Particle breakage and shakedown behavior of granular material under cyclic loading conditions

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Limestone aggregates are often disregarded for such applications due to their susceptibility to particle breakage and permanent deformation. This study presents an experimental investigation into the cyclic response of limestone ballast under loading conditions representative of heavy-haul freight operations. Long-term permanent deformation tests were conducted under varying cyclic stress ratios and confining pressures. Particle breakage was quantified using the Particle Breakage Index ( Bg ) and the Ballast Breakage Index ( BBI ), while single-particle crushing tests were performed to evaluate particle strength. The results identify a critical cyclic stress ratio ( n crit = 0.80) governing both permanent deformation and particle breakage. For cyclic stress ratios below this threshold, the material exhibited stable behavior (shakedown regime) and limited particle breakage. Conversely, for n crit ≥ 0.80, progressive deformation (plastic creep regime) and a marked increase in particle degradation were observed. Increased confinement significantly reduced degradation and promoted shakedown behavior, even under higher stress levels. These findings demonstrate that the cyclic stress ratio controls not only deformation behavior but also particle integrity, while enhanced confinement mitigates ballast degradation. The results support the conditional feasibility of limestone ballast for heavy-haul railway applications. Particle Breakage Cyclic stress ratio Shakedown Railway Ballast Limestone Heavy-haul railways Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction Heavy-haul railway operations impose severe cyclic stresses on ballast layers, accelerating degradation processes that control long-term track performance. As axle loads increase toward 40 t to improve freight productivity (Delgado et al., 2019 ), understanding the mechanisms controlling particle breakage becomes increasingly critical. Railway ballast performance is governed by the mechanical integrity of its particles, which controls stress–strain response, particle strength, volume change, permeability change, and pore pressure development (Shi et al., 2023 ). Under cyclic train loading, high stress concentrations develop within the ballast layer, particularly beneath sleepers where contact forces are greatest (Chrismer and Selig, 1993 ; Aikawa, 2015 ). When stress levels exceed typical service conditions, particle degradation accelerates, especially under heavy-haul loading (Marsal, 1967 ). Degraded ballast compromises drainage diminishes lateral stability and increases settlement susceptibility, while under wet conditions, fouled material may act as a lubricant, significantly reducing shear strength and overall stability (Tutumluer et al., 2025 ). For tracks supported by stiff subgrades, the ballast layer typically contributes the majority of vertical track deformation, with approximately 50–70% of total settlement originating within the ballast layer (Selig and Waters, 1994 ). Ballast behavior depends strongly on particle durability; consequently, high-quality igneous and metamorphic rocks such as basalt, granite, quartzite, gneiss, dolomite, and rhyolite are typically specified for railway applications (Indraratna, 2016 ). Limestone ballast, in contrast, is often restricted due to its susceptibility to rainfall-induced degradation (Guo et al., 2022 ) and comparatively low abrasion resistance (Selig and Waters, 1994 ). The plastic deformation response of railway ballast is strongly governed by the stress state imposed during cyclic loading, particularly the cyclic stress ratio ( n ), defined as the ratio between the applied cyclic stress ( q cyc ) and the monotonic stress at failure ( q f ). Several researchers have shown the existence of a threshold value, referred to as the critical cyclic stress ratio ( n crit ), below which ballast behavior remains predominantly elastic, a condition commonly described as shakedown (Werkmeister et al., 2001 ). Reported values of n crit for railway ballast are relatively consistent. Suiker et al. ( 2005 ) observed shakedown behavior for n < 0.82, with higher ratios leading to the plastic creep regime. Similar trends were reported by Delgado et al. ( 2021 ) for reduced-scale ballast specimens, with n crit = 0.85. Malisetty et al. (2022) identified n crit = 0.80 for typical Australian ballast (Lackenby et al., 2007 ). For limestone ballast, De Andrade et al. ( 2025 ) reported that cyclic stress ratios above 0.84 resulted in a transition to the plastic creep regime. Despite its recognized role in governing ballast deformation regimes, the relationship between cyclic stress ratio and particle breakage evolution remains poorly understood. This study aims to evaluate the suitability of limestone ballast, which is often disregarded for railway applications, by investigating the relationship between cyclic stress ratio (n) and particle breakage. It further examines whether an optimal cyclic stress ratio exists at which particle breakage remains limited, enabling the identification of a threshold stress level beyond which excessive ballast degradation occurs. A series of large-scale cyclic triaxial tests were conducted to evaluate long-term permanent deformation under varying cyclic stress ratios and confining pressures. Different confinement levels were adopted to represent field strategies used to enhance track confinement. The applied stress conditions were representative of heavy-haul freight operations involving axle loads of 32.5 and 40.0 tonnes, as well as milder and more severe operational scenarios. Particle breakage was quantified using the Particle Breakage Index (Bg) (Marsal, 1967 ) and the Ballast Breakage Index (BBI) (Indraratna et al., 2005 ), while individual particle strength was evaluated through single-particle crushing tests. 2. Experimental Program 2.1 Materials and methods The experimental program used a limestone ballast meeting AREMA No. 4 grading requirements (AREMA, 2020). This gradation is specified for mainline railway tracks and provides a relatively uniform particle size distribution (Fig. 1 a). Detailed physical and morphological characterization of the aggregate is available in De Andrade et al. ( 2024 ); key descriptors are summarized here for completeness. The material satisfied the index-property requirements of Brazilian (ABNT, 2021) and U.S. specifications (AREMA, 2020), except for the proportion of non-cubic particles (Table 1 ). AIMS-based imaging indicated predominantly low-to-moderate surface texture and sub-rounded angularity, while sphericity was mostly low (flattened/stretched). These characteristics may increase susceptibility to abrasion and particle breakage under repeated loading. Table 1 Limestone ballast index parameters Requirements Limestone ABNT (2021) AREMA (2020) Particle specific gravity ( G s ) 2.7 2.6 2.6 Water absorption (%) 0.06 < 2 < 2 Los Angeles abrasion (%) 22 < 30 < 30 Average particle shape Cubic Cubic Cubic Non-cubic particles (%) 18 < 15 < 5 Weather resistance (%) 4.75 (63.5 to 38 mm) < 10 < 5 1.90 (38 to 19 mm) 3.47 (19 to 12.5 mm) Large-scale triaxial specimens were prepared to ensure representative particle interaction and reduce boundary effects. Cylindrical specimens measuring 300 mm in height and 150 mm in diameter were adopted (Fig. 1 b). This geometry satisfies the recommended aspect ratio ( H/D = 2.0), which limits end restraint effects (Bishop and Green, 1965 ), while the specimen diameter substantially exceeded the maximum particle size ( D/ dₘₐₓ ≥ 6.0), ensuring representative particle-scale behavior (Skoglund et al., 2000 ). Ballast specimens were densified through controlled vibration to achieve uniform packing and representative particle interlock. Conditioning prior to cyclic loading promoted stabilization of the initial fabric and reproduction of post-tamping void ratios (Anderson and Fair, 2008 ; Indraratna and Nimbalkar, 2013 ; Indraratna et al., 2013 ; Indraratna et al., 2015 ; Sun et al., 2016 ; Delgado et al., 2021 ). A detailed description of the preparation and conditioning procedures is provided in De Andrade et al. ( 2025 ). Axial strains were measured using two internal displacement transducers mounted diametrically opposite along the specimen height. This configuration reduces measurement errors associated with external instrumentation and enables accurate detection of small cyclic deformations. The monotonic shear strength of the limestone aggregate has been previously characterized (De Andrade et al., 2025 ), enabling the present study to concentrate on degradation mechanisms. The material exhibited a critical state friction angle ( φ′ cv ) of 50.7ºand a corresponding critical state friction coefficient ( M ) of 2.08. Figure 2 compares the shear strength response, expressed in terms of principal stress ratio at failure ( σ ’ 1 / σ ’ 3 ) f as a function of effective confining pressure, with results reported for fresh and recycled ballast (Indraratna and Salim, 2001 ), scaled-down granite and steel slag ballast (Delgado et al. 2021 ), and rockfill materials (Marsal, 1967 ; Marschi et al., 1972 ; Charles and Watts, 1980 ). A reduction in the principal stress ratio at failure with increasing confinement was observed, which is consistent trends reported for other granular materials. The limestone ballast exhibited shear strength behavior comparable to recycled ballast and reduced-scale ballast materials reported in the literature. 2.2 Mechanical response and degradation behaviour of limestone ballast The following sections present an experimental evaluation of limestone ballast, focusing on mechanical response, permanent deformation behaviour, and particle breakage under cyclic loading. 2.2.1 Long-term permanent deformation Long-term permanent deformation (PD) tests were conducted using different deviatoric stress levels while maintaining a constant confining pressure. Table 2 summarizes the main experimental conditions adopted in the PD tests. The present study extends previous findings (De Andrade et al. 2025 ) by introducing a lower confinement level (σ₃ = 40 kPa), enabling evaluation of confinement effects and the relationship between cyclic stress ratio and particle breakage. Each PD test was conducted up to one million loading cycles. Although tests PD4 and PD7 were interrupted after 4.5 × 10⁵ and 9.6 × 10⁵ cycles, respectively, due to unexpected power outages, the results remained suitable for evaluating ballast performance. Tests PD6 and PD10 were performed using a cyclic deviatoric stress of 280 kPa, representative of 32.5 t/axle loads, but under different confining pressures. Test PD11 employed a cyclic deviatoric stress of 350 kPa, representative of a 40.0 t/axle loading conditions. These stress levels were derived from empirical formulations proposed by Talbot ( 1918 ) and Schramm ( 1961 ). Similar deviatoric stress magnitudes were adopted by Delgado et al. ( 2021 ) to simulate 32.5 t/axle and 40.0 t/axle loads. Thus, the applied stress range encompassed realistic railway loading conditions as well as less severe and more demanding scenarios. Table 2 Experimental program for permanent deformation tests Triaxial Test e 0 N σ 3 (kPa) q cyc (kPa) σ 1 /σ 3 n PD1 0.82 10 6 40 80 3.00 0.27 PD2 0.84 10 6 40 120 4.00 0.40 PD3 0.85 10 6 40 160 5.00 0.53 PD4 0.79 4.5 x 10 5 40 200 6.00 0.67 PD5 0.82 10 6 40 240 7.00 0.80 PD6 0.73 10 6 40 280 8.00 0.93 PD7 0.74 9.6 x 10 5 40 320 9.00 1.07 PD8 0.81 10 6 70 140 3.00 0.29 PD9 0.82 10 6 70 210 4.00 0.44 PD10 0.79 10 6 70 280 5.00 0.58 PD11 0.78 10 6 70 350 6.00 0.73 PD12 0.78 10 6 70 402 6.74 0.84 PD13 0.75 10 6 70 420 7.00 0.89 Note : e 0 = Initial void ratios; N = Number of cycles; σ 3 = Confining pressure; σ 1 = Major principal stress. Permanent deformation tests were performed under sinusoidal vertical cyclic loading at a frequency of 5 Hz. This frequency is consistent with that observed in heavy-haul wagons with a bogie distance of approximately 4 meters, operating at speeds up to 80 km/h (Delgado et al., 2019 ). Confining pressures of 40 kPa and 70 kPa were adopted, which fall within the realistic range of 10–70 kPa reported by Indraratna et al. ( 2013 ), and are consistent with the experimental measurements of 18–60 kPa reported by Selig and Waters ( 1994 ). Increased confinement simulates reinforcement strategies such as reduced sleeper spacing, increased shoulder ballast height, intermittent shoulder restraints, or geosynthetic layers at the ballast–capping interface. These measures can improve track performance by reducing particle breakage and enhancing bearing capacity and resilient response (Lackenby et al., 2007 ). Granular material behavior under repeated loading may exhibit either stable or unstable responses, depending on the magnitude of the applied cyclic stress. Dawson and Wellner ( 1999 ) proposed a method to evaluate strain accumulation and identify shakedown behavior in granular materials. Their approach involves plotting the rate of permanent vertical strain against accumulated permanent vertical strain. According to their findings, materials exhibiting satisfactory long-term performance tend toward stable behavior, characterized by permanent vertical strain rates on the order of 10 –10 per cycle. This framework provides a basis for interpreting the deformation regimes observed in the present study. Figure 3 presents the assessment of shakedown behavior based on the criterion proposed by Dawson and Wellner ( 1999 ) for both confining pressures. The permanent deformation tests showed that permanent vertical strain increased with higher cyclic deviatoric stress levels. Under a confining pressure of 40 kPa, specimens tested at lower stress levels (PD1–PD4) exhibited similar deformation behavior, stabilizing after limited vertical strain accumulation and indicating a transition to the shakedown regime. In contrast, higher stress levels (PD5–PD7) resulted in continued strain accumulation, consistent with the plastic creep regime. Under 70 kPa confinement, a stabilizing trend in permanent strains was observed for PD8–PD11, whereas PD12 and PD13 exhibited ongoing strain accumulation, indicating a plastic creep regime. As discussed previously, permanent deformation of ballast is primarily influenced by the cyclic stress ratio imposed during loading. The plastic creep regime observed under higher loading conditions is associated with elevated cyclic stress ratios imposed on the ballast. The trends shown in Fig. 3 for both confining pressures support the existence of a critical cyclic stress ratio ( n crit ) of approximately 0.80, delineating the transition between stable and unstable behavior of the limestone ballast. When the cyclic deviatoric stress reached roughly 80% of the ballast shear strength (e.g., PD5), permanent strains no longer stabilized, indicating a transition toward the plastic creep regime. These findings are consistent with the results reported by Suiker et al. ( 2005 ), Delgado et al. ( 2021 ), and Malisetty et al. (2022). Overall, the results suggest a fundamental response largely governed by the imposed cyclic stress ratio, consistent with observations reported for ballast materials with different lithologies, gradations, and specimen scales. Tests conducted under higher confinement (70 kPa), adopted to simulate reinforcement strategies aimed at improving track confinement, revealed a clear tendency toward stabilization of permanent deformations. For stress conditions representative of a 32.5 t/axle loading scenario, test PD10 exhibited a cyclic stress ratio of 0.58—well below the critical threshold of 0.80—indicating that the shakedown regime was achieved. In contrast, PD6 showed a tendency toward transition to the plastic creep regime, associated with the higher cyclic stress ratio applied. Furthermore, the increased confining pressure demonstrated that even under stress levels representative of heavier loading conditions, such as those applied in PD11 corresponding to 40.0 t/axle, the ballast exhibited a tendency toward shakedown behavior. These results suggest that this limestone aggregate may be considered suitable for heavy-haul railway ballast applications at both 32.5 t/axle and 40.0 t/axle, provided that appropriate reinforcement strategies are implemented to enhance track confinement. 2.2.3 Single-particle crushing strength The crushing strength of the limestone ballast was evaluated through a series of single-particle crushing tests (Fig. 4 ). Each test was performed using a uniaxial loading frame at constant strain rate of 1.27 mm/min, compressing individual particles between two steel platens under monotonic loading. The initial particle diameter was measured as the vertical distance between platens. Axial load and platen displacement were continuously recorded until rupture. This procedure is analogous to that used in Brazilian test tensile strength for concrete. The crushing strength was calculated as: $${\sigma}_{f}=\frac{{F}_{f}}{{d}^{2}}\left(1\right)$$ where: F f is the maximum load corresponding to particle rupture and d is the initial particle diameter. Several tests were performed, but some results were excluded due to: (i) particle rupture along preferential planes caused by pre-existing discontinuities, and (ii) breakage of particle edges not representative of full crushing failure. As a result, 35 particles with nominal diameters ranging from approximately 10 mm to 50 mm were successfully tested, as shown in Fig. 5 . The results indicate that crushing strength decreases with increasing particle size. This trend is attributed to greater susceptibility to internal flaws in larger particles, which facilitates rupture under load (Lade et al., 1996 ). Similar observations have been reported for various granular materials (McDowell and Bolton, 1998 ; Nakata et al., 2001 ; Indraratna and Salim, 2003 ; Delgado et al., 2021 ). 2.2.4 Particle breakage in cyclic loading After the permanent deformation tests, the specimens were re-sieved to quantify particle breakage using two indices: the breakage index Bg proposed by Marsal ( 1967 ) and the Ballast Breakage Index ( BBI ) introduced by Indraratna et al. ( 2005 ). Marsal’s method evaluates breakage by calculating the percentage mass difference retained on each sieve ( ΔWk ) between the initial and final particle size distributions. The Bg index corresponds to the sum of the positive mass differences. The BBI was developed specifically for railway ballast and is determined from the area between the initial and final PSD curves, bounded by an upper limit representing the practical breakage potential of ballast particles. Larger particles were found to be more susceptible to breakage than smaller ones (Fig. 6 ). For clarity, only tests conducted under 40 kPa confinement are presented. This trend is consistent with the lower crushing strength of larger particles, as evidenced by the single-particle crushing tests. Similar observations have been reported by Salim ( 2004 ), Al-Saoudi and Hassan ( 2014 ), Hussaini et al. ( 2015 ), and Indraratna et al. ( 2016 ), who also identified higher breakage rates among larger particles following cyclic loading. Figure 7 presents the breakage indices BBI and Bg as a function of the cyclic stress ratio. The results indicate that particle breakage is strongly governed by the cyclic stress ratio and that a critical threshold exists below which degradation remains limited. A distinct transition in breakage behavior is observed around the critical value ( n crit = 0.80). For n < 0.80, breakage remained relatively low, consistent with the stabilization of permanent deformation and attainment of the shakedown regime (Fig. 3 ). In contrast, for n ≥ 0.80, both BBI and Bg increased sharply, indicating intensified particle degradation. This shift is consistent with the transition to the plastic creep regime observed in the permanent deformation tests. These results demonstrate that the cyclic stress ratio governs not only the plastic deformation behavior but also the structural integrity of ballast particles under repeated loading. A reduction in breakage indices was observed in tests conducted under higher confining pressures, consistent with the trends identified in the shakedown analysis (Fig. 3 ). For instance, tests PD6 and PD10, both representing loading conditions equivalent to 32.5 t/axle, showed that PD10, performed under 70 kPa confinement, exhibited substantially lower breakage indices ( Bg = 1.7%, BBI = 3.4%) than PD6 conducted under 40 kPa ( Bg = 9.2%, BBI = 15.5%). This behavior may be associated with the Optimum Degradation Zone concept proposed by Indraratna et al. ( 2005 ). As confinement increases, the ballast assembly tends to develop a more efficient packing structure, promoting a more uniform distribution of internal contact stresses and increasing interparticle contact areas. Consequently, localized stress concentrations – commonly associated with particle breakage – are reduced. In addition, the coordination number, defined as the average number of contact points per particle, may increase slightly. These findings highlight the effectiveness of increased confinement in mitigating ballast degradation and enhancing performance under heavy-haul loading. Figure 8 illustrates representative ballast particles at the conclusion of the long-term permanent deformation tests. The dominant degradation mechanism observed at both confinement levels was rounding, or "chipping" (Bach, 2013 ) in which particle edges and corners were progressively worn due to high contact stresses and shear forces (Fig. 8 a). As a result, particle angularity decreased, while overall particle size and shape remained relatively unchanged. As shown in Fig. 8 b, particle fragmentation, whereby a particle splits into several medium-sized fragments, was observed only in a limited number of particles. This observation is consistent with the findings of Sun et al. ( 2014 ), who reported that at frequencies below 20 Hz, ballast degradation is primarily characterized by attrition of asperities and corner breakage. 3. Conclusions This study presents an experimental investigation into the geomechanical behavior of limestone ballast for application in heavy-haul railway tracks. Cyclic triaxial tests and single particle crushing tests were conducted to assess long-term permanent deformation and particle breakage. Based on the experimental findings, the following conclusions are drawn: A critical cyclic stress ratio ( n crit ) of 0.80 was identified, defining a governing threshold for both permanent deformation behavior and particle breakage. This value is consistent with results reported for ballast materials with different lithologies, particle size distributions, and specimen scales, suggesting that this represents a fundamental mechanical response of granular materials under cyclic loading. For cyclic stress ratios below this threshold, limestone ballast exhibited stabilization of permanent deformation (shakedown regime) and limited particle breakage. Conversely, for n ≥ 0.80, a transition to an unstable response was observed, characterized by progressive permanent deformation (plastic creep regime) and a substantial increase in particle breakage indices. The limestone aggregate investigated can be considered suitable for railway ballast in heavy-haul freight operations involving axle loads of 32.5 t and 40.0 t, provided that reinforcement strategies aimed at increasing track confinement are implemented. Increased confinement reduced ballast degradation and improved mechanical performance under heavy-haul loading conditions. Crushing strength tests revealed that larger limestone particles tend to exhibit lower strength, making them more susceptible to degradation under high stress levels. This mechanical vulnerability aligns with the significant particle breakage observed in the permanent deformation tests. The experimental investigation provided a consistent and mechanistically grounded assessment of limestone ballast performance under heavy-haul loading conditions, highlighting the importance of laboratory investigations for evaluating ballast behavior at high axle loads. Although limestone ballast has traditionally been discouraged due to its susceptibility to particle degradation—effects also observed in this study under low confinement—the results demonstrate that these limitations can be effectively mitigated through increased track confinement. By identifying a critical cyclic stress ratio governing both permanent deformation and particle breakage across different ballast lithologies, particle size distributions, and specimen scales, this study supports the conditional feasibility of limestone ballast for demanding railway applications. Nevertheless, further research is required to strengthen the link between laboratory-scale observations and long-term field performance. These findings provide valuable insight for the design and maintenance of heavy-haul railway track systems. Nomenclature BBI Ballast breakage index Bg Marsal’s particle breakage index C c Coefficient of uniformity C u Coefficient of curvature d Initial particle diameter D Specimen diameter d max Maximum particle diameter e 0 Initial void ratio F f Maximum load in single particle crushing strength test G s Particle specific gravity H Specimen height M Critical state friction coefficient n Cyclic stress ratio N Number of load cycles n crit Critical cyclic stress ratio PD Permanent deformation PSD Particle size distribution q cyc Cyclic deviatoric stress q f Deviatoric stress at failure ΔW k Percentage difference retained on each sieve ε p Permanent vertical strain σ 1 Major principal stress σ 3 Confining pressure σ f Crushing strength φ’ cv Friction angle at the critical state Declarations Author Contribution Guilherme Faria Souza Mussi de Andrade: conceptualization, data curation, formal analysis, investigation, methodology, writing – original draft. Bruno Teixeira Lima: funding acquisition, supervision, validation, resources, writing – review and editing. Antonio Carlos Rodrigues Guimarães: supervision, validation, writing – review and editing. Acknowledgments This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. Data Availability The data were deposited into Postgraduate Program in Civil Engineering (PGECIV) at Rio de Janeiro State University and are available at the following URL: https://www.pgeciv.uerj.br/teses References ABNT (Associação Brasileira de Normas Técnicas) (2021) Via férrea - Lastro ferroviário - Requisitos e método de ensaio (NBR 5564). Rio de Janeiro, Brazil (In Portuguese). Aikawa, A. (2015). Dynamic characterisation of a ballast layer subject to traffic impact loads using three-dimensional sensing stones and a special sensing sleeper. 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Deformation and degradation aspects of ballast and constitutive modelling under cyclic loading. Ph.D. thesis, University of Wollongong. Schramm, G. (1961). Permanent Way Technique and Permanent Way Economy. Otto Elsner Verlagsgesellschaft, Dieburg, Germany. Selig, E. T. and Waters, J. M. (1994). Track geotechnology e substructure management , Thomas Telford, London. Shi, C., Fan, Z., Connolly, D. P., Jing, G., Markine, V. and Guo, Y. (2023). Railway ballast performance: recent advances in the understanding of geometry, distribution and degradation. Transportation Geotechnics , 41, 101042. https://doi.org/10.1016/j.trgeo.2023.101042 Skoglund, K. A., Hoseth, S. and Værnes, E. (2000). Development of a large triaxial cell apparatus with variable deviatoric and confining stresses. In Proceedings of the 5th International Symposium on Unbound Aggregates in Roads (Unbar-5) , Nottingham, UK, 145–152. Suiker, A. S. J., Selig, E. T. and Frenkel, R. (2005). Static and cyclic triaxial testing of ballast and subballast. Journal of Geotechnical and Geoenvironmental Engineering , 131(6), 771–782. https://doi.org/10.1061/(ASCE)1090-0241(2005)131:6(771 ). Sun, Q. D., Indraratna, B. and Nimbalkar, S. (2016). Deformation and degradation mechanisms of railway ballast under high frequency cyclic loading. Journal of Geotechnical and Geoenvironmental Engineering , 142(1), 04015056.https://doi.org/10.1061/(ASCE)GT.1943-5606.0001375 . Sun, Q. D., Indraratna, B. and Nimbalkar, S. (2014). Effect of cyclic loading frequency on the permanent deformation and degradation of railway ballast. Geotechnique , 64(9), pp. 746–751. https://doi.org/10.1680/geot.14.T.015 Talbot, A. N. (1918). Stresses in railroad track: reports of the Special Committee on Stresses in Railroad Track. In Proceedings of the AREA: First Progress Report. American Railway Engineering Association , Washington, DC, USA, vol. 19, pp. 873–1062. Tutumluer, E., Wang, H., Husain, S. F., Kong, T., Kim, Y., Ding, K., Qamhia, I. I.A., Wilk, S. and Li, D. (2025). A comparative study of new ballast and recycled ballast generated from various maintenance activities. Transportation Engineering , 20, 100321. https://doi.org/10.1016/j.treng.2025.100321 . Werkmeister, S., Dawson, A. R. and Wellner, F. (2001). Permanent deformation behavior of granular materials and the shakedown concept. Transportation Research Record , 1757(1), 75–81. https://doi.org/10.3141/1757-09 . Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9139205","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":609287434,"identity":"e17cda3c-72c8-4688-875c-5743c141f494","order_by":0,"name":"Guilherme Faria Souza Mussi de Andrade","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0ElEQVRIiWNgGAWjYFACxgYQycMvAeZJyBCvRXIGmCXBQ7xlBjcgmglrkY9Ibt3M86dOxvh28/FHN2oseBjYDx/dgE+L4Y3Ettu8bYd5zO4cS2zOOQZ0GE9a2g28WmaAtDQc4DG7kWPYnMMG1CIBZBPUAnQYj/EMkJZ/RGiRlwBpYWPmMZAAasltI0KLAc/DtptzgX6RuJGWODu3T4KHjZBf5NvTn91486fOnn9G8oHPOd/q5PjZDx/Db8sBdBE2fMrBtjQQUjEKRsEoGAWjAABa1kdO47keZQAAAABJRU5ErkJggg==","orcid":"","institution":"Rio de Janeiro State University","correspondingAuthor":true,"prefix":"","firstName":"Guilherme","middleName":"Faria Souza Mussi","lastName":"de Andrade","suffix":""},{"id":609287435,"identity":"9f132115-8ce0-4ba9-9c25-3f6c727d1aa4","order_by":1,"name":"Bruno Teixeira Lima","email":"","orcid":"","institution":"Rio de Janeiro State University","correspondingAuthor":false,"prefix":"","firstName":"Bruno","middleName":"Teixeira","lastName":"Lima","suffix":""},{"id":609287436,"identity":"1ef14f05-4841-408c-a218-8d6735c645be","order_by":2,"name":"Antonio Carlos Rodrigues Guimarães","email":"","orcid":"","institution":"Military Institute of Engineering","correspondingAuthor":false,"prefix":"","firstName":"Antonio","middleName":"Carlos Rodrigues","lastName":"Guimarães","suffix":""}],"badges":[],"createdAt":"2026-03-16 14:39:40","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9139205/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9139205/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105177161,"identity":"60b3a74c-d1b9-480f-8fa3-d56a9f2a88e9","added_by":"auto","created_at":"2026-03-23 06:17:55","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":153162,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Limestone ballast PSD curve; (b) cyclic triaxial apparatus with limestone ballast specimen\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9139205/v1/b4249919dcbbc311a6c4d745.jpg"},{"id":105563980,"identity":"001ad303-dc7f-4179-9f91-ed6b20e78495","added_by":"auto","created_at":"2026-03-27 12:48:21","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":103163,"visible":true,"origin":"","legend":"\u003cp\u003eShear strength of limestone ballast (after De Andrade et al., 2025) compared with ISAC and granite scaled ballast (after Delgado et al., 2019), as well as fresh and recycled full-scale ballast and rockfill materials (after Indraratna et al., 2011; Salim, 2004).\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9139205/v1/9fc62c97c654ba2f7bc94b03.jpg"},{"id":105177166,"identity":"25cc49d9-92ed-407f-a4a1-02b85c0d8b32","added_by":"auto","created_at":"2026-03-23 06:17:55","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":173860,"visible":true,"origin":"","legend":"\u003cp\u003eShakedown occurrence of the limestone aggregate: (a) \u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e = 40 kPa; (b) \u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e = 70 kPa\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9139205/v1/cd88150f0523fa6473240e97.jpg"},{"id":105177162,"identity":"ab5b22a1-dab0-44da-9613-b7a2759eb8ef","added_by":"auto","created_at":"2026-03-23 06:17:55","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":81272,"visible":true,"origin":"","legend":"\u003cp\u003eSingle particle crushing test\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9139205/v1/8d987194b10b02ffd2a1a038.jpg"},{"id":105177168,"identity":"90082123-bfe3-4424-9048-11fb7e3eae80","added_by":"auto","created_at":"2026-03-23 06:17:56","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":47077,"visible":true,"origin":"","legend":"\u003cp\u003eSingle particle crushing strength test results.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9139205/v1/e4646b267405eb0a5547a04d.jpg"},{"id":105177169,"identity":"7b872e9c-2989-49d4-a17d-01f1eadd7e89","added_by":"auto","created_at":"2026-03-23 06:17:56","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":102141,"visible":true,"origin":"","legend":"\u003cp\u003eDetermining the breakage index \u003cem\u003eBg\u003c/em\u003e\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9139205/v1/95ef5a5807d8a538a1133d6c.jpg"},{"id":105177163,"identity":"543c7074-6d34-417e-a444-52c465c0650f","added_by":"auto","created_at":"2026-03-23 06:17:55","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":120560,"visible":true,"origin":"","legend":"\u003cp\u003eBreakage indices results: (a) \u003cem\u003eBBI\u003c/em\u003e; (b) \u003cem\u003eBg\u003c/em\u003e\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9139205/v1/9a508ea136daf4b0b9ac754f.jpg"},{"id":105177165,"identity":"e725cd1d-18b7-481a-ab3c-4cc38970d21f","added_by":"auto","created_at":"2026-03-23 06:17:55","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":78705,"visible":true,"origin":"","legend":"\u003cp\u003eBallast particle degradation at the end of the permanent deformation test: (a) Rounding; (b) Fragmentation\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9139205/v1/d2fab456bbb99f3662dae46d.jpg"},{"id":107487566,"identity":"0e09e3a7-fb23-47d6-9609-48e7fb429533","added_by":"auto","created_at":"2026-04-22 02:42:07","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1272629,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9139205/v1/68914f73-0494-45a9-94c4-160680d62428.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Particle breakage and shakedown behavior of granular material under cyclic loading conditions","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eHeavy-haul railway operations impose severe cyclic stresses on ballast layers, accelerating degradation processes that control long-term track performance. As axle loads increase toward 40 t to improve freight productivity (Delgado et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), understanding the mechanisms controlling particle breakage becomes increasingly critical.\u003c/p\u003e \u003cp\u003eRailway ballast performance is governed by the mechanical integrity of its particles, which controls stress\u0026ndash;strain response, particle strength, volume change, permeability change, and pore pressure development (Shi et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Under cyclic train loading, high stress concentrations develop within the ballast layer, particularly beneath sleepers where contact forces are greatest (Chrismer and Selig, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1993\u003c/span\u003e; Aikawa, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). When stress levels exceed typical service conditions, particle degradation accelerates, especially under heavy-haul loading (Marsal, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e1967\u003c/span\u003e). Degraded ballast compromises drainage diminishes lateral stability and increases settlement susceptibility, while under wet conditions, fouled material may act as a lubricant, significantly reducing shear strength and overall stability (Tutumluer et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). For tracks supported by stiff subgrades, the ballast layer typically contributes the majority of vertical track deformation, with approximately 50\u0026ndash;70% of total settlement originating within the ballast layer (Selig and Waters, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e1994\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eBallast behavior depends strongly on particle durability; consequently, high-quality igneous and metamorphic rocks such as basalt, granite, quartzite, gneiss, dolomite, and rhyolite are typically specified for railway applications (Indraratna, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). Limestone ballast, in contrast, is often restricted due to its susceptibility to rainfall-induced degradation (Guo et al., \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) and comparatively low abrasion resistance (Selig and Waters, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e1994\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe plastic deformation response of railway ballast is strongly governed by the stress state imposed during cyclic loading, particularly the cyclic stress ratio (\u003cem\u003en\u003c/em\u003e), defined as the ratio between the applied cyclic stress (\u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003ecyc\u003c/em\u003e\u003c/sub\u003e) and the monotonic stress at failure (\u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e). Several researchers have shown the existence of a threshold value, referred to as the critical cyclic stress ratio (\u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrit\u003c/em\u003e\u003c/sub\u003e), below which ballast behavior remains predominantly elastic, a condition commonly described as shakedown (Werkmeister et al., \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). Reported values of \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrit\u003c/em\u003e\u003c/sub\u003e for railway ballast are relatively consistent. Suiker et al. (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) observed shakedown behavior for \u003cem\u003en\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.82, with higher ratios leading to the plastic creep regime. Similar trends were reported by Delgado et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) for reduced-scale ballast specimens, with \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrit\u003c/em\u003e\u003c/sub\u003e = 0.85. Malisetty et al. (2022) identified \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrit\u003c/em\u003e\u003c/sub\u003e = 0.80 for typical Australian ballast (Lackenby et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). For limestone ballast, De Andrade et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) reported that cyclic stress ratios above 0.84 resulted in a transition to the plastic creep regime. Despite its recognized role in governing ballast deformation regimes, the relationship between cyclic stress ratio and particle breakage evolution remains poorly understood.\u003c/p\u003e \u003cp\u003eThis study aims to evaluate the suitability of limestone ballast, which is often disregarded for railway applications, by investigating the relationship between cyclic stress ratio (n) and particle breakage. It further examines whether an optimal cyclic stress ratio exists at which particle breakage remains limited, enabling the identification of a threshold stress level beyond which excessive ballast degradation occurs. A series of large-scale cyclic triaxial tests were conducted to evaluate long-term permanent deformation under varying cyclic stress ratios and confining pressures. Different confinement levels were adopted to represent field strategies used to enhance track confinement. The applied stress conditions were representative of heavy-haul freight operations involving axle loads of 32.5 and 40.0 tonnes, as well as milder and more severe operational scenarios. Particle breakage was quantified using the Particle Breakage Index (Bg) (Marsal, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e1967\u003c/span\u003e) and the Ballast Breakage Index (BBI) (Indraratna et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2005\u003c/span\u003e), while individual particle strength was evaluated through single-particle crushing tests.\u003c/p\u003e"},{"header":"2. Experimental Program","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Materials and methods\u003c/h2\u003e \u003cp\u003eThe experimental program used a limestone ballast meeting AREMA No. 4 grading requirements (AREMA, 2020). This gradation is specified for mainline railway tracks and provides a relatively uniform particle size distribution (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea). Detailed physical and morphological characterization of the aggregate is available in De Andrade et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2024\u003c/span\u003e); key descriptors are summarized here for completeness. The material satisfied the index-property requirements of Brazilian (ABNT, 2021) and U.S. specifications (AREMA, 2020), except for the proportion of non-cubic particles (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). AIMS-based imaging indicated predominantly low-to-moderate surface texture and sub-rounded angularity, while sphericity was mostly low (flattened/stretched). These characteristics may increase susceptibility to abrasion and particle breakage under repeated loading.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eLimestone ballast index parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eRequirements\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLimestone\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eABNT (2021)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAREMA (2020)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParticle specific gravity (\u003cem\u003eG\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWater absorption (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLos Angeles abrasion (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage particle shape\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCubic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCubic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCubic\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNon-cubic particles (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eWeather resistance (%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.75 (63.5 to 38 mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u0026lt;\u0026thinsp;5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.90 (38 to 19 mm)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.47 (19 to 12.5 mm)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eLarge-scale triaxial specimens were prepared to ensure representative particle interaction and reduce boundary effects. Cylindrical specimens measuring 300 mm in height and 150 mm in diameter were adopted (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb). This geometry satisfies the recommended aspect ratio (\u003cem\u003eH/D\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.0), which limits end restraint effects (Bishop and Green, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1965\u003c/span\u003e), while the specimen diameter substantially exceeded the maximum particle size (\u003cem\u003eD/ dₘₐₓ\u003c/em\u003e \u0026ge; 6.0), ensuring representative particle-scale behavior (Skoglund et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). Ballast specimens were densified through controlled vibration to achieve uniform packing and representative particle interlock. Conditioning prior to cyclic loading promoted stabilization of the initial fabric and reproduction of post-tamping void ratios (Anderson and Fair, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Indraratna and Nimbalkar, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Indraratna et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Indraratna et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Sun et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Delgado et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). A detailed description of the preparation and conditioning procedures is provided in De Andrade et al. (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Axial strains were measured using two internal displacement transducers mounted diametrically opposite along the specimen height. This configuration reduces measurement errors associated with external instrumentation and enables accurate detection of small cyclic deformations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe monotonic shear strength of the limestone aggregate has been previously characterized (De Andrade et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2025\u003c/span\u003e), enabling the present study to concentrate on degradation mechanisms. The material exhibited a critical state friction angle (\u003cem\u003eφ\u0026prime;\u003c/em\u003e\u003csub\u003e\u003cem\u003ecv\u003c/em\u003e\u003c/sub\u003e) of 50.7\u0026ordm;and a corresponding critical state friction coefficient (\u003cem\u003eM\u003c/em\u003e) of 2.08. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e compares the shear strength response, expressed in terms of principal stress ratio at failure (\u003cem\u003eσ\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026rsquo;\u003c/em\u003e\u003c/sup\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e/ σ\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026rsquo;\u003c/em\u003e\u003c/sup\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e)\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e as a function of effective confining pressure, with results reported for fresh and recycled ballast (Indraratna and Salim, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2001\u003c/span\u003e), scaled-down granite and steel slag ballast (Delgado et al. \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), and rockfill materials (Marsal, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e1967\u003c/span\u003e; Marschi et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1972\u003c/span\u003e; Charles and Watts, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1980\u003c/span\u003e). A reduction in the principal stress ratio at failure with increasing confinement was observed, which is consistent trends reported for other granular materials. The limestone ballast exhibited shear strength behavior comparable to recycled ballast and reduced-scale ballast materials reported in the literature.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Mechanical response and degradation behaviour of limestone ballast\u003c/h2\u003e \u003cp\u003eThe following sections present an experimental evaluation of limestone ballast, focusing on mechanical response, permanent deformation behaviour, and particle breakage under cyclic loading.\u003c/p\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e2.2.1 Long-term permanent deformation\u003c/h2\u003e \u003cp\u003eLong-term permanent deformation (PD) tests were conducted using different deviatoric stress levels while maintaining a constant confining pressure. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e summarizes the main experimental conditions adopted in the PD tests. The present study extends previous findings (De Andrade et al. \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) by introducing a lower confinement level (σ₃ = 40 kPa), enabling evaluation of confinement effects and the relationship between cyclic stress ratio and particle breakage.\u003c/p\u003e \u003cp\u003eEach PD test was conducted up to one million loading cycles. Although tests PD4 and PD7 were interrupted after 4.5 \u0026times; 10⁵ and 9.6 \u0026times; 10⁵ cycles, respectively, due to unexpected power outages, the results remained suitable for evaluating ballast performance. Tests PD6 and PD10 were performed using a cyclic deviatoric stress of 280 kPa, representative of 32.5 t/axle loads, but under different confining pressures. Test PD11 employed a cyclic deviatoric stress of 350 kPa, representative of a 40.0 t/axle loading conditions. These stress levels were derived from empirical formulations proposed by Talbot (\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e1918\u003c/span\u003e) and Schramm (\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e1961\u003c/span\u003e). Similar deviatoric stress magnitudes were adopted by Delgado et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) to simulate 32.5 t/axle and 40.0 t/axle loads. Thus, the applied stress range encompassed realistic railway loading conditions as well as less severe and more demanding scenarios.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental program for permanent deformation tests\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTriaxial Test\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eN\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e (kPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003ecyc\u003c/em\u003e\u003c/sub\u003e (kPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e/σ\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.27\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e160\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.53\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4.5 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e240\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e7.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.80\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e8.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e9.6 x 10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e9.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e3.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.44\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e280\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.58\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e350\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e402\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e6.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.84\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePD13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e420\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e7.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"7\"\u003e\u003cem\u003eNote\u003c/em\u003e: \u003cem\u003ee\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;Initial void ratios; \u003cem\u003eN\u0026thinsp;=\u003c/em\u003e\u0026thinsp;Number of cycles; \u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003e3\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;Confining pressure; \u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;\u003cem\u003e=\u003c/em\u003e\u0026thinsp;Major principal stress.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003ePermanent deformation tests were performed under sinusoidal vertical cyclic loading at a frequency of 5 Hz. This frequency is consistent with that observed in heavy-haul wagons with a bogie distance of approximately 4 meters, operating at speeds up to 80 km/h (Delgado et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Confining pressures of 40 kPa and 70 kPa were adopted, which fall within the realistic range of 10\u0026ndash;70 kPa reported by Indraratna et al. (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), and are consistent with the experimental measurements of 18\u0026ndash;60 kPa reported by Selig and Waters (\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e1994\u003c/span\u003e). Increased confinement simulates reinforcement strategies such as reduced sleeper spacing, increased shoulder ballast height, intermittent shoulder restraints, or geosynthetic layers at the ballast\u0026ndash;capping interface. These measures can improve track performance by reducing particle breakage and enhancing bearing capacity and resilient response (Lackenby et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2007\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eGranular material behavior under repeated loading may exhibit either stable or unstable responses, depending on the magnitude of the applied cyclic stress. Dawson and Wellner (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) proposed a method to evaluate strain accumulation and identify shakedown behavior in granular materials. Their approach involves plotting the rate of permanent vertical strain against accumulated permanent vertical strain. According to their findings, materials exhibiting satisfactory long-term performance tend toward stable behavior, characterized by permanent vertical strain rates on the order of 10\u003csup\u003e\u0026ndash;10\u003c/sup\u003e per cycle. This framework provides a basis for interpreting the deformation regimes observed in the present study.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents the assessment of shakedown behavior based on the criterion proposed by Dawson and Wellner (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) for both confining pressures. The permanent deformation tests showed that permanent vertical strain increased with higher cyclic deviatoric stress levels. Under a confining pressure of 40 kPa, specimens tested at lower stress levels (PD1\u0026ndash;PD4) exhibited similar deformation behavior, stabilizing after limited vertical strain accumulation and indicating a transition to the shakedown regime. In contrast, higher stress levels (PD5\u0026ndash;PD7) resulted in continued strain accumulation, consistent with the plastic creep regime. Under 70 kPa confinement, a stabilizing trend in permanent strains was observed for PD8\u0026ndash;PD11, whereas PD12 and PD13 exhibited ongoing strain accumulation, indicating a plastic creep regime.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs discussed previously, permanent deformation of ballast is primarily influenced by the cyclic stress ratio imposed during loading. The plastic creep regime observed under higher loading conditions is associated with elevated cyclic stress ratios imposed on the ballast. The trends shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e for both confining pressures support the existence of a critical cyclic stress ratio (\u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrit\u003c/em\u003e\u003c/sub\u003e) of approximately 0.80, delineating the transition between stable and unstable behavior of the limestone ballast. When the cyclic deviatoric stress reached roughly 80% of the ballast shear strength (e.g., PD5), permanent strains no longer stabilized, indicating a transition toward the plastic creep regime. These findings are consistent with the results reported by Suiker et al. (\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2005\u003c/span\u003e), Delgado et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), and Malisetty et al. (2022). Overall, the results suggest a fundamental response largely governed by the imposed cyclic stress ratio, consistent with observations reported for ballast materials with different lithologies, gradations, and specimen scales.\u003c/p\u003e \u003cp\u003eTests conducted under higher confinement (70 kPa), adopted to simulate reinforcement strategies aimed at improving track confinement, revealed a clear tendency toward stabilization of permanent deformations. For stress conditions representative of a 32.5 t/axle loading scenario, test PD10 exhibited a cyclic stress ratio of 0.58\u0026mdash;well below the critical threshold of 0.80\u0026mdash;indicating that the shakedown regime was achieved. In contrast, PD6 showed a tendency toward transition to the plastic creep regime, associated with the higher cyclic stress ratio applied.\u003c/p\u003e \u003cp\u003eFurthermore, the increased confining pressure demonstrated that even under stress levels representative of heavier loading conditions, such as those applied in PD11 corresponding to 40.0 t/axle, the ballast exhibited a tendency toward shakedown behavior. These results suggest that this limestone aggregate may be considered suitable for heavy-haul railway ballast applications at both 32.5 t/axle and 40.0 t/axle, provided that appropriate reinforcement strategies are implemented to enhance track confinement.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.2.3 Single-particle crushing strength\u003c/h2\u003e \u003cp\u003eThe crushing strength of the limestone ballast was evaluated through a series of single-particle crushing tests (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Each test was performed using a uniaxial loading frame at constant strain rate of 1.27 mm/min, compressing individual particles between two steel platens under monotonic loading. The initial particle diameter was measured as the vertical distance between platens. Axial load and platen displacement were continuously recorded until rupture. This procedure is analogous to that used in Brazilian test tensile strength for concrete. The crushing strength was calculated as:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$${\\sigma}_{f}=\\frac{{F}_{f}}{{d}^{2}}\\left(1\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere: \u003cem\u003eF\u003c/em\u003e\u003csub\u003e\u003cem\u003ef\u003c/em\u003e\u003c/sub\u003e is the maximum load corresponding to particle rupture and \u003cem\u003ed\u003c/em\u003e is the initial particle diameter.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eSeveral tests were performed, but some results were excluded due to: (i) particle rupture along preferential planes caused by pre-existing discontinuities, and (ii) breakage of particle edges not representative of full crushing failure. As a result, 35 particles with nominal diameters ranging from approximately 10 mm to 50 mm were successfully tested, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The results indicate that crushing strength decreases with increasing particle size. This trend is attributed to greater susceptibility to internal flaws in larger particles, which facilitates rupture under load (Lade et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1996\u003c/span\u003e). Similar observations have been reported for various granular materials (McDowell and Bolton, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Nakata et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Indraratna and Salim, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2003\u003c/span\u003e; Delgado et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.2.4 Particle breakage in cyclic loading\u003c/h2\u003e \u003cp\u003eAfter the permanent deformation tests, the specimens were re-sieved to quantify particle breakage using two indices: the breakage index \u003cem\u003eBg\u003c/em\u003e proposed by Marsal (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e1967\u003c/span\u003e) and the Ballast Breakage Index (\u003cem\u003eBBI\u003c/em\u003e) introduced by Indraratna et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). Marsal\u0026rsquo;s method evaluates breakage by calculating the percentage mass difference retained on each sieve (\u003cem\u003eΔWk\u003c/em\u003e) between the initial and final particle size distributions. The \u003cem\u003eBg\u003c/em\u003e index corresponds to the sum of the positive mass differences. The \u003cem\u003eBBI\u003c/em\u003e was developed specifically for railway ballast and is determined from the area between the initial and final PSD curves, bounded by an upper limit representing the practical breakage potential of ballast particles.\u003c/p\u003e \u003cp\u003eLarger particles were found to be more susceptible to breakage than smaller ones (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). For clarity, only tests conducted under 40 kPa confinement are presented. This trend is consistent with the lower crushing strength of larger particles, as evidenced by the single-particle crushing tests. Similar observations have been reported by Salim (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2004\u003c/span\u003e), Al-Saoudi and Hassan (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), Hussaini et al. (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), and Indraratna et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), who also identified higher breakage rates among larger particles following cyclic loading.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e presents the breakage indices \u003cem\u003eBBI\u003c/em\u003e and \u003cem\u003eBg\u003c/em\u003e as a function of the cyclic stress ratio. The results indicate that particle breakage is strongly governed by the cyclic stress ratio and that a critical threshold exists below which degradation remains limited. A distinct transition in breakage behavior is observed around the critical value (\u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrit\u003c/em\u003e\u003c/sub\u003e = 0.80). For \u003cem\u003en\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.80, breakage remained relatively low, consistent with the stabilization of permanent deformation and attainment of the shakedown regime (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). In contrast, for \u003cem\u003en\u003c/em\u003e\u0026thinsp;\u0026ge;\u0026thinsp;0.80, both \u003cem\u003eBBI\u003c/em\u003e and \u003cem\u003eBg\u003c/em\u003e increased sharply, indicating intensified particle degradation. This shift is consistent with the transition to the plastic creep regime observed in the permanent deformation tests. These results demonstrate that the cyclic stress ratio governs not only the plastic deformation behavior but also the structural integrity of ballast particles under repeated loading.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA reduction in breakage indices was observed in tests conducted under higher confining pressures, consistent with the trends identified in the shakedown analysis (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). For instance, tests PD6 and PD10, both representing loading conditions equivalent to 32.5 t/axle, showed that PD10, performed under 70 kPa confinement, exhibited substantially lower breakage indices (\u003cem\u003eBg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.7%, \u003cem\u003eBBI\u003c/em\u003e\u0026thinsp;=\u0026thinsp;3.4%) than PD6 conducted under 40 kPa (\u003cem\u003eBg\u003c/em\u003e\u0026thinsp;=\u0026thinsp;9.2%, \u003cem\u003eBBI\u003c/em\u003e\u0026thinsp;=\u0026thinsp;15.5%). This behavior may be associated with the Optimum Degradation Zone concept proposed by Indraratna et al. (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). As confinement increases, the ballast assembly tends to develop a more efficient packing structure, promoting a more uniform distribution of internal contact stresses and increasing interparticle contact areas. Consequently, localized stress concentrations \u0026ndash; commonly associated with particle breakage \u0026ndash; are reduced. In addition, the coordination number, defined as the average number of contact points per particle, may increase slightly. These findings highlight the effectiveness of increased confinement in mitigating ballast degradation and enhancing performance under heavy-haul loading.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e illustrates representative ballast particles at the conclusion of the long-term permanent deformation tests. The dominant degradation mechanism observed at both confinement levels was rounding, or \"chipping\" (Bach, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) in which particle edges and corners were progressively worn due to high contact stresses and shear forces (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003ea). As a result, particle angularity decreased, while overall particle size and shape remained relatively unchanged. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003eb, particle fragmentation, whereby a particle splits into several medium-sized fragments, was observed only in a limited number of particles. This observation is consistent with the findings of Sun et al. (\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), who reported that at frequencies below 20 Hz, ballast degradation is primarily characterized by attrition of asperities and corner breakage.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3. Conclusions","content":"\u003cp\u003eThis study presents an experimental investigation into the geomechanical behavior of limestone ballast for application in heavy-haul railway tracks. Cyclic triaxial tests and single particle crushing tests were conducted to assess long-term permanent deformation and particle breakage. Based on the experimental findings, the following conclusions are drawn:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eA critical cyclic stress ratio (\u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrit\u003c/em\u003e\u003c/sub\u003e) of 0.80 was identified, defining a governing threshold for both permanent deformation behavior and particle breakage. This value is consistent with results reported for ballast materials with different lithologies, particle size distributions, and specimen scales, suggesting that this represents a fundamental mechanical response of granular materials under cyclic loading. For cyclic stress ratios below this threshold, limestone ballast exhibited stabilization of permanent deformation (shakedown regime) and limited particle breakage. Conversely, for \u003cem\u003en\u003c/em\u003e\u0026thinsp;\u0026ge;\u0026thinsp;0.80, a transition to an unstable response was observed, characterized by progressive permanent deformation (plastic creep regime) and a substantial increase in particle breakage indices.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe limestone aggregate investigated can be considered suitable for railway ballast in heavy-haul freight operations involving axle loads of 32.5 t and 40.0 t, provided that reinforcement strategies aimed at increasing track confinement are implemented. Increased confinement reduced ballast degradation and improved mechanical performance under heavy-haul loading conditions.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eCrushing strength tests revealed that larger limestone particles tend to exhibit lower strength, making them more susceptible to degradation under high stress levels. This mechanical vulnerability aligns with the significant particle breakage observed in the permanent deformation tests.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThe experimental investigation provided a consistent and mechanistically grounded assessment of limestone ballast performance under heavy-haul loading conditions, highlighting the importance of laboratory investigations for evaluating ballast behavior at high axle loads. Although limestone ballast has traditionally been discouraged due to its susceptibility to particle degradation\u0026mdash;effects also observed in this study under low confinement\u0026mdash;the results demonstrate that these limitations can be effectively mitigated through increased track confinement. By identifying a critical cyclic stress ratio governing both permanent deformation and particle breakage across different ballast lithologies, particle size distributions, and specimen scales, this study supports the conditional feasibility of limestone ballast for demanding railway applications. Nevertheless, further research is required to strengthen the link between laboratory-scale observations and long-term field performance. These findings provide valuable insight for the design and maintenance of heavy-haul railway track systems.\u003c/p\u003e"},{"header":"Nomenclature","content":"\u003cp\u003e\u003cem\u003eBBI\u003c/em\u003e Ballast breakage index\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eBg\u003c/em\u003e Marsal\u0026rsquo;s particle breakage index\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eC\u003csub\u003ec\u003c/sub\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/em\u003eCoefficient of uniformity\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eC\u003csub\u003eu\u003c/sub\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/em\u003eCoefficient of curvature\u003c/p\u003e\n\u003cp\u003e\u003cem\u003ed\u003c/em\u003e Initial particle diameter\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eD\u003c/em\u003e Specimen diameter\u003c/p\u003e\n\u003cp\u003e\u003cem\u003ed\u003csub\u003emax\u003c/sub\u003e\u003c/em\u003e Maximum particle diameter\u003c/p\u003e\n\u003cp\u003e\u003cem\u003ee\u003csub\u003e0\u003c/sub\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/em\u003eInitial void ratio\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eF\u003csub\u003ef\u003c/sub\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/em\u003eMaximum load in single particle crushing strength test\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eG\u003csub\u003es\u003c/sub\u003e\u003c/em\u003e Particle specific gravity\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eH\u003c/em\u003e Specimen height\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eM\u003c/em\u003e Critical state friction coefficient\u003c/p\u003e\n\u003cp\u003e\u003cem\u003en\u003c/em\u003e Cyclic stress ratio\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eN\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/em\u003eNumber of load cycles\u003c/p\u003e\n\u003cp\u003e\u003cem\u003en\u003csub\u003ecrit\u003c/sub\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/em\u003eCritical cyclic stress ratio\u003c/p\u003e\n\u003cp\u003e\u003cem\u003ePD\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/em\u003ePermanent deformation\u003c/p\u003e\n\u003cp\u003e\u003cem\u003ePSD\u0026nbsp; \u0026nbsp; \u0026nbsp;Particle size distribution\u003c/em\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eq\u003csub\u003ecyc\u003c/sub\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/em\u003eCyclic deviatoric stress\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eq\u003csub\u003ef\u003c/sub\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/em\u003eDeviatoric stress at failure\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u0026Delta;W\u003csub\u003ek\u003c/sub\u003e\u003c/em\u003e Percentage difference retained on each sieve\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u0026epsilon;\u003csub\u003ep\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/sub\u003e\u003c/em\u003ePermanent vertical strain\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u0026sigma;\u003csub\u003e1\u003c/sub\u003e\u003c/em\u003e\u003cem\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u0026nbsp;\u003c/em\u003eMajor principal stress\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u0026sigma;\u003csub\u003e3\u003c/sub\u003e\u003c/em\u003e Confining pressure\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u0026sigma;\u003csub\u003ef\u003c/sub\u003e\u003c/em\u003e\u003cem\u003e\u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp; \u0026nbsp;\u003c/em\u003eCrushing strength\u003c/p\u003e\n\u003cp\u003e\u003cem\u003e\u0026phi;\u0026rsquo;\u003csub\u003ecv\u003c/sub\u003e\u003c/em\u003e Friction angle at the critical state\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eGuilherme Faria Souza Mussi de Andrade: conceptualization, data curation, formal analysis, investigation, methodology, writing \u0026ndash; original draft. Bruno Teixeira Lima: funding acquisition, supervision, validation, resources, writing \u0026ndash; review and editing. Antonio Carlos Rodrigues Guimar\u0026atilde;es: supervision, validation, writing \u0026ndash; review and editing.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eThis study was financed in part by the Coordena\u0026ccedil;\u0026atilde;o de Aperfei\u0026ccedil;oamento de Pessoal de N\u0026iacute;vel Superior \u0026ndash; Brasil (CAPES) \u0026ndash; Finance Code 001.\u003c/p\u003e \u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data were deposited into Postgraduate Program in Civil Engineering (PGECIV) at Rio de Janeiro State University and are available at the following URL: https://www.pgeciv.uerj.br/teses\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eABNT (Associa\u0026ccedil;\u0026atilde;o Brasileira de Normas T\u0026eacute;cnicas) (2021) \u003cem\u003eVia f\u0026eacute;rrea - Lastro ferrovi\u0026aacute;rio - Requisitos e m\u0026eacute;todo de ensaio\u003c/em\u003e (NBR 5564). 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Permanent deformation behavior of granular materials and the shakedown concept. \u003cem\u003eTransportation Research Record\u003c/em\u003e, 1757(1), 75\u0026ndash;81. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.3141/1757-09\u003c/span\u003e\u003cspan address=\"10.3141/1757-09\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Particle Breakage, Cyclic stress ratio, Shakedown, Railway Ballast, Limestone, Heavy-haul railways","lastPublishedDoi":"10.21203/rs.3.rs-9139205/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9139205/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe geomechanical performance of railway ballast is critical to the long-term stability of heavy-haul track systems. Limestone aggregates are often disregarded for such applications due to their susceptibility to particle breakage and permanent deformation. This study presents an experimental investigation into the cyclic response of limestone ballast under loading conditions representative of heavy-haul freight operations. Long-term permanent deformation tests were conducted under varying cyclic stress ratios and confining pressures. Particle breakage was quantified using the Particle Breakage Index (\u003cem\u003eBg\u003c/em\u003e) and the Ballast Breakage Index (\u003cem\u003eBBI\u003c/em\u003e), while single-particle crushing tests were performed to evaluate particle strength. The results identify a critical cyclic stress ratio (\u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrit\u003c/em\u003e\u003c/sub\u003e = 0.80) governing both permanent deformation and particle breakage. For cyclic stress ratios below this threshold, the material exhibited stable behavior (shakedown regime) and limited particle breakage. Conversely, for \u003cem\u003en\u003c/em\u003e\u003csub\u003e\u003cem\u003ecrit\u003c/em\u003e\u003c/sub\u003e \u0026ge; 0.80, progressive deformation (plastic creep regime) and a marked increase in particle degradation were observed. Increased confinement significantly reduced degradation and promoted shakedown behavior, even under higher stress levels. These findings demonstrate that the cyclic stress ratio controls not only deformation behavior but also particle integrity, while enhanced confinement mitigates ballast degradation. The results support the conditional feasibility of limestone ballast for heavy-haul railway applications.\u003c/p\u003e","manuscriptTitle":"Particle breakage and shakedown behavior of granular material under cyclic loading conditions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-23 06:17:50","doi":"10.21203/rs.3.rs-9139205/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0a2d0bbb-4de9-411b-b082-299695b3b9ca","owner":[],"postedDate":"March 23rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-04-20T18:39:29+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-23 06:17:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9139205","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9139205","identity":"rs-9139205","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}