A calculation method for the horizontal displacement of a pile based on fiber optic sensing

Abstract

The present invention discloses a method for calculating the horizontal displacement of a pile based on fiber optic sensing, comprising the following steps: Step 1: By arranging two parallel fiber optic sensor lines with multiple equally spaced nodes on the pile and setting fiber optic sensors at each equally spaced node, the measured axial strain data at different equally spaced nodes of the pile is obtained; Step 2: Based on the relationship between difference and derivative, the matrix relationship between axial strain and the horizontal displacement of the pile is obtained; Step 3: According to the force condition at the bottom of the retaining pile, the boundary conditions are determined; Step 4: The boundary conditions obtained in Step 3 are applied to the matrix relationship between axial strain and the horizontal displacement of the pile obtained in Step 2, and the axial strain is transformed into the horizontal displacement through inverse transformation; With this method, the present invention can quickly obtain the pile displacement value, which is convenient for engineering personnel to judge the deformation degree of the pile. The adopted assumption conditions are consistent with the actual situation, the implementation process is simple and easy, and the operability is strong, ensuring the safe construction of the project.

Description

Technical Field

[0001] Embodiments of the present invention belong to the field of geotechnical engineering. More specifically, the present invention relates to a method for calculating the horizontal displacement of a pile based on fiber optic sensing technology. Background Art

[0002] As an important part of the engineering monitoring system, the sensing and monitoring technology provides support and guarantee for collecting and obtaining accurate and reliable basic data such as formation, structural deformation, and stress during the engineering construction process. During the construction process of underground engineering, risk accidents often occur suddenly. However, traditional monitoring means are time-consuming and laborious, affected by environmental factors, and have a large amount of human interference, making it difficult to meet the technical requirements of dynamic and continuous construction in geotechnical engineering. Therefore, there is a great need to adopt some new sensing technologies and methods to make up for these deficiencies to meet the requirements of dynamic and continuous construction in geotechnical engineering.

[0003] Advanced fiber optic sensing technology has the advantages of strong anti-interference ability, high precision, good stability, waterproof and moisture-proof, long durability, easy installation, the ability to realize long-distance and large-range surface monitoring, and good integratability. It has gradually become a new means for the health and safety monitoring of civil engineering and can well make up for the deficiencies of traditional monitoring technologies. Introducing fiber optic sensing technology into the construction monitoring of geotechnical engineering provides accurate and reliable monitoring data for the dynamic risk assessment of geotechnical engineering, timely feedback, and guidance for construction, thus ensuring the safe, economical, and effective implementation of geotechnical engineering construction, which is of great significance.

[0004] During the process of foundation pit excavation and unloading, the supporting structure will deform under the action of the lateral pressure of the surrounding soil, and the magnitude of its deformation is related to the safety of the supporting structure and the overall stability of the foundation pit. As the main monitoring item for the construction monitoring of the foundation pit, the value of the horizontal displacement of the pile changes with the excavation of the foundation pit and is an important indicator for inspecting the safety status of the retaining structure. Therefore, the horizontal displacement of the pile can be monitored by installing a fiber Bragg grating sensing array in the foundation pit retaining pile. However, during the monitoring process, what the fiber Bragg grating sensor senses is the axial strain at a certain point, and what is actually required in the actual monitoring is the horizontal displacement value. Therefore, a calculation method is needed to realize the conversion from the fiber axial strain to the horizontal displacement of the pile. Summary of the Invention

[0005] Aiming at the above defects or improvement requirements of the prior art, the purpose of the present invention is to provide a calculation method for converting the axial strain obtained by fiber optic sensing technology into the horizontal displacement of a pile.

[0006] To achieve the above object, the present invention relates to: a method for calculating the horizontal displacement of a pile based on fiber optic sensing, including the following steps:

[0007] Step 1: By arranging two parallel optical fiber sensor lines with multiple equally spaced nodes on the pile body, and setting optical fiber sensors at each equally spaced node, the measured axial strain data at different equally spaced nodes of the pile body is obtained;

[0008] Step 2: According to the relationship between difference and derivative, the matrix relationship between axial strain and horizontal displacement of the pile body is obtained;

[0009] Step 3: According to the force condition at the bottom of the retaining pile, the boundary conditions are determined;

[0010] Step 4: Apply the boundary conditions obtained in Step 3 to the matrix relationship between axial strain and horizontal displacement of the pile body obtained in Step 2, and convert the axial strain into horizontal displacement through inverse transformation.

[0011] Furthermore, the optical fiber sensor is an optical fiber Bragg grating sensor.

[0012] Furthermore, Step 2 includes the following steps:

[0013] Step 2.1. Set the step length of equally spaced nodes on the optical fiber sensor line as h, and obtain the first-order, second-order, and n-order forward differences corresponding to different positions. The relationship between difference and derivative is as shown in Equation 1;

[0014] Δ n f k =h n f (n) (ξ), where ξ ∈ (x k , x k+1 ) (1)

[0015] Step 2.2. According to Equation 1, there is Δ 2 f=h 2 f”(ξ), and the expansion is shown in Equation 2;

[0016]

[0017] Step 2.3. Transform Equation 2 to obtain the relationship expression between the horizontal displacement and strain of the pile body as,

[0018]

[0019] Step 2.4. Express Equation 3 in matrix form:

[0020]

[0021] In the formula: x k is the coordinate corresponding to the position of the equally spaced node, k = 0, 1, 2,..., n;

[0022] f x , f x+h—Deflection value of the fixed end, f x+ih (i = 2, 3, 4, …, (n + 1));

[0023] n—Number of sensors;

[0024] h—Distance between adjacent sensors, i.e., equal - distance node step size;

[0025] d—Distance between sensors at the same horizontal position on two measuring lines;

[0026] ε ai , ε bi —Strain value monitored by the i - th fiber optic sensor starting from the bottom of the pile, i = 1 ~ n.

[0027] Furthermore, the specific method for clarifying the boundary conditions in step 3 according to the stress condition at the bottom of the retaining pile is as follows:

[0028] In actual engineering, the bottom of the retaining pile will be embedded in the bedrock, so the contact between the pile body and the bedrock can be understood as rigid, that is, the displacement and rotation angle at the pile end are both 0, and the retaining pile can be simplified into a cantilever beam structure; this is boundary condition one;

[0029] Assume the starting point coordinate x = 0, and the bottom of the retaining pile is a fixed end. There is a grating virtual point at the same fiber Bragg grating layout spacing along the bottom direction of the retaining pile, and the corresponding displacement can also be regarded as 0. In this way, assume the displacement at the starting point f 0 is the displacement at the virtual point, then f h is the deflection value of the fixed end of the retaining pile; Therefore, there is f 0 = f h = 0, this is boundary condition two.

[0030] Furthermore, step 4 includes the following steps:

[0031] Step 4.1. Combining the boundary conditions obtained in step 4, the first and second columns in formula 4 can be ignored and rewritten in the following form:

[0032]

[0033] Step 4.2. The coefficient matrix of formula (5) is a square invertible matrix. Through inverse transformation, the axial strain can be converted into horizontal displacement, as shown in formula 6:

[0034]

[0035] Finally, by solving formula 6, the horizontal displacements corresponding to different positions of the pile body can be obtained.

[0036] Generally speaking, compared with the prior art, the above - mentioned technical solution conceived by the present invention can achieve the following beneficial effects:

[0037] (1) The method for calculating the horizontal displacement of a pile based on fiber optic sensing of the present invention adopts assumption conditions consistent with the actual situation, and the implementation process is simple and easy to operate with strong operability;

[0038] (2) The method for calculating the horizontal displacement of a pile based on fiber optic sensing of the present invention can quickly obtain the displacement value of the pile, which is convenient for engineers to judge the deformation degree of the pile and ensure the safe construction of the project. Description of the Drawings

[0039] Figure 1 is a schematic diagram of the layout of pile fiber optic sensors in a preferred embodiment of the present invention;

[0040] Figure 2 is Figure 1 the schematic cross-sectional structure diagram of A-A;

[0041] Figure 3 is a schematic diagram of the deflection curve in a preferred embodiment of the present invention; Detailed Embodiment

[0042] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0043] Please refer to Figure 1 - Figure 2 , which specifically relates to a method for calculating the horizontal displacement of a pile based on fiber optic sensing, including the following steps:

[0044] Step 1: Use fiber optic sensors to arrange two symmetrically centered measuring lines a and b in the pile, and measure the axial strain ε of each point by the measuring lines a and b a , ε b . The schematic diagram of the deflection curve is shown in the appendix Figure 3 . In the figure, FBG is the abbreviation of the fiber optic sensor, a and b are the two fiber optic sensor measuring lines respectively, P is any point on the central axis of the pile, u is the deflection value corresponding to point P, and α is the inclination angle of any point on the deflection curve.

[0045] Step 2: Take the step size of equidistant nodes as h, then x k = x 0 + kh (k = 0, 1, 2,..., n) (x k is the coordinate corresponding to the fiber optic sensing measurement point position). Assume that the function value at the x k point is f k = f(x k ), and call Δf k = fk+1 -f k is the first-order forward difference of x with step size h; similarly, Δ k f 2 f k =Δf k+1 -Δf k is the second-order difference at x k . Generally, Δ n f k =Δ n-1 f k+1 -Δ n-1 f k is the nth-order difference at x k . There is also the following relationship between the difference and the derivative:

[0046] Δ n f k =h n f (n) (ξ), where ξ ∈ (x k , x k+1 ) (1)

[0047] Therefore, Δ 2 f = h 2 f”(ξ), that is

[0048]

[0049] Therefore, the expression for the relationship between the horizontal displacement and strain of the pile body is

[0050]

[0051] The above equation can be expressed in matrix form

[0052]

[0053] In the formula: f x , f x+h —deflection values at the fixed end, f x+ih (i = 2, 3, 4, …, (n + 1));

[0054] n—the number of sensors;

[0055] h—the distance between adjacent sensors;

[0056] d—the distance between sensors at the same horizontal position on two measuring lines;

[0057] ε ai , ε bi —strain values measured by the ith fiber Bragg grating sensor starting from the pile bottom, i = 1 to n.

[0058] Step 3: Define the boundary conditions. To solve Equation 4 and obtain the horizontal displacement values at different positions of different pile bodies, it is necessary to define the boundary conditions required for calculating Equation 4, and at least two boundary conditions are needed. In actual engineering, the bottom of the retaining pile is generally embedded in the bedrock to a certain depth, so the contact between the pile body and the bedrock can be understood as rigid, that is, the displacement and rotation angle at the pile tip are both 0, and the retaining pile can be simplified into a cantilever beam structure. This is the first boundary condition.

[0059] Step 4: Make the following assumptions: Assume that x = 0, and the bottom of the retaining pile is a fixed end. There is a virtual grating point at the same fiber Bragg grating layout spacing along the bottom direction of the retaining pile, and the corresponding displacement can also be regarded as 0. In this way, assume that the starting point f 0 is the displacement at the virtual point, then f h is the displacement value at the fixed end of the retaining pile. Therefore, there is f 0 = f h = 0, this is the second boundary condition.

[0060] Step 5: Combine the boundary conditions obtained in Steps 3 and 4, then the first and second columns in Equation 4 can be ignored and rewritten in the following form:

[0061]

[0062] The coefficient matrix of the above formula is a square matrix and invertible. Through inverse transformation, the axial strain can be transformed into horizontal displacement, as shown in Equation 6:

[0063]

[0064] Finally, by solving Equation 6, the horizontal displacements corresponding to different positions of the pile body can be obtained.

[0065] Through this method, the displacement value of the pile body can be quickly obtained, which is convenient for engineers to judge the deformation degree of the pile body, ensure the safe construction of the project, and improve the construction quality and safety.

[0066] It is easy for those skilled in the art to understand that the above is only a preferred embodiment of the present invention and is not used to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for calculating the horizontal displacement of a pile based on fiber optic sensing, characterized in that, it includes the following steps: Step 1: By arranging two parallel fiber optic sensor lines with multiple equally spaced nodes on the pile, and setting fiber optic sensors at each equally spaced node, the measured axial strain data at different equally spaced nodes of the pile is obtained; Step 2: According to the relationship between difference and derivative, the matrix relationship between axial strain and pile horizontal displacement is obtained; Step 3: According to the force condition at the bottom of the retaining pile, the boundary conditions are determined; Step 4: Apply the boundary conditions obtained in Step 3 to the matrix relationship between axial strain and pile horizontal displacement obtained in Step 2, and convert the axial strain into horizontal displacement through inverse transformation; The said Step 2 includes the following steps: Step 2.

1. Set the step size of equally spaced nodes on the fiber optic sensor line as h, and calculate the first-order, second-order, and n-order forward differences corresponding to different positions. The relationship between difference and derivative is as shown in Equation (1); Δ n f k = h n f (n) (ξ), where ξ ∈ (x k , x k+1 ) (1) Step 2.

2. According to Equation (1), there is Δ 2 fk = h 2 f′(ξ), and the expansion is shown in Equation (2); Step 2.

3. Transform Equation (2). Two symmetrically arranged measuring lines a and b are laid out in the pile using fiber optic sensors, and the axial strain ε at each point is measured by the measuring lines a and b a , ε b , that is, the axial strain at each point on the measuring line a is ε a , and the axial strain at each point on the measuring line ε b is ε b ; Obtain the relationship expression between the horizontal displacement and strain of the pile as, Step 2.

4. Express Equation (3) in matrix form: where: x k is the coordinate of the equally spaced node k, where k = 0, 1, 2, …, n; f k , f k+ih — displacement values at point k and point k + ih, where i = 1, 2, 3, 4, …, (n + 1); n—the number of sensors; h—the distance between adjacent sensors, that is, the step size of equally spaced nodes; d—the distance between sensors at the same horizontal position on the two sensor lines; ε ai , ε bi — are the strain values monitored by the i-th fiber optic sensor starting from the bottom of the pile for the measuring lines a and b respectively, where i = 1, 2, 3, 4, …, n; f k is the function value at point k; Δ n f k = Δ n-1 f k+1 - Δ n-1 f k is the n-th order difference at point k; f(ξ) is the function value at point ξ, where point ξ is any point between x k and x k+1 any point between them.

2. The method for calculating the horizontal displacement of a pile based on fiber optic sensing according to claim 1, characterized in that , the fiber optic sensor is a fiber Bragg grating sensor.

3. The method for calculating the horizontal displacement of a pile based on fiber optic sensing according to claim 1, characterized in that , the specific method for determining the boundary conditions in Step 3 according to the force condition at the bottom of the retaining pile is: In actual engineering, the bottom of the retaining pile will be embedded in the bedrock, so the contact between the pile and the bedrock can be understood as rigid, that is, the displacement and rotation angle at the pile end are both 0, and the retaining pile can be simplified into a cantilever beam structure; this is the first boundary condition; Assume that the starting point coordinate x = 0, and the bottom of the retaining pile is a fixed end. There is a grating virtual point at the same fiber Bragg grating layout spacing along the bottom direction of the retaining pile, and the corresponding displacement can also be regarded as 0. In this way, assume the starting point f 0 is the displacement at the virtual point, then f h is the displacement value of the fixed end of the retaining pile; therefore, there is f 0 = f h = 0, which is the second boundary condition.

4. The method for calculating the horizontal displacement of a pile based on fiber optic sensing according to claim 1, characterized in that , the said Step 4 includes the following steps: Step 4.

1. Combining the boundary conditions obtained in Step 4, the first and second columns in Equation (4) can be ignored and rewritten in the following form: Step 4.

2. The coefficient matrix of Equation (5) is a square invertible matrix, and the axial strain can be converted into horizontal displacement through inverse transformation, as shown in Equation (6): Finally, by solving Equation (6), the horizontal displacements corresponding to different positions of the pile can be obtained.

Images