Abstract
To investigate the actual working mechanism of anti-slide piles, an integrated monitoring system combining distributed fiber Bragg grating (FBG) sensors and flexible inclinometers was deployed in a highway landslide control project. FBG cables and inclinometer tubes were implanted in one single-row cantilever pile (No.20) and two double-row portal-frame piles (No.48 front-row and No.71 rear-row) with anchor cables, allowing for simultaneous measurement and comparative study of the internal force (bending moment) and deformation (displacement) fields. The results reveal that single-row piles exhibit a tightly coupled internal force-deformation relationship, with coincident bending moment and displacement inflection points. In contrast, double-row piles display a systematic decoupling: peak bending moments shift to greater depth while maximum displacements remain shallow, caused by load redistribution through the capping beam. Safety evaluation shows that the measured maximum bending moments utilize only 7.06%–10.75% of the design capacity, confirming linear elastic behaviour and substantial safety reserves. The study demonstrates the value of multi-source data fusion for structural diagnosis and performance optimization in slope engineering.
1 Introduction
With the frequent occurrence of global climate change and extreme weather events, the long-term stability of highway cutting slopes in mountainous areas is the core issue to ensure operational safety (; ; ). Anti-slide piles, especially anchor anti-slide piles, are the key retaining structures for the treatment of large-scale landslides. Their design is usually based on simplified geological models and load assumptions (; ; ). However, under complex geological conditions and variable environmental loads, the actual stress state of the pile, the distribution of landslide thrust and the load transfer path are often deviated from the design expectations. Therefore, it is of great theoretical and practical significance to reveal the ' internal force-deformation ' response mechanism of anti-slide piles through advanced in-situ monitoring methods for evaluating their working performance, optimizing design theory and ensuring engineering safety.
The traditional anti-slide pile monitoring technology mainly depends on inclinometer, steel bar m and earth pressure box (; ; ). The inclinometer can effectively obtain the lateral displacement profile of the pile along the depth, and is a classical tool to judge the position and deformation mode of the slip surface. However, the inclinometer data reflect the ' deformation ' results of the structure, and it is difficult to directly and accurately quantify the ' internal force ' distribution of the pile body. Although the steel bar gauge can measure the local stress, its ' point ' measurement characteristics are difficult to capture the continuous distribution of the bending moment of the pile body, and are susceptible to electromagnetic interference, zero drift and other problems, and the long-term stability is not good. In recent years, the distributed sensing technology represented by fiber Bragg grating (FBG) has brought a revolutionary breakthrough for structural health monitoring in geotechnical engineering. FBG can realize long-distance, high-density and quasi-distributed strain measurement by sensing the wavelength drift caused by the axial strain of the optical fiber. It has the advantages of high precision, strong anti-interference ability and good durability. In particular, the weak reflection fiber grating technology allows thousands of sensing points to be multiplexed on a single fiber, which provides the possibility to realize the fine characterization of the full-length internal force distribution of the anti-slide pile (; ; ; ). At the same time, as a mature technology for monitoring the horizontal displacement of deep soil, the flexible inclinometer can directly reflect the position, shape and deformation development trend of the sliding surface.
In addition to FBG, other distributed optical fiber sensing techniques such as Brillouin optical time-domain reflectometry (BOTDR) and time-domain reflectometry (TDR) have also been applied in geotechnical monitoring. BOTDR can achieve fully distributed strain measurement over tens of kilometers with a spatial resolution on the order of 1 m, while BOTDA systems may reach a few centimeters. However, BOTDR typically has lower strain measurement accuracy (∼20 με) compared to FBG (∼1 με). TDR detects localized shear deformations through cable impedance changes but provides limited quantitative strain profiles. In this study, FBG was selected for its high precision, immunity to electromagnetic interference, and quasi-distributed capability at 1 m intervals, which adequately captures the bending moment distribution of the pile (total length 22–30 m). The spatial resolution is sufficient to identify the slip surface location and major curvature changes, and the installation of FBG chains is more straightforward than continuous BOTDR fibers in heavily reinforced pile cages.
However, most of the current studies either use FBG alone to monitor internal forces, or use inclinometers alone to monitor deformation (; ; ; ). It is not sufficient to carry out in-depth collaborative analysis of two kinds of data with different sources and physical meanings, and to establish the internal relationship and mutual verification mechanism of ' internal force-deformation '. It is still a weak link in the current research to construct a linkage interpretation framework for the ' internal force-deformation ' response of anti-slide piles to comprehensively and dynamically evaluate their working conditions. This synergy can not only verify the reliability of the monitoring results, but also reveal the internal relationship between the landslide thrust transmission mechanism, the pile force mode and the deformation characteristics. In addition, for the ' internal force-deformation ' response correlation mode of anti-slide piles, especially under different structural forms (such as single-row cantilever piles and double-row portal piles), whether this correlation is ' tight coupling ' or ' partial decoupling ', and how its internal mechanism is affected by the pile-soil-anchor cable cooperative work, there is still a lack of empirical research and theoretical explanation based on long-term field monitoring data.
Based on this, this paper takes a cutting slope with complex geological conditions and multiple treatment in a mountainous expressway in eastern Guangdong as the engineering background. Distributed FBG sensing cables and flexible inclinometer tubes are arranged in typical sections, and long-term collaborative monitoring of single-row and double-row anchor anti-slide piles has been carried out for more than 1 year. In this paper, the spatial and temporal distribution of pile bending moment is inverted by FBG strain data. Combined with the inclinometer data, the sliding surface is identified and the deformation characteristics are analyzed. The difference of synergistic mechanism between single and double row piles in ' internal force-deformation ' response is compared and analyzed. Based on the monitoring data, the structural safety state of the anti-slide pile is quantitatively evaluated. The research results aim to provide an innovative and data-driven analysis method and technical paradigm for the performance evaluation and scientific maintenance of slope reinforcement projects.
2 Project overview and monitoring system construction
2.1 Engineering geology and landslide characteristics
The avalanche occurred on a roadway in eastern Guangdong’s mountainous region prone to erosion. The slope strata have a typical ternary structure: upper loose accumulation body, intermediate weak interlayer, and underneath shattered bedrock. The landslide area is seen in Figure 1. Details are as follows: (1) The sliding body consists of Quaternary gravelly silty clay and extensively weathered argillaceous siltstone with a loose structure and high permeability. (2) The major sliding zone forms in the completely weathered mudstone layer, which is soft plastic-plastic, resulting in a regional hydraulic weak surface. (3) The slide bed is medium-weathered mudstone and sandstone, with a fragmented but overall stable rock mass. The geological structure impacts how easily the slope slides along the weak interlayer during rainwater infiltration, which may promote the deeper potential sliding surface. This multi-slip surface and hydrological sensitivity allow the retaining structure to sustain dynamic and non-uniform complicated stresses, providing a typical and complex geological prototype for this study’s monitoring and analysis.
FIGURE 1
2.2 Design of governance engineering and collaborative monitoring scheme
In light of the aforementioned landslide, this article investigates the H2 landslide as the object, and the regional location number is altered from DZK19 + 640 to DZK19 + 780. The slope remediation project uses the grading support approach. In this research, two representative parts are chosen for detailed monitoring. Section A (secondary platform) uses a single row of circular anchor cable anti-slide piles (pile diameter 2.5m, pile length 22m, and No.20 pile as the monitoring object). Section B (five-stage platform) uses double-row portal anchor cable anti-slide piles. The pile concrete’s strength grade is C30, and the main reinforcing is HRB400 steel bars. Figure 2 shows the plan portion of the H2 landslide anti-slide pile. All anti-slide piles are circular reinforced concrete sections with a diameter of 2.5 m. The concrete strength grade is C30 (elastic modulus 30 GPa), and the longitudinal reinforcement is HRB400 steel. Detailed cross-sectional information will be used in Section 3.1 for bending moment inversion.
FIGURE 2
The primary monitoring technique attempts to provide a synchronized strain-displacement-environment sensing system (see
Figure 3for the monitoring arrangement schematic).
A FBG sensor network. In the pile reinforcement cage’s binding stage, the FBG sensing cables were firmly tied to the longitudinal main reinforcements on two opposite sides of the circular pile cage: the mountain side and the road side (i.e., the extreme tension/compression fibers under the primary sliding direction). This two-plane arrangement suffices to capture the maximum tensile and compressive strains needed for bending moment inversion according to beam theory. Sensors were not installed on the inclinometer tube because the flexible inclinometer tube is decoupled from the pile body after grouting and primarily measures the soil-pile composite displacement rather than the pile’s own axial strain. The sensing locations are separated by 1.0 m, allowing for quasi-continuous distributed monitoring of the pile body’s full-length axial strain. The spatial resolution satisfies the requirements for accurate bending moment inversions.
A flexible inclinometer displacement monitoring system. To get the pile-soil composite’s deep horizontal displacement field, the high-precision flexible inclinometer tube is mounted parallel to the FBG cable and fastened to the steel cage.
Environmental factor monitoring. Rainfall and groundwater level data at the pile site are recorded simultaneously as load input variables.
FIGURE 3
The 1-m spacing was determined based on the total pile length and the expected spatial scale of the slip surface and bending moment variation. For piles longer than 20 m, the curvature changes induced by landslide thrusts typically extend over several meters; thus, a 1-m interval is sufficient to reconstruct the bending moment profile with acceptable accuracy while avoiding excessive sensor count and data complexity. Although BOTDA systems can offer spatial resolutions as fine as 2 cm, such dense sensing is not necessary for capturing the global mechanical behavior of the pile. Moreover, the FBG quasi-distributed array used here provides higher strain measurement precision (∼1 με) than most BOTDA-based dynamic measurements, which is crucial for the reliable inversion of bending moments. The chosen configuration balances monitoring effectiveness, system cost, and installation practicality in a heavily reinforced concrete pile.
Following the concrete pouring of the pile body, all sensors form an integrated monitoring system, ensuring the total unity of the space-time benchmark and laying the groundwork for the joint decoupling and analysis of multi-source data. The integrated monitoring officially commenced in March 2025 and lasted for over 14 months until May 2026. During this period, FBG strain data and deep horizontal displacement data were both automatically collected at a frequency of once per day, while rainfall data was recorded synchronously on an hourly basis.
3 Analysis of internal force evolution mechanism of pile based on FBG
3.1 Mechanical interpretation of distributed sensing data from strain to bending moment
Because the FBG sensing cable is tightly and continuously bound to the longitudinal reinforcing bars, and the reinforcing bars are fully bonded with the surrounding concrete (no slip assumed under service loads), the strain measured by the FBG fiber is considered equal to the strain of the reinforcing bar at that point. Under the plane-section assumption, the axial strain of the bar represents the extreme fiber axial strain of the concrete section. Hence, the measured fiber strain ε(z) is directly adopted as the pile’s axial strain at the sensor location. It should be emphasized that the elastic modulus E in Equation 1 is the elastic modulus of the pile concrete (30 GPa for C30), not the modulus of the optical fiber cable. The fiber is merely a sensing element; its small stiffness does not affect the pile’s mechanical response, and using the pile’s modulus in the strain-to-moment conversion is mechanically correct.
FBG directly detects the axial strain ε(z) of optical fibers. To reveal the pile’s stress condition, convert it to bending moment M(z). According to the plane section assumption and linear elastic constitutive relation in material mechanics, for the circular section, the tension on the pile’s side is positive and the compression is negative (). Figure 4 shows the deformation pattern of the pile under horizontal load. The bending moment of the pile may be calculated using the strain values of the a- and b-planes, the elastic modulus of the pile, and the moment of inertia of the section, as indicated in Equation 1:where εa(z) is the strain measured by a-plane grating fiber; εb(z) is the strain measured by the b-plane grating fiber; D is the spacing of symmetrical grating fiber; E is the elastic modulus of the pile; and I(z) is the moment of inertia of the pile section at the depth of z, which is a constant value for the pile with equal section.
FIGURE 4
In this simplified mechanical model, the pile is considered as a vertical cantilever beam with its bottom end fully fixed in the stable bedrock, while the top may be free (single-row cantilever pile) or elastically restrained by anchor cables and capping beam (double-row system). The actual deformation curve is not simply linear; the sketch only illustrates the sign convention for strain measurement.
3.2 Internal force-deformation response mechanism of single row anti-slide piles
Based on the bending moment distribution of the pile body obtained by inversion of distributed FBG sensing data (Figure 5), the dynamic evolution law of the working state of No.20 single-row anchor cable anti-slide pile with hydrological season is revealed, as well as its internal relationship with deformation response.
FIGURE 5
It should be noted that the simplified deflected shape in Figure 4 is for illustration only and does not imply zero bending moment at the pile bottom. In fact, for a pile fixed at its tip, the bending moment at the fixed end is generally non-zero due to the resisting moment from the bedrock. The measured non-zero bending moment around 20–22 m (Figure 5) is consistent with this fixed-end condition and reflects the actual embedded response of the pile.
3.2.1 Evolution of bending moment distribution and hydrological driving force
During the monitoring period, the bending moment distribution of the pile body varied dramatically and consistently (Figure 5). During the dry season, the bending moment is spread in a conventional ‘S' shape throughout the depth, indicating that the pile body is primarily controlled by a single potential sliding surface, displaying a distinct cantilever beam stress profile. After entering the flood season, the distribution pattern systematically transforms to the ‘U' shape, indicating that the negative bending moment of the pile top and the positive bending moment of the middle and lower parts of the pile both increase at the same time, while the bending moment of the middle part (about 5–12 m depth) decreases relative. The primary mechanical aspect of this morphological transition is that rainwater penetration increases the saturation of the slope’s shallow soil and reduces matrix suction, resulting in increased shallow landslide thrust near the pile top (0–4 m). This causes the pile to transition from a single point control mode, which mostly bears medium and deep thrust in the dry season, to a composite force mode, which bears both shallow and deep thrust in the flood season. The bending moment sign at the top of the pile shifts from positive to negative, indicating that the pile body in this area transitions from tension to compression, while the side represents the mechanical behavior of the shallow soil as it moves forward.
3.2.2 Pile force partition and mechanism based on synergistic response
Combined with the bending moment time series curve (shown in Figure 5) and the synchronously obtained deep displacement data, the pile body can be divided into four sections with different mechanical response mechanisms, thereby clarifying the synergistic mechanism of internal force-deformation.
3.2.2.1 Active sliding response zone (0–4 m)
The bending moment and horizontal displacement of this portion have a strong positive connection and synchronization with rainfall intensity. This nomenclature indicates that the bending moment in this segment is actively modulated by the prestressed anchor cables rather than solely driven by the landslide thrust, representing a unique dynamic regulation mechanism. This shows that this depth range is located in an active shallow sliding body, whose mechanical behavior is directly regulated by changes in pore water pressure. As an external excitation, the rainfall event causes the thrust acting on the pile (manifested as bending moment) and the soil’s shear deformation (manifested as pile displacement) to occur almost simultaneously and in the same direction, resulting in a typical load input-structure response direct coupling mode.
3.2.2.2 Prestress regulation zone (5–10 m)
In this area, there is a consistent negative connection between the change in bending moment and the trend in rainfall, which serves as an important mechanical feedback loop. The mechanism is as follows: as shallow thrust rises, the anchor cable attached to the pile top is further tensioned, and the anchor cable tension Pa grows passively. This increased strain will create an extra bending moment Ma in the middle of the pile (5–10 m), opposing the direction of the landslide thrust bending moment Ms. The measured bending moment at this depth may be stated as Mmeasured = Ms-ηMa (where η represents the bending moment effect coefficient linked to depth). This phenomenon is essentially the dynamic modulation of the pile body’s internal force distribution via the chain feedback of deformation-tension-bending moment by the anchor cable as an active constraint element, which is the core cooperative working mechanism of the anchor cable anti-slide pile, as opposed to the ordinary anti-slide pile.
3.2.2.3 Stable anchorage zone (11–17 m)
The bending moment amplitude in this portion is minimal and steady, with a weak link to rainfall. Synchronous displacement data demonstrate that deformation in this depth range approaches zero. This shows that the pile body has passed through the sliding surface and is securely immersed in the stable sliding bed, primarily giving an anti-rotation embedding effect. The modest bending moment variation in this location is mostly generated by the deformation of the top pile body, which is induced by the coordinated deformation of the elastic foundation beam, rather than by external hydrological forces.
3.2.2.4 Sensor anomaly zone (less than 18 m)
The bending moment around the depth of 18 m shows a continual aberrant rise that deviates from the higher trend, although the inclination displacement data at the same location is stable. Given the sensor’s proximity to the pile’s bottom, it is susceptible to damage throughout the construction process. It has been found that this anomaly is more likely to be produced by damage or drift of the local sensor grating than by the actual mechanical phenomena. This scenario also demonstrates the value of joint monitoring. Independent deformation data may efficiently identify and eliminate abnormalities in a single internal force data set, ensuring the dependability of the result.
In summary, for No.20 single-row piles, the bending moment distribution of FBG inversion and the displacement distribution measured by the inclinometer are very consistent in both space (inflection point position) and time (response phase to rainfall). This demonstrates a tightly coupled synergistic response relationship between the internal force (bending moment) field and the deformation (displacement) field of the pile body caused by the landslide thrust as the input load in the cantilever single-row anti-slide pile, which is consistent with classical beam bending theory. This coupling relationship offers a solid theoretical foundation for determining the position of the sliding surface and evaluating the trustworthiness of other data using one data set.
3.3 Cooperative working mechanism and internal force-deformation response of double-row anti-slide pile system
The bending moment distribution (shown in Figure 6) and reaction mechanism of the double-row portal frame anti-slide pile system made up of No.48 (front row) and No.71 (back row) piles differ significantly from those of the single-row piles. This is due not just to the double-row arrangement, but also to the substantial structural limitations imposed by the top portal coupling beam, which radically alters the load transfer path and pile force modes.
FIGURE 6
The bending moment distribution of double-row piles is a ‘S' shape with a comparable form and deepening range (as illustrated in Figure 7). Compared to single-row piles, the maximum bending moment point drops substantially downward (26 m for No.48 pile and 29 m for No.71 pile), showing that the pile body’s major stress area is less than 20 m beneath. This phenomenon demonstrates how the portal frame system successfully transmits and redistributes shallow load to the deeper pile body and front row piles via structural action, allowing for a wider range of pile-soil interaction depth. Furthermore, the bending moment distribution of double-row piles is highly stable during the monitoring period, with no dramatic seasonal morphological change compared to single-row piles, indicating that as a holistic structural system, it has greater self-regulation ability and overall stability in response to dynamic hydrological loads.
FIGURE 7
3.3.1 Load transfer path and internal force redistribution mechanism
The transmission and redistribution path of landslide thrust in the system may be clearly illustrated using a synergistic analysis of the bending moment amplitude, sign, and evolution process of the front and rear piles (refer to Figure 7). Rainfall is selected as the primary correlating variable because it directly controls the fluctuation of groundwater level and pore water pressure, which are the main driving forces for landslide thrust variations. Presenting bending moment evolution against rainfall clearly illustrates the hydrological sensitivity of the pile internal force and the time-lag effect of deep sliding surfaces, thus revealing the load transfer mechanism under environmental loading.
Rear row piles serve as the primary bearing body. In the shallow layer up to the first slip surface area (0–16 m), the bending moment amplitude of No.71 back row pile is much greater than that of No.48 front row pile, and it is positively connected with rainfall. This convincingly demonstrates that the landslide thrust first acts directly on the back row pile, making it the’main pile’ under active earth pressure.
The transfer of force to the deep and front rows. The thrust is not supported only by the back row piles. The bending moment of the front row piles varies substantially in the transition zone, which is 14–24 m deep, and the stress on the mountainside progressively shifts from tension to compression. This crucial characteristic implies that the push is transferred via two paths: a) The pile-soil-pile interaction transmits some of the horizontal load to the front row piles; b) The rigid coupling beam at the top distributes some of the load from the back row piles to the front row piles in the form of axial pressure and bending moment. At this level, the front row piles progressively transition into a stress condition dominated by axial pressure and supplemented by bending, reflecting the portal frame structure’s supporting and pulling coordination mechanisms.
Synergistic effect of a deep sliding surface. For a clearer illustration of the structural load transfer mechanism, a conceptual schematic diagram (Figure 8) is introduced to summarize the main thrust redistribution path: Landslide thrust → Rear-row pile (primary bearing) → Rigid capping beam (axial force and bending moment transfer) → Front-row pile (compression-bending composite response). At depths of 25–30 m, the bending moment responses of the front and back piles show simultaneously (albeit the amplitude is small), indicating a deep potential slip surface. Its reaction is slightly positive linked with rainfall and lags behind, indicating that deep groundwater dynamics have long-term control over the mechanical characteristics of the sliding surface.
FIGURE 8
3.3.2 Internal force-deformation response mode decoupling
In contrast to single-row piles’ internal force-deformation tight coupling, the double-row pile system exhibits substantial decoupling. For example, the highest bending moment point of the No.48 front row pile is at a depth of 26 m, but its largest horizontal displacement area is in the shallow layer of 0–10 m; the same is true for the No.71 rear row pile. The separation of the internal force peak and the deformation peak in space is an unavoidable mechanical feature of the portal frame structure system.
The fundamental cause is that the pile body’s border conditions have altered. The stiff coupling beam joins the tops of the front and back piles, which is equal to adding an elastic rotation restriction to a single pile, preventing it from being a free cantilever. Under this restriction, the deflection curve form of the pile body changes, the maximum bending moment points shifts downward, and the displacement of the pile top is controlled, but the relative displacement of the shallow pile body may be more visible. As a result, decoupling is simply the reconstruction of a single component’s force-deformation connection using the structural system effect (portal frame constraint), and it is an advanced version of the entire system working together to optimize the internal force distribution. This knowledge provides a critical criterion for determining whether the structural system performs its anticipated function normally using monitoring data.
To summarize, the double-row portal anti-slide piles effectively transmit and redistribute landslide thrust via the systematic cooperative working mechanism of ‘back row bearing main thrust-coupling beam adjustment distribution-front row cooperative pressure’. The findings indicate that the internal force distribution is deep and stable, which increases the structure’s capacity to withstand overturning and overall stability. The typical decoupling of the internal force field and displacement field response is the crucial fingerprint for determining if the structural system is operating appropriately. A multi-line of defense with deep and shallow combinations is established. The back row piles regulate the shallow slip surface, while the front and back rows work together to control the deep slip surface, increasing system redundancy.
3.4 The commonness and systematic difference of response mechanism in single-row and double-row anti-slide piles
Based on the fusion analysis of optical fiber and inclinometer data, this study uncovers the underlying similarities and differences in the reaction mechanism of anti-slide piles with diverse structural forms from the standpoint of ‘internal force-deformation’ synergy. The hydrological cycle serves as the common external stimulation that drives the reaction of the two types of piles, and the multi-source data mutual feedback validates the collaborative monitoring method’s universality and dependability. The structural topology is what causes the essential difference. Single-row cantilever piles have a direct landslide thrust transmission channel, with internal force and deformation being intimately connected in time and space. The mechanism is transparent, making it easy to set the sliding surface and invert the push. The double-row gantry piles form a high-order, statically indeterminate spatial cooperative system. The rigid connecting beam reconstructs the load transfer channel, causing thrust to be redistributed across the “back row-coupling beam-front row,” spatially decoupling the single pile’s peak internal force and deformation. This decoupling is not an anomaly; rather, it is an advanced expression of the system’s general cooperation and stress state optimization. It is a key fingerprint that indicates whether it regularly performs its design purpose. The two common collaborative reaction mechanisms explained in this work provide a theoretical foundation for the mechanism diagnosis and performance evaluation of anti-slide piles using monitoring data.
4 Collaborative response mechanism of deep displacement and internal force distribution
In this Section, the internal correlation mode between the internal force field and the deformation field of anti-slide piles with different structural forms under the action of landslide thrust is analyzed using the fusion analysis of the deep displacement of the pile body and the distributed optical fiber strain monitoring data, in order to reveal their respective structural response mechanisms. The inclination monitoring data demonstrate that (as shown in Figure 9), all pile displacements exhibit a pattern of attenuation down depth, confirming the mechanical condition dominated by bending. The displacement curve of the No.20 single-row pile shows prominent inflection points at depths of 3–5 m and 7–9 m, with a total displacement of up to 15.2 mm. In the double-row pile system, the displacement of No.71 pile in the back row (10.8 mm) is significantly greater than that of No.48 pile in the front row (4.9 mm), and the depth range of the significant development area of the two displacements differs, indicating a load distribution imbalance in the system.
FIGURE 9
The geographical comparison between the depth of the displacement mutation point and the depth of the inflection point of the FBG-inverted bending moment distribution indicates two basically distinct synergistic response mechanisms, with the difference originating in the structural system itself. For the No.20 single-row pile, the displacement mutation point (3–5 m, 7–9 m) in the main sliding direction corresponds to the bending moment inflection point (3–5 m, 10–12 m) in space. This correlation demonstrates that, in the statically determinate cantilever beam model, the cross-section bending moment induced by landslide thrust is the primary source of the pile body’s particular curvature and displacement distribution.
The inflection point of displacement indicates an abrupt shift in curvature of the pile deflection curve, which should be at the zero point of shear force (equivalent to the extreme point of bending moment) in principle. The spatial consistency of monitoring data demonstrates that the stress and deformation of single-row piles adhere to classical beam theory, with a direct and translatable tight coupling relationship between the internal force distribution and the deformation form. This linkage allows one set of monitoring data to be used to calibrate or interpret another set of data, as well as give dual proof for correct sliding surface position identification.
In double-row piles, the peak response of displacement and bending moment are spatially separated. For example, the considerable displacement of the No.48 front row pile is centered in the shallow layer of 0–10 m, while the bending moment peak area is found in the deep layer of 20–30 m; the No.71 rear row pile exhibits similar features. This decoupling phenomenon is an unavoidable consequence and distinguishing characteristic of the portal statically indeterminate structure system’s cooperative work. The mechanical root is that the stiff connecting beam exerts substantial limitations on the pile top, altering the boundary conditions of the single pile. The landslide thrust mostly affects the rear row piles. Part of the load is conveyed to the front row piles via pile-soil contact (soil arching effect), while the remaining portion is transformed into axial force and bending moment via the connecting beam for redistribution. During this process, the stress in the front row piles shifts from simple bending to compression-bending composite state, causing the deformation form to be modulated by the stiffness distribution and load transfer path of the entire structure rather than just the local bending moment. As a result, the geographical difference between the internal force peak and the displacement peak is not only an anomaly, but also intuitive indication that the load is successfully dispersed throughout the system, with structural redundancy playing a role.
The foregoing study findings demonstrate that the internal force-deformation synergy concept is critical to understanding the structural behavior of anti-slide piles. For single-row piles, the tight coupling model validates the design calculation model’s applicability, and its monitoring goal is to determine whether the coupling relationship exists. For double-row piles, response decoupling is the typical working mode. The key to monitoring is determining if the decoupling features are obvious and the path of load redistribution is smooth. By analyzing these two models using data fusion, monitoring can be elevated from a single-point safety judgment to a diagnostic level of whether the overall working behavior of the structural system conforms to the design mechanism, providing a more solid foundation for the project’s performance evaluation and maintenance decisions.
It is worth noting that the anti-slide piles are massive reinforced concrete structures with a diameter of 2.5 m. The steel reinforcement cage, as an integral part of the pile, significantly increases the flexural stiffness of the section but does not alter the fundamental soil failure mechanism. The landslide thrust and soil movement are governed by the global pile-soil relative stiffness and the shear strength of the surrounding soil, not by the local presence of steel bars. The FBG sensors measure the pile’s internal strain response, which reflects the overall soil-structure interaction. Therefore, the interpretation of failure mechanisms based on pile bending moments and displacements is not affected by the reinforcement, as the pile acts as a rigid element relative to the soft sliding mass. Nevertheless, we acknowledge that in small-scale model tests, reinforcement might influence localized soil arching; however, for full-scale in-situ piles, this effect is negligible.
5 Evaluation of working state and safety reserve of anti-slide pile
Based on an in-depth analysis of the ‘internal force-deformation’ synergistic response mechanism, this Section quantitatively compares the measured maximum bending moment of the pile body obtained by distributed FBG inversion with the design bending capacity calculated using the section limit equilibrium theory, allowing for an objective and quantitative evaluation of the structural safety state of the three anti-slide piles. This evaluation not only verifies design safety, but it also provides a final mechanical interpretation of the structure’s actual stress level as shown by the aforementioned joint monitoring data. This project’s anti-slide pile is made of circular reinforced concrete, and the flexural capacity of the normal section must be calculated taking into account the combined action of the concrete compression zone and the steel tension and compression zone. Referring to the appropriate design theory (; ), the ultimate bending moment Mmax may be determined using Equation 2:where fc is the design value of axial compressive strength of concrete; fy is the design value of tensile strength of longitudinal reinforcement; A is the cross-sectional area of anti-slide pile; r is the radius of circular anti-slide pile; rs is the circumferential radius of the center of the longitudinal reinforcement; α is the central angle corresponding to the cross-sectional area of the compressed concrete, and α ≥ 2π/3.5; θ is the central angle of the corresponding tensile steel bar, which can be taken as 2π/6 ∼ 2π/3, generally 0.5π; Atension is the cross-sectional area of the tensile reinforcement arranged along the perimeter of the anti-slide pile in the range of the central angle; and Acompression is the cross-sectional area of the tension bar arranged along the periphery of the pile within the range of the central angle.
Substituting the aforesaid design parameters into Equation 2, the design value of the ultimate flexural bearing capacity of the single pile is computed as Mmax = 25,089.1 kN⋅m. This is the benchmark for evaluating the safety status of the pile structure. The FBG monitoring system measures the maximum bending moment (Mmax) of each pile during the observation time and compares it to the intended bearing capacity (Mmax). The bending moment utilization rate is calculated as η = Mmax,measured/Mmax. The findings are shown in Table 1. The quantitative assessment results (η < 11%) constantly reveal that under the current load situation, the material stress level of all monitoring piles is substantially lower than their design strength, and the structure is in a state of exceptionally adequate safety reserve. This finding is consistent with the synergistic response mechanism described in Section 3, and it has an obvious mechanical relevance.
TABLE 1
| No. | Pile type | Measured maximum bending moment Mmax, measured (kN·m) | Bending moment utilization η (%) | Safety status evaluation |
|---|---|---|---|---|
| 20 | Single-row pile | 2,697.9 | 10.75 | High safety reserve |
| 48 | Double-row piles (front row) | 2,224.3 | 8.87 | High safety reserve |
| 71 | Double-row piles (back row) | 1772.4 | 7.06 | High safety reserve |
The measured maximum bending moment and safety state evaluation of anti-slide pile.
The significant safety margin serves as the foundation for linearizing the cooperative response: the exceptionally low bending moment use indicates that the pile’s concrete and steel bars are mostly in the linear elastic working stage. This is the mechanical state required for the above-mentioned ‘internal force-deformation’ connection to be obvious and stable (whether tight coupling or system decoupling). Under these conditions, both the theoretical Equation 2 and the monitoring data inversion results are very reliable.
The differences in safety factors between pile kinds reflect the system’s division of work. The rear row pile (No.71) had the lowest usage rate (7.06%), followed by the front row pile (No.48) at 8.87% and the single row pile (No.20) at 10.75%. This gradient aligns with the load transfer route. The rear row pile, being the primary bearing body, carries a heavy load, yet the safety margin is the greatest due to the high design bearing capacity. The arrangement shares the front row piles, thus reducing the real force. Single-row piles are loaded individually, and their utilization rate is among the highest in the system. In terms of safety reserve, it has been quantitatively proven that the double-row portal frame system optimizes load distribution in each component through synergy, hence improving overall safety.
In conclusion, this Section quantitatively compares the extreme value of’internal force’obtained by collaborative monitoring with the theoretical’resistance ', which not only confirms the current extremely high safety of the project from the most fundamental strength level, but also links the safety factor with the’internal force-deformation’collaborative response mechanism, and clarifies that sufficient safety reserve is the internal guarantee to maintain the exp The assessment results serve as a critical quantitative foundation for assessing long-term service performance and determining operational and maintenance decisions for the slope treatment project.
6 Conclusion
The major results of this work are based from the joint monitoring and fusion analysis of FBG and inclinometer data for single and double row anchor cable anti-slide piles.
The integrated FBG-inclinometer system provides full-depth, synchronous acquisition of bending moment and displacement fields. For single-row cantilever piles, internal force and deformation are tightly coupled in space and time, with coincident inflection points enabling reliable slip surface identification and mutual verification between the two data types.
The double-row portal-frame piles exhibit a systematic decoupling response: the peak bending moment is shifted to greater depth (20–30 m) while maximum horizontal displacement remains concentrated in the shallow layer (0–10 m). This separation originates from the thrust redistribution path “rear pile → rigid capping beam → front pile”, which transforms the front pile into a compression-bending composite member. Such decoupling is a characteristic fingerprint of normal structural system operation.
The measured maximum bending moments of all monitored piles utilize only 7.06 %–10.75% of the design flexural capacity, confirming a linear elastic state and substantial safety reserves. The gradient of utilization ratios (rear row < front row < single row) quantitatively demonstrates the load-sharing optimization of the portal-frame system, which directly underlies the observed decoupled response pattern.
This study demonstrates multi-source data deep fusion and long-term in-situ verification, although the present study has several limitations. The 1-m FBG spacing may not capture localized strain concentrations smaller than this scale, although the global bending behavior is adequately recovered. The strain compatibility assumption (concrete–rebar–fiber) holds under service loads but requires validation if cracks develop. The installation of the reinforcement cage and instruments may slightly disturb the surrounding soil; however, for large-diameter piles, this effect is considered insignificant. The monitoring period, although over 1 year, did not encompass extreme hydrological events, warranting continued observation to verify the long-term mechanisms. In the future, it will be important to conduct ultra-long-term monitoring, increase the deep coupling of monitoring data and numerical models, and investigate intelligent diagnostic and early warning systems based on machine learning.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
LF: Conceptualization, Data curation, Formal Analysis, Methodology, Writing – original draft. HJ: Methodology, Resources, Software, Validation, Writing – review and editing. SM: Investigation, Project administration, Software, Visualization, Writing – original draft. NB: Data curation, Funding acquisition, Methodology, Writing – original draft. WY: Formal Analysis, Investigation, Methodology, Supervision, Writing – original draft. YZ: Funding acquisition, Methodology, Validation, Writing – original draft. NW: Data curation, Funding acquisition, Methodology, Software, Writing – review and editing. FW: Conceptualization, Data curation, Funding acquisition, Writing – original draft, Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This work presented in this paper was funded by National Natural Science Foundation of China (No.52578452), Henan Province Science and Technology Research Project (262102320027) and Guangdong Communications Group Project (JT2024YB44). The authors are grateful to the editor and reviewers for discerning comments on this paper.
Conflict of interest
Author LF was employed by Guangdong Communications Industrial Investment Co., Ltd.
Authors HJ and SM were employed by Guangdong Dachao Expressway Co., Ltd.
Authors NB, WY, and YZ were employed by Guangdong Hualu Transportation Technology Co., Ltd.
Author NW was employed by China Railway Northwest Research Institute Co., Ltd.
The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
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Summary
Keywords
anti-slide pile, collaborative monitoring, fiber bragg grating (FBG), internal force-deformation response, landslide thrust, structural health monitoring
Citation
Feng L, Jian H, Mengyang S, Biao N, Yuhang W, Zhao Y, Wenqing N and Wenlin F (2026) Coupled internal force-deformation response of anti-slide piles based on optical fiber and inclinometer data fusion. Front. Mater. 13:1810532. doi: 10.3389/fmats.2026.1810532
Received
13 February 2026
Revised
07 May 2026
Accepted
08 May 2026
Published
26 May 2026
Volume
13 - 2026
Edited by
Erkan Oterkus, University of Strathclyde, United Kingdom
Reviewed by
Umar Zada, Polytechnic Institute of New York University, United States
Jian Cui, China Academy of Railway Sciences, China
Updates
Copyright
© 2026 Feng, Jian, Mengyang, Biao, Yuhang, Zhao, Wenqing and Wenlin.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Feng Wenlin, fengwenlin@hpu.edu.cn
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.