Research on a novel inclinometer based on distributed optical fiber strain and conjugate beam method

Journal Pre-proofs Research on a novel inclinometer based on distributed optical fiber strain and conjugate beam method Yan Zhou, Zheng Dongjian, Chen Zhuoyan, Liu Yongtao PII: DOI: Reference:

S0263-2241(19)31271-0 https://doi.org/10.1016/j.measurement.2019.107404 MEASUR 107404

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Measurement

Received Date: Revised Date: Accepted Date:

21 October 2019 12 December 2019 14 December 2019

Please cite this article as: Y. Zhou, Z. Dongjian, C. Zhuoyan, L. Yongtao, Research on a novel inclinometer based on distributed optical fiber strain and conjugate beam method, Measurement (2019), doi: https://doi.org/10.1016/ j.measurement.2019.107404

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Research on a novel inclinometer based on distributed optical fiber strain and conjugate beam method Yan Zhou1,2,3,Zheng Dongjian1,2,3 *,Chen Zhuoyan1,2,3,Liu Yongtao1,2,3 1.State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China; 2. College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China; 3. National Engineering Research Center of Water Resources Efficient Utilization and Engineering Safety, Hohai University, Nanjing 210098, China ;)

* Corresponding author at: Hohai University, 1 Xikang road, Nanjing, Jiangsu Province 210098, China Email address: [email protected] (Dongjian Zheng)

Abstract: The inclinometer is widely used in the deformation monitoring of civil and hydraulic engineering, but the manual observation required for existing traditional inclinometers is time-consuming, laborious and workload-intensive; an inclinometer with automatic monitoring is expensive, difficult to use for achieving distributed monitoring and shows poor instrument durability. To overcome the shortcomings of traditional inclinometers, a distributed optical fiber inclinometer (DOFI) is developed based on the conjugate beam method and distributed strain measurement technology. Compared to Euler-Benuli beam based converting method, the conjugate beam based method is more flexible and accurate to monitor the deformation of the slope under the heterogeneity geological conditions. Numerical simulation and laboratory tests show that the conjugate beam based inclinometer (DOFI) is effective, feasible and accurate. It can be used to quickly and accurately measure the deformation and direction of rock and soil mass, such as slope, and can realize long-term on-line monitoring.

Keywords: slope; deformation monitoring; inclinometer; optic distributed sensing; conjugate beam method

1.Introduction The inclinometer is widely used in the deformation monitoring of civil engineering and hydraulic engineering. This device is a kind of monitoring instrument for measuring horizontal displacement and azimuth angles of the points along inclinometer casing installed in civil engineering or slope. When the inclinometer is used, the sensor probe generally takes a fixed interval from the bottom to the top in the inclinometer tube to measure the change in angle between the axis of the inclinometer and the plumb line at each depth of the inclinometer tube. One then calculates the horizontal displacement of each fixed length and superimposes from the bottom of the inclinometer tube to obtain the horizontal total displacement of each measuring point relative to the fixed point at the bottom[1][2] .Since the 1950s, the inclinometer has been widely applied to the in situ monitoring field of civil engineering, slope and water conservancy projects, playing a very important role in ensuring construction and operational safety[3]. The traditional mobile and fixed inclinometers are commonly used instruments for monitoring the internal deformation of slopes. They have been widely used in slope monitoring and have achieved good monitoring results, such as the Zhujiadian landslide[4]of the Three Gorges Reservoir in China. The Ivanchi landslide[5] in the Dolomites of Italy and the Kovala landslide[6]. However, the traditional mobile inclinometer performs manual measurement on the entire depth of the inclinometer tube, which is time-consuming and labor-intensive manual observation, cumbersome operation steps, a large workload, and an inability to monitor in bad weather and under dangerous working environment. It is difficult to realize distributed monitoring with poor instrument durability, the measurement accuracy is not high, and online monitoring cannot be realized, and the fixed inclinometer has the problems of high cost and small number of monitoring points. It is also not easy for both kind of inclinometers to accurately determine the exact location of the landslide surface.

Therefore, it is necessary to develop a new type of inclinometer that is more usable. As a new stage of sensing technology, slope deformation measurement technology based on light and sound sensing theory has gradually emerged. Castañeda et. al,

[7]

used an three dimensional laser scanner to measure soil

erosion for the first time, what underpins optical technologies as an option for three-dimensional measurement of information. Gernot Michlmayr et al.[8] applied distributed acoustic sensing (DAS) technology to measure the precursor acoustic emission (AE) released before the landslide collapse in the laboratory. DAS based on optical fiber technology can realize acoustic emission measurement with high spatial and temporal resolution over a large distance. The aim is to study AE as a precursor of slope failure and evaluate the potential of landslide warning based on this technique. Thereinto, optical fiber sensing technology has such characteristics as high sensitivity, low monitoring cost, convenient remote and long-term monitoring[9]. As a feasible infrastructure health monitoring technology, distributed brillouin fiber optic sensor has superior performance in strain and temperature measurement than traditional sensors[10], distributed optical fiber is not environmentally demanding and this new monitoring

technology integrating sensing and transmission has been increasingly favored by the civil and hydraulic engineering fields[11][13]. Consequently, at present, optical fiber sensing technology has been applied in monitoring slope deformation. In 1978, Mendez[14]used fiber optic sensors in the monitoring of concrete structures for the first time. Subsequently, researchers from various countries promoted the use of fiber optic sensing technology in civil and hydraulic engineering; Shunji, Kato et al.[15]monitored the deformation of a road slope in Japan, installed the sensing fiber in a plastic tube, and arranged the plastic tube in a "W" plane on the slope surface to sense the deformation of the slope; Bao-jun Wang et al.[16]wove the sensing fiber into a grid shape and arranged it onto the surface of an indoor sand slope model for a loading test, with BOTDR technology being used to monitor the tiny strain of the fiber and obtain the distributed micro strain cloud chart of each point in the fiber sensing network, which showed well the strain of the slope model in the process of a landslide; Ding yong et al.[17] designed a set of fiber-optic sensor networks with the crossconnection of each part as a fishing net, which can be directly buried at a certain depth under the surface of the slope and used to accurately monitor the surface deformation of the slope in view of the fact that the one-dimensional optical fiber cannot accurately reflect the failure and deformation of the slope. Experimental results show that the fiber optic sensor network is very sensitive to deformation, can detect minimal external forces, and can accurately track the abnormal strain area; To verify whether the optical fiber sensing technology based on BOTDR can be used for bridge health monitoring, Shi Bin et al.[18] laid distributed optical fibers onto the steel and concrete surfaces of reinforced concrete beams. Resistance strain gauges were pasted onto the top surface of concrete beams and the surface of two longitudinal main bars. Distributed optical fibers and resistance strain gauges were both used to monitor the strain of concrete beams under a step-by-step loading test. The comparison between BOTDR and resistance strain gauge showed that the test results for BOTDR technology are accurate enough to be applied to bridge health monitoring; For the internal deformation monitoring of the slope, many reinforced concrete structures are buried deep in the rock and soil, and the deep deformation of slope can be obtained by measuring the deformation of reinforced concrete structures. Liu jie et al.[19]pasted the sensing fiber onto the surface of an inclined pipe and monitored the displacement of the deep slope rock and soil mass through the strain distribution of the sensing fiber. The indoor simulation test showed that the horizontal displacement at any point of the inclined pipe could be accurately obtained from the strain of the fiber; Zhang[20], Wang et al [21]and many scholars have attempted to propose fiber optic inclinometers based on FBG sensing technology, but the FBG sensor is connected in series by wavelength division multiplexing technology, and the monitoring data are still a series of strain values of discrete points, which can only be used to achieve quasi-distributed monitoring. And this kind of inclinometer is relatively expensive and has few measuring points as a quasi-distributed technology, a small number of fiber Bragg gratings is not easy to accurately determine the specific position of the

sliding surface. With the development of distributed optical fiber strain measurement technology, some scholars have developed several methods based distributed optical fiber strain for monitoring slope deformation.The distributed optical fiber monitoring system can only provide the strain change, but can not provide the displacement information which is also concerned in the process of deformation monitoring[22], so they proposed various mathematical methods for transforming strain into displacement response

[23].

For example, Pei Huafu et al. [24] and Wang et al.

[21]

used FBG

strain sensor to measure the internal strain of the slope and used the difference equation method to convert the strain measured by the FBG strain sensor into the displacement along the inclined casing. Ding Yong et al

[25][26]

applied the

distributed sensing optical fiber to monitor the deformation state of the SMW pile and used the classical double integral method based on Euler-Bernoulli beam theory assumptions of hard soil model. Luigi Zeni et al.

to transform the strain into displacement information under the [27]

developed a fiber optic based inclinometer for remote monitoring

of landslides and compared with traditional inclinometers. The test result shows the displacements provided by the optical fiber sensors are underestimated. The maximum deviation is about 15% in laboratory and the trend along the tube is obviously different in field. Therefore, the inclinometer based on distributed optical fiber strain and its traindeformation converting algorithm need further study deeply. In this paper, a new distributed optical fiber inclinometer (DOFI) adapted to complex geological conditions is developed based on distributed optical fiber strain and conjugate beam method. It can realize automatic observation of slope deformation with arbitrary tube length. At the same time, the numerical simulation and physical model test of the new type inclinometer are carried out, and the accuracy of the measured values based on the conjugate beam method was compared with based on the Euler-Benulli beam method, which verifies the feasibility of the new type of optical fiber inclinometer. It provides a reliable basis for the practical application of the distributed optical fiber inclinometer (DOFI). 2. The principle of PPP-BOTDA The Pulse pre-pump Brillouin Optical Time Domain Analyzer (PPP-BOTDA) is a distributed optical fiber sensing technology based on Brillouin scattering. Based on the stimulated brillouin scattering (SBS) effect, the technique injects pump light and probe light at both ends of the fiber, and adding a beam of pre-pump light to excite phonons. When the frequency difference between pump light and detection light is equal to the brillouin frequency shift in a certain region, SBS is generated in that region and energy transfer will occur between the two beams[28]; one then calculates the strain value of the optical fiber based on the corresponding relationship between the frequency shift and strain[29][30]. As an updated version of the Brillouin optical time-domain analysis technique (BOTDA), its spatial resolution and measurement accuracy have been further improved. When the temperature and strain of the structure under test changes [31],

the variation of the Brillouin frequency shift can be expressed as vB  Cv   Cvt T

(1)

namely,

（ , T0）+ B  , T ）= （0 B

（ （  , T ） B  , T） T + B  T

(2)

where （ is the Brillouin frequency shift when the fiber strain is  and the temperature is T ;（0 is the B ,T0） B  ,T） Brillouin frequency shift when the fiber strain is 0 and the temperature is T0 ;

 and T are the strain and temperature

variations, respectively; （  ,T） is the strain coefficient, which is approximately 493 MHz; （  , T）T is the B B temperature coefficient, approximately 1.1 MHz/K, and K is the thermodynamic temperature unit, and the numerical value is 1.1 MHz/K=1.1 MHz/℃.

Fig. 1. The principle of PPP-BOTDA 3. DOFI design and sensing rod deflection calculation 3.1 Design of the DOFI The DOFI developed in this paper is mainly composed of four parts: an easily deformed sensing rod, ordinary single-mode fiber, protective sleeve and pulley device, as shown in Figure 1(a). The main body of the inclinometer is a sensing rod that is easy to deform. The stiffness should be small to ensure that it is easy to deform the rod under stress. The ordinary single-mode fiber is attached to the outer surface of the easily deformable sensing rod in the four directions adjacent to 90°. For the mobile inclinometer, the optical fiber is smoothly connected at the bottom of the sensing rod, and a flexible protective cover can be set on the outside of the sensing rod pasted with the optical fiber. To facilitate the DOFI to move in the inclinometer tube without changing direction, it is necessary to bury the inclinometer tube and set two pulleys at each end of the sensing rod. In practical engineering applications, the pulley of the DOFI should be aligned with the groove of the inclinometer tube such that the inclinometer can move freely in the inclinometer tube. For the fixed inclinometer, the fiber of the multi-section inclination-measuring sensing rod can be connected together in series through the fiber connection flange, and the extra fiber from the top is connected to the measuring instrument, which monitors the strain of each measuring point of the sensor rod. The specific arrangement is shown in Fig. 1 (b).

(a)Diagram of the DOFI

(b) DOFI on-site embedding scheme Fig. 2. Design and installation of the DOFI When deformation occurs inside the slope, the rock and soil will extrude the inclinometer tube, and the DOFI installed in the inclinometer tube will also deform at the same time. Since the slop, tube and rod are in close contact, the displacement detected by the DOFI can be regarded as the horizontal displacement occurring inside the slope. During monitoring, the strain value of each measuring point of the optical fiber on the surface of the inclinometer sensing rod is measured by a measuring instrument. Through the conjugate beam method, the relationship between the strain value and the deflection value of the inclinometer sensing rod is derived to calculate the deflection value for each measuring point, i.e., the horizontal displacement inside the slope rock and soil mass. The deduction process used to determine the relationship between the deflection and strain of the sensing rod is briefly described below. 3.2 Sensing rod deflection calculation

For the deflection calculation of cantilever beam based strain, the classical double integral method based on EulerBernoulli beam theory is usually used to transform the axial strain into deflection of cantilever beam, and suppose the bending distribution along the cantilever beam is a triangle, which is not always reasonable. The conjugate beam method can be used to calculate the deflection of straight beam with uniform and non-uniform cross-section. It is simple and wide applicability. The two methods are briefly introduced as follows. 3.2.1 Conjugate beam method The conjugate beam method shows that the bending moment distribution of the real beam has a one-to-one correspondence with the load distribution of the virtual beam. The deformed axis of the DOFI is a smooth continuous curve, which meets the assumption of a plane section and ignores the influence of shear on the bending moment. The bending moment distribution

M  x ,

the strain distribution   x  , the deflection distribution

wx

and the curvature

distribution k  x  on the actual beam have the following relationship with the equivalent load distribution bending moment distribution

M x 

q  x 

and the

on the conjugate beam. k x 

d 2wx dx

2

=

M x EI



 x y

 q  x  =

d 2M x

(3)

dx 2

First, the DOFI sensing rod at the very bottom is taken for research. Since the sensing rod is fixed in stable rock and soil mass, the boundary condition of the sensing rod is that the bottom displacement

w1 is zero and the deflection

angle  1 is zero. It can be assumed that the sensing rod is a cantilever beam. According to the corresponding relation supported by the conjugate beam, the real and virtual beam model of the cantilever beam is shown in Fig.3. Assuming that the length of the cantilever beam is L , the beam components are divided into n equidistant elements by the sampling interval of the distributed optical fibers. The unit length is l  L / n , the unit number

i

ranges from 1 to n ,

and the node number p ranges from 1 to n  1 . According to the conjugate beam method[32], the virtual bending moment generated at the node p (2  p  n ) of the virtual beam can be calculated as p 1 1 M p  l 2 qi ( p  i+ ) 2 i 1

Suppose

i1(x)

and

(4)

i2(x) are the strain value monitored at the optical fiber tension side and compressed side of

the cantilever beam unit i ; y ( x) is the distance from the monitoring point of the tension-side fiber to the neutral axis during the deformation process. Then, there is qi  i yi , and the distance

yi of the fiber monitoring point to the neutral

axis is a fixed value R , and the deflection at the node p obtained using equation (4) is

wp 

L2 p1  2  i  1  i   1 ( p i  ） 2  n R i1  2 2 

(5)

Equation (5) shows that the deflection of any point on the structure is only related to the length of the member, the distance from the position of the optical fiber to the neutral axis of the member section, unit division accuracy and the corresponding strain values and has nothing to do with the size and distribution range of the load. Therefore, as long as the structural units are divided reasonably and the structural strain is accurately measured, the deformation of the structure can be accurately calculated.

(a)Schematic diagram of a cantilever real beam (b) Schematic diagram of a cantilever virtual beam Fig. 3. Schematic diagram of the cantilever beam conjugate beam method

Fig. 4. Schematic diagram of flexural members

Fig. 5. Displacement of the Kth sensing rod

The deflection calculation for a DOFI sensing rod was studied above. The actual geotechnical engineering needs to observe the deep internal deformation. For example, when a geotechnical slope is monitored by an inclinometer, the depth of the inclinometer tube can reach more than tens of meters. At this time, several inclinometer sensing rods can be closely connected to form a distributed inclinometer sensor bar (Fig. 2 (b)), which enables one to continue monitoring the deeper internal deformation. If the inclinometer composed of N sensing rods is regarded as a cantilever beam as a whole and the strain in the two directions of each sensing rod is substituted into equation (5), then the actual deflection values of each measuring point of all N inclinometer sensing rods can be calculated. As shown in Fig. 5, let the ydirection displacement of point j of the Kth (K=1,2,…,N)inclinometer sensing rod be wykj (z direction displacement is wzkj), then

wykj  wy ,k 1   y ,k 1l j  wykjp

(6)

In this formula, wy,k ― 1 and θy,k ― 1 is the y-direction deflection displacement and deflection angle of the k-1th

inclinometer sensing rod at the boundary with the kth root, respectively, lj is the length from point j of the Kth sensing rod to the junction of the Kth sensing rod and the k-1th sensing rod, wykjp is the displacement of the j point caused by deflection deformation of the Kth sensor rod itself. Let the angle between the total deflection of a point on the member and the z-axis be  as showed fig.4, then tan   wy wz . Similarly, the deflection direction of any measurement point can be derived from the strain value of the

optical fiber, and the sliding azimuth angle  of the node can be obtained. Let the Angle between the total deflection of a point on the member and the Z-axis be  , and the sliding azimuth of this node is as follows:

 =arctan

wy wz

+LZ

（7）

Where 𝑤y、 𝑤z are the deflections of the y direction and the z direction of a certain node, and 𝐿Z is the azimuth of the z direction. 3.2.2 Euler-Bernoulli beam theory For the cantilever beam shown in Figure 4, the normal strain value of any section x of the cantilever beam can be obtained from the Euler-Bernoulli beam theory [33]:

  y, z , x   a( x) y  b  x  z  c  x 

(8)

In this formula,   y, z, x  is the strain value at the  y, z  point of the section x ; a( x)、b  x  、c  x  are the coefficient values corresponding to the section x . The coefficient values a、 b and c of any section x of the cantilever beam can be solved by the three equations through the strain values at three positions. From the stress distribution of the entire cross section, combined with the material mechanics formula, the bending moment components M y and M z of the y and

z axes can be obtained.

M y  x     E  y、z、x  zdA

(9)

M z  x     E  y、z、x   ydA

(10)

A

A

In this formula, E is young's modulus of cantilever beam material. Under the appropriate boundary conditions, the following two differential equations are integrated on x to calculate the deflection values in both directions of arbitrary section x .

M y  x   EI  wz   x 

(11)

M z  x   EI  wy   x 

(12)

EI  wz  x    ( M y  x  dx)dx  Cz x  Dz

(13)

EI  wy  x    ( M z  x  dx)dx  Cy x  Dy

(14)

Among them, w is the deflection of the cantilever beam; wz   x  is the second derivative of wz  x  ; I is the moment of inertia of the cantilever beam; C and D are parameters determined by boundary conditions. Provided the bending moment is distributed roughly in a right triangle along the x direction, by integrating the cantilever beam in the x direction, the displacement of any section x in both directions can be obtained. M  0 x2 (15) wy  x   Z 3EI

wz  x  

M y  0 x2 3EI

(16)

Among them, M y  0  and M Z  0  are bending moment components M y and M z at the fixed end. 3.3 Discussion and Comparison In practical engineering, the tube of measuring displacement is usually as deep as several tens of meters. Both of the material characteristics and geological structure of the slop along the direction of the tube is often varied, so the load distribution on the tube or sensing bar is complicate. It is difficult to determine the bending moment distribution along the direction of the tube. Under the triangle distribution assumptions, based on the Euler-Benuli beam strain-deflection converting method, the displacement of the measuring point's cross section can be obtained by integrating the boundary conditions. However, it is obvious that the calculation error will gradually increase with the sensing bar length increases, that is, the longer the measurement length, the larger the error caused. The displacement obtained by Eq. (13) and Eq.(14) along the tube dozens of meters long would have a large error accumulation. The conjugate beam method calculates the displacement value by the fiber strain segment. The difference of the strain distribution of each segment can reflect the variation of the slop geological conditions. It is not necessary to assume that the bending moment is distributed roughly in a right triangle along the fiber optic inclinometer sensing bar, and the calculation results are closer to the actual situation. In the following, the strain-deflection converting accuracy based on the conjugate beam method is analyzed and compared with based on the Euler-Bernoulli beam method theoretically. It is assumed that the error of the measurement result is only caused by the strain error, and the measured error obeys the normal distribution. For the Euler beam theory, the beam of length L is also divided into n small units of length l for convenience  

1

comparison, node P normally can be expressed as Pi   i   l . According to the trapezoidal formula, the deformation 2 

value y p of the node P can be expressed in discrete form as: yp =

p 1  l2  1   2 p  3   2 1  1 1     2  p   1  p    4  p  i     2  i   1  i    ,  i  1  n  8R  2 i 1  

(17)

The result of i (x) still obeys the normal distribution, and the standard deviation S1 of y p can be obtained by using the formula of normal distribution S1 =

l2 R

p  4 p 2  1  1 24



 2 p  3 64

2

1

(18)



For the conjugate beam method, the standard deviation S2 of y p is: S2 =

S = 1  S2

l2 R

p  4 p 2  1  1

(19)



24





3 2  2 p  3  1 8 1 p  4 p 2  1  1

p  4 p 2  1  1 

(20)

By comparison, it can be found that  is greater than 1, indicating that the monitoring standard deviation S2 of the conjugate beam method is always smaller than the standard deviation S1 of the Euler beam method. For the strain value with its own error, with the accumulation of error, the deviation between the deformation data obtained by the Euler beam method and the actual value is larger and larger, and does not converge. However, the accuracy of conjugate beam method used in this paper is much higher than that of Euler beam method. 4. Verification of two calculation methods In order to analyze the strain-deflection converting accuracy of the above two calculation methods, the verification

is carried out by a combination of numerical simulation and laboratory test. 4.1 Numerical simulation of displacement The numerical model shown in Fig. 6(a) is established using ABAQUS. Optical fiber inclinometer sensing bar was considered as linear elastomer, elastic modulus is 600MPa, Poisson's ratio is 0.17, and optical fibers with diameter of 0.12mm are arranged in four directions. Fiber bonding length is 1m, elastic modulus is 40 GPa, Poisson's ratio is 0.20. Considering that the slop is elastoplastic material, the slope materials constitution follows the Mohr-Coulomb model, the slope materials elastic modulus is 5GPa, and the Poisson's ratio is 0.35. The contact relation between the fiber optic inclinometer sensing bar and the rock or soil inside the slope is modeled. The tangential behavior is selected as a hard contact with a coefficient of friction of 0.6 in the tangential direction. The slope stability is analyzed by the strength reduction method, and the strength reduction coefficient Fr is 0.5, 0.75, 1, 1.25, 1.5, 1.75 and 2.0, respectively. The meshing of the slope and the fiber optic inclinometer is shown in Fig. 6(a). Fig. 6(b) is a displacement cloud diagram of the slope and inclinometer sensing bar when Fr is 2.0.

(a) Slope and fiber optic inclinometer model diagram

(b) Displacement cloud image of rock and soil body and displacement cloud diagram of fiber optic inclinometer Fig.6 Slope FE model and displacement cloud map

The numerical analysis result of the deflection of the fiber sensing bar under different fr is the actual deformation value of the slop. The strain value of the optical fiber on the surface of the sensing bar is taken as the strain monitoring value. The deflection values of the inclinometer are calculated by Euler beam theory and conjugate beam method respectively, and then compared with the actual deflection value of the numerical simulation to analyze the straindeflection converting accuracy. The comparison results are shown in Figure 7. It can be seen from the figure that the results obtained by the two methods are close in the region near the fixed end of the sensing bar. The deflection value calculated by the conjugate beam method oscillates up and down the actual deflection curve, and the difference between the strain converting deflection value based on conjugate beam method and the numerical analysis deflection value is small, and the maximum relative error is only 4.8%. And the farther the measuring point on the sensing bar is from the fixed end, the larger the displacement error calculated by the Euler beam theory, but the displacement error calculated by the conjugate beam method is still Small, and the calculation accuracy based on conjugate beam method is relatively high.

Fig.7 Comparison of numerical simulation displacement calculation 4.2 Test verification 4.2.1 Fabrication of the Test Platform In order to further verify the feasibility and accuracy of the DOFI strain-deflection converting accuracy based on the conjugate beam method and the Euler-Benuli beam theory in slop deformation monitoring, an indoor measurement test simulating the actual slop deformation was carried out. Referring to Fig. 2(a), a DOFI is fabricated by arranging the single mode fiber in four directions of a polyurethane rod. In order to facilitate the measurement of deflection, a deflection measuring device is specially designed, which is composed of three narrow thin steel plates, a variable radius disk support and a bottom plate. At the same time, in order to simulate the load applied of DOFI in the slope, try to divide the DOFI into five sections, place springs at the junctions of each section. The spring is used to simulate the action of rock-soil mass on the sensing bar of the inclinometer. Fig.8 is a schematic diagram of the measuring device. In this experiment, the PPP-BODTA monitoring equipment adopts the NBX-6050A optical nanometer instrument developed by Neubrex Corporation of Japan. This device’s maximum measuring length is 25 km, the strain measurement range is -3%~4%, the strain accuracy is ±7.5  , and the minimum sampling interval can reach 1 cm, which can meet the needs of strain measurement in slope engineering. The sampling interval for this test is 5 cm, and the spatial resolution is 10 cm. 4.2.2 Test scheme To facilitate the experiment, only one DOFI sensing rod was used for the test; the main body of the sensing rod was a solid polyurethane rod with a diameter of 45 mm and length of 1000 mm. The Corning SMF-28e ordinary singlemode white tight-fitting optical fiber is applied with a certain prestress realized by stretching, and adhered to the polyurethane rod in four directions with AB glue. The effective bonding length in each direction is 1 m, and some optical fibers are reserved for connecting the measuring instrument. The polyurethane rod is cylindrical and its surface is relatively smooth. To prevent the dial indicator deviating from the sensing rod, a 50×50 mm plexiglass sheet is pasted on each measuring point of the sensing rod, with the pointer of the dial indicator sliding only on the glass sheet so as not to affect the measurement results. During the test, the DOFI is placed vertically on the measuring device, and the bottom end is fixed by the disc support. The whole system can be considered as a cantilever beam fixed at one end, with each narrow steel plate with a distance of 120cm from top to bottom. The deflection value of the sensing rod is measured with five dial gauges with a distance of 100cm from top to bottom of each narrow steel plate. In practical engineering, the main direction of the inclinometer tube displacement is not necessarily along the inclinometer tube groove, so the direction and displacement are generally determined by measuring two sets of data for mutually perpendicular grooves. To conform to the displacement of the inclinometer in practical engineering, a two-

way deflection measurement test is needed. The loading direction can be along any direction between the two groups of dial indicators, and three stages of loads was applied along any direction in this test. When the dial indicator reading does not change after each loading, the reading is recorded. The strain value and Brillouin frequency shift of distributed optical fibers on sensing rod surface are measured by NBX-6050A, and the specific test arrangement is shown in Fig. 9. By conjugate beam method and Euler beam method, the strain values of optical fibers are converted into deflection values in two directions. Comparing with the actual deflection values in two directions measured by the percentile meter, the calculation accuracy of the two methods can be analyzed.

Fig. 8 Schematic diagram of deflection measuring device Fig. 9 Test arrangement Table 1 Basic parameters of NBX-6050a

Technical indicators Measurement wavelength/nm Range of frequency scanning/GHz Range of strain measuring/με Distance sampling resolution/cm Spatial resolution/cm Accuracy of strain meaurement/με Time for measurement/s 4.2.3 Test results and analysis

Performance parameters 1550±2 9～13 -30000～+40000 （-3～4％) 5cm（Minimum value） 10,20,50,100 ±7.5 0.1

The strain sensitivity coefficient of a distributed fiber strain sensor varies depending on the base material and the bonding process. Therefore, it is necessary to perform an indoor calibration test on the DOFI before the test to obtain the strain sensitivity coefficient. In the calibration test, it is observed that the fiber strain is linear with the Brillouin shift. The correlation coefficient R2 is above 0.99, and there is no hysteresis or fatigue effect. It is proved that the performance is good and can be used for measurement. Without considering the cross-sensitivity of temperature to strain,

the

relationship

between

the

 v  486.4  M H z     10826.37 M H z

Brillouin

frequency

shift

and

the

applied

tensile

strain

is

.During the test, a point was taken at an interval of 5 cm for measurement,

with the 1-m-long fiber optic on the sensing rod having a total of 20 segments. The strain values obtained by the DOFI are transformed to displacement by the conjugate beam method (CBM) and the Euler-Benuli beam method (E-B), and compared with the actual displacement values measured by the respective points of the dial indicator. For comparison, the displacement of the two directions at each measurement point (Fig. 9) was statistically analyzed, and the relative error (RE), mean error (MRE), and standard deviation (SD) were used to compare the advantages and disadvantages of

two methods. The Comparison results is shown in Table 2. In order to facilitate the intuitive comparison of test results, the measured results were drawn as the relationship between measuring points and deflections, as shown in Fig. 10. Fig. 10 (a) shows the comparison results of deflection values calculated by two deflection conversion methods in the Z direction and those measured by the dial indicator. Fig. 10(b) shows the comparison results of deflection values calculated by two deflection conversion methods in the Y direction and those measured by the dial indicator. It can be seen from Fig. 10 that the deflection value calculated by the CBM is very close to the measured value of the dial indicator. The theoretical calculation results of E-B show that the error is small at the point close to the fixed end, but the farther away the measurement point is from the fixed end, the greater the deviation between the calculated value and the measurement value of the dial indicator. Table 2 calculates the measurement errors of the two methods. Table.2 Test deflection measurement data sheet

Measuring point 1 2 3 4 5

Direction y z y z y z y z y z

Dial indicator mm 0.79 1.39 2.76 4.55 5.69 10.16 9.40 16.90 13.23 25.20

SD MRE

(a) Z-direction deflection

RE（％）

CBM mm

E-B mm

CBM

E-B

0.80

0.81

2.12

3.26

1.34 2.64 4.32 5.96 10.70 9.10 17.64 13.79 24.22

1.46 2.59 4.21 6.03 9.53 8.66 18.30 14.86 28.15

-3.42 -4.37 -5.08 4.79 5.35 -3.25 4.47 4.25 -3.91 4.20mm 4.10

5.12 -6.13 -7.34 5.82 -6.25 -7.91 8.34 12.33 11.71 7.66mm 7.42

(b) Y-direction deflection

Fig.10 Comparison results of Y and Z deflection under three stages of loads Table 2 calculates the measurement errors of the two methods. As can be seen from table 1, the results calculated by CBM are obviously superior to those calculated by E-B method. The standard deviation of the results calculated by the CBM is 4.20mm, and the relative error ranges from 2.12% to 5.35%, which is within the allowable measurement

requirements. The standard deviation of the results calculated by E-B theory is 7.66mm, and the relative error ranges from 3.26% to 12.33%, most of which exceed the allowable measurement error. At the same time, it can be seen that the DOFI measurement error does not increase with the increase of the deflection. Even in the case of large deflection, the measurement accuracy is still stable, there is no problem that the measurement deflection is underestimated, and the relative error still remains at about 5%. DOFI is also more suitable than other inclinometers [27] for measurements of the actual slopes with greater deflection. Above all, the proposed measurement technology is verified in the laboratory conditions. And the usability of this technology in real conditions is not much different from in the laboratory conditions. But obviously, some factor would affect the signal to noise ratio and measurement uncertainty such as the optic fiber connecting, breaking and optic bending loss as well as the optical fiber bonding or embedding technics and the sensing bar material, so it is important to install and protect the system properly and calibrate by calibration optical fiber in time. Moreover the proposed measurement technology is focus on only one point installed clinometer tube. The challenge is how to properly establish an interior and surface deformation sensing network based on distribute optic fiber for the whole slope Meanwhile, taking the advantage of distribute optic fiber monitoring, to forecast slope fail time, range of influence and its consequence would be the important directions of further research. 5 Conclusions In this paper, based on the superiority of distributed optical fiber sensing materials, a new DOFI is developed for internal deformation monitoring of the slop. Based on the conjugate beam method, the relationship between optical fiber strain and inclinometer displacement is derived. Numerical simulation and laboratory tests were performed, and the strain-deflection converting accuracy based on conjugate beam method and E-B beam method is compared by the combination of finite element numerical simulation and indoor measurement test, and the following conclusions were obtained:

(1)Based on the relationship between beam strain and deflection, the DOFI can be used to measure internal deformation of rock and soil mass. The laboratory test shows that it is simple and convenient to calculate beam deflection deformation from the distributed fiber strain and that it is easy to conduct distributed measurement of deflection deformation. The displacement obtained by the test is very close to the actual deflection measured by the dial indicator. The measurement by the DOFI has high accuracy and stable measurement accuracy. (2)Based on conjugate beam method (CBM), the relationship between fiber optic strain and inclinometer displacement is more accurate and reasonable. The calculation accuracy of conjugate beam method is verified by finite element numerical simulation and indoor measurement test. It has good applicability to actual structural deformation monitoring. Compared with Euler-Bernoulli beam method, the displacement calculation accuracy based on CBM is higher. The novel inclinometer based on distributed optical fiber strain and conjugate beam method can realize the automatic observation of slope deformation at any inclined hole depth. (3)The DOFI can be used to realize remote and inaccessible the deep displacement and its direction measurement quickly and accurately for rock-soil body, soft soil foundation, dam and other fields. And enable distributed real-time on-line monitoring that is time-saving, labor-saving and safe. Especially in complex electromagnetic, chemical and water environments or when electrical sensors (such as flammable and explosive environments) are not allowed, this inclinometer is more adaptable than traditional electrical sensors. Acknowledgments The work was supported by National Key R&D Program of China (2018YFC1508603), National Natural Science Foundation of China (Grant Nos. 51579085, 51779086, 51579086), Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (YS11001).

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CRediT author statement

Yan Zhou: Conceptualization, Methodology, Software, Validation，Formal analysis，Investigation, Writing- Original draft preparation, Writing- Reviewing and Editing Zheng Dongjian: Conceptualization, Methodology, Investigation, Resources, Supervision, Project administration, Funding acquisition Chen Zhuoyan: Visualization, Data curation Liu Yongtao: Visualization, Data curation [34]

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. [35]

No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work. [36]

Highlights: 1) An optical fiber inclinometer was developed based on the conjugate beam method. 2) The CBM strain-deflection algorithm was discussed and compared theoretically. 3) The simulation and test were carried out to verify the CBM based inclinometer. 4）CBM based DOFI is more flexible and accurate than EBM based. [37]