Monitoring shear deformation of sliding zone via fiber Bragg grating and particle image velocimetry

Deyng Wng ,Honghu Zhu,b,* ,Guyu Zhou ,Wenzho Yu ,Bojun Wng ,Wnhun Zhou

a School of Earth Sciences and Engineering,Nanjing University,Nanjing,210023,China

b Institute of Earth Exploration and Sensing,Nanjing University,Nanjing,210023,China

c State Key Laboratory of Internet of Things for Smart City,University of Macau,Macau,China

Keywords: Landslide Shear band Fiber bragg grating (FBG)Particle image velocimetry (PIV)Sinusoidal model Strain-displacement proportional coefficient

ABSTRACT Monitoring shear deformation of sliding zones is of great significance for understanding the landslide evolution mechanism,in which fiber optic strain sensing has shown great potential.However,the correlation between strain measurements of quasi-distributed fiber Bragg grating (FBG) sensing arrays and shear displacements of surrounding soil remains elusive.In this study,a direct shear model test was conducted to simulate the shear deformation of sliding zones,in which the soil internal deformation was captured using FBG strain sensors and the soil surface deformation was measured by particle image velocimetry(PIV).The test results show that there were two main slip surfaces and two secondary ones,developing a spindle-shaped shear band in the soil.The formation of the shear band was successfully captured by FBG sensors.A sinusoidal model was proposed to describe the fiber optic cable deformation behavior.On this basis,the shear displacements and shear band widths were calculated by using strain measurements.This work provides important insight into the deduction of soil shear deformation using soil-embedded FBG strain sensors.

1.Introduction

Landslide is one of the most serious geological disasters and poses a significant threat to human safety and infrastructure operations on an annual basis worldwide (Kogure and Okuda,2018;Schulz et al.,2018).The landslide movements are mainly dominated by the shear deformation behaviors of sliding surfaces or zones (Alshibli et al.,2003;Scaringi et al.,2018).Therefore,an extensive understanding of sliding surface deformation is of great importance for performing stability assessments of slopes and early warning of landslide events.

Modern techniques for capturing landslide deformation can be divided into two types,i.e.surface monitoring and subsurface monitoring.Surface measuring techniques,e.g.photogrammetry(Baldi et al.,2008),global navigation satellite system (GNSS)(Mantovani et al.,2022),and synthetic aperture radar(SAR)(Cenni et al.,2021),can only obtain local and regional displacements,and the measuring accuracy highly relies on meteorological conditions and site environments.In contrast,geotechnical instruments for measuring subsurface movements,e.g.inclinometers (Yan et al.,2020) and extensometers (Corominas et al.,2000),enable the measurement of subsurface displacements and the identification of potential sliding surfaces,but they can hardly perform large-scale,long-distance and real-time monitoring (Zhu et al.,2017a).Therefore,there is an urgent need to develop more advanced measurement methods of soil shear deformation to reveal the failure modes of the soils in the sliding zone.

In recent years,fiber optic sensing technologies have been successfully applied to geohazard monitoring(Iten,2011;Klar et al.,2014;Damiano et al.,2017;Schenato et al.,2017;Cao et al.,2022;Zhu et al.,2022a).Compared with the abovementioned sensors,fiber optic sensors offer a variety of benefits,such as high resistance to corrosion,high precision,and miniature size.In particular,they can sensitively measure strain and temperature distributions along a long distance like human nerves (Zhu et al.,2017a,b,2022b).For landslides,they are frequently deployed in boreholes to detect vertical strain profiles due to shear movements (Sun et al.,2014;Kogure and Okuda,2018;Zhang et al.,2018;Ye et al.,2022;Wang et al.,2023).Since the fiber optic sensors can only measure axial strains along their total lengths,a reliable conversion model between the measured strains and shear displacements is essential.In Japan,a full-scale test was conducted by Sugimoto et al.(2001) to investigate the feasibility of soil-embedded fiber optic (FO) cables for shear deformation detection.However,they only conducted a qualitative experimental study.In Switzerland,Hauswirth et al.(2012) performed a shear model test in laboratory and used strain integration-based shear displacements to estimate landslide movements.Based on these works,Zhang et al.(2018)innovatively proposed the longest-path and shortest-path models for calculating soil shear displacements using strain measurements.The reliability of the proposed method was verified by the test results of Sugimoto et al.(2001) and field monitoring data of a reservoir landslide.In the experimental and theoretical studies of Wu et al.(2020) and Wang et al.(2023),more factors were considered,and the relevant algorithms were further improved for the convenience of field application.

The distributed fiber optic sensing (DFOS) used in the abovementioned studies provided valuable insights into understanding sliding zone behaviors and landslide triggering mechanisms.However,due to the limitations in the scanning rates of the DFOS systems and the high cost involved,capturing dynamic deformations and evaluating slope stability in real time are challenging.On the contrary,fiber Bragg grating (FBG) enables realtime and long-term monitoring with higher measurement accuracy and frequency and lower budgets.Dozens or hundreds of FBG sensors can be connected in series to form a quasi-distributed sensing array with the aid of wavelength or time division multiplexing techniques (Zhu et al.,2017a,b).In the past few decades,FBG sensors have been successfully used to perform continuous monitoring of a variety of geotechnical infrastructures,such as slopes (Huang et al.,2012;Ye et al.,2022),foundations (Cao et al.,2022),tunnels (Wang et al.,2013;Zhu et al.,2022b),and underground pipelines(Wang et al.,2021).Previous studies indicate that soil-embedded FBG sensors can sensitively detect soil deformation patterns by measuring strain variations.However,few attempts have been made to determine the quantitative relationship between FBG strain measurements and soil shear displacements,which is essential for the development of FBG-based landslide deformation monitoring systems.

On the other hand,particle image velocimetry (PIV),as a popular noncontact measurement method,can identify the soil deformation fields by comparing the movement of pixels in different photographs.Using this method,Zhang et al.(2019)investigated the pattern of horizontal and vertical displacement fields beneath a loaded strip footing and found that the soil deformation pattern resembled those in the classical Prandtl slipline theory.Sun et al.(2020) measured the deformation fields of a geogrid-reinforced model slope and established a relationship between geogrid characteristic strains and factors of safety of the slope.In recent years,this technique has been widely used in laboratory model tests for investigating soil-structure interaction mechanisms.Huang et al.(2021)and Li et al.(2022)employed the PIV technique to evaluate the uplift performance of pipes buried in flat ground and slopes,respectively,and the influence factors of peak uplift resistance and soil failure mode are systematically explored.Different from fiber optic sensors that can only measure one-dimensional tensile or compressive strains and may have interface slipping problems during monitoring,PIV can accurately and reliably obtain soil strain fields.Therefore,it is an important supplement and verification method for fiber optic sensors in laboratory model tests and also can be used to study the deformation compatibility between FO cables and surrounding soil (Wu et al.,2020).

In this study,FBG and PIV are combined to characterize the soil shearing process in a direct shear model test.The shear failure patterns of the soil mass were summarized.A shape-based calculation method was proposed to analyze strain measurements for estimating shear displacements.The feasibility of this approach was verified by the experimental results.

2.Methodology

FBG and PIV are two advanced measurement techniques for measuring soil deformation.The former is used to measure the soil internal deformation,whereas the latter is used to obtain the surface deformation information.The combination of two measurement techniques enables the acquisition of multiple parameter including soil surface displacement fields,strain fields,and internal soil strain distribution.

2.1.Working principle of FBG

Since the birth of the first FBG sensor in the 1970s,FBG sensors have been widely used as strain or temperature sensors for geotechnical monitoring(Zhu et al.,2017b).As shown in Fig.1,the refractive index will typically alternate over a defined length,which is given by

Fig.1.Principle of the FBG sensing technique.

where λBis the Bragg wavelength,and the typical values are between 1510 nm and 1590 nm;neis the effective refractive index of the grating in the fiber core;and Λ is the grating period.

When a broadband input signal is injected into the fiber and interacts with the grating,only the wavelength of λBcan be backreflected without any perturbations in the other wavelengths.The Bragg wavelength of the reflected light of an FBG sensor has a linear relationship with strain and temperature:

where Δε is the change in the axial strain in the FO cable;and ΔTis the change in the environmental temperature;andcεandcTare the calibration coefficients for strain and temperature,respectively.Several gratings with various Bragg wavelengths can be inscribed along the same fiber,which is called multiplexing.The reflected signal includes a series of different Bragg wavelengths.Multiplexing is the key advantage of FBG because it enables quasidistributed measurement.The typical values ofcεandcTare 0.78 and 6.67 ×10-6°C-1,respectively.

2.2.Working principle of PIV

PIV is an efficient noncontact technique for measuring surface deformation of a medium (Zhang et al.,2019;Wang et al.,2021).This technique was originally proposed to measure instantaneous velocities of fluids and later introduced to geotechnical applications by White et al.(2003).A series of photographs captured during a geotechnical model test is analyzed in sequence,starting with an initial reference image.For PIV analyses,the photograph is divided into a series of subsets.Each reference subset is allowed to deform using image-intensity interpolation techniques to improve the correlation between reference and target subsets (Stanier et al.,2016).The displacement vector of the target patch is obtained by locating the peak of the autocorrelation function of each subset between images 1 and 2,as shown in Fig.2.The soil deformation can be obtained by comparing the coordinates of each patch within the images of the sequences.

Fig.2.Schematic illustration of the PIV technique.

3.Laboratory model tests

3.1.Test materials

A series of direct shear model tests has been conducted in this study.The soil used in the test was clean river sand,which was collected from the Yangtze River,Nanjing,China.The grain size distribution of the soil is presented in Fig.3.The soil has an effective particle size(d10)of 0.18 mm,a mean particle size(d30)of 0.29 mm,and a constrained particle size (d60) of 0.35 mm.The test soil is classified as poorly graded coarse sand(ASTM D2487-17,2017).By using direct shear tests,the friction angle of the sand at a relative density,Dr,of 23% was measured to be 32°.The normal stresses on the soil specimens in these direct shear tests were set to 100,200,300 and 400 kPa,and the loading rate was 0.02 mm/min (ASTM D6528-17,2017).The basic physical and mechanical properties of the test soil are listed in Table 1.

Table 1Physical and mechanical properties of the test soil.

Fig.3.Grain size distribution of the test soil.

Two strain sensing cables with serially connected four FBG strain sensors were prepared for soil deformation monitoring.The bare FBGs were 0.25 mm in diameter and 15 mm in grating length.All sensors were calibrated in laboratory before the tests.The average calibration coefficients for strain and the monitoring accuracy of the FBG sensors were 0.78 and±0.8×10-6,respectively.According to Iten(2011)and Zhang et al.(2019,2020),the slipping problems of the cable-soil interface can be solved by adding anchors to the cables.Therefore,heat-shrink tubes were mounted on the cable surface with a spacing of 85 mm.These tubes have outer layers formed by radiation cross-linked polyolefins,and inner layers of hot melt adhesive,with a total length of 30 mm and an outer diameter of 1.5 mm before being heated by the fusion splicer.Since the laboratory temperature was kept at 26°C during the tests,the influence of temperature variations on the FBG strain measurements was neglected.

3.2.Test setup

The test setup is shown in Fig.4.The test equipment consisted of a shear box,in which the soil specimen was placed,and several sensors.The interior dimensions of the shear box were 760 mm long,380 mm wide,and 120 mm high.It was divided transversely into two halves.Shear force was applied by moving one-half of the box relative to the other to induce failure in the soil specimen.

Fig.4.Test setup (unit: mm): (a) Photograph of the test devices,(b) A region of interest (ROI) for PIV analysis,and (c) Layout of the FBG sensing array in plan view.

The soil was manually tamped every 10 mm to a height of 80 mm.At a height of 40 mm from the bottom of the box,two FBG arrays(labeled SOF-1 and SOF-2)were carefully laid on the surface and embedded FO cables with a length of 680 mm were passed through pre-fabricated holes on the sidewalls of the shear box with a diameter of 1 mm (as shown in Fig.4b).The soil was then filled while ensuring that the FBG arrays remained in place.The dry density and moisture content of the soil were 1.6 g/cm3and 3%,respectively.To enhance the texture of the exposed soil face,four lines with red fine sand were laid on the surface,which effectively improved the precision of image-based deformation analyses.

In addition to the FBG strain sensors,two dial indicators were installed on the shear box to measure the shear displacements,as shown in Fig.4a.The displacements of the shear box were collected by a data acquisition system for subsequent processing.A highprecision Canon EOS 600D digital camera was placed above the whole set to take continuous photographs for analyses using the GeoPIV-RG software.The camera was set to ISO 800,aperture f/5.6,and exposure time 1/40 s during the test.For PIV analyses,the region correlation threshold and overall correlation threshold were set to 0.9 and 0.75,respectively,to avoid the phenomenon of blank values (Stanier et al.,2016).An NZS-FBG-A02 FBG sensing interrogator,produced by Suzhou NanZee Sensing Technology Co.,Ltd.,China,was used to continuously collect the fiber optic monitoring data at a frequency of 1 Hz.Detailed information on the FBG sensing interrogator is listed in Table 2.

Table 2Detailed information of the FBG sensing interrogator.

3.3.Test program

In a drained direct shear test,the loading rate is generally set to 0.8 mm/min to reduce the generation and dissipation of excess pore water pressure in the soil(Zhou et al.,2010;ASTM D6528-17,2017).To replicate this condition,a transverse loading rate of 0.5 mm/min was applied on the right half of the shear box during the model tests(Wu et al.,2020).Real-time data collection was performed by all sensors throughout the test,while the digital camera continuously recorded the deformation information of the soil mass.

4.Test results

4.1.FBG results

In this study,several direct shear model tests were conducted.Fig.5 shows the typical monitoring results of the FBG sensing arrays.To show the test results more clearly,only a part of the data from a large number of strain measurements are selected to plot figure.In Fig.5,the dashed lines represent the boundary between the left and right halves of the shear box.Considering that the measuring range of the FBG strain sensor was-0.0035-0.0035,the maximum transverse displacements for analyses were chosen as 20 mm in the tests.As shown in Fig.5a,the tensile strains of the FBG sensors gradually accumulated with the development of soil transverse displacements.When the shear displacements were smaller than 6 mm,the dominant discontinuity of strains was concentrated in a small zone in the vicinity of the predefined shear plane,suggesting that the strain variations were caused by the formation of the shear plane.The soil mass at the central axis displaced transversally and stretched the FBGs toward both sides,thus inducing tensile strains in the FBGs.In addition,soil shear failure occurs along the boundary between the left and right halves of the shear box.Therefore,the shear deformation propagated almost along the center of the FBG arrays,indicating the high accuracy of FBG-based measurements.

Fig.5.Distribution of strains measured during the direct shear test: (a) SOF-1 and (b) SOF-2.

The strain distributions along each FBG sensing array were successfully recorded during the tests.The following generalizations can be developed from Fig.6 regarding the variation in measured strains with shear displacements.The strain-displacement proportional coefficientkis defined as the ratio of the strain change to the change in soil shear displacement,which is expressed by

Fig.6.Strain versus shear displacement curves during the direct shear test: (a) SOF-1 and (b) SOF-2.

The soil deformation process can be divided into two phases.In phase I,the measured strain increased slightly with the increasing displacement.However,it increased abruptly under sustained shearing in phase II.A possible explanation for this phenomenon was the development of plastic strains in the shear zone and shear softening behavior in the shear plane.Fig.7 shows a typical variation in the stress ratio and volume change with respect to the imposed horizontal displacement in a direct shear test (based on data from Shibuya et al.,1997).The soil response can be divided into four characteristic phases,i.e.elastic behavior,plastic behavior,softening behavior,and residual behavior.For the dense sand,the resisting shear stress increases with shear displacement until it reaches the peak shear strength.After failure stress is attained,the resisting shear stress gradually decreases as shear displacement increases (Das,2016).Therefore,the failure occurred along the predefined shear plane (Fig.5),resulting in a sudden increase in tensile strains of the FBGs.

Fig.7.Typical variation in the stress ratio and volume change with respect to horizontal displacement in a direct shear test (Shibuya et al.,1997).

Moreover,the strains measured by FBG-1,FBG-2,FBG-3,FBG-5,FBG-6 and FBG-7 were larger than those measured by FBG-4 and FBG-8,which could be attributed to the influencing range of the shear band.The FBG-4 and FBG-8 have the lowest strain increase rate during the test and may suffer from a relatively slight influence.The FBG strain measurements on SOF-1 show a sudden change when the transverse displacement was 7.5 mm.In contrast,such variations for SOF-2 mainly occurred at 10.5 mm,as shown in Fig.6b.The reason is that SOF-2 is far away from the position of the applied load,leading to the shear failure being slower than that of the soil surrounding SOF-1.Based on the above observation,the advantage of the FBGs is that in the case of dense sand,the process of soil shear failure can be observed and distinguished.

4.2.PIV results

To fully understand the strain distribution in the shear band,digital photographs of the soil were taken and evaluated with the PIV technique.An additional requirement that has to be considered is the optimal dimension of the analyzed region.The sample width should be reasonable to reduce the influence of the boundary effect between the soil mass and box sidewalls.Several tests were performed in advance,resulting in an optimal length and width of the specimen of 650 mm and 350 mm,respectively.

As shown in Fig.8a-d,the measured transverse displacements on the soil surface increased as the shearing process progressed.The transverse displacements on the soil surface were approximately in agreement with the readings of dial gages.In Fig.8a,the zone of abrupt change of soil displacements was mainly concentrated in the interface between the two half boxes(the predefined shear plane),resulting in compression and shearing of the localized soil mass.When the transverse displacement reached 10 mm,the soil mass pressed sideways from the end of the sample and exhibited a large deformation band in the soil mass(Fig.8b).As the transverse displacements increased,two shear slip surfaces slowly took form in the soil mass and formed a shear band with the shape of a spindle(Fig.8c).Finally,a secondary failure surface appeared in the spindle-shaped zone at the end of the direct shear test(Fig.8d).

Fig.8.Contours of soil transverse displacement calculated by PIV analyses.

To fully understand the shear failure behaviors of the soil in this test,soil shear strain fields were extracted and plotted in Fig.9.The shear strain contour plot in the soil mass at a right box moving displacement of 5 mm is shown in Fig.9a.In the early phase of the soil shearing,most of the soil mass was in an elastic state,and the shear deformation was concentrated only around the predefined shear plane.When the shear displacements reached 10 mm,the maximum shear strain of the soil was close to 35%.The shear strain zone was inclined and extended upward to the soil mass,indicating the formation of a plastic zone,as shown in Fig.9b.Then,the shear band in the soil propagated at an accelerating rate and finally extended two curved slip surfaces in the soil mass(Fig.9c and d).A Mohr’s circle can be drawn to represent this shear failure phase(Fig.10).As shear failure occurs,the transverse stress is allowed to increase,while the vertical stress on the shear band is assumed to remain unchanged.The forming slip surfaces show an angle of inclination θ with respect to the horizontal of 45°+φpeak/2(φpeakis the peak friction angle of the sand)(Wolf et al.,2003).As shown in Fig.9d,the angle of inclination is 61°with respect to the horizontal axis,and the maximum shear strain of the soil was approximately 65%.Moreover,the range of the shear band will not change significantly,but the shear strains of the internal soil mass will increase as the shear displacements increase.

Fig.9.Soil shear strains calculated by PIV analyses.

Fig.10.Mohr’s circle of soil elements on the slip surface.

Referring to Fig.6,FBG measurements can effectively identify the plastic and softening behaviors in the soil,with a sudden change in strain profile curves.These observations were consistent with shear strains determined via PIV analyses.Based on analyses of the displacement vector fields,the failure region in the soil mass looked like a spindle shape.The maximum shear strain is distributed on the shear plane.This was in accordance with the findings of Li et al.(2007).The distance between two slip surfaces can be roughly estimated and plotted in Fig.11.Notably,the shear band was not rigid.In addition to its shrinkage in size,tensile and compressive deformation existed within the shear band.

Fig.11.Soil shear strain at the locations of SOF-1 and SOF-2 via PIV analyses.

4.3.Validation of FBG strain measurements

To validate FBG strain measurements,it is essential to compare them with results obtained using other measurement methods.However,existing instruments such as linear variable displacement transducers,electric strain gages,and extensometers will inevitably disturb in situ stress and strain fields when deployed in geotechnical model tests(Iten,2011;Damiano et al.,2017).In this study,we adopted the analysis methods from previous studies (Zhang et al.,2016,2019;M?ller et al.,2022) and conducted an integrated FBG and PIV-based performance evaluation of soil shear deformation.

Fig.12 presents the strains measured by FBG arrays as well as equivalent strains determined via PIV analyses.It is found that the strain distribution pattern of the soil mass obtained by the two methods was similar.However,the strain magnitudes measured by the FBG sensors were much smaller.This was likely due to the deformation compatibility between the FBGs and soil.In this aspect,a pioneering study reported by Wu et al.(2020)pointed out that the cable-soil shear coupling coefficientKcan be adopted to evaluate the cable-soil coupling condition,which is expressed by

Fig.12.Qualitative comparison of FBG strain measurements with equivalent strains determined via PIV analyses.

wheredis the shear displacement(m);ε（x）is the measured strain along the FO cable (με);ais the boundary of shear-affected zone(m);andL0andLdare the cable lengths before and after soil deformation,respectively.The cable-soil coupling states under shearing conditions can be divided into three categories(i.e.cablesoil well-coupled state,cable-soil slipped state,and post-slippage state),and can be identified using the cable-soil shear coupling coefficient.

Based on the test results,the relationship between the cable elongations and soil transverse displacements on each FO cable was retrieved.As presented in Fig.13,SOF-1 and SOF-2 exhibit highR2values,verifying the results of Zhang et al.(2020)that tube anchors can improve cable-soil deformation compatibility.Thus,it can be inferred that SOF-1 and SOF-2 had not slipped from the surrounding soil throughout the whole shearing procedure and sustained the well-coupled state throughout the whole shearing procedure.Based on the above analyses,the following factors should also be noted when verifying the validity of FBG strain measurements via PIV analyses: (1) The assumed plane-strain condition cannot be completely assured during the tests.This could be ascribed to the bulge deformation at the soil surface,which leads to accumulative errors in the PIV measurement;(2)Using a quasi-distributed FBG array can only capture discrete information.Hence,PIV measurements can provide necessary complements for FBG sensors in laboratory tests.Moreover,the strain measured by the anchored FBG sensing array was further averaged over the anchor spacing.This issue deserves special attention and needs to be further investigated.deformation under shearing normal to the cable axis to estimate the tensile strains measured by FBGs.For this purpose,the sensing cable is assumed to deform in an S-shaped “shearing type”configuration,as shown in Fig.14.In this study,the shape of the sensing cable follows a sinusoidal model,and the corresponding equation is expressed as

Fig.13.Cable elongation versus shear displacement curves.

Fig.14.An analytical method for calculating shear displacements based on strain measurements:(a)Assumed shape function u(x)for the FO cable,and(b) Comparison of the transverse displacement of the FO cable from Eq.(5) and transverse displacement obtained by PIV analyses.

whereusis the shear displacement anddsis the length of the Sshaped deformed sensing cable at the initial cable configuration(m).Note thatxgoes from-ds/2 tods/2.Based on the analyses in Section 4.3,the sensing cable moves with the surrounding soil together and has the same deformation mode as the soil mass.

4.4.Quantitative evaluation of soil shear progressive failure

The displacement is the most straightforward physical parameter for characterizing the soil shear deformation behavior.Therefore,we develop a simplified formulation for sensing cable Therefore,the shape of the deformed FO cable is derived by PIV analyses from the assumed mathematical shape given by Eq.(5).

From Eq.(5),the increase in the FO cable length between two points atx=-ds/2 andx=ds/2 (FO cable stretching) is

Therefore,the corresponding axial strain of the FO cable εmat the origin of the coordinates is

Using the following series expansion

and keeping only the first two terms,the axial strain of the FO cable from Eq.(7) becomes

According to previous studies(Iten et al.,2008;Hauswirth et al.,2012;Wu et al.,2020),it is assumed that the maximum strain along the cable is located at the predetermined shear plane.Eq.(9)shows that the measured maximum strain is determined by the shear displacement and the width of the shear band.Based on the PIV analyses,the shear band widths increased synchronously with increasing shear displacements in the early shearing phase.However,a complete shear plane generally developed after the peak shear strength of the soil,and then the shear band width remained constant,while the measured maximum strain still increased with the shear displacement.This explains why the strain profile changed suddenly during the increase in shear displacement,as shown in Fig.6.Normally,strain localization,which is the consequence of progressive damage of the sliding surface,leads to the formation of a narrow shear band.Landslide movement may occur along this shear band,and trigger constant acceleration of the landslide mass (Lacroix et al.,2020).Hence,the development of measured strains can reflect the slow and rapid motions of landslides.Based on the above analyses,the shear band gradually formed in the soil mass after the shear stress reached the maximum value.Then,the soil shear displacement and measured strain corresponding to the inflection point in Fig.15 are defined asucriticaland εcritical,respectively.As shown in Fig.6,the values ofucriticalat the locations of SOF-1 and SOF-2 are 7.5 mm and 10.5 mm,respectively,which are smaller than the maximum shear displacement (i.e.20 mm).Therefore,the proposed straindisplacement proportional coefficientkcan be regarded as a discriminating indicator for identifying the evolutionary stages of landslide deformation,which proved to be a new way to forecast sliding events.

Fig.15.Measured strain versus shear displacement curve (Marone,1998;Moore and Iverson,2002).

In engineering practice,the strains measured by FBG sensors need to be converted to displacements to facilitate deformation and stability analyses.For this purpose,several analysis models have been proposed to calculate the soil shear displacements by measured strains,such as the triangle and arc models (Iten et al.,2008;Li et al.,2015;Zhang et al.,2018).The triangle and arc models assume that the deformation of the FO cable within the shear band is in a triangle or arc shape,respectively,as shown in Fig.16a and b.However,the calculation results of the triangle model may greatly deviate from the real values,which is mainly due to the simple hypotheses of the deformation patterns of FO cables.For the arc model,there are many parameters to be determined,resulting in lower computational efficiency of shear displacements in practical applications.

Fig.16.Deformation patterns of the FO cable embedded in the soil: (a) Schematic diagram of the soil shearing process,and (b) Two typical deformation patterns of the FO cable.

Based on the sinusoidal model mentioned above,the shear displacements can be obtained by FBG strain measurements after determining the length of the S-shape deformed sensing cableds(Eq.(9)).In the study of Zhang et al.(2018),dswas assumed to be the length of the affected sensing cable due to shearing in a straindistance plot.For the direct shear model tests in this study,dscan be obtained from FBG-measured strain profiles and displacement fields through PIV analyses.Therefore,dswas taken as 0.2 m at the initial phases (i.e.0 ＜us＜10 mm),while it was estimated to be 0.38 m after a complete shear band formed in the soil mass (i.e.10 mm ≤us≤20 mm).The shear displacements derived from these three models were plotted with respect to the displacements recorded by dial gages,as shown in Fig.17a-c.Overall,the shear displacements obtained from Eq.(9) agreed fairly well with the measured displacements,with an average relative error of 13.1%.Furthermore,the average relative errors of the triangle and arc models were 28.9% and 14.8%,respectively.This illustrates the effectiveness of the proposed method in this study.

Fig.17.Measured and calculated results of shear displacements:(a)Sinusoidal model,(b)Triangle model,and(c)Arc model.Black dashed line indicates 1:1 ratio and gray dashed lines indicate 1:1.2 and 1:0.8 ratios,representing a 20% uncertainty.

To date,most studies have used the computerized X-ray tomography or PIV techniques to investigate soil surface deformation(Shi et al.,1999;Hall et al.,2010),with only a few studies considering the internal movements of soil mass.In particular,measuring the formation of shear bands in soil is challenging.Hence,a preliminary attempt was made to calculate the shear band width using fiber optic strain measurements.It should be noted that the imperfect coupling between the soil mass and FO cables will cause a deviation in strain measurements(Zhang et al.,2020).For a poor coupling condition,there may be two additional deformed segments within stable and unstable soil masses.However,this situation was not considered here.

Fig.18 shows the shear band widths under various shear displacements calculated by Eq.(9).The shear band widths increased to a certain value with increasing shear displacements.The calculated shear band widths for the locations of SOF-1 and SOF-2 were nearly 23.6 cm and 30.8 cm,respectively (Fig.18).These results were consistent with the findings of PIV analyses,with a relative error below ±10%.However,the two FO cables differed in their development tendency due to soil anisotropy.Overall,this calculation method can be considered as an effective way to predict shear band widths under various shear displacements.

Fig.18.Comparison of the measured and calculated shear band widths.

5.Discussion

Based on the FBG monitoring results and PIV analyses,improved insight into the initiation and propagation of the shear band in the soil mass can be obtained.For PIV analyses,the displacement and strain fields of the soil surface were analyzed based on sequential photographs taken by a digital camera.The limitation of this technique is that it is unsuitable for monitoring the bulge deformation at the soil surface.For FBGs,our results imply that this technique can capture the formation of shear slip surfaces in sandy soil,which may provide new insights into the shear deformation mechanism of granular materials.

Fig.19 schematically shows the propagation of the shear band during the test.In the initial phase,the soil mass moved as a whole in response to shear displacements,and the soil mass was in a state of elasticity(Shibuya et al.,1997;Wolf et al.,2003;Das,2016).Due to the boundary constraints of the shear box,two inclined slip surfaces appeared in the soil mass near the box sides.Then,two symmetrical main slip surfaces,such as the shape of a spindle,formed in the soil mass as the shear displacement increased.In this case,the deformed soil mass can be classified into the active shear deformation zone,simple shear zone,and passive shear zone.Immediately after the peak resisting force,a single horizontal slip surface developed in the middle of the specimen,accompanied by a secondary slip surface in the soil mass (Rechenmacher and Finno,2004).Moreover,the monitoring results indicate that FBGs can be utilized to detect the plastic and softening behavior of the soil,which may provide new insights into the soil internal shear deformation.However,the shear deformation is also influenced by soil characteristics and test conditions.Poliakov et al.(1994) and Shi et al.(1999)found that the shear band formed spontaneously in the region in which plastic deformations occurred.These shear bands show an angle of inclination α with respect to the vertical of 45°+φ/2 ＜α ＜45°+v/2 (internal friction angle φ and angle of dilatancyv).Thus,further studies considering boundary conditions and material parameters are required to evaluate the influences of these parameters on the deformation mechanism of shear bands.

Fig.19.Possible deformation modes along potential slip surfaces.

Based on the above analyses and previous studies,we assumed that the sensing cable deformed in an S-shaped “shearing type”configuration and further validated this hypothesis via PIV analysis results.A sinusoidal model was proposed to calculate shear displacements and shear band widths based on FBG strain measurements.Furthermore,the strain-displacement proportional coefficientkcan be considered a crucial indicator for detecting the soil plastic and softening behavior and performing early warning of potential geohazards,such as landslides.Nevertheless,two points should be noted as having potential effects on the results of the calculated shear displacements.

(1) FBG strain measurements were further averaged over the anchor spacing,which may lead to an overestimation ofds.Sometimes,it is difficult to determine the value ofdsdue to the limited number of FBGs in field applications.The lengthdsis obtained by FBG measurements and PIV analyses in this study.Therefore,the proposed method should be further improved by advanced technologies with higher spatial resolutions,such as optical frequency domain reflectometry(OFDR).

(2) In this study,a straightforward shearing apparatus was adopted to investigate the soil shear deformation behavior using fiber optic sensors.For field applications,the actual pattern of deformed strain sensing cables subjected to shear movements is quite complicated and is influenced by many factors,such as the confining pressure,angle of shearing,soil properties,and structures of sensing cables.However,only one burial depth and one cable type is considered in the present study.Hence,further research should be carried out to test the usefulness of the proposed method under various confining pressures.

6.Conclusions

In this study,fully instrumented direct shear model tests were performed to investigate the initiation and propagation of shear bands in soil.Quasi-distributed FBG strain sensors were used to measure shear deformation,and the PIV technique was employed to verify the feasibility of this methodology.A sinusoidal model was proposed to convert FBG strain measurements into displacements and widths of the shear band.The following conclusions can be drawn from this study:

(1) Anchored FBG arrays were capable of capturing the formation of shear bands in soil.The maximum strain occurred near the center of the shear box and decreased towards both sides.The strain distributions clearly illustrated the accumulation of deformation in the shear band,which can be used to assess the development of soil shear failures.

(2) A sinusoidal model was proposed to convert FBG strain measurements into soil shear displacements and shear band widths in the cable-soil well-coupled state.The calculated shear displacements were close to the measured results,with a relative error below ±15%.

(3) The strain-displacement proportional coefficient can be considered an evaluation indicator for soil deformation phases.The variation trend of this parameter can well reflect the formation and evolution process of the shear band.This finding sheds light on the important role of FBG-based shear deformation measurements in landslide evaluation.

Declaration of competing interest

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.

Acknowledgments

This work was financially supported by the National Natural Science Foundation of China(Grant Nos.42225702 and 42077235)and the Open Research Project Program of the State Key Laboratory of Internet of Things for Smart City(University of Macau)(Grant No.SKL-IoTSC(UM)-2021-2023/ORP/GA10/2022).The authors thank Bao Zhu and Yuxin Gao,both from Nanjing University,for their assistance in the model tests.