Reinforcement Material Research Articles

Microbial-Induced Calcium Carbonate Precipitation and Basalt Fiber Cloth Reinforcement Used for Sustainable Repair of Tunnel Lining Cracks

The increasing problem of urban traffic congestion has led to the extensive use of underground tunnels. However, tunnel lining cracks pose a major threat to the integrity and safety of the structure. Although the traditional repair method is effective, it often requires higher construction technology and higher cost, and may cause damage to the concrete structure. In this study, microbial-induced calcium carbonate precipitation (MICP) was combined with basalt fiber cloth to repair and reinforce tunnel lining cracks. Bacillus pasteurii was used to optimize the microbial mineralization process, and the effectiveness of the method on cracks with different widths was evaluated using a water seepage test. In addition, the mechanical properties of the reinforced tunnel lining were tested. The microbial mineralization process effectively repaired cracks with widths of 1 mm, 2 mm, and 3 mm. The use of unidirectional basalt fiber cloth increased the bearing capacity of the strengthened member by 12.5%. The combined reinforcement method also enhances the deflection performance and alleviates the influence of water seepage on the bonding performance. This innovative and sustainable approach not only provides an effective solution for the repair of tunnel lining cracks, but also contributes to the broader field of eco-friendly building materials. This study highlights the potential of using this combination approach to improve the durability and performance of underground infrastructure.

Thermal Stress Analysis of Maxillary Dentures with Different Reinforcement Materials Under Occlusal Load Using Finite Element Method

The purpose of this study was to determine the effect of fiber reinforcement materials on the magnitude of stresses in a critical part of the maxillary denture base under thermal and occlusal load. Thermal stress analyses of the models were carried out using the finite element method. The models consisted of bone, soft tissue, interface gap, and maxillary dentures with and without reinforcements. A concentrated occlusal load of 230 N was applied bilaterally on the molar teeth. A 36 °C reference and 0 °C, 36 °C, and 70 °C variable ambient temperatures were applied to the models. CrCo, unidirectional and woven carbon/epoxy, unidirectional and woven glass/epoxy, and unidirectional and woven Kevlar/epoxy were used as reinforcing materials in the maxillary denture base made of PMMA (polymethyl methacrylate). Stress distributions on the maxillary denture’s midline and lateral line direction were evaluated. Maximum stresses in the incisal notch and the labial frenal notch of the maxillary denture were determined. Failure analysis of reinforcement materials used in maxillary dentures was carried out using the Tsai-Wu index criterion. The results obtained show that the thermal properties of reinforcement materials should be considered as an important criterion in their selection.

Evaluation of polyester high-tenacity fabric and carbon nanotube reinforcements for improving flexural response in concrete beams.

This research scrutinized the effectiveness of utilizing polyester high tenacity fabrics to enhance the functionality of concrete panels. Two distinct woven fabrics with comparable strength resistance were fabricated and assessed. Concrete beams were compared in their original form and those reinforced with woven fabrics, along with beams reinforced with carbon nanotubes (CNTs) (B, BC2, BC4, BS1, and BS2). Results indicated that the textile-reinforced concrete panels displayed notably greater energy absorption capabilities post-failure under flexural loads in comparison to the control and CNT-reinforced panels. This enhanced performance was credited to the development of multiple cracking patterns in the textile-reinforced panels. The flexural behavior of the textile-reinforced panels was characterized by four discernible phases: a linearly increasing segment, a crack propagation phase featuring multiple cracking, a post-cracking phase with reduced stiffness, and ultimately, failure due to fabric rupture or debonding. Conversely, the control and CNT-reinforced panels exhibited a more brittle response post-initial cracking, with a limited number of cracks and reduced deformation capacity. The performance of the textile samples was largely unaffected by their specific characteristics, except for the fabric wrapping angle. The introduction of 0.04% CNTs marginally enhanced crack flexural resistance compared to the control and 0.02% CNT panels, owing to the varied distribution of CNTs within the matrix. Overall, the textile-reinforced concrete panels demonstrated superior load-bearing capacity, ductility, and energy absorption when compared to the other reinforcement techniques examined.

Manufacturing Aluminum-Based Nanocomposites via Stir-Squeeze Casting Combined with Ultrasonication

This study successfully produced aluminum nanocomposites using a stir-squeeze casting process, both with and without ultrasonication (US) assistance. The matrix material utilized was scrap automobile wheel aluminum alloy (A356), with 1% SiC nano particles, averaging a size of 40 nm, serving as the reinforcement material. A comparison was made by also producing A356 aluminum casts with and without the use of US. The produced casts underwent thorough chemical and mechanical characterization, including optical and scanning microscopy, porosity measurement, hardness measurement, compression and tensile testing, as well as wear testing. Additionally, energy-dispersive X-ray spectroscopy (EDS) and X-ray diffraction (XRD) analyses were conducted to assess compositions and confirm the presence of SiC nano particles in the aluminum matrix. Porosity levels were slightly higher in the nanocomposite samples compared to pure matrix samples, attributed to the tendency of pore formation due to improper distribution of ceramic particles, resulting in clustering and agglomeration. However, significant reduction in porosity was observed with the application of ultrasonication, effectively breaking up clusters and agglomerations of reinforcement particles. Regarding mechanical properties, the A356+SiC sample with US exhibited the highest hardness (70.8 HRB), tensile strength (163.25 MPa), and compressive strength (387.2 MPa), along with the lowest abrasive wear loss (0.0017 g) among all types of casts produced in this study.

Free Vibration and Buckling Analyses of Functionally Graded Plates With Graphene Platelets Reinforcement

Abstract While existing research has focused on using graphene platelets (GPLs) as reinforcement for homogeneous matrices, this study proposes a new nanocomposite for plate structures consisting of GPLs incorporated into a conventional functionally graded matrix with the aim of enhancing their overall stiffness. The performance of such plates is evaluated via free vibration and buckling analyses in the present study. Note that the matrix phase is graded continuously with the power law distribution across the plate's thickness, whereas various GPL dispersion patterns along the thickness are studied. The material properties of the typical functionally graded matrix are determined by the rule of mixture, and then those of the composite are estimated by the modified Halpin–Tsai model as well as the rule of mixture. Based on Hamilton's principle and the novel four-unknown refined plate theory (RPT4), the governing equations of the plate are developed. The Navier-type solution scheme is then adopted to get the critical buckling load and natural frequency of the nanocomposite plate. Numerical findings are examined to evaluate the novel nanocomposite plate model, and a parametric study is also conducted. In addition, high-accurate results are provided via the Navier-type solution here as benchmark solutions for further studies on functionally graded material structures reinforced by GPLs.

Shrinkage behaviour of high-strength concrete plates reinforced with carbon textile reinforcement

Carbon textile reinforcement is a relatively new type of CFRP reinforcement which, when utilized with high-strength concrete, leads to the production of ultra-thin free-form concrete shells. However, such reinforcement usually suffers from weak resistance to compressive stresses, while high-strength concrete is susceptible to high shrinkage rates. This combination may lead to a boor shrinkage behaviour, and thus an excessive shrinkage-related craking. Therefore, this paper aims to study the shrinkage behaviour of high-strength concrete plates reinforced with carbon textile reinforcement. Additionally, the utilization of shrinkage-compensating concrete as a possible shrinkage mitigation method was also investigated. For this aim, twelve concrete plates of dimensions 500 mm × 150 mm x 30 mm were cast. The shrinkage and expansion behaviour of the specimens were monitored for six months using the distributed fibre optic sensor (DFOS) technology, and then all the specimens were tested till failure under a direct tension test. The results have revealed that the existence of textile reinforcement does not provide any significant resistance to the negative strains generated from the shrinkage of concrete, which, for restrained concrete plates, leads to the formulation of wide cracks. On the other hand, the utilization of shrinkage-compensating concrete not only eliminates the formulation of shrinkage-related cracks but also reduces the crack’s width resulting from the loading process by up to 35 % during all stages of loading as illustrated by the fibre optic sensors measurements. Additionally, shrinkage-compensating concrete exhibits a slightly higher compressive strength than normal concrete.

Green synthesis of multifunctional natural rubber-lignin nanocomposites: A sustainable approach for waste reduction

Lignin, a valuable biomaterial having an array of exciting properties is increasingly favoured as a reinforcement material in the fabrication of green composites. Reinforcement in biopolymers like natural rubber (NR) using lignin nanoparticles (LNP) is considered a hotspot today. In this study, LNP synthesized via the homogenization method was incorporated into natural rubber latex (NRL) using probe sonication, and NR/Lignin nanocomposites (NR/LNP) were fabricated using latex dipping method. The addition of LNP resulted in significant enhancements in mechanical and antibacterial properties, biodegradability, and ultraviolet (UV) blocking capabilities with the addition of 7 parts per hundred rubber (phr) of LNP, due to the uniform dispersion and effective interaction between NR and LNP. This research demonstrates a versatile pathway for integrating LNP into NR through a green method, enabling the production of eco-friendly NR nanocomposites for multifunctional applications. This pathway contributes to a safe disposal of NR based products.

Ecofriendly hybrid natural fiber reinforced polypropylene composites from biowastes

The used ground coffee waste (GCW) and tea leaf waste (TLW), the large wastes from the beverage process, were selected as natural reinforcement and natural pigment in the polypropylene (PP) matrix. In this work, the maleic anhydride polypropylene (MAPP) was added to the composites to develop the compatibility between fillers, fibers, and polymer matrix. The TLW/PP composites, GCW/PP composites, and GCW/TLW/PP hybrid composites were prepared in the ratio of TLW and GCW ranging from 0 to 30 wt% with the addition of MAPP at 5 wt% of fillers. The presence of GCW and TLW in the PP matrix decreased tensile properties and impact resistance but increased flexural modulus and hardness of PP at high concentrations of GCW and TLW. The increase in GCW and TLW concentration slightly reduced melting temperature but it enhanced the tensile and flexural modulus. Furthermore, it enhanced the hardness, thermal and rheological properties of the composites. The TLW/PP composites had better mechanical properties, and rheological properties than GCW/PP composites but thermal properties were quite similar. The mechanical properties of GCW/TLW/PP hybrid composites were better than those of GCW/PP composites but lower than those of TLW/PP composites. The rheological and thermal behaviour of hybrid composites were like that of TLW/PP composites. Incorporating MAPP improves the mechanical and rheological behavior of PP composites by enhancing the interaction among PP, GCW, and TLW. However, this addition does not significantly enhance the composites’ thermal properties. The optimum composite was hybrid composites of GCW/TLW/PP consisting of GCW of 10 wt%, TLW of 20 wt%, and MAPP of 1.5 wt% which presented good mechanical, thermal, and rheological properties. The mechanical properties of this hybrid composites were as follows: a tensile strength of 26.35 MPa, elongation at break of 10.91%, tensile modulus of 636.69 MPa, flexural strength of 45.57 MPa, flexural modulus of 3632.86 MPa, impact resistance of 12.72 kJ/m2, and a Shore D hardness of 76.15. The overall results showed that GCW and TLW can be used as reinforcement material and natural pigment in the polymer matrix.

Open source tool for Micro-CT aided meso-scale modeling and meshing of complex textile composite structures

Volumetric image-based modeling of textile reinforcements and composites is favored over ideal geometric modeling because of its ability to represent complex structures in sufficient detail. Although several approaches were devised, there is still a scarcity of dedicated tools capable of effectively transferring pertinent information from images to high-fidelity models. This work presents the open source project, PolyTex, a Python-based object-oriented application that establishes a streamlined and reproducible workflow for such tasks. Dual kriging serves as the foundational theory for the parametric approach developed to represent, simplify, and approximate the morphology and topology of fiber tows. The code takes two types of input, either an explicit representation of tow geometry using point clouds or implicit representations, such as image masks representing fiber tows separately with grayscale values. Tailored APIs allow for smooth integration between PolyTex’s modeling capabilities and the simulation environments offered by OpenFOAM and Abaqus. Case studies on virtual testing of textile permeability were presented to demonstrate this capability. The modular and object-oriented design makes PolyTex a highly reusable and extensible tool that allows users to create a customized pipeline.

A facile biomass-based coating for flax fabric toward plant fiber/biobased epoxy composite with enhanced fire safety

The natural abundance, biodegradability, and low density of plant fibers, together with biobased epoxy thermoset resin, have driven the increasing popularity of plant fiber/polymer composites (PFRPs) to wider applications in various industries. However, the striving for biomass-based flame retardants (FRs) treatment for PFRPs remained a bottleneck due to polymers’ inherent vulnerability against fire and the increasing environmental awareness. In this work, a facile two-step aqueous solution coating process was proposed for fabric surface treatment of flax fabric using fully biobased phytic acid and chitosan from polysaccharides. The treated flax fabric demonstrated self-extinguishing behavior when ignited and showed a decrease in peak heat release rate (PHRR) by 58% under combustion. The laminate produced by this treated flax fabric and biobased epoxy resin showed a decrease of PHRR by 36% and an increase of more than 200% for the time of torch fire burn-through, demonstrating intriguing flame retardance brought by only FRs treatment on flax fabric reinforcements. Various measurements were done to elaborate on the role of treated flax fabric in the flame retardancy of polymer composites.

Unveiling the untapped potential of Hibiscus Rosa-sinensis lignocellulosic fiber: A multifaceted characterization for advancing sustainable biocomposite applications

In the pursuit of sustainable advancements in bio-inspired fiber reinforced polymer composite materials, the exploration of novel natural fibers has become a focal point of research. This experimental study aims to elucidate the unexplored potential of Hibiscus Rosa-sinensis fiber (HRF) as a versatile reinforcement material for high-performance composites. Through an integrated approach, this research offers a meticulous analysis of the HRF's physico-chemical properties, and single fiber tensile strength. The crystalline structure are revealed by X-ray diffraction (XRD), thermal behavior are characterized through thermo-gravimetric analysis (TGA), and surface morphology has been visualized using field emission scanning electron microscopy (FESEM) studies. From the results, it is found that the HRF contains a cellulose content of 79.50 %, positioning it as a prime bast fiber among its counterparts. This composition is complemented by hemicellulose (10.36 %), lignin (4.62 %), wax (0.84 %), and ash (2.96 %). The Fourier-transform infrared spectroscopy (FTIR) spectra unveils the intricate functional groups present in the fibers. XRD analysis highlights a crystallinity index (CI) of 66.93 %, confirming a well-organized and structured crystalline arrangement. The thermal stability established through TGA underscores HRF's resilience up to 284 °C, presenting it is an optimal reinforcement material for bio-inspired green composites operating within 280 °C. The surface morphology of HRF is examined through FESEM and three-dimensional profiling, showcasing its inherent morphological intricacies. The multidimensional characterization provided herein contributes significantly to the evolving landscape of biocomposite research, fostering a platform for future advancements and innovations in HRF-based composite materials.

Indoor tests of sensor-enabled piezoelectric geocable–geogrid composite structure for slope rehabilitation and monitoring

Sensor-enabled piezoelectric geocables were combined with a geogrid to acquire a sensor-enabled piezoelectric geogrid (SPGG) based on the impedance–strain relationship. Tension, pullout, and straight shear tests were conducted on this SPGG configuration. The tension test results indicated that the tensile strain–normalized impedance curves were exponential in form within the first 7 % of strain and the rate of shift in impedance was independent of the tension loading rate. An excellent correspondence between the peak strength and impedance inflection point was observed in the results of the pullout and straight shear tests. Additional validation of the proposed SPGG was conducted through a collapse test of the reinforced soil slope model. The results indicated that the SPGG-obtained strains were similar to actual strain gauge measurements but provided a larger measurement range and that the SPGG was able to sense real-time vibrations during the slope collapse using a voltage analysis, confirming that the proposed SPGG can simultaneously provide soil reinforcement, strain monitoring of reinforcement materials, and vibration sensing. This research is expected to inform the development of a dynamic and static monitoring, large range, and accurate method for monitoring the conditions of reinforced soil over their entire lifecycles.

Synergic effect of nano sized ceramic powder of titanium dioxide and silver on AZ91D composites fabricated by friction stir processing

This study aims to observe the synergic effects of AgNPs/TiO2 on AZ91D hybrid composite fabricated via friction stir process. Nano-sized particles of titanium-di-oxide (TiO2) and silver (AgNPs) in powder form were utilized as reinforcement materials for fabricating mono and hybrid composites. The average size of the reinforcements was 80 nm. Friction stir processing (FSP) technique was done at constant parametric settings. Investigating the microstructure of the composites by optical microscope(OM) analysis showed a homogenous distribution of the incorporated particles in the AZ91D matrix. Scanning electron microscopy (SEM) analysis was done for fractography, which indicates ductile facture in all the specimens despite having any composition of reinforcements. However, rate of ductile fracture decreased with weight fraction of TiO2. Tensile strength and Micro-hardness measurements revealed enhancement in tensile properties i.e. ultimate tensile strength (UTS), yield strength(YS), percentage elongation(EL) and microhardness in all samples. The contribution of various strengthening mechanisms, i.e. Hall-patch, Orowan strengthening and thermal mismatch, were calculated for all samples and compared with actual values. Among strengthening mechanisms, Orowan strengthening is the most dominant. The modified Clyne method estimates the collective effect of various strengthening mechanisms to evaluate the theoretical YS for all samples. The maximum value of Yield strength (YS) is 175.612 MPa obtained for T-50-A-50. The maximum value for microhardness is obtained as 140.08 HV on Vickers scale for T-100-A-0 attributed to uniform dispersion of hard ceramic (TiO2) particles.

Experimental study on the static properties of bamboo fiber reinforced ultra-high performance concrete (UHPC)

Bamboo fiber, as a natural and sustainable material, offers low cost, high strength, and environmental benefits, showing significant potential in composite material reinforcement. This study investigates the effects of bamboo fiber on the static properties of ultra-high performance concrete (UHPC) through experimental research. Different fiber lengths (6 mm, 12 mm, 18 mm) and volume contents (0.5 %, 1.0 %, 1.5 %, 2.0 %) were examined for their impact on the workability, mechanical properties, and pore/void structure of UHPC. The results demonstrate that while bamboo fiber incorporation reduces workability, it significantly enhances compressive and flexural strengths. Specifically, a 21.9 % increase in compressive strength was achieved with 18 mm fibers at 1.0 % content, and a 40.5 % increase in flexural strength was observed with 18 mm fibers at 1.5 % content. Mercury intrusion porosimetry (MIP) and computed tomography (CT) revealed that longer fibers contribute to the formation of larger pores, affecting the void structure. Moreover, bamboo fibers degrade over time in alkaline environments, with a 5 % reduction in tensile strength after 28 days, but the crystallinity of the cellulose has increased. Based on the experimental results, 12 mm bamboo fibers at 1.0–1.5 % content provide the best balance of strength enhancement and workability, making them a promising reinforcement material for UHPC.

Synthesis and characterization of bacterial cellulose composite with graphite and TiO2-ZnO: structural and functional analysis

This research aims to synthesize and characterize a bacterial cellulose (BC)-based composite with graphite and TiO2-ZnO as reinforcement materials using ex-situ synthesis with CTAB as a surfactant. FTIR and SEM-EDS analysis revealed interactions between the matrix and the reinforcement materials, as well as irregular particle distribution in the BC/G-TiO2-ZnO composite. The addition of graphite to BC significantly increased the conductivity of the composite, while the addition of TiO2-ZnO had the opposite effect. The mechanical properties of the composite exhibited an inverse relationship with the conductivity parameter. Swelling tests indicated that pH and the addition of CTAB influenced the swelling behavior of the BC-based composite. The results of this study provide a strong foundation for the development of potential applications in the fields of electronics and pollutant filtration. The synthesis of this composite aims to harness the unique properties of BC, graphite, and TiO2-ZnO, creating a multifunctional material with potential uses in flexible electronics, sensors, biocompatible conductive materials, and advanced filtration systems.

Aluminum boron carbide metal matrix composites for fatigue-based applications: A comprehensive review

Metal matrix composites (MMCs), known for their low density and superior stiffness, have gained significant attention in various load bearing and fatigue-prone applications. These composites offer distinct advantages over traditional monolithic metals, including enhanced mechanical and tribological properties, making them prime candidates for lightweight structural applications. Among ceramic reinforcements, boron carbide stands out due to its lower density, high elastic modulus, excellent refractoriness, and superior hardness, positioning it as an ideal reinforcement material. This review delves into the processing techniques, material properties, and microstructural characteristics of boron carbide-reinforced MMCs, with a focus on aluminum LM6 alloy as the matrix. Additionally, the paper explores the latest advancements and emerging opportunities for employing these composites in fatigue-critical applications, highlighting their potential to revolutionize industries requiring high performance and durability under repeated loading conditions.

Effect of Alumina as Reinforcement on the Mechanical and Physical Properties of Recycled AA6061 Aluminium

The utilisation of reinforcement materials in aluminium metal matrix composites is widely used in the manufacturing sector due to their lightweight nature, excellent strength-to-weight ratio, enhanced fracture toughness, and improved mechanical properties. The purpose of this study is to investigate the effect of reinforcing alumina in recycled AA6061 aluminium on the properties of the resulting aluminium matrix composite. Various compositions of recycled AA6061 aluminium reinforced with alumina were prepared and analysed using the cold compaction method. The results show that the addition of alumina composition increases the hardness properties of the composite by up to 5 wt.% at 32.91 Hv compared to the unreinforced sample at 30.63 Hv, but the hardness decreases as the alumina mass composition increases. According to the analysis of physical properties, in comparison to the unreinforced sample, the density decreases with increasing mass composition of alumina up to 10 wt.%, which is from 2.4636 g/cm3 to 2.3014 g/cm3, respectively. In relation to the microstructure of the samples, the addition of alumina results in irregular shapes with larger pores. An increasing in the mass composition of alumina results in increased porosity and water absorption.

Investigations on the influence of thickness and preform structure on the mechanical performance of novel textile composites with woven Kevlar® fabric reinforcement and poly methylmethacrylate (Elium®) matrix

Abstract Elium (novel methyl methacrylate (MMA)) resin is a liquid thermoplastic resin curable at room temperature and a possible replacement for epoxies. The main objective of this work is to evaluate the mechanical characteristics of novel Kevlar fabric reinforced Elium composites with different thicknesses. The plain-woven structure Kevlar/Elium laminates were manufactured with 1.5 mm and 2.5 mm thicknesses through vacuum-assisted resin infusion moulding, where 8 and 12 layers of woven fabrics were used, respectively. The effect of laminate thickness was measured in terms of mechanical (tensile, flexural, shear, and dynamic mechanical analysis (DMA)) and physical (density and fibre volume fraction (FVF)) characteristics. The density of the laminates was found in the range of 1.18–1.31 g cm−3. FVF was 50.69 and 52.27% for 1.5 and 2.5 mm thick laminates, respectively. The composite with 1.5 mm thickness exhibited the highest tensile strength (667.9 MPa) and flexural strength of 330.7 MPa. Conversely, the highest interlaminar shear strength measured for 2.5 mm thick laminate is 16.5 MPa. The DMA analysis recorded the highest storage and loss modulus for 2.5 mm thickness laminates. The fractography analysis confirmed the quantified experimental observation of excessive interface debonding and delamination. Elium composites may be suitable for high-end structural applications, including marine and aircraft structures.

Production of (B4C+FeTi) reinforced and Fe based composites by mechanical alloying

Abstract In this study, the microstructure and mechanical performance of Fe-based composites reinforced by FeTi+B4C at various ratios were determined. The study was based on the production of Fe based nano carbide and boride (B4C, Fe2B, Fe7C3, TiB2) reinforced composites. Mechanical alloying technique was chosen to reduce the reinforcement material to nano size and distribute it homogeneously. Sintering temperature was used as 1,100 °C and sintering time as 2 h. The reionforcement “FeTi+B4C” ratio was raised up to 15 wt.%. The microstructure and phases of the composite samples were descrived by scanning electron microscopy, energy dispersive spectroscopy, X-RD analysis and hardness. The concentration of voids and the stiffness changes of the samples were determined. The size of TiC and TiB2 particles reduced significantly with the rise in B4C ratio. Since the hardness of TiB2 was less than that of the B4C matrix, the hardness reduced with increasing TiB2 ratio.

Study on the Interface Reinforcement Effect of Bamboo Grid in Filled Loess Embankment in a High and Steep Gully

A bamboo grid is a new type of reinforcement material, which can replace traditional geogrids in the reinforcement of embankments. In this study, the reinforcement effect of the bamboo grid that is only set at the interface between the filled and undisturbed soils of the filled loess embankment in a high and steep gully was investigated. The influence of reinforcement position and grid spacing on the reinforcement effect was studied by carrying out a large-scale direct shear test, numerical simulation, and field measurement. The results indicated that the bamboo grid could enhance the shear strength of the reinforcement interface. The interface shear strength first improved and then decreased with the decrease in grid spacing. The differential settlement was significantly reduced after the reinforcement of the bamboo grid at the interface. Compared with other reinforcement positions, setting the bamboo grid in the upper part of the embankment was the most efficient and economical. When the grid spacing became dense, the reinforcement effect was improved as the differential settlement decreased. However, the improvement in the reinforcement effect by decreasing the grid spacing was limited, which meant there was an optimal grid spacing.