Fiber Optic Strain Research Articles

Detection of matrix cracks in composite laminates using embedded fiber-optic distributed strain sensing

We used an optical frequency-domain reflectometry fiber Bragg grating (FBG) distributed strain measurement system to detect matrix cracks in carbon fiber-reinforced plastics. Load/unload tests were performed on cross-ply laminates under ambient-, high-, and low-temperature conditions using embedded 100mm gauge FBG sensors. We measured the strain distributed along the gauge and examined the crack initiation using optical microscopy and soft X-ray inspection. A peak appeared in the distributed strain corresponding to the occurrence of cracks. The strain distribution during crack initiation was calculated in each temperature range via finite element analysis and compared with the measurement results. We determined that the number and location of cracks can be determined by extracting the peaks from the distributed strain. However, the peaks in the distributed strain do not correspond to the occurrence of cracks that are close to each other, warranting a measurement method with a higher strain resolution.

Strain mode measurement of asphalt pavements using distributed fibre optic sensor data

This paper proposes a method for measuring strain modes in asphalt pavements using distributed fibre optic strain sensor data. A processing algorithm based on cross power spectral density (CPSD) was developed to utilize high spatial resolution strain data to determine the CPSD peak frequency and corresponding relative amplitude. The proposed method was applied in both laboratory and field settings, comparing the results of distributed fibre optic cables with those of accelerometers or theoretical solutions to validate accuracy. Local heating of asphalt structures was used to test the sensitivity of the measured strain modes to changes in material properties. The results demonstrate that different fibre optic cables can provide peak frequencies comparable to traditional accelerometers (±0.6 Hz). Additionally, they offer relative amplitude with a resolution of 1 cm, achieving a modal assurance criterion exceeding 0.95 when compared to theoretical strain mode shapes. The method also sensitively reflects material property changes at different positions within the asphalt structure. This indicates that the proposed approach can effectively measure strain modes in asphalt structures, offering a more detailed understanding of the distribution of structural properties compared to traditional methods.

Study on Coal Seam Roof Failure Based on Optical Fiber Acoustic Sensing and the Parallel Electrical Method

As China enters the stage of deep coal mining, the accidents caused by roof failure pose increasingly serious threats. Current research on roof failure zones often use single methods, but single geophysical data may result in multisolution issues during interpretation. This paper employed similar simulation experiments, exploring the strain failure characteristics and the changes in apparent resistivity caused by stress variations, taking the 11-3106 working face of a mining area as the research object. Through optical fiber strain and apparent resistivity, the locations and degrees of fracture in postmining rock strata were identified. The feasibility of using distributed optical fiber sensing and the parallel electrical method for qualitative and quantitative analysis of mining-induced fractures was verified. The results showed that optical fiber strain increased significantly at the location of rock fracture, with apparent resistivity anomalies rising correspondingly. The peak strain region corresponded well with the region of apparent resistivity anomalies. In a similar simulation with a geometric ratio of 1:100, the height of the caving zone was measured to be 31.65 cm, with a caving-to-mining ratio of 6.33. In the field working face, the caving zone height was 29.47 m, with a caving-to-mining ratio of 6.01, consistent with the actual conditions of the 11-3106 working face.

Ultrasensitive strain sensor of dual parallel FPIs utilizing femtosecond laser processing and Vernier effect

This study proposes and develops a highly sensitive fiber optic strain sensor utilizing femtosecond laser processing and the Vernier effect. The sensor features two parallel Fabry-Pérot interferometers (FPI), with each FPI consisting of an air bubble and a tapered fiber optic cascade. FPI 2 serves as the sensing cavity, while FPI 1 acts as the reference cavity. The strain sensing capability of a single FPI 2 is measured at 6.67 p.m./με, while the parallel configuration of FPI 2 with FPI 1 achieves a sensitivity of 68.3 p.m./με, resulting in an amplification of 10.24. Furthermore, the proposed sensor demonstrates excellent repeatability, low-temperature cross-sensitivity, simple fabrication, and cost-effectiveness, making it a promising tool for strain measurement applications.

Field monitoring and prediction of the thermal response of an in-service curved continuous welded rail using distributed fiber optic strain measurements

Field monitoring and prediction of the thermal response of an in-service curved continuous welded rail using distributed fiber optic strain measurements

Evolution mechanism of deviated well fiber-optic strain induced by single-fracture propagation during fracturing in horizontal wells

Considering the high construction cost of horizontal adjacent well monitoring and the lack of vertical adjacent well fiber optic for obtaining fracturing information, this paper proposes the use of deviated wells with fiber optics for monitoring purposes. To demonstrate the advantages of deviated well fiber optics and the feasibility of their deployment, this paper constructs a forward model based on the finite element coupled with cohesive element approach to simulate the strain induced by the propagation of a single hydraulic fracture in horizontal wells on deviated well fiber optics, and conducts a numerical simulation analysis of the strain induced by the propagation of a single hydraulic fracture on deviated well fiber optics. The results show that the strain evolution induced by single-fracture propagation in deviated well fiber optics can be divided into four stages: strain-enhancing, strain-converging, tensile strain-expanding, and linear strain-converging. The strain evolution characteristics of deviated well fiber optics are manifested as follows: a “heart-shaped” tensile strain convergence zone with a certain deviation appears in the middle, which subsequently converges into a tensile strain convergence band, with compressive strain convergence zones on both sides, and an expanding tensile strain convergence zone on the outer side of the compressive strain convergence band. The analysis finds that when the well inclination angle is greater than 45°, the strain response characteristics of deviated well fiber optics are mainly governed by the width expansion of the fracture, and when less than 45°, they are mainly governed by the height expansion of the fracture. Changes in the azimuth angle can cause a deviation of the “heart-shaped” tensile strain area and the compressive strain convergence zone in the fiber-optic strain waterfall plot, with larger deviations corresponding to smaller azimuth angles. The depth at which the deviated well fiber optics are deployed, reaching the depth of the horizontal section of the horizontal well, can reflect the upward expansion of the fracture height. The results of the analysis illustrate the advantages of deviated well fiber optics in obtaining both fracture width and height expansion information simultaneously and propose a method for selecting suitable deviated well fiber-optic construction parameters based on fracturing monitoring needs. This research can reduce the construction cost of deploying fiber optics in adjacent wells and has significant implications for guiding the layout of adjacent well fiber optics.

A strain transmissibility-based analysis approach for operational modal of concrete dam under nonstationary excitation

The transmissibility-based operational modal analysis (TOMA) method is attracting more attentions due to its relaxation of assumptions about excitation properties, making accurately identifying the modes of actual engineering structures possible. However, in specific application on distributed vibration responses of huge hydraulic structures excited by broad-spectrum non-stationary earthquake, more proper selections of data segmentations on two dimensions (along time or spatial axis) are needed. Based on the concept of distributed vibration sensing optical fiber strain transmissibility, the operational modal analysis model based on single reference and poly references transmissibility under the strain format and the corresponding solutions of model and modal parameters are studied. A false mode elimination method combined with the continuity of spatial distribution of optical fiber measurements, a response sequence set optimization method that comprehensively consider amplitude/PSD non-stationarity, and the principle about how to select (non) reference points (sets) considering the spatial distribution of measurement signal-to-ratio are further developed. The case study shows that the proposed combined method could improve the modal parameter identification accuracy of concrete dams under broad-spectrum non-stationary excitation, and the distributed optical fiber vibration sensing technology can provide a rich (non) reference point (set) selection combination for this method.

Measuring strain distributions in an asphalt pavement using fibre optic sensors under static loading by test vehicles

Understanding the in-situ structural behaviour of pavements plays an important role in road engineering. Hence, various measurement methods were developed in the past to get an insight into the response of roads to traffic loading. In the present study, distributed fibre optic strain sensors were embedded into a hot mix asphalt pavement. The sensors were used for strain measurements with high spatial resolution in order to assess its feasibility to gain the continuous strain distribution in the pavement under short-term static loading. In addition, the loading process was measured with high temporal resolution, indicating that – using shorter sensor lengths – vehicle passages could also be studied. The strain distributions gathered with this type of sensor were compared to the results of a simple finite element model and the effect of applying various sensor cables. In addition, new opportunities provided by distributed fibre optic sensors in road engineering are discussed.

Study of the evolution characteristics of fiber-optic strain induced by the propagation of bedding fractures in hydraulic fracturing

Shale reservoirs contain numerous bedding fractures, making the formation of complex fracture networks during fracturing a persistent technical challenge in evaluating shale fracture morphology. Distributed optical fiber sensing technology can effectively capture the process of fracture initiation and propagation, yet the evaluation method for the initiation and propagation of bedding fractures remains immature. This study integrates a distributed optical fiber sensing device based on optical frequency domain reflectometry (OFDR) with a large-scale true tri-axial fracturing physical simulation apparatus to conduct real-time monitoring experiments on shale samples from the Lianggaoshan Formation in the Sichuan Basin, where bedding is well-developed. The experimental results demonstrate that two bedding fractures in the shale sample initiated and propagated. The evolution characteristics of fiber-optic strain in a horizontal adjacent well, induced by the initiation and propagation of bedding fractures, are characterized by the appearance of a tensile strain convergence zone in the middle of the optical fiber, flanked by two compressive strain convergence zones. The initiation and propagation of the distal bedding fracture causes the fiber-optic strain in the horizontal adjacent well to superimpose, with the asymmetric propagation of the bedding fracture leading to an asymmetric tensile strain convergence zone in the optical fiber. Utilizing a finite element method coupled with a cohesive element approach, a forward model of fiber-optic strain in the horizontal adjacent well induced by the initiation and propagation of hydraulic fracturing bedding fractures was constructed. Numerical simulation analyses were conducted to evaluate the evolution of fiber-optic strain in the horizontal adjacent well, confirming the correctness of the observed evolution characteristics. The presence of a "wedge-shaped" tensile strain convergence zone in the fiber-optic strain waterfall plot, accompanied by two compressive strain convergence zones, indicates the initiation and propagation of bedding fractures during the fracturing process. These findings provide valuable insights for interpreting distributed fiber-optic data in shale fracturing field applications.

Evaluation of a Rapid Diagnostic Tool to Estimate Geometry Evolution of Multiple Simultaneously Propagating Fractures from Crosswell Fiber-Optic Strain Measurements

Summary Crosswell low-frequency distributed acoustic sensing (LF-DAS) strain rate measurements generate data useful for hydraulic fracture (HF) diagnostics. These data contain information about HF geometry; however, interpreting the data has relied on time-consuming and computationally expensive numerical interpretation methods. This study aims to evaluate the applicability of a rapid diagnostic tool, known as the “zero strain rate location method” (ZSRLM), for characterizing the geometry of multiple fractures propagating simultaneously. Simulations of multiple fracture propagation are conducted using a planar 3D multifracture simulator that incorporates 3D rock deformation, fluid flow in the wellbore, fluid leakoff, and multiscale fracture propagation regimes. A supertimestepping algorithm is used to solve the nonlinear parabolic equations governing fluid-driven fractures. The far-field strain profile induced by multiple propagating fractures along a crosswell fiber-optic cable is computed using the displacement discontinuity method (DMM). Various scenarios are simulated by adjusting key completion parameters, including the number of clusters, cluster spacing, in-situ stress states, and geomechanical properties. The ZSRLM is then applied to the computed strain field to estimate fracture extents and propagation rates. The accuracy of the ZSRLM is assessed by comparing the estimated fracture geometry parameters with the known simulated values. Our observations indicate that the ZSRLM is not effective when two or more fractures approach the observation well at similar times, as it becomes challenging to discern unique strain-rate converging patterns on waterfall plots for each fracture. However, when fracture arrivals at the monitor well are offset, distinct strain rate patterns emerge, enabling the application of the ZSRLM. Errors between simulated and estimated fracture extent propagation rates are quantified. Finally, the ZSRLM is applied to a field case involving multicluster fracture propagation, and the interpretation of the results is discussed in light of these findings. This research demonstrates the applicability of the ZSRLM for diagnosing the velocities and final extents of multiple fractures propagating simultaneously. The method offers a rapid means of characterizing stimulations using crosswell LF-DAS measurements, which can inform decisions regarding completion design, well spacing, and landing zone. The study contributes to the advancement of efficient fracture diagnostics in the industry, reducing the reliance on numerical interpretation methods.

Structural Diagnosis of Solid Rocket Motors Using Neural Networks and Embedded Optical Strain Sensors

The main failures that could deteriorate the reliable operation of solid rocket motors (SRMs) and lead to catastrophic events are related to bore cracks and delamination. Current SRMs’ predictive assessment and damage identification practices include time-consuming and cost-demanding destructive inspection techniques. By considering state-of-the-art optical strain sensors based on fiber Bragg gratings, a theoretical study on the use of such sensors embedded in the circumference of the composite propellant grain for damage detection is presented. Deep neural networks were considered for the accurate prediction of the presence and extent of the defects, trained using synthetic datasets derived through finite element analysis method. The evaluation of this combined approach proved highly efficient in discriminating between the healthy and the damaged condition, with an accuracy higher than 98%, and in predicting the extent of the defect with an error of 2.3 mm for the bore crack depth and 1.6° for the delamination angle (for a typical ~406 mm diameter grain) in the worst case of coexistent defects. This work suggests the basis for complete diagnosis of solid rocket motors by overcoming certain integration and performance limitations of currently employed dual bond stress and temperature sensors via the more scalable, safe, sensitive, and robust solution of fiber optic strain sensors.

Distributed fiber optic temperature and strain sensing in cementing and water injection: Insights to well integrity monitoring and multisensing optical fiber cable design

In this study, we installed two fiber optic cables with different designs into a new well, a soft-flat cable and a stainless-steel cable, for distributed fiber optic sensing in cementing and water injection. The two fiber cables were cemented behind casing and the soft-flat cable was used for temperature sensing in cementing as well as cement curing period. The high-speed Rayleigh scanning successfully visualized the cement front tracking from the combined effects of temperature and pressure changes by cement pumping. The temperature variations in cement curing reveled the cement volume and have the potential to identify defects in annular cement and formation damage caused by cementing. The water injection test for strain sensing was carried out with increasing injection rate from 100 L/min to 200 L/min. Strain profiles from the two fiber cables suggested that the strain responses reveal alternation of sand and silt, and reservoir heterogeneity. The water injection results showed that the measured strains of the two cables matched fairly well and the stainless-steel cable showed a high strain sensitivity responding to injection pressure (1 με/5 kPa). Comparison of strain measurement results of the two cables provided valuable insights for future strain fiber cable design. Strain sensing results also indicated a high capability to capture small pressure changes in the heterogeneous layers. Thus, our results demonstrate the high potential of using strain sensing for leak detection and well integrity monitoring in fluid injections, particularly for the long-term monitoring at CO2 storage site.

Geomechanics Modeling of Strain-Based Pressure Estimates: Insights from Distributed Fiber Optic Strain Measurements

Summary Rayleigh frequency shift distributed strain sensing (RFS-DSS) has been demonstrated as a potential technology for characterizing fracture geometries and optimizing the completion design in unconventional reservoirs. The combination of RFS-DSS strain and pressure gauge measurements has been reported recently in field applications (Dhuldhoya and Friehauf 2022; Haustveit and Haffener 2023) to characterize conductive fracture dimensions and production profiles. Haustveit and Haffener (2023) demonstrated a novel technique that uses RFS-DSS strain change during production, measured from a far-field observation well, to monitor the drain profile of a horizontal multistage well. The strain change and pressure change were strongly related during production, and this relationship was applied to continuously estimate pressure drawdown along the full length of the well. However, the sensitivity or influencing factors of the relationship between strain change and pressure change along the fiber are not yet fully understood. Therefore, the main objective of this study is to investigate the relationship between strain change and pressure change under various fractured reservoir conditions and provide guidelines for better utilizing this novel strain-pressure relationship to estimate conductive fractures and pressure profiles. We use a coupled geomechanics and fluid flow model to simulate the strain and pressure changes in the near-well and far-field regions during stable production and shut-in periods. A linear relationship is used to fit the strain change and pressure change data obtained from both producing and monitoring wells. We analyze the impact of various fracture properties [size and permeability of the stimulated reservoir volume (SRV) around fractures, fracture conductivity, fracture area, and skin factor] on the linear relationship based on the R2 value and fitting error. The relationship between the strain change and pressure change during the stable production obtained by our numerical study is consistent with the field measurements. The slope of strain change vs. pressure change during one day of production is significantly influenced by fracture properties. Overall, the monitoring well shows a stronger linear relationship than the producing well during both stable production and shut-in periods. A better linear relationship between the strain change and pressure change is associated with a larger fracture conductivity or larger fracture spacing scenario on both producing and monitoring wells during the stable production period. The cluster spacing affects the linear relationship between strain and pressure change during rock deformation. When cluster spacing is reduced, the nonlocal effect of deformation becomes more pronounced, resulting in a weaker linear relationship. During the shut-in period, the monitoring well exhibits a stronger linear relationship with a high R2 value and small fitting error compared to the producing well. The linear relationship obtained during the shut-in period is less reliable for the producing well. In cases of homogeneous fractures, where the fracture properties are uniform, the strain change and pressure change are similar, except for two outer fractures. This study provides a better understanding of the relationship between strain change and pressure change measured in the near-well and far-field regions during stable production and shut-in periods. The results of our study also demonstrate the potential for utilizing the RFS-DSS strain measurement to characterize the effective fracture and drainage dimensions.

Real-time monitoring of rock fracture by true triaxial test using fiber-optic strain monitoring in adjacent wells

The real-time monitoring of fracture propagation during hydraulic fracturing is crucial for obtaining a deeper understanding of fracture morphology and optimizing hydraulic fracture designs. Accurate measurements of key fracture parameters, such as the fracture height and width, are particularly important to ensure efficient oilfield development and precise fracture diagnosis. This study utilized the optical frequency domain reflectometer (OFDR) technique in physical simulation experiments to monitor fractures during indoor true triaxial hydraulic fracturing experiments. The results indicate that the distributed fiber optic strain monitoring technology can efficiently capture the initiation and expansion of fractures. In horizontal well monitoring, the fiber strain waterfall plot can be used to interpret the fracture width, initiation location, and expansion speed. The fiber response can be divided into three stages: strain contraction convergence, strain band formation, and postshutdown strain rate reversal. When the fracture does not contact the fiber, a dual peak strain phenomenon occurs in the fiber and gradually converges as the fracture approaches. During vertical well monitoring in adjacent wells, within the effective monitoring range of the fiber, the axial strain produced by the fiber can represent the fracture height with an accuracy of 95.6% relative to the actual fracture height. This study provides a new perspective on real-time fracture monitoring. The response patterns of fiber-induced strain due to fractures can help us better understand and assess the dynamic fracture behavior, offering significant value for the optimization of oilfield development and fracture diagnostic techniques.

The Impact of Liquids and Saturated Salt Solutions on Polymer-Coated Fiber Optic Sensors for Distributed Strain and Temperature Measurement.

The application of distributed fiber optic strain and temperature measurement can be utilized to address a multitude of measurement tasks across a diverse range of fields, particularly in the context of structural health monitoring in the domains of building construction, civil engineering, and special foundation engineering. However, a comprehensive understanding of the influences on the measurement method and the sensors is essential to prevent misinterpretations or measurement deviations. In this context, this study investigated the effects of moisture exposure, including various salt solutions and a high pH value, on a distributed strain measurement using Rayleigh backscattering. Three fiber optic sensors with different coating materials and one uncoated fiber were exposed to five different solutions for 24 h. The study revealed significant discrepancies (∼38%) in deformation between the three coating types depending on the surrounding solution. Furthermore, in contrast to the prevailing literature, which predominantly describes swelling effects, a negative deformation (∼-47 με) was observed in a magnesium chloride solution. The findings of this study indicate that corresponding effects can impact the precision of measurement, potentially leading to misinterpretations. Conversely, these effects could be used to conduct large-scale monitoring of chemical components using distributed fiber optic sensing.

Tensile modulus measurement of composite materials based on distributed optical fiber strain monitoring technology

In this paper, a method was proposed to measure the elastic modulus of each layer-material in multi-layer cylindrical structures by OFDR in a large temperature range. Distributed measurement technology was used to carry out accurate measurements of strain distribution and numerical value on specimens. The accurate force-strain relationship can be obtained if the specimen is small or there is inevitable non-uniformity on the specimen. In this paper, a tensile test platform was built, and the tensile tests of optical fiber (−51.6 °C to 82.15 °C), polymer double-layer specimen (−54 °C to 63 °C), and composite three-layer specimen (−46 °C to 62 °C) were carried out. The elastic modulus of the three kinds of material and their relationships with temperature were obtained. By comparing with the standard test results, the accuracy and reliability of the test were verified.

Distributed polymer optical fiber sensors using digital I-OFDR for geotechnical infrastructure health monitoring

We present a distributed polymer optical fiber sensor system for deformation monitoring of geotechnical infrastructure. The sensor system is based on the digital incoherent optical frequency domain reflectometry (I-OFDR) for the detection of local strain events along a perfluorinated polymer optical fiber (PF-POF) used as a sensing fiber. For the best possible load transfer, the PF-POFs were integrated onto geotextiles which pose a sensor carrier for the sensing fiber. By using elastic PF-POF instead of a standard glass fiber as a sensing fiber the strain range of geotextile-integrated fiber optic sensors could be extended up to 10 % in accordance with the end-user requirements. In order to reduce overall costs of the sensor system and achieve its robustness required for use on site, the standard vector network analyzer used by default was replaced by an integrated digital board for optical frequency domain analysis. This implementation showed a significant improvement in the dynamic range and sensitivity compared to the previous measurement system based on the conventional network analyzer. The functionality of the entire sensor system was proven in the field test during the installation of two geomats with integrated PF-POFs embedded into a road embankment in a section of the B 91 federal road near Werschen in the greater Leipzig area. To monitor the installation-related changes in the condition of both sensor-based geomats several control measurements on the embedded PF-POFs and co-integrated reference glass fibers were carried as the construction works progressed. The measurements recorded in the field confirm the great potential of the selected PF-POF used as the distributed fiber optic strain sensor. The future management of the remaining challenges of industrial strain-coupled sensor integration can result in a successful market launch of the PF-POF-sensor integrated into geosynthetics. The sensor system is ready to be used for practical application.

Distributed fiber optic strain sensing for structural health monitoring of 70 MPa hydrogen vessels

We report on the development and testing of 70 MPa hydrogen pressure vessels with integrated fiber optic sensing fibers for the automotive use. The paper deals with the condition monitoring of such composite pressure vessels using the optical backscatter reflectometry (OBR) which was applied for a distributed fiber optic strain sensing along fully integrated polyimide-coated single-mode glass optical fiber (SM-GOF). The sensing fibers were embedded into the vessel structure by wrapping them over the inside polymer liner during the manufacturing process of the outside carbon fiber reinforced polymer (CFRP). Detecting local strain events by the integrated fiber optic sensors might be an opportunity for monitoring the material degradation. Regarding the investigation of the ageing behavior, both ambient hydraulic cycling tests and slow burst tests were conducted on 70 MPa pressure vessels with embedded fiber optic sensors. The achieved results contribute to the knowledge about material fatigue to guarantee the safe usage during the entire lifetime of the composite hydrogen storage vessels. The presented work stands in context of the European Horizon 2020 research project SH2APED focused on the development of an innovative hydrogen storage system composed of an assembly of nine 70 MPa tubular pressure vessels used as an automotive battery pack.

Reliability Assessment of Fiber Optic Shape Sensing

Fiber optic shape sensing is a promising technology capable of enriching the field of Structural Health Monitoring (SHM), with many potential applications that expand the uses of distributed optical fiber sensors. The operational principle is based on the simultaneous strain acquisition from several optical fiber cores deployed in a single sensing cable (or multicore fiber). The parallel strain traces of these cores can be combined to extract curvature and torsion distributions along the sensing cable, that can be used for the three-dimensional reconstruction of the underlying shape. This study evaluates the reliability of fiber optic shape sensing for damage detection through the use of a model-assisted probability of detection framework specifically developed to simulate a carbon fiber-reinforced polymers specimen under quasi-static loading monitored by distributed optical fiber sensors based on Rayleigh backscattering. Specifically, we compare the performance of a traditional distributed optical fiber strain sensor with the one of a hypothetical distributed shape sensing cable (or multicore fiber). To perform this comparison, we redefine the damage index definition, which is usually based on the measured strain values, to make it compatible with shape sensing, where it can be defined in terms of curvature and torsion. With these preliminary results, we aim to evaluate whether shape sensing technology can be employed for damage detection to detect damage-related deformation, whether we can obtain better results compared to traditional optical fiber sensor applications, and discuss how damage metrics need to be modified. In future activities, these aspects will be further investigated taking into account other case studies and shape sensing configurations.

Shape Sensing of Resin Pipe with a Helical-winding Optical Fiber in Bending Test

In this study, we developed a shape-sensing technique for a pipe. An optical fiber was helically bonded on the outer surface of a resin pipe whose length, outer diameter and inner diameter are 3200 mm, 34 mm, and 26.6 mm, respectively. Firstly, four grooves were made on the surface along the pipe in a helical pattern with the same pitch of 360 mm. At the one pipe end, adjacent grooves were offset by 90 degrees and the offset was maintained along the pipe. The single-mode fiber was put into a groove and fixed by epoxy and then it was embedded into the adjacent groove. Consequently, the optical fiber was going back and forth twice along the pipe. At the pipe ends, there were stress-free fibers between the grooves. Shape sensing for the pipe is conducted as follows. 1. Strain distributions along the grooves are measured by a distributed fiber-optic strain sensing system. 2. The bending strain is extracted from the measured strain to calculate the curvature and bending angle. 3. The shape of the pipe is reconstructed based on the curvature and bending angle using the Frenet-Serret formulas. Three-point bending tests were conducted. In the tests, the pipe ends were clamped to be the fixed ends and a point load was applied to the pipe center. Strain distributions were measured by tunable wavelength coherent optical time domain reflectometry (TW-COTDR) or optical frequency domain reflectometry (OFDR). Then the pipe shape was reconstructed as described above. We compared the reconstructed shape with the deformation calculated by finite element analysis and the agreement was excellent. If we insert the developed pipe into a bedrock and reconstruct the pipe shape continuously, it is expected that we can detect cracks or damage in the bedrock. This approach is expected to make rock excavation constructions safer.