes the following steps: S401: Based on mechanics of materials, the relationship between bending moment and displacement is realized, and the bending moment of the pile cross-section is calculated. The calculation expression is as follows: ； In the formula, express Bending moment at elevation, This indicates the bending stiffness of the sheet pile, where This represents the elastic modulus of the steel sheet pile. Represents the moment of inertia of the cross section; S402: Based on mechanics of materials, this establishes a correlation between lateral pressure and bending moment, where lateral pressure... The calculation expression is as follows: ； In the formula, express Lateral pressure at elevation; S403: Discretization calculation of bending moment: Combined with the curvature of the pile cross section The expression for calculating the lateral pressure is obtained after discretization using the second-order three-point derivative. Substituting the calculation expression into the second-order three-point derivative formula, we obtain the bending moment calculation formula as follows: ； In the formula, Indicates elevation Bending moment at section, This represents the additional bending moment generated by lateral pressure. The additional bending moment is the cutoff error term, and the cutoff error is related to the step size. Proportional; S404: Moment rounding error correction; Moment rounding error The actual bending moment calculation formula is as follows: ； In the formula, Indicates the actual bending moment. Indicates the bending moment in step S403. The bending moment is calculated using the formula.

3. The method for calculating the curvature and bending moment of sheet piles according to claim 2, characterized in that, In S402, lateral pressure includes active earth pressure outside the foundation pit, water pressure, and temporary additional loads during construction.

4. A method for evaluating the stability of sheet piles, employing the method for calculating the curvature and bending moment of the sheet pile body as described in any one of claims 1-3, characterized in that, Includes the following steps: S01: Determine the allowable bending moment of the reduced pile wall design according to the principle of equal curvature; S02: Calculate the design allowable curvature based on the reduced design allowable bending moment; S03: Evaluate the stability of the sheet pile by comparing the actual curvature of the sheet pile body with the allowable curvature of the design and the actual bending moment with the allowable bending moment of the design.

5. The method for evaluating the stability of sheet piles according to claim 4, characterized in that, Based on the inversion results of measured data from multiple projects, the stiffness of a single sheet pile is calculated by reducing the stiffness of the composite pile wall by 50%.

6. The method for evaluating the stability of sheet piles according to claim 5, characterized in that, In S02, the allowable bending moment for the reduced pile wall design is... Based on the principle of constant curvature, the calculation expression is as follows: ； In the formula, This represents the maximum design bending moment value of a single pile. This indicates the allowable bending moment value for the pile wall design after reduction. Indicates the stiffness of a single pile. Indicates the stiffness of the pile wall after reduction; Calculate the allowable curvature of the sheet pile based on the design bending moment of a single sheet pile. The calculation expression is as follows: 。 7. The method for evaluating the stability of sheet piles according to claim 6, characterized in that, In S03, the stability evaluation of sheet piles is as follows: Based on the calculated actual curvature of the pile body Compared to the allowable curvature of the pile body design Based on the calculated actual bending moment of the pile body Compared with the allowable bending moment of the pile wall design Determine whether the sheet pile support structure is safe: when , At that time, the steel sheet pile support structure was assessed as safe; when , At that time, the steel sheet pile support structure was assessed as unsafe, and a danger warning was issued; when , Or when , At the same time, strengthen monitoring and reinforcement.

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