Influence of Moisture on the Shakedown Behavior of Fine Soils for Sustainable Railway Subballast Layers

Abstract

This study investigates the influence of moisture on the mechanical behavior of fine soil mixtures from the São Luís region, applied as subballast layers in railway track structures. Two samples were analyzed: a non-lateritic sandy soil (NA’, AM03) and a lateritic clayey soil (LG’, AM09). The research included physical and chemical characterization tests, as well as repeated load triaxial tests to determine the resilient modulus and shakedown limits, complemented by numerical simulations using the SysTrain 2.0 software. The samples showed average resilient modulus values of 577 MPa and 638 MPa, respectively. Tests were conducted under optimum moisture content and under moisture 1% above the optimum, induced by capillary rise in compacted samples. The results indicated that under 1% above optimum moisture, the shakedown limits were reduced by up to 50% for AM03 and 25% for AM09, demonstrating greater stability for the lateritic soil. In addition, it was observed that as stress ratios increased, the shakedown limits for both moisture conditions tended to converge. Numerical simulations confirmed the adverse influence of increased moisture on the occurrence of shakedown in both samples. For AM03, the simulations revealed progressive failure under elevated moisture, indicating a more severe stress redistribution within the subballast layer. In contrast, AM09 remained within the shakedown regime under both conditions, although it exhibited higher values of $S_1/S_{1\max }$ under moisture above optimum, suggesting a greater tendency toward plastic creep. These findings highlight the critical importance of moisture control for the sustainable performance of railway substructures. This study contributes to understanding environmental vulnerability in transportation infrastructure and supports the development of more resilient and sustainable railway systems.

1. Introduction

The railway subballast plays a fundamental role in the durability of track structures, acting as a load distribution and filtering layer, and contributing to the mechanical stability of the system [1,2,3]. Its performance is strongly affected by moisture variations and cyclic loading, which can accelerate permanent deformation and compromise structural integrity over time [4,5,6].

The mechanical behavior of subballast can be assessed through resilient modulus and permanent deformation tests [4,5,7,8], with resistance to permanent deformation being particularly important for the selection of quarry materials [9]. While Indraratna et al. [1] emphasize the role of subballast as a filtering and drainage layer, Guimarães [4] argues that it may be composed of fine lateritic soils, which do not necessarily exhibit drainage characteristics [5,9,10,11,12]. In contrast, AREMA [13] recommends that the subballast be sufficiently impermeable to prevent subgrade saturation, yet permeable enough to allow capillary rise.

Moisture variations caused by climate, infiltration, and groundwater fluctuations affect soil layers [14], leading to strength loss and the accumulation of permanent deformation over time. Several studies have confirmed the influence of moisture on the deformation behavior of railway subgrades [15], showing that changes in moisture content after compaction significantly impact the resilient modulus and bearing capacity [14,16]. When actual loading conditions exceed the original design assumptions, premature deterioration may occur [14], particularly in transition zones with inadequate drainage [17].

Numerous authors have investigated the mechanical performance of subballast materials under varying moisture conditions. Guimarães [18] examined the behavior of yellow clay under different moisture contents and compaction stress levels, while Thuler [19] observed that fine lateritic soils compacted at optimum moisture exhibited minimal deformation but performed poorly when compacted above the optimum. Menezes [14] emphasized the advantages of lateritic soils due to their low permeability and reduced sensitivity to moisture. Ribeiro [20] and Zhang [21] also demonstrated the detrimental effects of high moisture levels on strength and resilient modulus. Thom and Brown [22] associated high saturation and low permeability with reduced mechanical resistance, while Hashem and Zapata [23] proposed predictive models based on the degree of saturation and stress ratios. Li et al. [24] and Nazzal et al. [25] further confirmed that moisture significantly influences permanent deformation and shakedown thresholds.

Although many studies have adopted the SysTrain software to simulate railway behavior under various conditions [26,27,28,29,30,31,32], understanding the effects of integrating moisture content into shakedown-based analyses remains limited. This limitation restricts the predictive accuracy of long-term deformation behavior under realistic field conditions.

This study addresses this gap by combining experimental tests and finite element simulations using SysTrain 2.0 to investigate the influence of moisture content on the shakedown behavior of railway subballast layers. The working hypothesis is that increasing the moisture content promotes the accumulation of permanent deformation, thereby reducing the mechanical stability of the layer under cyclic loading. The results are expected to contribute to the development of more reliable design and maintenance strategies by incorporating moisture-sensitive parameters into the assessment of trackbed performance.

2. Materials and Methods

This research was carried out following the methodology outlined in the flowchart presented in Figure 1, which illustrates the steps taken throughout the study. Initially, fine soil samples were collected from the São Luís region. Two of these samples (AM03 and AM09) were subjected to a series of tests, including both physical characterization and mechanical performance evaluations. Both samples were compacted at their optimum moisture content. After compaction, sample AM09 underwent capillary wetting, resulting in a moisture content 1% above the optimum. In contrast, sample AM03 was tested while maintaining its optimum moisture level. The variation in shakedown limits was determined using laboratory-based experimental tests, enabling the assessment of the samples’ mechanical behavior under different moisture conditions. Furthermore, numerical simulations were conducted using Systrain 2.0 software to verify the occurrence of shakedown in the materials used as subballast. These simulations enabled the evaluation of permanent deformation conditions and the materials’ tendency toward shakedown, providing insights complementary to the experimental analysis.

2.1. Materials

São Luís island is located in the Maranhão Gulf, Brazil, forming a right angle in relation to the coastline. Its landscape is characterized by dunes and sandy beaches to the northeast of the island. The samples analyzed in this study comprise fine soils typical of the region, frequently found in the subgrade of highways and in exhausted soil deposits.

This research investigated two fine soil samples from different areas of São Luís and its surroundings. The selection of sampling points was based on tactile-visual analysis, prioritizing soils with lateritic characteristics. The disturbed samples were collected according to the NBR 9604 standard [33], which establishes guidelines for the opening of inspection pits and trenches, ensuring the proper collection of disturbed and undisturbed samples. Figure 2 shows the location of the sampling points for the studied samples.

2.2. Methods

2.2.1. Physical Characterization

The physical characterization of the soil was conducted through a series of laboratory tests, as presented in

Table 1. Laboratory tests and standards used.

Test	Standard
Real grain specific mass	NBR 6558 [34]
Grain size analysis	NBR 7181 [35]
Liquid limit	NBR 6459 [36]
Plastic limit	NBR 7180 [37]
Compaction test	NBR 7182 [38]
Mini-MCV	DNIT 259 [39]
Mass loss by immersion	DNER ME 256 [40]

.

The consistency limits, including the Liquid Limit (LL) and Plastic Limit (PL), were determined to classify the soil according to the HRB (Highway Research Board) and USCS (Unified Soil Classification System) standards.

The compaction test was performed to determine the optimum moisture content and maximum dry density, using 1000 cm³ cylindrical molds and manual compaction with a 2.5 kg rammer.

Additionally, the real specific gravity of the grains and granulometric analysis were performed to evaluate the soil density and particle distribution. The Mini-MCV and mass loss by immersion tests were also applied, enabling a more detailed assessment of the soil’s mechanical behavior. These procedures are essential to classify the materials according to the MCT (Miniature, Compacted, Tropical) methodology, which is specifically designed for tropical soils.

Lateritic soils are highly weathered materials typically found in tropical and subtropical regions, formed through intense chemical weathering under hot and humid conditions. This process, known as laterization, involves the leaching of silica and the accumulation of iron (${\mathrm{Fe}}_2{\mathrm{O}}_3$) and aluminum (${\mathrm{Al}}_2{\mathrm{O}}_3$) oxides. As a result, lateritic soils develop a characteristic microstructure with aggregated particles, low plasticity, low cation exchange capacity, and significant interparticle bonding due to sesquioxides. Geotechnically, they exhibit metastable behavior under unsaturated conditions, with their strength largely governed by suction and chemical bonding. However, this stability may significantly decrease when the soil becomes saturated. In contrast, non-lateritic soils rely more on friction and cohesion provided by clay minerals, without the microstructural cementation typical of lateritic materials.

Based on these characteristics, the MCT classification system proposed by Nogami and Villibor [41] categorizes tropical soils into two main groups: lateritic behavior (L) and non-lateritic behavior (N). This classification relies on granulometric properties combined with mechanical performance, further subdividing the soils according to the predominance of sandy, silty, or clayey fractions.

• Categories:

  –

  N—Soils with “non-lateritic” behavior

  ∗

  NA (Sands): Sands, Silty Sands, Silts (l)

  ∗

  NA’ (Sandy): Silty Sands, Clayey Sands

  ∗

  NS (Silty): Silts (k, m), Sandy and Clayey Silts

  ∗

  NG (Clayey): Clays, Clayey Sands, Silty Clays

  –

  L—Soils with lateritic behavior

  ∗

  LA (Sands): Sands with little clay

  ∗

  LA’ (Sandy): Clayey Sands, Clayey Sandy Soils

  ∗

  LG (Clayey): Clays, Clayey Sands

2.2.2. Chemical Characterization

The chemical characterization of the soils was performed using X-Ray Diffraction (XRD) tests to determine the mineralogical composition and better understand the nature of the analyzed materials.

To prepare the samples intended for XRD, the clay fraction was initially separated through a sedimentation process followed by centrifugation at 10,000 revolutions per minute for 10 min. The concentrated material was then spread on slides using the smear method, in order to orient the clay minerals. Figure 3 presents the principal steps involved in the preparation of the clay fraction samples, including the concentration of material at the bottom of the centrifuge tube and the production of oriented slides for subsequent XRD analysis.

The prepared slides were subjected to three different conditions for analysis: (i) natural condition, (ii) solvated with ethylene glycol (glycolated), and (iii) heated at 500 °C for 2 h in a muffle furnace. Prior to these steps, the samples were pre-dried for 24 h.

The XRD analysis was conducted using Bruker-D4 Endeavor equipment, utilizing Co K$\alpha$ radiation (40 kV/40 mA). The scan was performed in the range of 2° to 30° ($2\theta$ scale), with a speed of 1°/min. This test allowed for the qualitative and semi-quantitative identification of the minerals present in the material.

2.2.3. Mechanical Characterization

The mechanical behavior of the material was evaluated using Repeated Load Triaxial (RLT) tests to determine both the resilient modulus (RM) and the permanent deformation (PD). The tests were performed using the SIGEO (v.1.0) equipment (Figure 4), located at the Soil Laboratory of the Military Institute of Engineering (IME), Brazil.

The samples were prepared by homogenizing the material, storing it in hermetically sealed plastic bags (∼4 kg each), and conditioning it in a humidity chamber for at least 12 h. They were then compacted in cylindrical molds (100 × 200 mm) using Modified Proctor energy, applied with a 2.5 kg manual rammer over 10 layers, with 33 blows per layer. According to DNIT 134 [42] and DNIT 179 [43], the number of specimens varied depending on the type of test. For the resilient modulus test, all loading stages were applied sequentially to a single specimen per material. In contrast, for the permanent deformation and shakedown tests, a separate specimen was prepared for each stress condition, as required by the standard procedure.

Resilient Modulus

The RM tests were performed in duplicate (four specimens in total), following the DNIT 134 standard [42].

Table 2. Stress conditions for RM triaxial tests.

Confining Stress ${\mathit{\sigma }}_3$ (MPa)	Deviatoric Stress ${\mathit{\sigma }}_{\mathit{d}}$ (MPa)	Stress Ratio ${\mathit{\sigma }}_1/{\mathit{\sigma }}_3$
0.020	0.020	2
0.020	0.040	3
0.020	0.060	4
0.035	0.035	2
0.035	0.070	3
0.035	0.105	4
0.050	0.050	2
0.050	0.105	3
0.050	0.150	4
0.070	0.070	2
0.070	0.140	3
0.070	0.210	4
0.105	0.105	2
0.105	0.210	3
0.105	0.315	4
0.140	0.140	2
0.140	0.280	3
0.140	0.420	4

summarizes the combinations of confining stress (${\sigma }_3$) and deviatoric stress (${\sigma }_d={\sigma }_1-{\sigma }_3$) applied in the tests.

The results were processed using the Systrain 2.0 software (MRCalc tool), which provided the model parameters and correlation coefficients (R²). Among the evaluated models, the composite model proposed by Pezo [44] was adopted, as it is widely used for pavement design in Brazil.

Permanent Deformation and Shakedown

Permanent deformation (PD) tests were conducted under a loading frequency of 2 Hz (120 cycles per minute), using a servo-controlled piston. The stress conditions applied are presented in

Table 3. Stress conditions used for PD tests.

Sample	${\mathit{\sigma }}_1$ (kPa)	${\mathit{\sigma }}_3$ (kPa)	Stress Ratio (${\mathit{\sigma }}_1/{\mathit{\sigma }}_3$)
AM03	270	90	3
	240	80	3
	280	70	4
	240	60	4
	300	60	5
	250	50	5
	180	30	6
	120	20	6
AM09	330	110	3
	300	100	3
	320	80	4
	280	70	4
	300	60	5
	250	50	5
	300	50	6
	240	40	6

.

To refine the stress increments near the plastic shakedown boundary, the confining stress (${\sigma }_3$) was progressively increased in increments of 10 kPa. The shakedown classification was determined based on the accumulated permanent deformation between 3000 and 5000 cycles, as defined by the EN 13286-7 standard, according to the criteria in Equations (1) to (3):

$${\epsilon }_{5000}-{\epsilon }_{3000}<0.045\times {10}^{-3}:\mathrm{Plastic}\mathrm{shakedown}$$

(1)

$$0.045\times {10}^{-3}<{\epsilon }_{5000}-{\epsilon }_{3000}<0.4\times {10}^{-3}:\mathrm{Plastic}\mathrm{creep}$$

(2)

$${\epsilon }_{5000}-{\epsilon }_{3000}>0.4\times {10}^{-3}:\mathrm{Incremental}\mathrm{collapse}$$

(3)

where ${\epsilon }_{3000}$ and ${\epsilon }_{5000}$ are the permanent axial strains at the 3000th and 5000th load cycles, respectively.

Moisture Conditioning Procedure

Moisture variation was induced by capillary absorption, placing samples on a porous stone inside a container with water (Figure 5). It was observed that an increase of approximately 1% in moisture relative to the optimum led to excessive deformation, making the PD tests unfeasible. Therefore, a practical moisture limit was set at approximately 1% above the optimum moisture content for each sample.

During this process, the samples were rotated every 15–20 min to ensure a uniform moisture distribution without compromising their integrity. Total immersion time was 40 min for AM03 and 60 min for AM09.

Following moisture conditioning, samples were stored horizontally in a humidity chamber for 50 min before testing. PD tests were then repeated under this new moisture condition, applying 5000 load cycles. After testing, the samples were weighed while moist and then oven dried to determine their final moisture content.

2.3. Simulations Conducted

Numerical simulations were performed using the finite element method with the SysTrain 2.0 software [45]. Four scenarios were simulated to evaluate the performance of AM03 and AM09 as subballast layers, considering optimum moisture conditions and moisture contents above the optimum.

• Scenario 1: Simulation with AM03 as subballast at optimum moisture content, under the application of a 32.5 t/axle load.
• Scenario 2: Simulation with AM03 at 1% above optimum moisture content, under the application of a 32.5 t/axle load.
• Scenario 3: Simulation with AM09 as subballast at optimum moisture content, under the application of a 32.5 t/axle load.
• Scenario 4: Simulation with AM09 at 1% above optimum moisture content, under the application of a 32.5 t/axle load.

The scenarios were designed to evaluate the influence of moisture variation on the mechanical and structural behavior of the railway subballast. Comparing optimum and above-optimum moisture conditions is essential to understand the impact of moisture fluctuations on subballast performance, especially in tropical regions, where soil moisture can vary significantly throughout the year due to climatic conditions.

Figure 6a shows the three-dimensional finite element mesh used in the simulations, designed to reflect the transverse symmetry between the rails. This approach is essential for the accurate modeling of soil behavior under the characteristic loads of railway systems. Figure 6b illustrates the railway pavement, highlighting the distribution of loads applied by wagons with 32.5 t/axle, a typical scenario in heavy-haul railways, where the strength and deformation capacity of the subballast are constantly challenged.

In all simulations, the geometric configurations of the superstructure elements were kept constant. The infrastructure comprised several elements, the characteristics of which are detailed in

Table 4. Input parameters for the railway infrastructure simulation.

Element	Description
Rails	• Gauge: 1.6 m	• Elastic modulus: 210 GPa
	• Section: TR-68	• Poisson’s ratio: 0.3
	• Specific weight: 7867.01 kg/m3
Sleepers	• Prestressed concrete monoblock	• Trapezoidal section
	• Length: 2.8 m	• Height: 20 cm
	• Bottom width: 30 cm	• Top width: 28 cm
	• Specific weight: 2400 kg/m3	• Elastic modulus: 33 GPa
	• Poisson’s ratio: 0.2	• Spacing: 60 cm
Fastenings	• Spring element
	• Stiffness coefficient: 17,000 kN/m (x/y axes)
	• Stiffness coefficient: 170,000 kN/m (z axis)
Ballast	• Crushed stone	• Thickness: 30 cm
	• Shoulder: 40 cm width	• Slope (H:V) 1:1
	• Cross slope: 3% on both sides	• Specific weight: 1730 kg/m3
subballast	• Thickness: 25 cm	• Resilient clayey material
	• Nonlinear elastic behavior	• Shoulder: 50 cm width
	• Slope: 1:1.2 at the edges	• Cross slope: 1%
Subgrade	• Thickness: 300 cm	• Behavior: linear elastic
	• Resilient modulus: 100 MPa	• Shoulder: 2 m width
	• Slope: 1:1.5 at the edges	• Cross slope: 1%
Loading	• Hopper wagons	• Coupling-to-axle distance: 1.21 m
	• 2 bogies	• Axle spacing: 1.7 m
	• Bogie spacing: 13.945 m	• Axle load: 32.5 t/axle
	• Reference position: midpoint between sleepers	• Number of axles: 4
	• 1st selected axle: 3	• Symmetry: yes

.

3. Results and Discussions

3.1. Physical Characterization

The results of the physical characterization of the samples are presented in

Table 5. Compaction and characterization tests.

Sample	Proctor Compaction			Grain Size Distribution					Dr	Atterberg Limits			MCT	TRB	USCS
	Method	MDD (g/cm3)	OMC (%)	Coarse Sand (%)	Medium Sand (%)	Fine Sand (%)	Silt (%)	Clay (%)		LL (%)	PL (%)	PI (%)
AM O3	Modified	2.048	10.33	15	14	49	19	2	2.61	20.46	13.26	7.20	NA’	A-4	SM
AM O9	Modified	2.043	10.45	2	24	41	7	26	2.61	20.28	15.26	5.02	LG’	A-4	ML-CL

. This table displays the main parameters obtained from the compaction, particle size distribution, and Atterberg limit tests, as well as the soil classification according to the USCS and TRB systems. Notably, both soils exhibit distinct behaviors concerning particle size distribution and consistency limits. Figure 7 shows the MCT classification chart, complementing the data analysis.

The physical characterization parameters are essential for assessing the mechanical behavior of materials in railway pavements, especially when subjected to different moisture conditions.

The soils studied were classified as NA’ and LG’ according to the MCT classification, as shown in Figure 7. The modified Proctor compaction test revealed similar values of dry unit weight (MEAS) for samples AM03 and AM09, recording 2.048 g/cm³ and 2.043 g/cm³, respectively. The Atterberg limits of the samples indicated a plasticity index (PI) of 7.2% for AM03 and 5.02% for AM09, characterizing both materials as having low plasticity. According to the MCT classification (DNIT 259 [39]), soils with low plasticity tend to exhibit better compaction characteristics and greater volumetric stability. The particle size analysis showed that both samples have a predominance of fine sand, which directly affects their mechanical behavior under cyclic loading.

The optimum moisture content of the analyzed materials presented similar values, with 10.33% for the non-lateritic soil (NA’) and 10.45% for the lateritic soil (LG’). Studies such as that by Menezes et al. [14] indicate that non-lateritic soils may exhibit structural impairment when exposed to moisture content above optimum, resulting in a reduction of resilient modulus and an increase in permanent deformations. Conversely, the lateritic soil (LG’), characterized by a higher clay fraction, tends to present greater cohesion due to the presence of clay minerals such as kaolinite and goethite, which may confer improved mechanical performance when compacted. However, its susceptibility to moisture variation must also be considered, as excessive moisture may lead to a loss of strength. Thus, moisture control in railway infrastructure layers is essential to ensure long-term track stability, especially in tropical regions, where intense rainfall can cause significant fluctuations in soil moisture content. Garmabaki [46] emphasizes that climate change impacts railway infrastructure. In tropical regions, such as Brazil, significant climatic variations, including periods of heavy rainfall, can alter the moisture content of railway infrastructure layers.

3.2. Chemical Characterization

Figure 8 presents the XRD test results for the respective samples.

XRD analyses indicated that the samples contain illite and kaolinite as their predominant clay minerals. In the case of sample AM09, the presence of these minerals, especially illite, supports its classification as a lateritic soil, since this type of soil is characterized by the presence of more active minerals, as described by Nogami and Villibor [41].

However, although AM03 exhibited the same mineralogical composition, the MCT test results did not confirm that it exhibited typical lateritic soil behavior. This demonstrates that the presence of illite and kaolinite alone is not sufficient to define the lateritic nature of a soil, requiring the consideration of other parameters associated with mechanical behavior, as evaluated by the MCT methodology.

Thus, the results obtained are consistent with the MCT classification while enriching the soil analysis by highlighting the relevance of mineralogical composition. However, they also reinforce the need for an integrated approach that combines mineralogical and mechanical aspects to achieve more precise and reliable soil characterization.

3.3. Data Analysis of Triaxial Tests

3.3.1. Resilient Modulus

The RM of AM03 ranged from 359 MPa to 852 MPa, with an average value of 577 MPa, falling within the expected range for soils of this classification. Authors such as Indraratna et al. [1] report lower subgrade RM values often below 100 MPa in non-tropical countries, which highlights the superior resilient behavior of Brazilian tropical soils. Guimarães [18] found RM values ranging from 60 MPa to 900 MPa in various Brazilian soils, reinforcing the variability and robustness of these materials. Gomes et al. [47] further corroborate this, indicating that NA’ soils may exhibit average modulus values between 151 MPa and 553 MPa, demonstrating that the values obtained in the present study fall within the upper range of this estimate.

AM09 exhibited the highest average RM, with measured values ranging from 433 MPa to 998 MPa and an average value of 638 MPa, showing high variability. It is noteworthy that the RM values obtained in this study are higher than those reported by Guimarães [18], Delgado [48], and Gomes [47]. In both cases, it was verified that the deviator stress exerts a significant influence on the resilient behavior, as shown in Figure 9. For AM03, a coefficient of determination ($R^2$) of 0.9026 was observed, indicating a strong correlation between deviator stress and resilient modulus. On the other hand, AM09 presented an $R^2$ of 0.6642, suggesting a weaker, yet still significant, correlation.

3.3.2. PD and Shakedown

With the results from the PD tests, it was possible to establish the shakedown limit as recommended by the European standard EN 13286-7 [49]. The Werkmeister model [50] was adopted, in which the shakedown limits exhibit an exponential relationship between the applied stresses. For this study, shakedown limit curves were generated for the investigated soils (AMO3 and AM09).

Table 6. Shakedown Analysis.

Sample	Stress Ratio (${\mathit{\sigma }}_1/{\mathit{\sigma }}_3$)	Principal Stress ${\mathit{\sigma }}_1$ (kPa)	Confining Stress ${\mathit{\sigma }}_3$ (kPa)	${\mathit{\epsilon }}_{5000}-{\mathit{\epsilon }}_{3000}$	Behavior
AMO3	3	270	90	0.045	Plastic Creep
	3	240	80	0.021	Shakedown
	4	280	70	0.080	Plastic Creep
	4	240	60	0.012	Shakedown
	5	300	60	0.076	Plastic Creep
	5	250	50	0.019	Shakedown
	6	180	30	0.057	Plastic Creep
	6	120	20	0.019	Shakedown
AMO9	3	330	110	0.061	Plastic Creep
	3	300	100	0.040	Shakedown
	4	320	80	0.045	Plastic Creep
	4	280	70	0.029	Shakedown
	5	300	60	0.051	Plastic Creep
	5	250	50	0.028	Shakedown
	6	300	50	0.056	Plastic Creep
	6	240	40	0.033	Shakedown

presents the applied stresses, and Figure 10 shows the curves as a function of the principal stress and stress ratio.

The limiting curves were generated for stresses where the difference in accumulated deformation between 5000 and 3000 cycles was less than $0.045\times {10}^{-3}$, representing the shakedown curve, and for when this difference was greater than $0.045\times {10}^{-3}$ but less than $0.4\times {10}^{-3}$, representing the plastic creep curve. Then, through interpolation of the values, the average curve between these two stages was generated, which establishes the shakedown limit between ranges A and B. It can be said that the correlation coefficients found are acceptable—0.77 and 0.99.

When compared to the results presented by Werkmeister [50], the soils studied in this research exhibited higher shakedown limits than those observed in graded crushed stone. This improved performance, illustrated in Figure 10, can be attributed to two main factors: (i) from a chemical perspective, the significant presence of aluminum and iron oxides and hydroxides, commonly found in lateritic soils, which act as natural cementing agents; and (ii) from a physical perspective, the development of high suction stresses, resulting from the typical particle size distribution of tropical soils.

The comparative analysis of these two materials, based on the shakedown concept, proved to be effective for ranking them in terms of behavior under permanent deformation. The results indicate that the clayey lateritic soil tends to exhibit a more favorable performance. It should be emphasized, however, that this approach does not replace permanent deformation tests with a high number of load cycles, as recommended by the Brazilian standard. Nevertheless, it represents a practical and useful tool for the preliminary selection and comparison of layer behavior with regard to rutting resistance.

The concept of shakedown is traditionally applied to granular materials, which, after a certain number of load applications, tend to stabilize due to the interlocking of larger particles. In the case of soils, however, the accommodation of deformations occurs differently, influenced by factors such as chemical composition, particle size distribution, the presence of natural cementation, and the development of high suction stresses. These characteristics contribute to a more resistant behavior against permanent deformation.

Both analyzed soils exhibited significantly superior behavior compared to the reference material (granodiorite), as evidenced by considerably higher shakedown limits. This reflects their greater capacity to withstand repeated loading before entering a regime of permanent deformation.

As the stress ratio ${\sigma }_1/{\sigma }_3$ increases, there is a reduction in the maximum stress the material can withstand before yielding initiates. The shakedown limit curve clearly illustrates this transition, delineating the regions of stable behavior from those where the material enters a plastic creep regime.

3.3.3. Influence of Moisture Content

To simulate moisture variations occurring under real field conditions, particularly in regions subject to flooding or fluctuations in the groundwater level, tests were conducted with samples molded with moisture content approximately 1% above the optimum content, through capillary uptake. Similar approaches have been adopted by other authors. Latvala et al. [51] demonstrated that the cyclic loading resistance of aged sub-ballast materials significantly decreases with increasing water content, while Vandoorne et al. [52] emphasized the importance of measuring soil suction and temperature to better capture field moisture dynamics and their influence on the mechanical performance of railway formations.

Table 7. Results of triaxial tests.

Sample	Stress Ratio {${\mathit{\sigma }}_1/{\mathit{\sigma }}_3$}	Principal Stress ${\mathit{\sigma }}_1$ (kPa)	Confining Stress ${\mathit{\sigma }}_3$ (kPa)	${\mathit{\epsilon }}_{5000}-{\mathit{\epsilon }}_{3000}$	Behavior
AMO3	3	180	60	0.330	Plastic Creep
	3	150	50	0.080	Shakedown
	4	200	50	0.068	Plastic Creep
	4	160	40	0.020	Shakedown
	5	200	40	0.050	Plastic Creep
	5	150	30	0.027	Shakedown
	6	240	40	0.022	Plastic Creep
	6	180	30	0.013	Shakedown
AMO9	3	270	90	0.090	Plastic Creep
	3	240	80	0.031	Shakedown
	4	240	60	0.075	Plastic Creep
	4	200	50	0.034	Shakedown
	5	250	50	0.050	Plastic Creep
	5	200	40	0.041	Shakedown
	6	300	50	0.045	Plastic Creep
	6	240	40	0.020	Shakedown

presents the stress values used to obtain the permanent deformation curves after 5000 cycles, both for this induced condition and for the optimum moisture content condition. The corresponding graphs were generated based on these data, as illustrated in Figure 11, using the same methodology employed for the samples in the ideal condition.

The analysis of the effect of moisture variation is crucial for assessing the material’s response to changes in saturation conditions in the field, particularly for pavements constructed in coastal regions such as São Luís Island. Figure 12 presents a comparison of the shakedown limits obtained under the two moisture conditions for the studied samples.

For AM03 (NA’ Soil), it is observed that the shakedown limit curve, with moisture above optimum, showed a reduction of approximately 50% for a stress ratio of 4. Beyond this ratio, the difference between the curves becomes progressively smaller, being practically insignificant for a ratio of 7. This behavior suggests that the impact of increased moisture on the shakedown limit tends to diminish as the applied stress ratio increases.

In the case of AM09 (LG’ Soil), the results indicate a reduction in the shakedown limit between 20% and 25% when compared to those obtained at optimum moisture content. Similarly to Sample 3, it is observed that as the stress ratio increases, the shakedown limit of the sample with higher moisture content tends to approach the values obtained under ideal conditions.

These results reinforce the sensitivity of materials to moisture content, emphasizing the importance of considering hydrological variations in the mechanical behavior analysis of tropical soils, especially in pavement design projects in regions with high susceptibility to saturation.

AM03 exhibited a greater variation in the shakedown limit compared to AM09. This behavior may be associated with the lateritic characteristics of the LG’ soil (AM09), including the presence of aluminum hydroxides, which promote natural cementation and influence suction stresses. Although AM09 showed less sensitivity to moisture variation than AM03, both demonstrated a significant influence of this factor, as evidenced by the shakedown curves obtained according to the methodology of Werkmeister [50] and the EN 13286-7 standard [49].

The increase in moisture had an adverse effect on the behavior of the materials, promoting the development of plastic deformations and reducing the specimens’ ability to accommodate loads. This phenomenon compromises the long-term structural stability of subballast layers, particularly in situations where moisture control is not fully ensured.

To further investigate this behavior, the parameters $\alpha$ and $\beta$ presented in

Table 8. Values of the parameters $\alpha$ and $\beta$ for the different moisture conditions.

Moisture Content	Non-lateritic Sandy Soil (AM03)		Lateritic Clayey Soil (AM09)
	$\mathit{\alpha }$	$\mathit{\beta }$	$\mathit{\alpha }$	$\mathit{\beta }$
Optimum moisture	1550.6	−0.994	763.29	−0.422
Above optimum moisture	148.69	0.224	420.75	−0.229

were derived from experimental tests conducted on both soil samples. Based on the test results, shakedown limit curves were established for each moisture condition, and the parameters were obtained by fitting these curves to the experimental data. These values will be employed as input parameters in the Systrain software to simulate the shakedown behavior of the subballast layer within the numerical model. The simulations aim to assess the suitability of the materials under cyclic loading conditions, considering variations in moisture content, and to investigate their influence on the development of permanent deformations and the material’s capacity to achieve a stable response under repeated loads.

3.4. Simulation Results

The shakedown verification implemented in SysTrain is based on the equation proposed by Werkmeister [50] (Equation (4)):

$${\sigma }_{1\max }=\alpha {\left({\displaystyle \frac{{\sigma }_{1\max }}{{\sigma }_3}}\right)}^{\beta },$$

(4)

where ${\sigma }_{1\max }$ is the maximum axial stress from the repeated load triaxial test, ${\sigma }_3$ is the confining pressure, and $\alpha$ and $\beta$ are material parameters.

Within the Systrain framework, the shakedown verification is performed using the ratio $S_1/S_{1\max }$, which represents the relationship between the applied vertical stress, calculated as the sum of ${\sigma }_d$ and ${\sigma }_c$ and the maximum allowable axial stress, $S_{1\max }$. This maximum stress is determined using Equation (4), which defines ${\sigma }_{1\max }$ based on the confining pressure and the material parameters $\alpha$ and $\beta$.

For the condition to be considered acceptable, indicating that the soil is operating under a shakedown regime, the value of this ratio must be less than 1. Figure 13 and Figure 14 illustrate the behavior of Sample 3 when used as a subballast layer. Under these conditions, the criterion $S_1/S_{1\max }<1$ is decisive for identifying shakedown behavior. Figure 13 corresponds to Scenario 1, in which the material was compacted at optimum moisture content. Figure 14, in turn, represents Scenario 2, where the samples were initially molded at optimum moisture content but were subsequently subjected to moisture induction by capillarity, simulating conditions with moisture levels above the ideal.

It is observed that, in Scenario 1, part of the layer exhibits $S_1/S_{1\max }$ values lower than 1, indicating predominantly shakedown regime behavior. However, in the region directly beneath the loading axes, there is a concentration of stresses exceeding the shakedown threshold ($S_1/S_{1\max }>1$), suggesting that even under optimum moisture conditions, this zone may already be prone to progressive accumulation of deformations.

In contrast, in Scenario 2 (Figure 14), a more pronounced increase is observed in regions where $S_1/S_{1\max }$ exceeds 1.0, indicating a higher critical stress state compared to the previous condition. This behavior suggests that, under such circumstances, the soil becomes more vulnerable to progressive failure, potentially compromising the long-term structural stability of the railway pavement.

Additionally, the stress redistribution suggests a reduction in the material’s load-bearing capacity, reflecting the negative impact of excess moisture on the mechanical performance of the layer. The results confirm the hypothesis that moisture variation affects the mechanical behavior of the subballast, corroborating existing literature, which indicates that moisture contents above the optimum tend to reduce the structural strength of compacted soils due to the decrease in matric suction forces and increased lubrication between soil particles.

Furthermore, according to the simulations, the value of $S_{1\max }$ for Scenario 1 was 88.81 kPa, while for Scenario 2 it was 80.01 kPa. These results indicate that moisture conditions above the optimum reduce the maximum allowable stress for the shakedown regime, suggesting that the moisture content directly influences the mechanical performance of the railway subballast.

Figure 15 and Figure 16 illustrate the subballast performance in the two simulations conducted for sample AM09. Figure 15 corresponds to Scenario 3 (material compacted at optimum moisture content), while Figure 16 represents Scenario 4 (material compacted above optimum moisture content).

In this context, for the lateritic soil, it is observed that in both scenarios, the subballast layer remained within the shakedown regime, with $S_1/S_{1\max }$ values lower than 1. This indicates a predominantly stable behavior within that regime. The highest stress concentrations occur directly beneath the loading axes. However, a variation in the stress values is observed depending on the material’s moisture content. The layer with moisture above the optimum exhibited higher stress values compared to the one compacted at optimum moisture content, highlighting the change in the subballast’s mechanical behavior due to moisture.

Additionally, the stress redistribution indicates a reduction in the material’s load-bearing capacity. In Scenario 4, the most critical region extends over a larger area than in Scenario 3, highlighting the detrimental effect of excess moisture on the mechanical performance of the layer. The results reinforce the hypothesis that moisture variation significantly influences the mechanical behavior of the subballast, consistent with findings in the literature, which indicate that moisture levels above the optimum tend to reduce the structural strength of compacted soils. This reduction is attributed to decreased matric suction and increased lubrication between soil particles.

Furthermore, according to the simulations, the value of $S_{1\max }$ for Scenario 3 was 171.65 kPa, while for Scenario 4 it was 184.22 kPa. These results suggest that moisture conditions above the optimum limit the maximum allowable stress for the shakedown regime, reinforcing the importance of moisture control for the mechanical performance of the railway subballast.

4. Conclusions

This study investigates the influence of moisture content on the shakedown condition of railway subballast, focusing on its tendency toward permanent deformation under cyclic loading. Based on experimental tests and numerical simulations using the SysTrain 2.0 software, the mechanical behavior of two representative tropical soils was evaluated, highlighting the adverse effects of excess moisture on the structural stability of railway tracks.

Moisture variation proves to be a critical factor in the mechanical performance of the subballast, significantly affecting the shakedown limits. An increase of 1% in moisture content above the optimum reduces these limits by up to 50% in sample AM03 (non-lateritic sandy soil) and by 20–25% in AM09 (clayey lateritic soil), promoting cumulative plastic deformations. It should be noted that this conclusion is based on single tests per moisture condition, following the DNIT 179/2018 procedure, which requires one specimen per stress condition. Nevertheless, the magnitude of the observed reduction highlights the strong influence of moisture on the shakedown limits of the materials tested.

With an increase in the stress ratio (${\sigma }_1/{\sigma }_3$), a convergence trend is observed in the shakedown limits of the samples, indicating that higher levels of confinement mitigate the effects of moisture. Nevertheless, AM03 exhibits progressive failure under high moisture content, while AM09 remains within the shakedown regime, although it is more susceptible to yielding.

The simulations conducted in SysTrain 2.0 corroborate the experimental findings, showing a reduction in the maximum allowable stress within the shakedown regime: from 88.81 kPa to 80.01 kPa in AM03, and from 171.65 kPa to 164.22 kPa in AM09. AM09 demonstrates superior performance, with greater load-bearing capacity and lower variability, reinforcing the technical potential of lateritic soils as subballast material for railway infrastructure in tropical regions.

In light of these results, strict moisture control is recommended throughout the life cycle of railway infrastructure. Moisture content above the optimum compromises load-bearing capacity, accelerates yielding, and significantly reduces the durability of the pavement structure.