sensors Article

A New Measurement Approach for Small Deformations of Soil Specimens Using Fiber Bragg Grating Sensors Dong-Sheng Xu School of Civil Engineering and Mechanics, Huazhong University of Science and Technology, 1037 Luoyu Rd., Wuhan 430074, China; [email protected] Academic Editors: George Rodriguez, Joseba Zubia and Paulo S. André Received: 23 March 2017; Accepted: 29 April 2017; Published: 4 May 2017

Abstract: A measurement approach for small deformations of soil specimens has been proposed in this study. The proposed approach consists of a small deformation transducer (SDT) based on fiber Bragg grating sensors which could provide an alternative tool to measure local small deformations of a soil specimen with high accuracy. The working principle, design procedures, calibrations and applications of the SDT are presented. An analytical solution is derived to obtain the relationship between the small deformation of the transducer and the wavelength shift of the FBG sensor, which was further evident in the laboratory calibration tests. The measurement range and resolution of the SDT can be adjusted by choosing different length and thickness of the material. The SDT can achieve a strain resolution of 4.45 micro-strains for a soil specimen with 80 mm in height. Measurement errors and stability were also examined and the results show that the maximum measurement error was around 0.01 mm. The designed SDT was further installed in a modified triaxial apparatus. Three shearing tests under different confining pressures were conducted. Results measured by the newly developed SDT are analyzed with comparisons to the results using external linear variable differential transformer (LVDT) transducers. The results provide evidence that this measurement approach is suitable for measuring the local deformations of soil specimens with high accuracy and stability. Keywords: small deformation transducer; fiber Bragg grating (FBG); soil specimen; triaxial test

1. Introduction Knowledge about the small deformation behavior of gravel materials is essential for the design and safety control of geotechnical structures. Many researchers have highlighted the importance of accurate measurements of the small strains of gravel material, such as soil specimens and aggregate [1–3]. In the past few decades, various methods and techniques have been developed to measure small strain behavior, such as bender elements, the resonant column method, proximity transducers, miniature linear variable differential transformer sensors (mini-LVDTs), mini-inclinometers, Hall-effect transducers, local deformation transducers (LDTs), etc. [4,5]. Among these, the bender element and LDT are the most commonly used methods to measure soil small strain behavior. The bender element is an effective method to measure very small strain behavior of soil specimens by using shear waves [6]. However, the soil strain induced by the shear wave can only be estimated, for example, Dyvik and Madshus [7] regarded the strain value is in the range of 10−5 , while Leong et al. [8] and Pennington [9] estimated it around 10−6 . To overcome the above limitations of the bender element method, the LDT was developed to measure local strains in the range between 10−5 and 10−2 . The LDT not only can measure small soil strains with higher accuracy, but also measure continuous strains during the shearing phase. Thus, many miniature displacement devices were employed in the LDT for traxial test equipment (e.g., Jardine et al. [2], Clayton et al. [6], Hird and Yung [10], Goto et al. [11]). Goto et al. [11] Sensors 2017, 17, 1016; doi:10.3390/s17051016

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Sensors 2017, 17, 1016 et al. [11]). Goto

2 ofsmall 13 et al. [11] were the first to develop a LDT with strain gauges to measure local strains of soil specimens in a triaxial test machine. Later on, Dasari et al. [12] improved the accuracy with four strain gauges in one LDT and Yimsiri et al. [13] further developed a cantilever-based LDT were the first to develop a LDT with strain gauges to measure local small strains of soil specimens in with four strain gauges. However, the measurement accuracy by using strain gauge was limited due a triaxial test machine. Later on, Dasari et al. [12] improved the accuracy with four strain gauges in one to the electrical and mechanical noises. Dasari et al. [12] pointed out the total noise can reach 6.0 mV LDT and Yimsiri et al. [13] further developed a cantilever-based LDT with four strain gauges. However, at the beginning axial strain of 4 × 10−5 and then may increase with the increase of strain. Goto et al. the measurement accuracy by using strain gauge was limited due to the electrical and mechanical [11] summarized eight sources of errors for LDTs, including electrical and mechanical noises from noises. Dasari et al. [12] pointed out the total noise can reach 6.0 mV at the beginning axial strain of the system, hysteresis in calibration, changes of elastic behavior of the membrane and short circuit 4 × 10−5 and then may increase with the increase of strain. Goto et al. [11] summarized eight sources problems in the presence of high water pressure. Also, the self-weight of LDT devices will also of errors for LDTs, including electrical and mechanical noises from the system, hysteresis in calibration, reduce the measurement accuracy [14]. Thus, with the development of fiber optic sensors (FOS), it is changes of elastic behavior of the membrane and short circuit problems in the presence of high necessary to develop a new measurement approach to measure local deformations of soil specimens water pressure. Also, the self-weight of LDT devices will also reduce the measurement accuracy [14]. with FOS. Thus, with the development of fiber optic sensors (FOS), it is necessary to develop a new measurement In recent decades, FOS have been dramatically developed and widely applied in engineering approach to measure local deformations of soil specimens with FOS. practice [15–19]. Pei et al. [20] developed a FBG-based inclinometer and used it in field slope In recent decades, FOS have been dramatically developed and widely applied in engineering monitoring; Zhu et al. [21] applied FBG sensors to measure the internal displacement in a model practice [15–19]. Pei et al. [20] developed a FBG-based inclinometer and used it in field slope monitoring; dam. Compared with electrical strain gauges, the fiber optic sensors have obvious advantages, such Zhu et al. [21] applied FBG sensors to measure the internal displacement in a model dam. Compared as tiny size, high precision, resistance to electromagnetic interference, and a combination of sensing with electrical strain gauges, the fiber optic sensors have obvious advantages, such as tiny size, high and transmission. Thus, in this study, a small deformation transducer (SDT) is developed to precision, resistance to electromagnetic interference, and a combination of sensing and transmission. measure local deformation of soil specimens by using fiber Bragg grating (FBG) sensors. The aim of Thus, in this study, a small deformation transducer (SDT) is developed to measure local deformation this study is to provide an effective approach to obtain the soil behavior under small deformation of soil specimens by using fiber Bragg grating (FBG) sensors. The aim of this study is to provide conditions, because soils adjacent to, for example, a subway tunnel, deep excavation foundations an effective approach to obtain the soil behavior under small deformation conditions, because soils and retaining walls, is normally under small strain conditions. Thus, understanding soil small strain adjacent to, for example, a subway tunnel, deep excavation foundations and retaining walls, is normally behavior is essential for civil engineers. The proposed approach could provide an effective tool to under small strain conditions. Thus, understanding soil small strain behavior is essential for civil measure soil stress-strain behavior at small strain levels. In this paper, the design, working principle, engineers. The proposed approach could provide an effective tool to measure soil stress-strain behavior fabrication, and calibration of the SDT are elaborated. A triaxial test apparatus was modified to at small strain levels. In this paper, the design, working principle, fabrication, and calibration of the employ the SDT. Several triaxial tests were conducted to evaluate the performance of the modified SDT are elaborated. A triaxial test apparatus was modified to employ the SDT. Several triaxial tests test system with the SDT. were conducted to evaluate the performance of the modified test system with the SDT.

2. Principle of the Small Deformation Transducer 2. Principle of the Small Deformation Transducer Principles of the FBG Sensor 2.1.2.1. Principles of the FBG Sensor Figure 1 shows the working principle of the FBGAs sensor. shown inwhen the figure, when a Figure 1 shows the working principle of the FBG sensor. shownAs in the figure, a broadband broadband light source is passed through the FBG sensor, a narrow band light will be reflected. light source is passed through the FBG sensor, a narrow band light will be reflected.

Figure 1. Illustration of the working principle of FBG sensors. Figure 1. Illustration of the working principle of FBG sensors.

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The reflected wavelength λB has a relationship with the core index of refraction and grating The B has a relationship with the core index of refraction and grating period of reflected the index wavelength modulation,λwhich is expressed as follows: period of the index modulation, which is expressed as follows: λB =2n Λ (1) 2neefff f  (1) B where index of refraction and and Λ is the period period of indexofmodulation. The reflected where nneffeff isisthe thecore core index of refraction Λ isgrating the grating index modulation. The wavelength λ will change with the local strains and/or temperatures. The wavelength change ∆λ B B reflected wavelength λB will change with the local strains and/or temperatures. The wavelength induced byB strains and is given by [22]: change Δλ induced bytemperatures strains and temperatures is given by [22]: ∆λ B B 6 −6 1 ppe ]e ·ε+(α +  ξ ) T ∼ .78 +66.7 .7 × 1010 T∆T = [1 − ∆T =00.78ε λ B B

(2) (2)

where ξ are temperature effect-related coefficients; ∆T where pee is the elastic optical coefficient; α and ξ ΔT is the temperature temperature change. change. In this study, study, the the FBG FBG sensor sensor was was fabricated fabricated by by the the phase phase mask mask method. method. Detailed Detailed procedures procedures for fabricating FBG sensors were described by Xu [23]. Figure 2 shows a sketch sketch of of the the experimental experimental setup used to fabricate FBG sensors by a phase mask method. A bare optical fiber was put in front of the phase mask which which has hasaaspecified specifiedwavelength. wavelength.After Afterthe thefiber fiberwas was exposed a spatial pattern exposed toto a spatial pattern of of ultraviolet light, a specific Bragggrating gratingwavelength wavelengthwas waswritten writteninto intothe thefiber. fiber. Briefly, Briefly, the whole ultraviolet light, a specific Bragg fabrication procedures can be divided into three three stages: stages: (a) preparation of the photosensitive optical fiber; (b) creating creating aa Bragg Bragg grating grating using using the the phase phase mask mask method; method; and and(c) (c)thermal thermalannealing annealing[23]. [23].

KrF excimer laser UV-mirror

Cylindrical lens

Interrogator with broadband source

Bared photosensitive fiber (uncoated)

Phase mask

Plan view of phase mask Translator

Figure 2. Experimental setup for fabricating FBG sensors by the phase mask method [23]. Figure 2. Experimental setup for fabricating FBG sensors by the phase mask method [23].

2.2. 2.2. Principle Principle of of the the SDT SDT Figure Figure 33 shows shows aa diagram diagram of of the the working working principle principle of of the the designed designed SDT. SDT. The The main main components components of the SDT include a flexible bronze strip, two FBG sensors and two hinged attachments. of the SDT include a flexible bronze strip, two FBG sensors and two hinged attachments. The The two two hinged attachments serve to fix the strip to the soil specimen. FBG sensors were glued at the centre of hinged attachments serve to fix the strip to the soil specimen. FBG sensors were glued at the centre the bronze strip. Therefore, with the hinged attachment fixing device, the strip together with the FBG of the bronze strip. Therefore, with the hinged attachment fixing device, the strip together with the sensor can be deformed with the FBG sensor can be deformed withsoil thespecimen. soil specimen.

The working principle of the SDT is shown in Figure 4. According to the classic elastic equation of the beam, the deformation of the SDT can be determined with boundary conditions of x = 0, y = 0 and x = l, y = 0. The deformation of the SDT Δ can be expressed as:

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working SensorsThe 2017, 17, 1016 principle of the SDT is shown in Figure 4. According to the classic elastic equation 4 of 13 of the beam, the deformation of the SDT can be determined with boundary conditions of x = 0, y = 0 and x = l, y = 0. The deformation of the SDT l ∆ can be expressed as:

   q1  dy dx   l R l0 ∆ = 0 l 1 + 1(dy/dx )22 − l R l h1  dy dx  idx  l ≈ 0 0 1 + 221 (dy/dx )2 dx − l R1 l l = 12 0(dy/dx dy dx)22dx dx 2 0 2

Top cap

(3) (3)

Top cap

Bronze strip

l0

l1

FBG sensors Hinges

Pedestal

Pedestal

Axial deformation Initial Figure Figure 3. 3. Schematic Schematic illustration illustration of of working working principle principle of of the the SDT. SDT.

By considering the SDT deformed in the first model of bulking, the deflection curve y as By considering the SDT deformed in the first model of bulking, the deflection curve y as indicated indicated in Figure 4 is obtained as: in Figure 4 is obtained as: yy = (4)  c1 sin(πx/l  x l) (4)



1



Substituting Equation (4) to (3), we can get: Substituting Equation (4) to (3), we can get: . √ . 22 ∆ = (cc 4l or c = 2 l∆ π ) ( ) 1π 1 





1



 4l 

or c1  2 l 

The bending moment at the point x0 is expressed as: The bending moment at the point x0 is expressed as: M0 = EI (π/l )2 c1 sin(πx0 /l )



2

M 0  EI  l  c1 sin  x0 l 

(5) (5)

(6) (6)

The tangential stress at x0 on the surface of the strip is: The tangential stress at x0 on the surface of the strip is: σ0 = M0 t/2I

(7) (7) where ‘t’ is the thickness of the strip in this study. Combining Equations (5)–(7) and together with where ‘t’ is the thickness of the strip in this study. Combining Equations (5)–(7) and together with Hook’s law σ0 = Eε FBG , we have: Hook’s law  0  E FBG , we have:

 0  M 0t 2 I

 FBG 

  t    sin  x0 l  l  l 

(8)

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ε FBG Sensors 2017, 17, 1016

r   ∆ πt sin(πx0 /l ) = l l

(8) 5 of 13

x (b)

(a)

P P M y

y

P

P Figure 4. Working principle of the (a) deformed SDT;SDT; (b) force and moment balance withinwithin the Figure 4. Working principle of SDT: the SDT: (a) deformed (b) force and moment balance SDT. the SDT.

If the FBG sensor is glued at at x0 x= l/2, so that: If the FBG sensor is glued = l/2, so that: 0

r  B   t   (9) ∆ πt ∆λ  0.78 B B = 0.78 l  l  (9) λB l l where t and l are the thickness and length of the SDT, respectively. From Equation (9), it can be where t and l are the thickness and length of the SDT, respectively. From Equation (9), it can be found that the axial deformation Δ has a unique relationship with the wavelength shifts of the FBG found that the axial deformation ∆ has a unique relationship with the wavelength shifts of the FBG sensor. Therefore, the local axial deformations of the soil specimen can be obtained by the FBG sensor. Therefore, the local axial deformations of the soil specimen can be obtained by the FBG sensor. sensor. The derived theoretical relationship between the measured wavelengths of FBG sensors and The derived theoretical relationship between the measured wavelengths of FBG sensors and SDT SDT deformations could provide a useful basis of analyzing the experimental calibration results. In deformations could provide a useful basis of analyzing the experimental calibration results. In addition, addition, the theoretical analysis could help to design the SDT for various applications, such as the theoretical analysis could help to design the SDT for various applications, such as adjusting the adjusting the measurement accuracy and range though the parameter t and l for different conditions. measurement accuracy and range though the parameter t and l for different conditions. It can also It can also be obtain from the theoretical analysis that the sensitivity of the axial deformation Δ be obtain from the theoretical analysis that the sensitivity of the axial deformation ∆ measured by measured by the SDT can be increased by a larger thickness and shorter length of the SDT. From the the SDT can be increased by a larger thickness and shorter length of the SDT. From the assumptions assumptions of the theory, we can also understand that the SDT is limited to small deformation of the theory, we can also understand that the SDT is limited to small deformation measurements measurements as it was assumed to be deformed as a first model of bulking. However, the as it was assumed to be deformed as a first model of bulking. However, the measurement range of measurement range of deformation can be increased with larger length and a thin SDT material by deformation can be increased with larger length and a thin SDT material by considering Equation (9). considering Equation (9). It should be noted that if the FBG sensors are glued slightly off the center It should be noted that if the FBG sensors are glued slightly off the center of the strip (i.e., x0 6= l/2), of the strip (i.e., x0 ≠ l/2), the Equation (9) is only approximate, then a laboratory calibration test is the Equation (9) is only approximate, then a laboratory calibration test is necessary to verify the necessary to verify the relationship between the FBG sensor and the deformations. By considering relationship between the FBG sensor and the deformations. By considering the resolution of ∆λ is the resolution of ΔλB is 0.02 nm at the wavelength λB = 1550 nm according to the parameters ofB 0.02 nm at the wavelength λ = 1550 nm according to the parameters of optical interrogation system optical interrogation system Bused in this study (i.e., MOI SM130), the resolution of the SDT used in this study (i.e., MOI SM130), the−4 resolution of the SDT computed through Equation (9) is computed through Equation (9) is 3.55 × 10 mm, as the length and thickness of the SDT are 80 mm 3.55 × 10−4 mm, as the length and thickness of the SDT are 80 mm and 0.2 mm, respectively. Thus, if and 0.2 mm, respectively. Thus, if we used the SDT to measure a soil specimen with a height of 80 we used the SDT to measure a soil specimen with a height of 80 mm, the small strain resolution mm, the small strain resolution measured by the SDT is 4.45 micro-strains (με). measured by the SDT is 4.45 micro-strains (µε).

2.3. Fabrication of the SDT The schematic diagram of the SDT is presented in Figure 3. There are four steps to prepare the SDT. Firstly, the FBG sensors with wavelength between 1510 nm and 1590 nm were prepared. Secondly, a spring-bronze strip was fabricated with 80 mm in length, 3.0 mm in width and 0.2 mm in thickness. The strip should be pre-strained with around 100 με to improve the linear properties and reduce creep behavior. Then, the FBG sensors were carefully installed on the surface of the bronze strip at the central position. It should be noted that the FBG sensors should be in good contact with

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2.3. Fabrication of the SDT The schematic diagram of the SDT is presented in Figure 3. There are four steps to prepare the SDT. Firstly, the FBG sensors with wavelength between 1510 nm and 1590 nm were prepared. Secondly, a spring-bronze strip was fabricated with 80 mm in length, 3.0 mm in width and 0.2 mm in thickness. The strip should be pre-strained with around 100 µε to improve the linear properties and reduce creep behavior. the Sensors 2017, Then, 17, 1016 the FBG sensors were carefully installed on the surface of the bronze strip at 6 of 13 central position. It should be noted that the FBG sensors should be in good contact with the strip. the strip. the FBG were a thin of glue. Allconnected the sensors were Finally, theFinally, FBG sensors weresensors protected by aprotected thin layer by of glue. Alllayer the sensors were in series connected in series extended to the optical with an armed optical fiber. and extended to theand optical interrogator with aninterrogator armed optical fiber. 2.4. Calibration of of the the SDT SDT 2.4. Calibration ◦ C. Figure 5 The The SDTs SDTs were were calibrated calibrated in in the the laboratory laboratory with with aa constant constant temperature temperature of of 20 20 °C. Figure 5 shows The optical optical interrogation system with with four four optical optical channels, channels, shows the the setup setup of of the the calibration calibration test. test. The interrogation system wavelength resolution of of0.02 0.02nm, nm,and andthe the maximum scan frequency 1 kHz used in this study wavelength resolution maximum scan frequency of 1ofkHz used in this study was was supplied by Micron Optics Incorporation (Atlanta, GA, USA). The interrogator is connected supplied by Micron Optics Incorporation (Atlanta, GA, USA). The interrogator is connected totoa acomputer computerthrough throughananinternet internetcable. cable.As Asshown shownininthe theFigure Figure5,5,aaspecial special small small scale scale screw screw was was used used to control the deformation of the SDT. The deformation was measured by a LVDT with a resolution to control the deformation of the SDT. The deformation was measured by a LVDT with a resolution 6 m. The LVDT results were compared with the SDT. A separate temperature sensor can of 10−6−m. of 1 1 ××10 The LVDT results were compared with the SDT. A separate temperature sensor can be be used measure temperature anddeduct deductany anytemperature temperatureeffect effectififthere there are are large large temperature temperature used to to measure thethe temperature and fluctuations during the test. In other words, temperature compensation can be conducted witha fluctuations during the test. In other words, temperature compensation can be conducted with aseparate separateFBG FBGtemperature temperaturesensor. sensor.

Figure 5. 5. Setup the calibration calibration test. test. Figure Setup of of the

Figure 6 shows the calibration results of the SDT with loading and unloading cycles and Figure 6 shows the calibration results of the SDT with loading and unloading cycles and temperature effects. The wavelength shift (Wshif) represents the measured wavelength minus the temperature effects. The wavelength shift (Wshif ) represents the measured wavelength minus the initial wavelength of the FBG sensors. Figure 6a shows the relationship between the deformations of initial wavelength of the FBG sensors. Figure 6a shows the relationship between the deformations of the SDT and wavelength shift of the FBG sensor. The relationship is expressed as: the SDT and wavelength shift of the FBG sensor. The relationship is expressed as:

 

  0.13  0.0086  Wshif2  0.2W shif  2

(10) ∆ = 0.13 Wshi f + 0.2 Wshi f − 0.0086 (10) where Δ denotes the deformation of the SDT; Wshif is the wavelength shift of the FBG sensor. Based where denotes analysis, the deformation of the SDT; is thehas wavelength shift of the FBG Based on on the ∆previous the deformation ofW the a quadratic function withsensor. the wavelength shifSDT the analysis, the deformation of the SDT has a quadratic function withrelationship the wavelength shift shiftprevious of the FBG sensor. Thus, a polynomial function was used to fit the between of the FBG sensor. a polynomial function wasCalibration used to fit the relationship between deformation deformation of theThus, SDT and the wavelength shifts. results show that the fitting accuracy 2 =wavelength of SDT and(R the shifts.initial Calibration results show that theinfitting accuracy is quite is the quite high 0.996). A little hysteresis was observed this calibration, thus high it is 2 (R = 0.996).toAapply little initial hysteresis waswhen observed in this thus itcan is suggested to apply suggested an initial bending setting up calibration, the SDT which reduce the initial an initial bending when setting up the which can reduce the temperature hysteresis. The temperature effects on SDT the wavelength shifts (W shifinitial ) of thehysteresis. SDT was The calibrated in the effects on the wavelength (Wshif6b. ) ofItthe SDTthat wasthe calibrated in theoflaboratory and presented in laboratory and presented shifts in Figure shows wavelength the FBG sensor has a close Figure 6b. It showswith that the the surrounding wavelength of the FBG sensor hastake a close relationship with the linear relationship temperatures. If we the linear wavelength of temperature surrounding If we take the temperature at 20 ◦ C as the initial sensor at 20 temperatures. °C as the initial value, thewavelength relationshipofbetween the sensor wavelength shift Wshif (i.e.,value, FBG wavelength minus FBG wavelength at 20 °C) and the temperature can be expressed as:

Wshif  0.0099 T   0.1986

(11)

Thus, the wavelength shift induced by the temperature variations can be deducted by Equation (11) from the measured results of SDT. Figure 6c shows the residual analysis of

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the relationship between the wavelength shift Wshif (i.e., FBG wavelength minus FBG wavelength at 20 ◦ C) and the temperature can be expressed as: Wshi f = 0.0099( T ) − 0.1986

(11)

Thus, the wavelength shift induced by the temperature variations can be deducted by Equation (11) from the measured results of SDT. Figure 6c shows the residual analysis of polynomial fit in Figure 6a. The residual displacement of the SDT calculated by Equation (10) minus the measured displacement by LVDT shows the maximum measurement error is around 0.01 mm. From the calibration results, it can be found that the overall accuracy of the SDT is quite high. However, it Sensors 2017, 17, 1016 7 of 13 should be noted that the sensitivity of the SDT will be decreased if the deformation is too large. too large. Large deformation induce higher contact forcethe between the membrane andwhich the hinge Large deformation will inducewill higher contact force between membrane and the hinge will which will alsothe diminish theTherefore, accuracy. it Therefore, it is to suggested keep the displacement maximum displacement also diminish accuracy. is suggested keep theto maximum of the SDT of the SDT below 0.3 mm. below 0.3 mm.

Figure Figure 6. 6. Calibration Calibration results results of of the the SDT: SDT: (a) (a) calibration calibration results results of of SDT SDT deformation deformation versus versus wavelength wavelength shift shift of of the the FBG FBG sensor; sensor; (b) (b) calibration calibration results results of of wavelength wavelength shifts shifts versus versus temperatures temperatures changes; changes; and and (c) in figure figure (a): (a): residual residual of of displacement displacement versus versus wavelength (c) residual residual analysis analysis of of the the polynomial polynomial fit fit in wavelength shift, . shift, W Wshif shif .

2.5. 2.5. Stability Stability and and Error Error Analysis Analysis of of the the SDT SDT The SDT is is aa significant significant concern concern for for deformation deformation measurement. measurement. A The stability stability of of the the SDT A laboratory laboratory stability test of the SDT was conducted for a relatively long-time of 30,000 s. Figure 7a stability test of the SDT was conducted for a relatively long-time of 30,000 s. Figure 7a shows shows the the directly measured wavelength results of the SDTs. It shows that the measured wavelengths were very stable during 30,000 s. The measurement errors of the SDT come from two sources: the first is the calculation error based on Equation (10) and the second source is the measurement error of the FBG sensor. Based on the Equation (10), the standard measurement error from the SDT can be expressed as:

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directly measured wavelength results of the SDTs. It shows that the measured wavelengths were very stable during 30,000 s. The measurement errors of the SDT come from two sources: the first is the calculation error based on Equation (10) and the second source is the measurement error of the FBG sensor. Based on the Equation (10), the standard measurement error from the SDT can be expressed as:   ∂(∆)  · σ Wshi f σ∆ =  ∂ Wshi f

(12)

whereSensors σ∆ is2017, the17,standard error of the SDT; σ(Wshif ) is the error of wavelength of the FBG sensor. 1016 8 of 13

Figure 7. Performance examination of the designed SDT: (a) long-term measured wavelengths;

Figure 7. Performance examination of the designed SDT: (a) long-term measured wavelengths; (b) measured errors of the wavelength. (b) measured errors of the wavelength.

The directly measured error from the FBG sensor was examined in this study. The SDT was installed in a soil specimen andfrom continuous readings were under static condition. Figure 7b was The directly measured error the FBG sensor wastaken examined in this study. The SDT shows the taken readings of the FBG sensors under static condition. It can be found that the σ(W shif ) is 7b installed in a soil specimen and continuous readings were taken under static condition. Figure equal to ±0.0015 nm. Substituting Equation (10) into (11) the results of σ(Wshif), the standard error of the SDT can be obtained as:

 

  Wshif   0.00150.26Wshif  0.2  Wshif 

(13)

From Equation (13), as the maximum wavelength shift of the FBG sensor is 3 nm, the maximum

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shows the taken readings of the FBG sensors under static condition. It can be found that the σ(Wshif ) is equal to ±0.0015 nm. Substituting Equation (10) into (11) the results of σ(Wshif ), the standard error of the SDT can be obtained as:     ∂∆  σ Wshi f = ±0.0015 0.26Wshi f + 0.2 σ∆ =  ∂ Wshi f

(13)

From Equation (13), as the maximum wavelength shift of the FBG sensor is 3 nm, the maximum error of the results by the SDT is ±0.00147 mm. Sensors 2017,measured 17, 1016 9 of 13 3. Experimental Setup 3. Experimental setup 3.1.3.1. A Modified Test Apparatus A Modified Test Apparatuswith withSDT SDT AA modified used to to install installthe theSDT. SDT.The Theschematic schematic setup modifiedtraditional traditionaltriaxial triaxialapparatus apparatus was used setup of of thethe testtest apparatus is isshown andthen thenfixed fixedononthe thesurface surface apparatus shownininFigure Figure8.8.The The SDT SDT was was calibrated calibrated and of of thethe specimen twohinges. hinges.As Asmentioned mentioned early, an initial soso that thethe soilsoil specimen byby two initial bending bendingshould shouldbebeapplied applied that distance betweenthe thetwo twohinges hingeswas was kept kept 11 mm mm shorter bebe distance between shorter than than the thelength lengthofofthe theSDT. SDT.It Itshould should noted that the initial bending depends on the cyclic test settings, because the SDT will experience noted that the initial bending depends on the cyclic test settings, because the SDT will experience both both extension and compression duringtests. cyclic tests. Two SDTs were mounted on the of surface of the extension and compression during cyclic Two SDTs were mounted on the surface the specimen specimen in diametrically opposite to each other. The test system includes a triaxial test chamber in diametrically opposite to each other. The test system includes a triaxial test chamber with a loading withpressure a loading frame, pressure supply the SDT, fiber optic interrogator andthe frame, supply devices, the SDT, fiberdevices, optic sensing interrogator andsensing computer. In this study, computer. In this study, the external LVDT device was also used to measure the total deformation external LVDT device was also used to measure the total deformation of the soil specimen. The SDT of was the soil specimen. The SDT was used to measure the local deformation with the maximum strain up used to measure the local deformation with the maximum strain up to 0.3%. Three different tests were to 0.3%. Three different tests were conducted with different confining pressure. After the soil conducted with different confining pressure. After the soil specimen and the SDT were installed, the specimen and the SDT were installed, the chamber was mounted and filled with distilled water. chamber was mounted and filled with distilled water. Distilled water will be used to apply surrounding Distilled water will be used to apply surrounding pressures to the soil specimen as indicated in pressures to the soil specimen as indicated in Figure 9. A loading rate of 0.005 mm/min was applied Figure 9. A loading rate of 0.005 mm/min was applied to shear a completely decomposed granite to shear a completely decomposed granite (CDG) soil specimen under a constant confining pressure. (CDG) soil specimen under a constant confining pressure. During shearing process, both the SDT During shearing process, the SDT and the LVDT data were recorded. and the LVDT data wereboth recorded.

Figure 8. Schematic view of SDT test system in the modified testing apparatus. Figure 8. Schematic view of SDT test system in the modified testing apparatus.

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Axial pressure Top cap Optical sensing interrogator

Water pressure Fiber

Computer l0 FBG sensor

Hinge Membrane O-ring

A test apparatus with water pressure

Pedestal

Axial pressure

Figure9.9. Schematic Schematic diagram diagramof ofthe theSDTs SDTson onaasoil soilspecimen specimenin inaamodified modifiedtraxial traxialapparatus. apparatus. Figure

3.2. Properties of the Soil Specimen 3.2. Properties of the Soil Specimen The SDT was tested in a modified traxial apparatus for a completely decomposed granite The SDT was tested in a modified traxial apparatus for a completely decomposed granite (CDG) (CDG) soil. The tests were conducted by following guidelines of BS 1337-2, 1990; BS-1337, 1990; soil. The tests were conducted by following guidelines of BS 1337-2, 1990; BS-1337, 1990; BS-5930, 1999. BS-5930, 1999. The liquid limit (wL), plastic limit (wp), plasticity index (Ip) and the specific gravity (Gs) The liquid limit (wL ), plastic limit (wp ), plasticity index (Ip ) and the specific gravity (Gs ) were 31%, 21%, were 31%, 21%, 10%, and 2.59, respectively. The soil was classified as silty sand according to the 10%, and 2.59, respectively. The soil was classified as silty sand according to the USCS classification USCS classification (ASTM D 2487). The maximum dry density (MDD) and optimum moisture (ASTM D 2487). The maximum dry density (MDD) and optimum moisture content (OMC) of the soil content (OMC) of the soil were found to be 1.84 Mg/m3 and 13.5%, respectively, based on standard were found to be 1.84 Mg/m3 and 13.5%, respectively, based on standard compaction tests. compaction tests. 3.3. Test Procedures 3.3. Test Procedures The soil specimens were prepared by pretreating disturbed soil, mixing with water and The soil wereThe prepared pretreating disturbed soil,oven mixing withdays water and compacting to aspecimens target density. soil wasby over dried by keeping in the for three under to a target density. The soil wasdried oversoil dried bythen keeping in the for three days under a acompacting constant temperature of 104 ◦ C. The over was mixed withoven distilled water to achieve constant temperature of 104 °C. The over dried soil was then mixed with distilled water to an optimum moisture content of 13.5%. To ensure even water content, the soil was matured for achieve 24 h at optimum moisture content ensure even water content, the soil was matured 24 h ◦ C. TheTo aan constant room temperature of of 20 13.5%. prepared soil was then compacted in three layers in for a mold at a constant room of 20 and °C. The prepared soil was then compacted in three layers in 3a with dimension of 50temperature mm in diameter 100 mm in height to achieve a dry density of 1.75 Mg/m mold with dimension of 50 mm in diameter and 100 mm in height to achieve a dry density of 1.75 3 (i.e., 95% of the maximum dry density of 1.84 Mg/m ). 3 3). Mg/m 95% ofwas theproperly maximum dry density of 1.84 Mg/m The(i.e., specimen mounted on a modified triaxial apparatus and sealed in a latex rubber The specimen was properly mounted on a modified triaxial sealedinin a latex membrane with O-rings. Two SDTs were installed on the surface of theapparatus specimen and as shown Figure 9. rubber membrane with O-rings. Two SDTs were installed on the surface of the specimen as shown in Each SDT was attached on the membrane by employing two metal hinges which were glued on the Figure 9. Each wasepoxy attached onAfter the membrane byand employing two metal hinges which were membrane with aSDT special resin. the specimen SDTs were installed, the outer chamber glued on the membrane with a special epoxy resin. After the specimen and SDTs were installed, the was filled with distilled water. Then, the specimen was saturated under a confining pressure of 50 kPa outer chamber was filled with distilled water. Then, the specimen was saturated under a confining and back pressure of 45 kPa. After completion of saturation, the specimen was consolidated with of 50 kPa and back pressure of consolidation 45 kPa. After iscompletion of saturation, specimen was apressure target isotropic confining pressure. The finished when the degreethe of consolidation consolidated with a target isotropic confining pressure. The consolidation is finished when the is found to be 95%. The specimen was then sheared with a shearing rate of 0.005 mm/min under degree of consolidation is found to be 95%. The specimen was then sheared with a shearing rate of a constant confining pressure. During shearing, the readings of the SDTs and external LVDTs were 0.005 mm/min under aby constant pressure. During shearing, the readings of the SDTs and continuously recorded the dataconfining logger and a computer. external LVDTs were continuously recorded by the data logger and a computer.

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4. Test Results and Discussions 4. Test Results and Discussions Figure 10 shows three stress-strain results of the SDTs and the external LVDTs under constant Figure 10 showsofthree stress-strain results the In SDTs andtothe externalaLVDTs under constant confining pressures 50 kPa, 100 kPa, and 200ofkPa. order facilitates detailed performance confining pressures of the 50 kPa, 100ofkPa, and 200 kPa. In orderare to facilitates a detailed performance evaluation of the SDT, results stress-strain relationship plotted using different maximum evaluation of theand SDT, the of results stress-strain relationship plotted using different maximum scales (i.e., 0.1% 0.5%) axial of strain (as depicted in Figureare 10a,b). From Figure 10b, the external scales (i.e., 0.1%measure and 0.5%)the of axial strain (as depicted in Figureof10a,b). From Figure 10b,and the external LVDT cannot strain below 0.01% because the bending errors system LVDT cannot measure the strain below 0.01% because of the bending errors and system compliances. compliances. It is observed that the local SDT results are appreciably smaller than the external LVDT It is observed thatThe the same local SDT resultsfrom are appreciably the external measurements. measurements. findings literature smaller [2,6,11]than indicated that LVDT the external LVDT The same findings fromstrains literature [2,6,11] indicated theand external LVDT overestimates the overestimates the axial because of the bendingthat errors system compliances. Goto et al.axial [11] strains because of the bending errors and system compliances. Goto et al. [11] found that the axial strain found that the axial strain measured by external device was almost twice higher than the strain device was almost twice than the strain measured localdeformations deformation measured by external local deformation transducer. As higher the SDT is proposed to measurebylocal transducer. As the SDT is proposed local deformations soil specimen of soil specimen as indicated in Figureto9, measure the current LVDTs cannot beof directly installedas at indicated the same in Figure of 9, the SDT current LVDTs be due directly installed the same of the SDT in the positions in the soil cannot specimen to the limitedat space of thepositions triaxial apparatus and soil specimen to the limited space of the apparatus and the specimen. The independent specimen. Thedue independent comparison of triaxial the SDT was conducted in the calibration tests as comparisoninofthe theprevious SDT wassections. conducted in the testscompared as elaborated the previous sections. elaborated Here, the calibration SDT was only withinexternal LVDTs which Here,also the SDT was only compared external LVDTs which were also reported in the literature [6,11]. were reported in the literaturewith [6,11].

Figure 10.Stress-strain Stress-strainrelationship relationship between deviator andstrain axialunder straindifferent under confining different Figure 10. between deviator stressstress and axial confining pressures: (a) Strain scale of 0 to 1%; (b) Strain scale of 0 to 0.1%. pressures: (a) Strain scale of 0 to 1%; (b) Strain scale of 0 to 0.1%.

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The accuracy of the SDT depends on several factors, such as: (1) the resolution of the FBG sensors; (2) the resolution of the fiber optic sensing interrogator; (3) the calibration coefficient; (4) the glue quality of the FBG sensor and the hinges; (5) any creep errors introduced between the membrane and the soil specimen. The items (1) and (2) are sources of errors common in any FBG sensor and also in traditional electrical transducers. The initial hysteresis is negligible and can be reduced by applying initial bending when setup the SDT during the test. The contact force between hinges and membrane increases with the deformation of SDT, which may further lead to the creep in hinges. However, the creeps of the hinges were examined by Goto et al. [11]. The results indicated that the rate of creep of the hinges introduced between the membrane and the soil specimen was 1 µm per day. Thus, considering the testing period for a standard soil test, the creep effect is negligible. Considering the described factors, it can be concluded that the SDT can be used effectively to measure the small strain behavior of soil specimens with good accuracy. 5. Conclusions In this study, a measurement approach for small deformations of soil specimens was proposed. A small deformation transducer (SDT) has been designed, fabricated, calibrated and installed in a modified triaxial apparatus. An analytical solution has been developed to obtain the relationship between the wavelength shifts of the FBG sensors and the local deformations of the SDT. The calibration test of the SDT proves that it can be used to measure local deformations and enables it to determine soil strength and stiffness at small strain levels. The SDT was employed in a modified triaxial test for measuring the small deformation behavior of soil specimens under different confining pressures. Different confining pressure tests were conducted and the results prove that the SDT works well in the presence of water. The SDT is more feasible to be used for local deformation measurements of soil specimens in a triaxial apparatus as it has obvious merits such as light weight, high accuracy, resistance to corrosion and ease of handling. It can be hoped that the SDT can be further developed for investigating the small deformation behavior of other materials such as rock and concrete under different loading conditions. Acknowledgments: The financial supports of a research grant of National Natural Science Foundation of China (project No. 51508215) and the Fundamental Research Funds for the Central Universities, HUST (The Huazhong University of Science and Technology, project No. 2017KFYXJJ138 ) are gratefully acknowledged. Author Contributions: D.-S.X. designed the experiments, analyzed the data and wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

Simpson, B.; O’Riordon, N.J.; Croft, D.D. A computer model for the analysis of ground movements in London Clay. Geotechnique 1979, 29, 149–175. [CrossRef] Jardine, R.J.; Symes, M.J.; Burland, J.B. The measurement of soil stiffness in triaxial apparatus. Geotechnique 1984, 34, 323–340. [CrossRef] Simpson, B. Retaining Structures: Displacement and Design. Geotechnique 1992, 42, 541–576. [CrossRef] Gasparre, A.; Coop, M. Techniques for performing small-strain probes in the triaxial apparatus. Geotechnique 2006, 56, 491–495. [CrossRef] Scholey, G.K.; Frost, J.D.; Presti, D.C.F.L.; Jamiolkowski, M. A review of instrumentation for measuring small strains during triaxial testing of soil specimens. Geotech. Test. J. 1995, 18, 137–156. Clayton, C.R.I. Stiffness at small strain: research and practice. Geotech. 2011, 61, 5–37. [CrossRef] Dyvik, R.; Madshus, C. Laboratory Measurements of Gmax Using Bender Elements. Adv. Eng. 1985, 161, 117–137. Leong, E.C.; Yeo, S.H.; Rahardjo, H. Measuring shear wave velocity using bender elements. Geotech. Test. J. 2005, 28, 488–498. Pennington, D.S.; Nash, D.F.T.; Lings, M.L. Anisotropy of G0 Shear Stiffness in Gault Clay. Geotechnique 1997, 47, 391–398. [CrossRef]

Sensors 2017, 17, 1016

10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.

21. 22. 23.

13 of 13

Hird, C.C.; Yung, P.C.Y. The Use of Proximity Transducers for Local Strain Measurements in Triaxial Tests. Geotech. Test. J. 1989, 12, 292–298. Goto, S.; Tatsuoka, F.; Shibuya, S.; Kim, Y.S.; Sato, T. A Simple Gauge for Local Small Strain Measurement in the Laboratory. Soils Found. 1991, 31, 169–180. [CrossRef] Dasari, G.R.; Bolton, M.D.; Ng, C.W.W.N. Small Strain Measurement Using Modified LDTs; Report CUED/D/-SOILS/TR275 Geotechnical Group; Cambridge University: Cambridge, UK, 1995. Yimsiri, S.; Soga, K.; Chandler, S.G. Cantilever-Type Local Deformation Transducer for Local Axial Strain Measurement in Triaxial Test. Geotech. Test. J. 2005, 28, 445–451. Ibraim, E.; di Benedetto, H. New Local System of Measurement of Axial Strains for Triaxial Apparatus Using LVDT. Geotech. Test. J. 2005, 28, 436–444. Alwis, L.; Sun, T.; Grattan, K.T.V. Optical fibre-based sensor technology for humidity and moisture measurement: Review of recent progress. Measurement 2015, 46, 4052–4074. [CrossRef] Ho, Y.T.; Huang, A.B.; Lee, J.T. Development of a fibre Bragg grating sensored ground movement monitoring system. Meas. Sci. Technol. 2006, 17, 1733–1740. [CrossRef] Xu, D.S.; Yin, J.H.; Cao, Z.Z.; Wang, Y.L.; Zhu, H.H.; Pei, H.F. A new flexible FBG sensing beam for measuring dynamic lateral displacements of soil in a shaking table test. Measurement 2013, 46, 200–209. [CrossRef] Zhu, H.H.; Shi, B.; Yan, J.F.; Zhang, J.; Zhang, C.C.; Wang, B.J. Fiber Bragg grating-based performance monitoring of a slope model subjected to seepage. Smart Mater. Struct. 2014, 23, 095027. [CrossRef] Zhu, H.H.; Shi, B.; Yan, J.F.; Zhang, J.; Wang, J. Investigation of the evolutionary process of a reinforced model slope using a fiber-optic monitoring network. Eng. Geol. 2015, 186, 34–43. [CrossRef] Pei, H.F.; Yin, J.H.; Zhu, H.H.; Hong, C.Y.; Wei, J.; Xu, D.S. Monitoring of lateral displacements of a slope using a series of special fibre Bragg grating-based in-place inclinometers. Meas. Sci. Technol. 2012, 23, 025007. [CrossRef] Xu, D.S.; Yin, J.H. Analysis of excavation induced stress distributions of GFRP anchors in a soil slope using distributed fiber optic sensors. Eng. Geol. 2016, 213, 55–63. [CrossRef] Hill, K.O.; Fujii, F.; Johnson, D.C.; Kawasaki, B.S. Photosensitivity on optical fiber waveguides: Application to reflection filter fabrication. Appl. Phys. Lett. 1978, 32, 647–649. [CrossRef] Xu, D.S. Development of Two Optical Fiber Sensing Technologies and Applications in Monitoring Geotechnical Structures. Ph.D. Thesis, The Hong Kong Polytechnic University, Hong Kong, China, 2014. © 2017 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).