Application of Distributed Fiber Optic Sensing Technique to Monitor Stability of a Geogrid-Reinforced Model Slope

Abstract

The development of the smart geosynthetics in recent years has shown tremendous potential with regard to its capability to strengthen geotechnical structures and, meanwhile, evaluate the local strains/stresses. This paper introduced the application of a distributed monitoring system to monitor a laboratory model slope reinforced with smart geogrids, in which the coherent optical frequency domain reflectometry technology (C-OFDR) was used to continuously monitor the geogrid deformations under different surcharge loadings. It showed that the measured results using C-OFDR technology were generally consistent to those from the fiber Bragg grating (FBG) sensors; however, C-OFDR has other significant advantages over the FBG technology. Empirical relationships between the geogrid characteristic strain measured by the C-OFDR sensors and the factor of safety calculated by the conventional limit equilibrium method were established, making it possible to use the geogrid characteristic strain to monitor the slope stability. This study proved the effectiveness of the distributed C-OFDR sensing technology in monitoring the geogrid-reinforced slope stability in the laboratory scale, a critical stepping stone to extend this technology to the field.

Introduction

In the infrastructure and construction engineering, the potential geo-hazards including the instability of artificial fill slopes pose a serious threat to human life and property. It is a common practice to use horizontal layers of geogrids to improve the performance of artificial fill slopes, due to its low cost, easy installation, and significant reinforcement effect. Many researchers have conducted model and field tests to investigate the stability behavior of reinforced slopes. The strain magnitude and distribution pattern in the soil reinforcement has been found to be closely related to the slope stability [1,2,3]. Therefore, accurate estimation of the tensile deformation/forces developed in the geogrid under working conditions is critical to the design and assessment of the reinforced fill slopes.

In the previous studies, electrical strain gauges were often bonded directly to geogrid longitudinal members to investigate the deformation behaviors of the geogrid in the slope. For example, Gnanendran et al. (2001) installed paired strain gauges along the length of geogrid to study the performance of the reinforced sand slope [4]. A highly elongated strain gauge was used by Bathurst et al. (2003) to find a nonlinear relationship between the local and global strains of the geogrid [5]. Since these conventional transducers include electrical sensing elements, they often encounter difficulties in practice, such as poor waterproof, poor corrosion resistance, and susceptible to electromagnetic interference (EMI). All these limitations could impact the accuracy and reliability of the strain measurements. In addition, the representativeness of the monitoring data is also constrained by the layout number of the sensing point.

Over the past few decades, the fiber optic sensing (FOS) technology has been developed rapidly [6]. Owing to its unique advantages, such as long-term stability and durability, non-electric, tiny size, high sensitivity, flexibility, and immune to water and EMI over traditional electric sensors, the potential of fiber optic sensors in various engineering monitoring applications has been widely recognized [7,8,9]. Geogrids as well as other geosynthetics integrated with optical fiber sensors have also been investigated in various geotechnical applications in recent years. Among these studies, the FOS technologies used can be generally classified into two categories. One is called quasi-distributed FOS monitoring method typified by fiber Bragg grating (FBG) technology [10], and the other is called fully distributed FOS (DFOS) monitoring method. By combining the wavelength and time division multiplexing techniques, the FBG technology enables dozens of sensors to be connected in series and has evolved as one of the most popular types of FOS. Its effectiveness has been well documented and a few related international codes have been published. However, due to the high price compared to traditional strain gauges, the FBG technology is suitable for small-scale applications, such as laboratory researches, for the time being. The DFOS monitoring method can continuously and simultaneously measure strains at points distributed along the optical fibers over the kilometer range. Unlike FBG sensors which need special processing methodology, the core of strain optical sensing fiber is same with the ordinary communication fibers, which makes it relatively cheap. Hence, the DFOS technology has been increasingly used for the monitoring of various field reinforced slopes in the constructions of highways, railways, dams, and other infrastructures. The distributed silica optic fibers and polymer optic fibers have been embedded into smart Geogrids for BOFDA (Brillouin Optical Frequency Domain Analysis) and OTDR (optical time domain reflectometry) based strain monitoring of dikes and slopes [11,12,13]. BOTDR (Brillouin optical time domain reflectometry) has also been used to obtain the distributed strain variations of geogrids monitor within model slope and reinforced soil walls in the field, respectively [14, 15]. However, these early reported DFOS based technology could not realize accurate measurement of local deformation due to its relatively low spatial resolution. C-OFDR (coherent optical frequency domain reflectometry) technique is a novel type of DFOS technology which can achieve highly precise measurement with high spatial resolution (≤ 1 cm) [16]. The C-OFDR enables the optical fiber to act as a truly distributed sensor; thereby more accurate measurements of local geogrid strain distributions are expected.

In this paper, a geogrid reinforced sand slope model test subjected to various vertical surcharge loads was conducted in the laboratory. The geogrid was integrated with distributed optical fiber sensors on the surface and its strain distribution was measured with C-OFDR instrument. To verify the reliability of the C-OFDR technology, FBG strain gauges were also attached to the geogrid layers for the comparisons. Using the conventional limit equilibrium method for slope stability analysis, the factor of safety of the model slope and its relationship with the geogrid characteristic strain has been established. The results clearly demonstrated the effectiveness of C-OFDR sensing technology being used to monitor and evaluate the stability of reinforced fill slopes.

C-OFDR technology

When a swept frequency pulse propagates along the core of an optical fiber, Rayleigh backscattering lights are generated due to small random variations of density and composition within the fiber. For each individual fiber, the backscattered signal forms a random but static pattern that can be regarded as a “fingerprint” of the fiber and obtained by interrogation method of OFDR. By means of windowing the spatially highly resolved backscattered data over a length \({\delta }_{x}\) in the distance domain (gauge length /spatial resolution), and converting it into the frequency domain using the Fourier transform, a spectral shift \(\Delta v\) between two measurements can be found by a cross-correlation analysis of the data. A distributed measurement is obtained by compiling the spectral shifts in all intervals along the fiber. There is a linear relationship between the spectral shift ∆v and the changes of strain \(\Delta \varepsilon \) and temperature \(\Delta T:\)

$$ \Delta v = C_{\varepsilon } \Delta \varepsilon + C_{T} \Delta T, $$
(1)

where \({C}_{\varepsilon }\) and \({C}_{T}\) are calibration constants. More details about the fundamentals and operating principles of C-OFDR systems can be found in [16, 17].

Laboratory model test

Material and equipment

Silty sand with its grain size distribution shown in Fig. 1 was used to construct the model slope. The unit weight and water content of the sand was controlled around 14 kN/m3 and 3%.

Fig. 1
figure1

Particle size distributions of the test sand

The glass fiber biaxial geogrid with a mesh size of 15 × 15 mm was used in this study (Fig. 2a). Three geogrid samples were used to conduct uniaxial tensile testing to obtain the mechanical properties of the geogrids. Only the transverse direction of the biaxial geogrids was tested as the geogrids undertake tensile loadings in this direction in the model slope testing and both the FBG and distributed optical fiber sensors would be installed along this direction. As illustrated in Fig. 2b, the present geogrids had a mean yield point elongation around 2.09% and tensile strength of 47.80 kN/m.

Fig. 2
figure2

a Geogrid sample. b Tensile loading-strain curves of Geogrid sample

A small-scale model test of a geogrid reinforced slope was conducted in an organic glass chamber, as shown in Fig. 3. The size of the slope model was 0.8 m long, 0.4 m wide, and 0.45 m in height. The slope inclination was 45°. A hydraulic jack which rested on a 25 cm long strip iron plate was used to apply surcharge load on the slope crest. Two layers of glass fiber geogrid were marked as upper Geogrid A and lower Geogrid B.

Fig. 3
figure3

General set-up of Geogrid-reinforced slops test (unit: cm). a Photograph. b Diagrammatic sketch

As shown in Fig. 2a, distributed strain sensing optical fiber (Corning φ 250 μm G652 single mode bare fiber without jacket) and FBG sensors were directly attached to the surface of the geogrid by epoxy resin glue. Figure 4 shows the general arrangement of the distributed optical sensing fiber and FBG sensors on Geogrid A and Geogrid B.

Fig. 4
figure4

General arrangement of distributed optical fiber and FBGs (unit: cm). a Geogrid. b Geogrid B

The C-OFDR based commercial distributed strain monitoring instrument used in the present test is OSI-S interrogator manufactured by Wuhan Junno Tech Corp. of China. It can achieve ultra-high spatial resolution (gauge length) adjustable from 1 mm to 1 cm. Experiments have demonstrated that accuracy and repeatability of the instrument decrease as the gauge length decrease. Here, the spatial resolution 1 cm of this C-OFDR interrogator was adopted to achieve optimal measuring accuracy of ± 1 με. For a continuous measurement, the measurement interval of the sampling rates in this test is 1 cm. For comparison purpose, the FBG device used in the model test was SM125 optical sensing interrogator manufactured by Micron Optics Inc., USA, which also has the accuracy of ± 1 με [18].

Testing Procedures

In the construction of the model slope, the sand was laid out in a series of horizontal layers of 10 cm thick. Each layer was tamped uniformly with a tamping rod to the prescribed thickness. Repeating the procedure until the designed height of the model slope was reached. During the construction process, Geogrid A and Geogrid B were installed at the specified heights of the slope. Special attention was paid to keep the geogrid flat and stretched when filling sand. Finally, redundant sand was excavated in the chamber to form the designed slope shape with shoulder, slope and toe. A thin layer of petroleum grease was applied to reduce the effect of the friction between the sand and the walls of model chamber.

In the model test, to investigate the deformation behavior of the geogrid reinforced slope, the surcharge load was applied by a hydraulic jack on the crest of the slope with its magnitude increasing step by step from 0.5kN, 1kN, 1.5kN, 2kN, 3kN, 4kN to 5kN.

Testing Results and Analyses

Failure of Geogrid-Reinforced Slope

Figure 5 is the relationship between the surcharge load and the settlement of the strip iron plate on the crest of the reinforced slope in the test. Under each level of the loading, a series of high-resolution digital photographs were taken with a digital camera for one side of the slope, which captured the failure of the slope as shown in Fig. 6. Two obvious circular cracks observed in the slope above the upper geogrid are slip surfaces, which indicates a general shear failure mechanism of the reinforced slope. The shear outlet of the lower slip surface (the major one) was located at the intersection of the Geogrid A and the slope surface.

Fig. 5
figure5

load-settlement curves

Fig. 6
figure6

Failure of slope in the test. a Side view. b Top view

By treating the deformation of soil as a low-speed flow process, the DIC (Digital Image Correlation) technique has been successfully used to monitor the deformation of the visible rock/soil surface. In our test, Ncorr, a 2D subset-based DIC software package, was utilized to study the development of slope deformation and slip surface quantitatively [19]. Figure 7 presents the horizontal and vertical displacement distributions of soil particles under the surcharge load of 1.5 kN. In the test, two visible cracks were formed and then gradually evolved into major slip surfaces with the increase of the surcharge load. It was interesting to find that the soil movement was largely restrained by the geogrid. The relatively large soil displacement mainly occurred near the slope surface, beneath the strip loading plate, and above the upper Geogrid A. The large horizontal displacements of the soil concentrate on the empty face of the slope, which is consistent with the slope failure mode observed in the test.

Fig. 7
figure7

Deformation field of slope measured by DIC. a Horizontal displacement. b Verticla displacement (unit: pixel)

Strain Monitoring Results

Despite the high accuracy and good repeatability of C-OFDR technology, the measured strain data in the test usually do not manifest as smooth curves. The measurement is also influenced by some other factors, such as testing environment, discontinuities in soil deformation, non-uniformity of sensor installation. For the data analysis purpose, in this work, the polynomial curve fitting based on the least square method was adopted to process the measured strain data [20]:

$$ {\text{s}}_{{\text{f}}} (x) = \sum\limits_{{\text{i } = \text{ 0}}}^{{\text{n}}} {{\text{p}}_{{\text{i}}} {\text{x}}^{{\text{i}}} } , $$
(2)

where \({\text{s}}_{{\text{f}}} (x)\) is the fitted strain value at distance x from the left side of the test model, and pi is the coefficient to be determined.

Figure 8 shows the fitting results of the geogrid strains using Eq. (2). Usually using a polynomial with higher degree would yield better fitting effect. However, for the present problem, it was observed that as the degree of the polynomial increases to a certain value, the fitting effect tends to be stable and the further improvement is limited. The root mean square error (RMSE) was used here to evaluate the fitting effects of different polynomials:

$$ RMSE = \sqrt {\frac{1}{n}\sum\limits_{i = 1}^{n} {\left( {f(x_{i} ) - s_{f} (x_{i} )} \right)^{2} } } , $$
(3)

where n is the number of geogrid strain sensing points, xi is the coordinate of the ith measurement point, \(f(x_{i} )\) is the measured strain value at point xi, and \(s_{{\text{f}}} \left( {x_{i} } \right)\) is the fitted strain value at point xi.

Fig. 8
figure8

Geogrid strains fitted with polynomials of different degree. a Geogrid A. b Geogrid B

As shown in Fig. 9, the RMSE decreases fast with the increase in the degree of the fitting polynomial only when the polynomial degree is less than 8 for Geogrid A and less than 6 for Geogrid B, respectively. Therefore, an 8th degree polynomial curve was adopted to fit the C-OFDR measured geogrid strain data for both Geogrid A and Geogrid B. Zero strain was assumed under the condition prior to the application of the surcharge load after the slope construction.

Fig. 9
figure9

RMSE of different polynomials fitting result

Figure 10 illustrates the geogrid strain distributions measured by the C-OFDR sensors. To verify the reliability of the C-OFDR measurements, the comparisons between the processed C-OFDR and FBG strain distributions are shown in Fig. 11. The results indicate that the overall trend of C-OFDR measured values is consistent to the FBG measurements. As expected, the geogrid strains increase as the surcharge load increases. Tensile strains of the upper Geogrid A are much larger than those of the lower Geogrid B at the same loading level. The maximum tensile geogrid strain was observed at the middle of Geogrid A right below the center of the loading strip plate, and the strain magnitude decreases when moving away from the middle of the geogrid. While for Geogrid B, the maximum tensile strain was nearly below the left edge of the loading plate.

Fig. 10
figure10

Strain of geogrids under surcharge loads. a Geogrid A. b Geogrid B

Fig. 11
figure11

Comparison between C-OFDR and FBG strain sensor test results

It is worth pointing out that, as a quasi-distributed monitoring method, FBG measurements lost a few local features of geogrid strain distributions whereas the distributed C-OFDR monitoring method can fully reflect the overall deformation characteristics. It is also observed that the FBG readings on some points are much smaller than the C-OFDR readings. For example, the FBG sensor B4 readings were much smaller than the corresponding C-OFDR readings and were questionable as they had little change under all surcharge loads. The phenomenon that relatively small strains measured by point strain gauges and relatively large strains by distributed FOS gauges at the same locations were also reported in Yashima’s work [15]. The differences of these readings have not been fully explained. The installation error, bond length, strain transfer error on point sensors, and other reasons may contribute to the difference [21, 22].

Stability evaluation of geogrid reinforced sand slope

The limit equilibrium method is a widely used conventional method for the slope stability analysis in the practice of geotechnical engineering. In this work, the Entry and Exit method in SLOPE/W (Geo-Slope International Ltd., 2007) was used to locate the critical slip surface [23]. The loading area is where the trial slip surfaces will likely enter the ground surface, while the intersection of the Geogrid A and the slope surface is where they will exit. A series of direct shear tests were conducted, and the cohesion and friction angle of the silty sand for the slope modeling were determined as 2 kpa and 25°. Then the factor of safety was calculated using the Bishop’s simplified method to assess the stability of the reinforced model slope under the surcharge loadings [24, 25]. The factor of safety Fs can be expressed by

$$ {\text{F}}_{{\text{s}}} = \frac{{\sum {\frac{1}{{m_{{\theta_{i} }} }}[c{\text{l}}_{i} + W_{i} \tan \varphi ]} }}{{\sum {W_{i} \sin \theta_{i} } }} $$
(4)
$$ m_{{\theta_{i} }} { = }\cos \theta_{i} + \frac{\tan \varphi }{{{\text{F}}_{{\text{s}}} }}\sin \theta_{i} , $$
(5)

where Wi is the weight of an individual slice of the slope mass and the surcharge load on the surface of the slope is equated to a portion of the weight of the corresponding slice; θi and li are the base inclination and width of an individual slice; c and φ are cohesion and internal friction angle of slope mass. Fs is computed through an iterative procedure with an initial guess value, since it appears on both sides of Eq. (4).

As the slope stability condition depends on the applied surcharge load, the geogrid characteristic strain induced by the surcharge loads may be closely related to the factor of safety of the model slope. Zhu et al. found a good empirical relationship between the factor of safety and characteristic strain (maximum and average horizontal strain) of soil mass at different elevation for both unreinforced and soil nailed model slopes [26, 27], that is

$$ F_{s} = a \left (\epsilon \right)^{b}. $$
(6)

where a and b are fitting constants to be determined, ε is the characteristic strain of slope soil mass. Analogously, in this paper, either the geogrid maximum strain or the geogrid average strain was adopted as a geogrid characteristic strain to be correlated to the factor of safety of the reinforced slope.

Figure 12 shows the curve fitting of the model test results using Eq. (6), in which the measured maximum and average geogrid strains from Geogrid A or Geogrid B, or the average values of Geogrid A and Geogrid B were taken as the geogrid characteristic strain, respectively. It is observed that the factor of safety of the slope decreases as the geogrid characteristic strain increases. The high correlation coefficients indicate that all the six geogrid characteristic strains are closely related to the factor of safety of the slope. Among them, the maximum strain of Geogrid A seems to have the best fit possibly because of its most sensitive response to the applied surcharge load. Therefore, it might be adequate to install DFOS sensors only on the upper one or two geogrids to monitor the stability of a locally loaded reinforced slope in the engineering practice.

Fig. 12
figure12

Relationships between the factor of safety and geogrid characteristic strain. a Maximum and average strains of Geogrid A. b Maximum and average strains of Geogrid B. c Average of maximum and average strains from Geogrid A and Geogrid B

Figure 13 illustrates the relationship between the applied surcharge load, the geogrid maximum strain, and the factor of safety of the reinforced model slope. In practice, after the reliable relationship between the geogrid maximum strain and the factor of safety of the slope is determined, the geogrid maximum strain continuously measured by the C-OFDR technology may be used as a stability/instability index of the geogrid reinforced slope.

Fig. 13
figure13

Relationship between the surcharge load, maximum strain and factor of safety

Conclusions

A geogrid-reinforced model slope constructed with silty sand was subjected to an increasing static surcharge load in the laboratory. In the test, a full-distributed optical sensing system based on the C-OFDR sensing technology was used to continuously measure the longitudinal strain distribution of the geogrid. The main observations, implications and conclusions can be summarized as below:

  • The C-OFDR based distributed fiber optic sensors can be employed to obtain the geogrid strain distributions effectively.

  • The C-OFDR technology can fully reflect the overall deformation characteristics without missing any key strain features, which is a significant advantage over the quasi-distributed monitoring method FBG.

  • The real-time monitored geogrid characteristic strains may be used to evaluate the stability of the geogrid reinforced slopes after the empirical relationship between the geogrid characteristic strain and the factor of safety of the slope has been determined.

  • The C-OFDR sensing technology was only applied to monitor the laboratory scale geogrid reinforced slope. Future work is needed to study the feasibility of applying this novel technology to the field scale cases.

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Acknowledgements

The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (Grant Nos. 41877244, 41702315), MWR Center for Levee Safety and Disease Prevention Research Open Project Fund (2019014).

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Sun, Y., Cao, S., Xu, H. et al. Application of Distributed Fiber Optic Sensing Technique to Monitor Stability of a Geogrid-Reinforced Model Slope. Int. J. of Geosynth. and Ground Eng. 6, 29 (2020). https://doi.org/10.1007/s40891-020-00209-y

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Keywords

  • Geogrid
  • Slope
  • Distributed fiber optic sensing
  • Strain
  • Stability analysis