A method for measuring stress under steel strand anchor based on ultrasonic reflection coefficient

Abstract

The present invention discloses a method for measuring stress under a steel strand anchor based on ultrasonic reflection coefficient, which belongs to the technical field of steel strand stress detection. The method comprises the following steps: installing an ultrasonic detection device on the non-contact interface between the anchor plate and the anchor pad, exciting ultrasonic waves with the ultrasonic detection device to measure the transmitted wave, using the reflected signal of the stress-free and contact-free anchor plate as the incident signal, using the fundamental frequency amplitude of the reflected signal after the anchor plate and the anchor pad contact as the reflected signal, and calculating the first-order interface stiffness K1 between the anchor pad and the anchor plate according to a preset algorithm. A power function model is used between the interface contact stiffness and the contact force, and the effective stress P0 between the anchor plate and the anchor pad is calculated according to a preset algorithm. The present invention only needs to use an ultrasonic method to measure the ultrasonic reflection coefficient between the anchor and the anchor pad on the actual prestressed beam. According to the relationship between the calibrated reflection coefficient and the interface contact force, the effective stress under the anchor can be measured.

Description

Technical Field

[0001] The invention belongs to the technical field of steel strand stress detection, and in particular relates to a method for measuring stress under a steel strand anchor based on ultrasonic reflection coefficient. Background Art

[0002] Prestressed structural systems and cable-bearing structural systems are the structural forms currently relied upon by large-span beam bridges, arch bridges, cable-stayed bridges, and suspension bridges. During the long-term service of bridges, degradation of structural performance due to material degradation, environmental erosion, shrinkage creep, load disturbances, and the like is inevitable. Monitoring the true stress state of key load-bearing components such as prestressed steel strands and cables is a key basis for evaluating bridge safety and durability. Currently, the accuracy of the vibration frequency-based measurement method for long cables can meet engineering requirements. However, the accuracy of short cable force measurement is low due to the influence of multiple factors such as the boundary conditions and bending stiffness of the cables. Even more difficult is the lack of an effective method for monitoring the prestress of the steel strands of prestressed beam bridges.

[0003] Both parallel steel cables and stranded steel cables are designed to withstand axial tension. The cable force is ultimately transmitted through anchor plates at each end to anchor pads embedded in the beam. The anchor pads then transmit the force to the beam, supporting its own weight and various vehicle loads. Therefore, a new research approach is needed to monitor cable force changes by measuring the contact force between the anchor plates and the pads within the cable anchoring system. This contact force provides a more direct estimate of the actual forces acting on the beam than the cable force. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to provide a stress measurement method under the steel strand anchor based on the ultrasonic reflection coefficient. In order to propose a new research idea, the cable force change is monitored by measuring the contact force between the anchor plate and the anchor pad in the cable anchoring system, so as to more directly reflect the evaluation value of the actual force acting on the beam.

[0005] In order to achieve the above object, the present invention provides the following technical solutions:

[0006] The present invention provides a method for measuring stress under a steel strand anchor based on ultrasonic reflection coefficient, comprising the following steps:

[0007] S1: An ultrasonic detection device is installed on the non-contact interface between the anchor plate and the anchor pad. The ultrasonic detection device excites ultrasonic waves to measure the transmitted wave. The reflected signal of the stress-free and non-contact anchor plate is used as the incident signal, and the fundamental frequency amplitude of the reflected signal after the anchor plate and the anchor pad contact is used as the reflected signal. The first-order interface stiffness K1 between the anchor pad and the anchor plate is calculated by the following formula:

[0008]

[0009] Where Z1 and Z2 are the acoustic impedances of anchor plate 3 and anchor pad 1, respectively, |R| is the reflection coefficient, and ω is the angular frequency.

[0010] S2: The following power function model is used between the interface contact stiffness and the contact force to calculate the effective stress P0 between the anchor plate 3 and the anchor pad 1:

[0011]

[0012] Where C and m are constants related to the material.

[0013] Furthermore, by Taylor expanding the contact force function P(h) of the interface to the second order at h=h0, we can obtain:

[0014] P(h)=P0-K1(h-h0)+K2(h-h0) 2

[0015] And the effective stress P0 between the anchor plate 3 and the anchor pad 1 is calculated by the power function model between the interface contact stiffness and the contact force in step S2:

[0016]

[0017] Where K2 is the second-order nonlinear stiffness, and C and m are constants related to the material.

[0018] The beneficial effects of the present invention are:

[0019] The present invention only needs to use an ultrasonic method to measure the ultrasonic reflection coefficient between the anchor and the anchor plate on the actual prestressed beam, and the effective stress under the anchor can be measured according to the relationship between the calibrated reflection coefficient and the interface contact force.

[0020] Other advantages, objectives and features of the present invention will be described in the following description and will be apparent to those skilled in the art to some extent, or those skilled in the art can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0022] Figure 1 Schematic diagram of the conversion of the anchor plate-anchor pad contact interface into a two-dimensional contact interface model in an embodiment of the present invention;

[0023] Figure 2 Schematic diagram of the relationship between reflection coefficient and stress in an embodiment of the present invention, DETAILED DESCRIPTION

[0024] like Figures 1-2 As shown, the present invention provides a method for measuring stress under a steel strand anchor based on ultrasonic reflection coefficient, comprising the following steps:

[0025] Before the trial begins:

[0026] A steel strand is passed through the center hole of the anchoring system formed by connecting the anchor plate 3 and the anchor pad 1 and anchored with a clip. A tension load is applied to the anchor plate 3 by a hydraulic jack, so that an under-anchor contact force is generated between the anchor plate 3 and the anchor pad 1.

[0027] Before the test began, the hydraulic jack applied a pre-tensioning load of 1.4KN, and then gradually loaded the load from 26.4KN to 184.7KN. The loading process is shown in Table 1 below:

[0028] Table 1 Load level settings

[0029]

[0030] Experimental implementation phase:

[0031] In the first step, an ultrasonic detection device is installed on the non-contact interface between the anchor plate 3 and the anchor pad 1. The ultrasonic detection device is used to excite ultrasonic waves and measure the reflected waves. The reflected signal of the stress-free and non-contact anchor plate is used as the incident signal, and the fundamental frequency amplitude of the reflected signal after the anchor plate 3 and the anchor pad 1 are used as the reflected signal. The first-order interface stiffness K1 between the anchor pad 1 and the anchor plate 3 is calculated using the following formula:

[0032]

[0033] Where Z1 and Z2 are the acoustic impedances of anchor plate 3 and anchor pad 1, respectively, |R| is the reflection coefficient, and ω is the angular frequency.

[0034] The ultrasonic detection device includes: a signal generator, an excitation sensor, a receiving sensor, a signal collector, and an oscilloscope. The working process of the ultrasonic detection device is: a set of 500kHz, 15-cycle, 10Vp-p sinusoidal pulse signals is manually triggered by the signal generator. After the ultrasonic wave is excited by the excitation sensor, the receiving sensor and the signal collector receive the reflected signal as the incident wave for calculating the reflection coefficient. The center frequency of the excitation sensor is 500KHz, and the receiving sensor uses a broadband sensor with a frequency response range of 100KHz-1000KHz.

[0035] In the implementation process, the anchor contact interface is simplified into a two-dimensional contact interface model. Assuming that the displacement and stress on the contact interface are continuous, the first-order contact stiffness K1 between the anchor plate 1 and the anchor plate 3 is expressed by the following formula:

[0036] K1=-dP0 / dh

[0037] Where P0 is the nominal contact stress between the anchor plate and the anchor pad, h is the displacement between adjacent surfaces, and d is the derivative sign;

[0038] Assuming that the contact interface between anchor plate 1 and anchor plate 3 can transmit transient stress, and that both anchor plate 1 and anchor plate 3 are made of ideal elastic medium, the displacement field of incident acoustic wave U0 and the displacement field of reflected wave U can be determined by the following formula: R and the transmitted wave displacement field U T :

[0039] U0=exp{iω(tx / c1)}

[0040] U R =Rexp{iω(t+x / c1)}

[0041] U T =Texp{iω(tx / c2)}

[0042] Where R and T are complex coefficients, representing the amplitudes of the reflected wave and the transmitted wave, respectively; C1 and C2 are the wave velocities of the sound wave propagating in anchor plate 1 and anchor plate 3, respectively; i is the imaginary number sign, ω is the angular frequency, t is the propagation time of the ultrasonic wave, and x is the propagation distance of the ultrasonic wave.

[0043] Then, the displacement fields of anchor plate 1 and anchor plate 3 are:

[0044] U1=exp{iω(tx / c1)}+Rexp{iω(t+x / c1)}

[0045] U2=U T

[0046] The interface gap distance h can be expressed as: h = U2(0,t)-U1(0,t)

[0047] If the contact surface spacing increases, the expression becomes positive; the stress fields in anchor plate 1 and anchor plate 3 are:

[0048]

[0049]

[0050] Where Z1 and Z2 are the acoustic impedances of the anchor plate 3 and the anchor pad 1, respectively; E1 and E2 are the elastic moduli of the anchor plate 3 and the anchor pad 1, respectively;

[0051] The relationship between the interface contact stress and contact stiffness is:

[0052] σ=K1h=K1[U2(0,t)-U1(0,t)]=K1(TR-1)exp(iωt)

[0053] Since stress can be transferred instantly from anchor plate 3 to anchor plate 1, the boundary condition is defined as the three stresses σ1, σ2, and σ are equal at the boundary, that is, σ1(0,t)=σ2(0,t)=σ(t)

[0054] According to the above formula, we can get iωZ1(R-1)=-iωZ2T=K1(TR-1)

[0055] The calculation formula for the reflected wave amplitude R is obtained as follows:

[0056] The reflection coefficient R can be expressed as:

[0057] In the second step, the following power function model is used between the interface contact stiffness and the contact force to calculate the effective stress P0 between the anchor plate 3 and the anchor pad 1:

[0058]

[0059] Where C and m are constants related to the material.

[0060] Since the reflection coefficient |R|<1, and the expression under the radical here should be greater than 0, then R 2 (Z1+Z2) 2 -(Z1-Z2) 2 > 0, that is, (Z1-Z2)(Z1+Z2)<R<1. In order to obtain the relationship between the linear stiffness and reflection coefficient of the contact interface in general, the linear stiffness K1 is derived with respect to the reflection coefficient |R| to obtain:

[0061]

[0062] Obviously, (Z1-Z2) 2 -(Z1+Z2) 2 <0, that is, dK1dR<0, so for the contact between the anchor plate 3 and the anchor pad 1, the first-order stiffness of the contact interface decreases with the increase of the reflection coefficient.

[0063] In this scheme, the anchoring system of the strand line 2 and the two-dimensional contact interface model are as follows: Figure 1As shown, the anchor plate 1 is embedded in the concrete beam, and the steel strand 2 is connected to the anchor plate 3 through a conical clip. Under the force of the steel strand 2, an annular contact area is formed between the anchor plate 3 and the anchor plate 1. The steel strand 2, anchor plate 3, anchor plate 1 and the beam form a series force transmission system. The direct contact force between the anchor plate 3 and the anchor plate 1 is measured, which is not only the effective anchor stress of the steel strand, but also the real prestress of the beam. When ultrasonic waves are incident from the annular contact area of ​​the anchor plate 3, part of the wave will pass through the contact interface into the anchor plate 1 and continue to propagate, and part will be reflected by the contact interface and transmitted back to the anchor plate 3; the reflected waveform is affected by the contact stiffness of the interface, and the interface contact stiffness is related to the interface contact force. By analyzing the reflected wave of the interface, the effective prestress of the steel strand can be measured; by conducting tests under three working conditions, the following results are obtained: Figure 2 The relationship between the reflection coefficient and stress under different contact force states is shown in the figure. It can be seen from the figure that the reflection coefficient decreases with the increase of stress. This is because the increase in stress causes the micro-asperities on the contact surface to deform, the actual contact area increases, the transmitted wave component of the ultrasonic signal through the interface increases, and the reflected wave component decreases; but the shapes of the micro-asperities on the anchoring interface are hemispheres of different sizes, and the deformation of the micro-asperities is not linearly related to the contact force. As the contact force increases, the deformation increment of the micro-asperities will become smaller and smaller, and gradually approach zero, and the reflection coefficient at this time will also tend to a stable value; among them, the contact interface of the CC specimen is rough, the contact interface of the SC specimen is medium rough, and the contact interface of the SS specimen is smooth; under the same stress state, the reflection coefficient of the rough contact interface is larger than that of the smooth contact interface, and the smoother the contact interface, the greater the compressive stress required for its reflection coefficient to converge. This is because, when the same compressive stress is applied, the actual contact area of ​​the rough interface micro-protrusion is smaller than that of the smooth interface, so the reflection coefficient of the rough contact interface is larger than that of the smooth interface. As the stress increases, the deformation of the rough interface micro-protrusion is larger and it is easier to reach the elastic limit. However, a greater stress is required to make the smooth interface micro-protrusion reach the deformation limit state.

[0064] Through the above method, this solution only needs to use the ultrasonic method to measure the ultrasonic reflection coefficient between the anchor plate 3 and the anchor pad 1 on the actual prestressed beam. According to the relationship between the calibrated reflection coefficient and the interface contact force, the effective stress under the anchor can be measured.

[0065] In one embodiment of the present invention, the following formula is obtained by performing Taylor expansion on the contact force function P(h) of the interface at h=h0:

[0066] P(h)=P0-K1(h-h0)+K2(h-h0) 2

[0067] Where h is the displacement between adjacent surfaces; K1 is the first-order linear stiffness, and K2 is the second-order nonlinear stiffness;

[0068] Among them, the stiffness of the interface is regarded as the differential equation of P(h), then K1 and K2 can be expressed as:

[0069]

[0070] The effective stress P0 between anchor plate 3 and anchor pad 1 is calculated using the power function model between the interface contact stiffness and the contact force:

[0071]

[0072] Where K2 is the second-order nonlinear stiffness, and C and m are constants related to the material.

[0073] In this solution, the calculation accuracy of the effective stress P0 can be improved by performing Taylor expansion of the interface contact force function P(h) around h=h0 to the second order.

[0074] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present invention.

Claims

1. A method for measuring stress under steel strand anchor based on ultrasonic reflection characteristics, characterized in that: The following steps are involved: S1: Install an ultrasonic detection device on the non-contact interface between the anchor plate and the anchor pad. Measure the transmitted wave after exciting the ultrasonic wave with the ultrasonic detection device. Take the reflected signal of the stress-free and non-contact anchor plate as the incident signal, and the fundamental frequency amplitude of the reflected signal after the anchor plate and the anchor pad contact as the reflected signal. Calculate the first-order interface stiffness between the anchor pad and the anchor plate using the following formula: K 1: Where, and are the acoustic impedances of the anchor plate (3) and the anchor pad (1), |R| is the reflection coefficient, is the angular frequency; S2: The interface contact stiffness and contact force are modeled using the following power function to calculate the effective stress between the anchor plate and the anchor pad. P 0 : Where C and m are constants related to the material.

2. The method for measuring stress under an anchor of a steel strand based on ultrasonic reflection characteristics according to claim 1, characterized in that: By putting the interface contact force function P(h) in h = h Performing Taylor expansion to the second order at 0 yields: The effective stress between the anchor plate and the anchor pad is calculated by the power function model between the interface contact stiffness and the contact force in step S2. P 0 : Where, K 2 is the second-order nonlinear stiffness, C and m are material-related constants, and h is the displacement between adjacent surfaces.

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