Assessing the Impact of Sand-Induced Ballast Fouling on Track Stiffness and Settlement

Abstract

This study investigates the impact of sand-induced ballast fouling on railway track performance, focusing on track stiffness (modulus), settlement, and overall degradation. The research utilized an 18-cubic-foot ballast box designed to replicate real-world track conditions under controlled laboratory settings. A key focus was quantifying voids within clean ballast to establish baseline characteristics, which provided a foundation for evaluating the effects of sand fouling. Two distinct test series were conducted to comprehensively analyze track behavior. The first series investigated pre-existing fouling by thoroughly mixing sand into the ballast to achieve uniform fouling levels. The second series simulated natural fouling processes by progressively adding sand from the top of the ballast layer, mimicking real-world conditions such as those in sandy environments. These methodologies allowed for detailed analysis of changes in track stiffness, deflection, and settlement under varying fouling levels. The findings demonstrate a direct correlation between increasing sand fouling levels and heightened track stiffness and settlement. Dynamic load testing revealed that as void spaces were filled with sand, the track’s flexibility and drainage capacity was significantly compromised, leading to accelerated degradation of track geometry. Settlement patterns and deflection data provided critical insights into how fouling adversely affects track performance. These results contribute significantly to understanding the broader implications of sand-induced fouling on track degradation, offering valuable insights for railway maintenance and design improvements. By integrating void analysis, test series data, and load-deflection relationships, this study provides actionable recommendations for enhancing railway infrastructure resilience and optimizing maintenance strategies in sandy terrains.

1. Introduction

1.1. Ballast Fouling and Its Implications on Track Performance

A railway track comprises three foundational substructure layers: ballast, sub-ballast, and subgrade. Ballast, a granular material consisting of angular aggregates ranging in size from 10 mm to 60 mm, plays a critical role in distributing cyclic loads generated by trains to the underlying substructure layers [1,2,3]. This material enhances load-bearing capacity, provides effective drainage, and is cost-efficient. Additionally, it encases the ties, ensuring both vertical and lateral stability for the track structure [1,3,4]. Furthermore, ballast mitigates the effects of dynamic loads by contributing to the overall resilience of the track system [2,5,6].

The functions of ballast extend beyond load distribution. It maintains track geometry, such as cross-level, alignment, and surface [7]. The void spaces between particles ensure effective water drainage and prevent the growth of vegetation. Moreover, ballast insulates the track from electrical interference, maintaining the reliability of power systems [1]. Its granular composition allows for easy rearrangement during maintenance, such as tamping, and provides storage capacity for fouling materials [2,7,8].

Fouling occurs when the void spaces in ballast are filled with finer materials, such as sand, which adversely impacts its mechanical properties. Fouling affects the distribution of track support, compromises drainage, and accelerates settlement, leading to increased maintenance demands [9,10]. Over time, fouling degrades the load distribution capacity of ballast, reduces lateral stability, and exacerbates permanent deformation [5,10]. Furthermore, fouling accelerates ballast degradation, diminishing its ability to distribute loads and facilitate drainage effectively [11].

1.2. Track Stiffness and Settlement

Railway networks traversing sandy terrain often encounter added hurdles impacting both maintenance and operations. Among these challenges lies the issue of ballast fouling, wherein the ballast layer becomes contaminated with sand, filling the interstitial spaces between particles [8]. This occurrence diminishes track flexibility, consequently augmenting track stiffness (denoted as $k$), representing the vertical displacement under applied force, typically measured in lb/in [12,13]. The ingress of sand into the ballast layer, either through infiltration or wind-borne deposition, amplifies track stiffness by reducing vertical displacement [12,14].

Zakeri et al. [12] conducted a field study to examine the impact of rail support modulus variations on a ballasted track. Employing the Zarembski and Choros [15] method, rail support modulus was calculated. The study involved collecting five samples from four different areas with varying fouling percentages (12%, 18.9%, 27.5%, 50.7%, and 62.7%) and calculating the resulting rail support modulus under repeated heavy axle loads. Comparative analysis was then conducted with similar studies in non-sandy regions. The findings illustrate a clear trend: as ballast fouling increases, so does the stiffness magnitude.

Estaire et al. [14] investigated track stiffness in sand-fouled ballast using large-triaxial and CEDEX Track Box (CTB) tests. In the large-triaxial test, seven tests from clean ballast to 100% fouling showed a consistent initial modulus up to 70% fouling but a significant increase for fouling levels greater than 70%. CTB tests revealed visibly fouled ballast at 85% and 100% levels. Stiffness remained stable up to 70% fouling but increased by 25% at higher levels, aligning with large-triaxial results.

Heydari et al. [16] examined the influence of ballast fouling on vertical and shear interlocking stiffness through experimental and numerical approaches in a controlled laboratory environment utilizing a ballast box. Their findings revealed that higher levels of fouling significantly compromised interlocking mechanisms, resulting in substantial alterations to both vertical and shear stiffness, with pronounced declines in shear stiffness as contamination intensified.

Ballast fouling also induces settlement, also termed permanent deformation, which encompasses the total settlement across ballast, sub-ballast, and subgrade layers, quantified in inches. This phenomenon emerges within substructure layers due to imposed loads, engendering differential settlements that lead to track geometry defects. Fouling may engender either an escalation or reduction in volume change rate and plastic strain accumulation [2].

Settlement can incur geometric deformations, intensifying with increasing fouling [2]. Research undertaken by Kashani et al. [17] to assess the impact of fouled ballast under heavy axle loads and high traffic conditions indicates that while settlement increases with higher fouling levels, the settlement rate remains relatively stable. Echoing Kashani’s findings, Han et al. [18] corroborate an augmentation in settlement with escalating fouling. Similarly, an investigation conducted on the South African Railway to probe the effects of coal-contaminated ballast on track settlement via a large-scale box test aligns with these conclusions, revealing a proportional rise in settlement with increasing fouling. Notably, this study demonstrates that settlement escalates from 11% to 40% as fouling percentages increase by 10% [19].

1.3. Research Objectives

This paper investigates the impact of sand infiltration into ballast voids on track stiffness and settlement. The study involves a series of laboratory tests conducted using a ballast box to evaluate these effects under two distinct methodologies. The first methodology simulates various scenarios where sand is already present between ballast particles at different levels, providing insight into pre-existing conditions. The second methodology simulates the gradual accumulation of sand over time within a real track environment, reflecting the ongoing process of sand-filling ballast voids. Through these approaches, the study aims to understand how sand influences the mechanical behavior of railway tracks, with a focus on both stiffness and settlement.

1.4. Hypothesis

The infiltration of sand into ballast voids alters the mechanical behavior of railway tracks, primarily by increasing track stiffness and settlement. This phenomenon leads to uneven distribution of dynamic loads across the track structure, exacerbating the rate of track geometry degradation. It is hypothesized that higher levels of sand infiltration will:

• Significantly influence track stiffness by reducing the flexibility of the ballast layer, potentially causing localized stiffness variations that accelerate structural fatigue.
• Increase settlement rates due to compromised load distribution, leading to a differential settlement that negatively impacts track alignment and stability.
• Impair drainage efficiency, further accelerating ballast fouling and promoting conditions that aggravate track deterioration over time.
• Alter the relationship between applied load and deflection, affecting the dynamic response of the track system and leading to higher maintenance demands.

This study aims to test these hypotheses under controlled laboratory conditions, providing insights into how sand fouling directly contributes to track degradation mechanisms.

2. Materials and Methods

2.1. Test Setup

Many ballast boxes have been developed for different research purposes, as discussed in the literature. For example, Selig [2] constructed a ballast box to study ballast breakage, volume change, and the shear strain mechanism responsible for vertical plastic strain development. However, subsequent research conducted by Kashani et al. [17], using a finite element model to calibrate Selig’s ballast box, highlighted some limitations, such as increased plastic deformation, tie rotational instability, reduction in ballast strength capacity, punching shear at the sample depth, and uncontrolled drainage. Kashani et al. [17] found that increasing the dimensions of Selig’s ballast box by 50%—resulting in approximate dimensions of 52 in × 33 in × 20.5 in—could mitigate these shear stress issues.

Taking these findings into account, the dimensions of the ballast box in this study were chosen to strike a balance between practical laboratory constraints and the need to minimize the limitations noted in prior research. Additionally, wood was selected as the construction material for its ability to replicate field-like boundary conditions while being cost-effective and easy to fabricate.

To examine the correlation between ballast fouling from sand infiltration and various track parameters such as deflection, stiffness, settlement, and degradation, a ballast box was fabricated at the Civil Engineering Structures Laboratory of the University of Delaware (Figure 1A–C). This box emulates real track conditions and is subjected to a specific load akin to that generated by train wheels. Its dimensions measure 48 inches in length, 36 inches in width, and 18 inches in height, housing 18 cubic feet of railway ballast. Within the ballast, a segment of the railroad superstructure was assembled, featuring a partial timber tie measuring 7 inches by 9 inches and spanning 3 feet in length, a section of rail (132 RE rail) approximately 12 inches long, and a plate affixed with two cut spikes at the top. It is noteworthy that the ballast box lacks a subgrade (soil) layer in its construction.

Loading was facilitated by a Material Testing Systems (MTS) Series 244 actuator possessing a dynamic and static capacity of 55 kilo-pound force (kips) in both tension and compression. The test frequency was contingent upon the size of the valve servo system. The particular unit employed featured two 15 gallons per minute (gpm) servo valves, enabling it to conduct higher frequency tests. The test configuration is depicted in Figure 1A–C Instrumentation, which includes the load and deflection measurement system integrated within the dynamic loading actuator itself, positioned in the middle of the rail section. Additionally, six Linear Variable Differential Transformers (LVDTs) were strategically positioned for further data collection (See Figure 1C).

2.2. Application of the Beam on Elastic Foundation BOEF Theory

To evaluate track performance under traffic-induced stress, particularly the dynamic wheel loads exerted by rail vehicles, the Beam on Elastic Foundation (BOEF) model was employed. This model, first introduced by Winkler in 1867 [20], conceptualizes the rail as a continuously supported beam resting on a uniform elastic foundation. The track stiffness (lb/in)—a fundamental parameter—correlates with the applied load and resultant track deflection, typically measured at a specified location relative to the load application point. Zarembski and Choros [15] further developed methodologies for computing the vertical track modulus, utilizing load and deflection data collected either in field or laboratory conditions. In these approaches, the track modulus signifies the vertical deflection of the track under load, distributed along the track’s length and measured in lb/in/in.

The load conditions were structured to mimic the passage of heavy axle load freight traffic on a rigid, stiff track structure at low speeds. Since no long rail was available, it was necessary to determine an appropriate load applied to the tie, leading to a reduction in the wheel load. Four stiffness scenarios were considered: 1000 lb/in/in, 5000 lb/in/in, 10,000 lb/in/in, and 13,000 lb/in/in at a speed of 40 mph. This setup aimed to measure rail deflection and ascertain the load transferred from the rail to the tie, as outlined in

Table 1. Load regime at three different stiffness scenarios.

	Inputs	Units	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Actual Lab Test
Rail Detail	Rail Type	RE	132	132	132	132	132
	Moment of Inertia ($I$)	in4	87.90	87.90	87.90	87.90	87.90
Tie Detail	Tie Spacing	in	19.5	19.5	19.5	19.5	19.5
Car Detail	Car Weight	lb	286,000	286,000	286,000	286,000	286,000
	Number of Axles	-	4	4	4	4	4
	Number of Wheels	-	8	8	8	8	8
	Wheel Diameter	in	36	36	36	36	36
	Speed $V$	mph	40	40	40	40	79
Load Regime	Static Load ($P_{Static}$)	lb	35,750	35,750	35,750	35,750	35,750
	Dynamic Load ($P_{Dynamic}$)	lb	48,858	48,858	48,858	48,858	61,639
	Load Ratio (${\displaystyle \frac{P_{dynamic}}{P_{static}}})$	-	1.37	1.37	1.37	1.37	1.72
	Track Stiffness ($k$)	lb/in/in	1000	5000	10,000	13,000	12,821
	Modulus of Elasticity ($E$)	lb/in2	30,000,000	30,000,000	30,000,000	30,000,000	30,000,000
Max. Results	$\beta$	1/in	0.01755	0.02624	0.03120	0.03332	0.03
	Max. Deflection ($w_{max}$)	in	0.429	0.128	0.076	0.063	0.080
	Max. Moment ($m_{max}$)	ln.lb	696,099	465,510	391,445	366,594	464,095
	Max. Pressure	psi	429	641	762	814	1023
	Max. Tie Bearing Force	lbf	8573	12,820	15,246	16,279	19,955
	Max. Load % for individual tie	%	17.55%	26.24%	31.20%	33.32%	32.37%

and Figure 2. The vertical deflection ($w$) was measured at the actuator, ensuring accuracy and consistency in data collection during the experimental process. Consequently, deflections of 0.429 in, 0.128 in, 0.076 in, and 0.063 in were calculated for the four scenarios, accompanied by tie bearing forces of 8573 lbf, 12,820 lbf, 15,246 lbf, and 16,279 lbf, respectively.

Given that estimated tie bearing forces exceeded 8500 lbf, Scenario 4 was established with a stiffness of 13,000 lb/in/in to serve as a basis for applying a 20,000 lbf tie bearing force, which was validated through actual lab testing. To further evaluate this setup, the tie-bearing load was increased to 20,000 lb, and the corresponding stiffness value was measured at this load.

To better understand the relationship between applied load, track stiffness, and rail deflection, the BOEF model was applied in this study. The fundamental equation governing the BOEF method is:

$$q\left(x\right)=EI{\displaystyle \frac{\left(d^{4}w\left(x\right)\right)}{d{x}^4}}+kw\left(x\right)$$

(1)

where:

• $q$: The vertical loading at point $x$
• $EI$: Flexural rigidity of the rail
• $w$: The vertical deflection of rail at point $x$
• k: Stiffness

Track stiffness ($k$) is derived using the following relationship:

$$k={\displaystyle \frac{P}{a Ʃ(w_1-w_0)}}$$

(2)

where:

• $P$: The dynamic load of a given wheel
• $a$: Tie spacing
• $w_1-w_0$: Difference in vertical deflection at specified points

The deflection of the rail ($w\left(x\right)$) can be calculated as:

$$w(x)={\displaystyle \frac{P\beta }{2k}} e^{-\beta x} [cos(\beta x)+sin(\beta x)]$$

(3)

with the flexural rigidity parameter $\beta$ defined as:

$$\beta =∜k/4EI$$

(4)

2.3. Load Regime and Dynamic Impact Assessment

The dynamic impact formula prescribed by the American Railway Engineering and Maintenance-of-Way Association (AREMA) was employed to compute the vertical load for the design. Considering the highly rigid track conditions depicted by the ballast box (Figure 1A,B), the chosen loading regime for this test series involved a maximum vertical load of 20,000 lb (20 kips) at a test frequency of 0.2 Hz (equivalent to 720 cycles per hour). The dynamic load ($P_{dynamic}$) can be calculated using the following equation, which incorporates the effects of speed ($V$ = 40 mph) and wheel diameter ($D$ = 36 inches). This formula, recommended by AREMA, is an empirical method extensively used in railway engineering for accurately estimating dynamic load conditions in various track designs.

$$P_{dynamic}=\left(1+{\displaystyle \frac{33V}{100D}}\right)\times P_{static}$$

(5)

• $P_{dynamic}$: The dynamic load
• $V$: Speed
• $D$: Wheel diameter
• $P_{static}$: The static load

Equation (5) is derived from the AREMA Manual of Railway Engineering (2010), Volume 1, Page 1-2-20 [21].

Following a successful test run, the load-deflection analysis revealed a maximum deflection of 0.08 inches at a load of 20,000 lb Utilizing the collected data and substituting them into the BOEF equation facilitated the determination of track stiffness. Furthermore, both the dynamic load and speed could be assessed. Using the parameters from

Table 2. Rail type with its specifications and the load.

Giving Data	Value	Unit
Rail type	132 RE	-
Static load ($P_{static}$)	35,750	lb
Tie spacing ($a$)	19.5	in
Wheel diameter	36	in
Modulus of Elasticity ($E$)	30,000,000	lb/in2
Moment of Inertia ($I$)	87.9	in4
Measured deflection ($w$) in lab	0.08	in
Applied load	20,000	lb

, which outlines the rail type specifications and the load, a 36-ton axle load with a 36-inch wheel diameter traversing a 132 RE rail type at a 20,000 lb load resulted in a deflection of 0.08 inches. The findings in

Table 3. BOEF analysis results and parameter derivations.

Results	Value	Unit
$\mathrm{T}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{k}\mathrm{S}\mathrm{t}\mathrm{i}\mathrm{f}\mathrm{f}\mathrm{n}\mathrm{e}\mathrm{s}\mathrm{s} \left(k\right)$	12,821	lb/in/in
$\beta$	0.03	1/in
Dynamic load ($P_{dynamic}$)	61,639	lb
Load ratio	1.72	-
Speed ($V$)	79	mph
Base pressure	1023	psi
Max. applied load	20,000.00	lb
Max. load % for individual tie	32.37%	%

, which present the BOEF analysis results, indicate that the track stiffness is 12,821 lb/in/in, with a dynamic load of 61,639 lb, equating to a ratio of 1.72 to the static load. This configuration is intended to simulate a track operating at 79 mph. The load transfer from the wheel to the tie accounts for 32.37%.

2.4. Methodology

The methodology employed in this research leverages the principles of track response mechanics, primarily focusing on track stiffness and the Beam on Elastic Foundation (BOEF) theory. Furthermore, the study introduces track settlement mechanics to delineate the degradation rate and associated maintenance-related behavior. The deflection data is also utilized to estimate permanent settlement as a function of varying proportions of sand-induced ballast fouling. These findings hold promise in establishing a statistical correlation between permanent settlement and fouling percentage due to repeated applied loads, offering insights for predicting maintenance intervals. The project comprises two distinct test series as outlined in Section 2.5, each characterized by a unique preparation technique, although the method of calculating the total voids between ballast particles remains consistent across both series.

Quantify the Total Voids Between Ballast Particles

To quantify the total voids within the ballast particles in a clean ballast state, three samples were loaded into three buckets to determine the void volume. The materials utilized in this investigation included ballast, water, sand, a volumetric container, and Large-scale. The procedures were divided into five steps as follows:

Step 1: Measuring the weight of dry and wet ballast:

This step began by recording the dry weight of the ballast sample. Since dry ballast is prone to moisture absorption, its actual weight could change upon contact with water. To mitigate this, the ballast was submerged in a water basin after the dry weight measurement. Its wet weight was then recorded after submersion to account for water absorption. Although complete water absorption was not guaranteed, this step ensured that the ballast weight stabilized and minimized further absorption during subsequent stages.

$$W_d=W_t-W_c$$

(6)

where:

• $W_d$: Weight of the ballast in a dry condition.
• $W_t$: Total weight of the ballast and container (before subtracting the container weight).
• $W_c$: Weight of the empty container.

Step 2: Mixing ballast sample with water:

After recording the wet weight of the ballast, it was placed into a container. Using a volumetric measure, water was gradually added until the container was completely filled to the brim, ensuring that all void spaces within the ballast were fully saturated.

Water was specifically chosen for this process due to its fluidity, allowing it to flow easily and permeate the interstitial gaps between the ballast particles. This ensured an accurate measurement of the void volume, as the amount of water added directly corresponded to the void spaces within the ballast.

$$W_a=W_{wet}-W_d$$

(7)

where:

• $W_a$: Weight of water absorbed by the ballast.
• $W_{wet}$: Weight of the ballast after absorbing water.
• $W_d$: Weight of the ballast in a dry condition.

Step 3: Measuring the total weight:

The total weight of the container and its contents was calculated using the following formula:

$$W_{total}=W_c+W_d+W_a+W_w$$

(8)

where:

• $W_{total}$: Total weight of the container and its contents.
• $W_c$: Weight of the empty container.
• $W_d$: Weight of the ballast in a dry condition.
• $W_a$: Weight of water absorbed by the ballast.
• $W_w$: Weight of water filling the voids in the ballast.

Step 4: Calculate the total void volume:

The total void volume was determined by dividing the weight of water filling the voids ($W_w$) by the net weight of water required to completely fill the container ($W_f$)

$$Voi{d}_{total}\left(\%\right)={\displaystyle \frac{W_w}{W_f}}\times 100$$

(9)

where:

• $W_w$: Weight of water filling the ballast voids.
• $W_f$: Total weight of water required to completely fill the container.

The average void percentage from the three samples was found to be 49.07% of the container volume (

Table 4. Average voids’ volume based on three different samples.

Total Voids’ Volume
	Sample 1	Sample 2	Sample 3	Average
Ballast net weight (lb)	71.25	72.8	72.5	72.18
Water net weight (lb)	47.05	47.1	47.09	47.08
Sand net weight (lb)	63.6	63.4	63.9	63.63
Ballast weight filled with water (lb)	96.35	97.75	97.0	97.03
Adding water weight (lb)	23.35	23.2	22.8	23.10
Water volume (in3)	10.60	10.67	10.50	10.59
Total voids’ volume %	49.63%	49.26%	48.31%	49.07%
Weight of sand at (49.07%) (lb)	31.56	31.23	30.87	31.22

).

Step 5: Determining the actual weight of sand representing the total void volume:

To calculate the sand weight representing 100% void saturation, the container was filled with sand, and its total weight ($W_t^{sand}$) was measured (

Table 5. The volumetric Container dimension is used to calculate the volume of the voids.

Volumetric Container Dimensions
Height (in)	14.5
Diameter (in)	12
Area (in2)	113.04
Volume (in3)	1302.84
Weight (lb)	1.75

). Using the voids percentage from Step 4, the weight of sand equivalent to 49.07% of the container volume was calculated as:

$$W_s=Voi{d}_{total}\left(\%\right)·W_t^{sand}$$

(10)

where:

• $W_s$: Weight of sand filling the ballast voids.
• $W_t^{sand}$: The total weight of sand required to fill the container completely.

Based on the void percentage from Table 4, the ballast volume within the ballast box was calculated (

Table 6. Box dimensions include the ballast volume and sand volume.

Box Dimensions
Width	in	36
Long	in	48
Height	in	18
Box volume	in3	31,104
Ballast and sand weight to fill the box	lb	2468.68
Ballast ratio	%	50.93%
Void ratio	%	49.07%
Ballast weight to fill 50.93% of the ballast box	lb	1723.30
Sand weight to fill 49.07% of the ballast box	lb	745.37

), and the fouling level distribution was determined from the ballast box dimensions (

Table 7. Fouling distribution based on the ballast box dimensions.

Fouling Distribution (%)	Sand Weight (lb)
0%	0.00
10%	74.54
25%	186.34
50%	372.69
75%	559.03
100%	745.37

).

2.5. Lab Tests

In this study, two distinct series of tests were performed to evaluate the behavior of ballast under various fouling conditions. The first series involved a more straightforward, consolidated approach, while the second series adopted a progressive method to simulate gradual fouling. Both series were designed to assess the performance of the ballast over multiple load cycles, providing comprehensive data on its behavior.

The first approach represented ballast that had already been placed and consolidated, examining track behavior in terms of stiffness and permanent settlement under repeated load as its voids filled with fouling material. The second approach simulated real-life conditions in desert areas, where wind-blown sand gradually increases the fouling from the top. It is important to note that in both series of tests, the ballast box did not include a subgrade layer (soil); it was solely composed of the ballast layer.

The ballast box was loaded using the lab’s dynamic load actuator to establish a load-deflection relationship as a function of load magnitude and loading frequency. Tests were conducted with varying fouling levels to examine the influence of sand infiltration on ballast performance. The fouling levels tested were as follows:

• Clean ballast (0% Fouling)
• 10% Fouling
• 25% Fouling
• 50% Fouling
• 75% Fouling
• 100% Fouling

Each test consisted of 3500 load cycles. Stiffness results were calculated from load cycle 0 to load cycle 3000 to focus on the stabilized loading region, whereas settlement results were analyzed across the entire range of cycles from 0 to 3500.

This experiment was repeated for each fouling level, and the test results underwent both statistical and engineering analyses and were compared with stiffness and deflection data from the literature.

2.5.1. Series 1—Unconsolidated Tests

In Series 1, the test procedure began by filling the ballast box with ballast. This method was used to accurately incorporate sand that represented the desired fouling percentages for each trial. The ballast was added in multiple layers, each layer being mixed thoroughly with sand in a cement mixer to ensure even distribution. The ballast mixture was then placed into the ballast box, layer by layer, to create a consistent and controlled test environment.

Subsequently, the mixture was distributed over the ballast box after multiple runs through the cement mixer. Each layer was manually tamped with 100 hits over the entire surface layer to ensure even distribution and leveling, exerting force cautiously to avoid excessive pressure on the ballast and prevent external influences. This meticulous procedure was repeated for each layer until the ballast box was completely filled.

Next, a steel plate was positioned onto the ballast box, followed by the application of actuator force at an extremely low frequency of 0.2 Hz and a magnitude of 1000 lbs. for a total of 50 cycles. This step ensured uniform conditions across all experiments in Series 1.

Subsequently, the railroad tie, previously mounted with the rail, plate, and cut spikes, was placed in the middle of the ballast area, oriented perpendicular to the actuator rod simulating the train wheel. Six LVDTs were strategically placed: two at the ends of the rail, two at the ends of the plate, and the remaining two at the end of the tie. Additionally, the actuator rod was affixed to the middle of the rail head.

Finally, a vertical load of 20,000 lbs. (20 Kips) at a test frequency of 0.2 Hz (720 cycles per hour) was applied until 3000 load cycles were completed. Upon completion of the test, the LVDTs and actuator rod were removed.

The ballast box was emptied and separated from the sand in preparation for the next test, varying from 0% to 100% fouling levels. It is worth noting that the steps involving the cement mixer and sand were omitted when testing clean ballast, specifically during the 0% fouling test.

2.5.2. Series 2—Progressive Tests

In Series 2, the steps closely resemble those of Series 1, maintaining the same magnitude for each step. However, there are two key distinctions in the Series 2 protocol: the method of mixing sand with ballast and the utilization of the steel plate.

In Series 2, the sand was mixed with the ballast differently compared to Series 1. Additionally, the steel plate was used only once, specifically during the Clean Ballast test (0% fouling). This approach was chosen because the ballast was not removed between tests in Series 2. Instead, the tests were conducted continuously until 21,000 load cycles were completed.

In this series of tests, clean ballast remained in the track, and sand was incrementally added from the top of the ballast layer in predefined percentages. After the addition of each level of sand, the system was subjected to 3500 cycles of loading before the next increment of sand level was added. For instance, to increase the fouling from 10% to 25%, the initial 10% of sand, approximately 0.6 cubic feet, was first added to the clean ballast layer. After completing 3500 load cycles, an additional 1 cubic foot of sand was added, bringing the total to 1.6 cubic feet or 25%, and the system underwent another 3500 cycles. This process continued, with each addition increasing the sand percentage until the 100% fouling condition was reached.

3. Results

3.1. Stiffness

Track stiffness can be determined as outlined in the methodology section. For each test series, a load-deflection graph was generated across the complete range of loading cycles (Figure 3A) [22]. This facilitated the calculation of stiffness (modulus), defined here as the alteration in deflection under load per unit length of track, expressed as lb/in/in.

The resultant load-deflection and deflection-time graphs are depicted in Figure 3A and Figure 3B, respectively. The initial stiffness is readily discernible [22].

Initially, average stiffness was computed over the entire set of loading cycles [22]. However, due to substantial initial deflections observed during testing (Figure 3A,B), it was determined that a more meaningful average stiffness could be derived by excluding the initial loading cycles.

Consequently, the final stiffness values were calculated based on the average load-deflection behavior for cycles 1000 through 3000 (Figure 4C). Hence, the stiffness for both series was calculated in three distinct stages:

• Stage 1 (full load cycles): Stiffness was computed from cycle 1 to cycle 3000.
• Stage 2 (initial load cycles): Stiffness was calculated from cycle 1 to cycle 500.
• Stage 3 (excluding initial cycles): Stiffness was determined from cycle 1000 to cycle 3000.

Figure 4A–C display the test outcomes for the spectrum of fouling conditions ranging from 0% to 100%. It is important to note that all deflections presented in these figures are measured at the actuator positioned at the top of the rail head.

3.2. Series 1—Stiffness Results

The average stiffness was computed for Series 1 across the range of 1000 to 3000 load cycles, plotted as a function of percent sand fouling. In this particular fouling configuration, the stiffness remains relatively constant, exhibiting minor fluctuations within the range of ±3% (Figure 5,

Table 8. Stiffness results (lb/in/in) for three different stages—Actuator measurement—Series 1.

Series 1—Track Stiffness
Fouling %	Cycles	Average Track Stiffness ($\mathit{k}$) (lb/in/in)
0%	0–500	11,023
	0–3000	12,236
	1000–3000	12,544
10%	0–500	11,703
	0–3000	12,517
	1000–3000	12,732
25%	0–500	11,001
	0–3000	11,960
	1000–3000	12,195
50%	0–500	11,246
	0–3000	12,382
	1000–3000	12,702
75%	0–500	11,011
	0–3000	11,825
	1000–3000	12,054
100%	0–500	11,435
	0–3000	12,234
	1000–3000	12,465

) [22].

3.3. Series 2—Stiffness Results

Average stiffness was computed for Series 2 across the full range of load cycles, represented as a function of percent sand fouling (

Table 9. Stiffness results (lb/in/in) for three different stages—Actuator measurement—Series 2.

Series 2–Track Stiffness
Fouling %	Cycles	Average Track Stiffness ($\mathit{k}$) (lb/in/in)
0%	0–500	11,026
	0–3000	12,306
	1000–3000	12,580
10%	0–500	11,762
	0–3000	12,826
	1000–3000	13,050
25%	0–500	11,691
	0–3000	12,414
	1000–3000	12,575
50%	0–500	11,755
	0–3000	12,944
	1000–3000	13,186
75%	0–500	13,185
	0–3000	13,772
	1000–3000	13,921
100%	0–500	12,431
	0–3000	13,163
	1000–3000	13,314

) [22]. It is noteworthy that this type of fouling implementation aligns more closely with real-world scenarios observed in desert-type areas [22].

Moreover, stiffness results consistently indicate an increase in the modulus (stiffness per unit length) with the escalation of sand fouling levels [22]. Upon fitting a linear trend to the dataset, encompassing data from the hydraulic actuator and six LVDTs (Figure 6,

Table 10. Series 2—Stiffness for different fouling levels.

Track Stiffness—Series 2
Linear equation	$k=m\times x+b (\mathrm{l}\mathrm{b}/\mathrm{i}\mathrm{n}/\mathrm{i}\mathrm{n})$
Where:
$k$ is the stiffness	$x$ is the fouling level
Slope ($m$)	Y-intercept ($b$)
1562.8	12,562

), the analysis elucidated the correlation between stiffness and fouling as follows:

The R² value corresponding to the correlation between stiffness and fouling was found to be 74.5%, indicating a good correlation between this relationship and the test data.

3.4. Stiffness Discussion

The observed stiffness behavior of the track, relative to sand fouling, exhibited notable differences depending on how the fouling was introduced into the test. In Series 1, where fouling was introduced in a “homogeneous” manner during the ballast installation in the ballast box, the stiffness remained relatively consistent with varying levels of sand fouling [22]. This finding resembled observations from another laboratory test conducted by J. Estaire and M. Santana [14].

However, when the sand was introduced in a manner consistent with real-world scenarios, i.e., from the top and allowed to consolidate under simulated traffic loading, the stiffness exhibited an increase with higher percentages of sand fouling [22]. This stiffening behavior with escalating levels of sand fouling in the ballast aligns with the results conducted by Zakeri [12] and Heydari et al. [16], which showcased findings from a series of field measurements of track modulus as a function of sand fouling.

3.5. Settlement Results

Settlement, also referred to as permanent settlement, encompasses the overall settling occurring across the ballast, sub-ballast, and subgrade layers, quantified in inches. Several factors contribute to settlement, such as the type of ballast, the control of void volumes by ballast size, the properties of the soil involved, and the applied loading.

The outcomes of the ballast box tests are portrayed in terms of load deflections relative to fouling levels. It is crucial to highlight, as previously stated, that the ballast box lacks a subgrade (soil) layer in both test series. Thus, this test focuses on the settlement of the ballast.

3.6. Series 1—Settlement Results

Series 1 comprises unconsolidated tests, each running for 3500 cycles. The data derived from the ballast box tests was graphed in terms of load-deflection (Figure 3A) and deflection-load cycles (Figure 7).

In reference to the settlement outcomes of Series 1 (

Table 11. Settlement results in (inches)–Actuator measurement—Series 1.

Fouling %	Cycles	Settlement (in)
0%	3500	0.576
10%		0.580
25%		0.579
50%		0.640
75%		0.943
100%		1.078

), the data was gathered through the utilization of a hydraulic actuator, which was responsible for exerting a cyclic force on the rail. Table 11 displays the results of all six tests conducted in Series 1.

The settlement results consistently show an increase in settlement (inches) with the escalation of sand fouling levels. Upon fitting an exponential trend to the obtained data (Figure 8,

Table 12. Series 1—Settlement for different fouling levels.

Track Settlement—Series 1
Exponential equation	$S=a\times e^{bx} \left(\mathrm{i}\mathrm{n}\right)$
Where:
$S$ is the settlement	$x$ is the fouling level
$\mathrm{Initial} \mathrm{settlement} (a$)	$\mathrm{Growth} \mathrm{Rate} (b$)
0.5274	0.6792

), encompassing data from the hydraulic actuator, the analysis elucidated the correlation between settlement and fouling as follows:

The R² value corresponding to the correlation between settlement and fouling was found to be 91.9%, indicating an excellent correlation between this relationship and the test data.

3.7. Series 2—Settlement Results

Series 2 depicts the progressive tests where fouling is incremented every 3500 cycles. Consequently, the settlement-load cycles (Figure 9) facilitate the determination of settlement amounts. This measurement captures the final deflection observed after the completion of the load series following 3500 cycles.

Table 13. Settlement results in (inches)–Actuator measurement—Series 2.

Fouling %	Cycles	Settlement (in)
0%	3500	0.580
10%		0.829
25%		1.070
50%		1.193
75%		1.623
100%		3.023

presents the settlement data for all tests conducted in Series 2 over 3500 cycles. The settlement results consistently demonstrate a rise in settlement (inches) with the escalation of sand fouling levels.

Upon fitting an exponential trend to the collected data (

Table 14. Series 2—Settlement for different fouling levels.

Track Settlement—Series 1
Exponential equation	$S=a\times e^{bx} \left(\mathrm{i}\mathrm{n}\right)$
Where:
$S$ is the settlement	$x$ is the fouling level
$\mathrm{Initial} \mathrm{settlement} (a$)	$\mathrm{Growth} \mathrm{Rate} (b$)
0.6489	1.4217

, Figure 10), encompassing data from the hydraulic actuator, the analysis reveals the correlation between settlement and fouling as follows:

The R² value corresponding to the correlation between settlement and fouling was found to be 94.6%, indicating an excellent correlation between this relationship and the test data.

3.8. Settlement Discussion

The settlement pattern observed in Figure 7 and Figure 9, representing settlement-load cycles in relation to sand fouling, remains consistent across both Series 1 and Series 2, irrespective of the method of sand introduction.

In Series 1, where fouling was uniformly introduced during ballast installation in the ballast box, settlement increases with higher levels of fouling sand. The most substantial settlement occurs during the initial cycles, typically spanning from cycle 5 to cycle 20.

The initial settlement rate undergoes a significant spike within a single cycle, exhibiting variability across various tests (Figure 11A).

As depicted in Figure 11A, the timing of the initial settlement varies across different tests within this series. Notably, in all tests, except for the 10% fouling test, the initial settlement occurs within a single cycle. For instance, in the 100% fouling test, the initial settlement commences at cycle 9 and concludes at cycle 10. However, in the 10% fouling test, the initial settlement spans from cycle 10 to cycle 11, albeit briefly. Subsequently, another settlement event transpires from cycle 11 to cycle 12 to complete the initial settlement. It is essential to highlight that the brief initial settlement observed in the 10% fouling test appears anomalous and could potentially skew the results when compared to others. Contrary to the hypothesis suggesting that settlement increases with higher fouling levels, the 10% fouling test exhibits higher settlement levels compared to the 0%, 25%, and 50% fouling tests. This outcome contradicts the expectation that it would fall between the settlement levels of the 0% fouling test and the 25% fouling test, as illustrated in Figure 11B.

Figure 11C indicates a discrepancy in the load applied by the hydraulic actuator during cycle 10, where only a 4000 lb load was experienced instead of the full load of 20,000 lb. This deviation from the expected load may have implications for the settlement behavior observed during this cycle and should be considered when analyzing the results.

Figure 11D illustrates the exclusion of the short settlement observed during cycle 10 from subsequent load cycles. To ensure consistency and facilitate analysis, all tests were aligned to commence from the same settlement cycle, specifically cycle number 4. Discarding some initial cycles did not affect the overall settlement results, ensuring the reliability and accuracy of the analysis.

After addressing the issue of short settlement in the 10% fouling test and aligning all tests to a common reference point, the results confirm that the settlement observed in the 10% fouling test falls between the settlement levels observed in the 0% fouling and 25% fouling tests. This outcome aligns with the initial hypothesis, as depicted in Figure 11E.

In summary, the settlement rate exhibits a consistent increase, albeit at a slower rate, across the different fouling levels. This pattern is reminiscent of observations made in the FAST track by Selig [2], where the settlement rate showed a significant increase during the initial 3 million gross tons (MGT) before continuing to rise at a slower rate over time.

In Series 2, where fouling is incrementally introduced from the top layer of the ballast, the settlement outcomes from the actuator were graphically represented to showcase the relationship between settlement and fouling levels, as depicted in Figure 12. This visual representation offers insights into how settlement changes with varying degrees of fouling within the ballast.

The settlement trends portrayed in Figure 12 demonstrate the evolution of settlement patterns throughout 3500 cycles for each fouling level. As observed, a distinct initial settlement phase exists during the early cycles, which is succeeded by a gradual but consistent escalation in settlement rates. This consistent trend persists across all experiments conducted in both Series 1 and Series 2, emphasizing the enduring influence of fouling on settlement dynamics over the testing period.

In Series 2, from the second test (with 10% fouling) to the fourth test (with 50% fouling), the initial settlement appears relatively minor. This phenomenon arises because Series 2 follows a progressive testing approach, where significant initial settlement in the uncompacted ballast already occurred during the initial test with clean ballast or 0% fouling. Notably, despite this reduced initial settlement, the settlement pattern remains consistent across all tests conducted within Series 2.

Surprisingly, tests representing 75% and 100% fouling exhibit substantial initial settlement, contrary to expectations for progressive tests. In such tests, the ballast is anticipated to have compacted, with voids filled by sand. However, the notable settlement observed in these tests may be attributed not only to the ballast but also to settlement in the sand layer, as the sand is driven into the voids or the tie burrows into the sand.

Given that the sand remains predominantly on the ballast surface without infiltrating deeply, it contributes significantly to the observed settlement.

Although Series 2 involves progressive testing, Figure 13 provides a breakdown of settlement for each test individually. Notably, settlement diminishes in each test before experiencing a subsequent increase at the 75% fouling mark. This suggests that the settlement observed at this stage may be primarily due to the crosstie settling into the sand layer that has yet to penetrate the underlying ballast.

Figure 14A, depicting the scenario with 75% fouling, illustrates that the sand fails to penetrate down to the ballast post-test. Nonetheless, it does indicate the crosstie’s subsidence into the ballast, as evidenced by the presence of dots on the sand surface. These dots signify that some sand has indeed infiltrated into the ballast voids, albeit in smaller quantities, while the majority remains on the surface. This behavior mirrors findings from previous studies such as Estaire and Santana CEDEX Track Box investigations [14], where sand was observed to predominantly remain on the ballast surface rather than infiltrating down to deeper layers, particularly when fouling levels reached 85% to 100%.

In Figure 14B, illustrating the scenario with 100% fouling, it is evident that the sand has not permeated down to the ballast, and there are no visible dots on the surface. This indicates that the voids in the upper layer of ballast have likely been compacted and occupied by sand from prior tests. This observation aligns with the findings of the Estaire and Santana CEDEX Track Box studies [14], which reported similar behavior in situations where sand predominantly remained on the surface without significant infiltration into the underlying ballast layer.

4. Conclusions

This study provides an in-depth analysis of track stiffness and settlement behavior under varying sand fouling conditions through two distinct series of tests.

4.1. Stiffness Findings

The analysis of stiffness under different fouling conditions revealed notable differences based on how fouling was introduced. In Series 1, where fouling was introduced homogeneously during ballast installation, the stiffness remained relatively constant with minor fluctuations. This consistency aligns with laboratory findings from other studies. However, in Series 2, which simulated real-world conditions by incrementally adding sand fouling from the top and consolidating it under load, stiffness increased with higher fouling levels. This increase in stiffness with escalating sand fouling aligns with field observations and underscores the significant impact of fouling introduced in a manner that mimics real-world scenarios.

4.2. Settlement Findings

The settlement behavior, characterized by permanent settlement, showed a consistent increase with higher fouling levels in both test series. Series 1 tests indicated substantial initial settlement, primarily within the first few cycles, with settlement rates leveling off thereafter. In contrast, Series 2 tests, which progressively introduced fouling, exhibited a distinct initial settlement phase followed by a consistent increase in settlement rates over subsequent cycles. This behavior suggests that the method of fouling introduction significantly influences initial settlement patterns, with more realistic fouling methods resulting in higher initial settlements due to sand infiltration into ballast voids.

4.3. Overall Implications

The study’s findings highlight the importance of considering the method of fouling introduction when evaluating track performance. Homogeneous fouling introduction during ballast installation resulted in relatively stable stiffness but did not accurately reflect real-world conditions where sand accumulates progressively. In contrast, the more realistic fouling method used in Series 2 provided a closer approximation of in-service conditions, demonstrating increased stiffness and settlement rates with higher fouling levels.

These insights are crucial for railway maintenance and track design, emphasizing the need for realistic fouling simulations in laboratory tests to better predict track performance under actual operating conditions. Understanding the effects of fouling on track stiffness and settlement can inform maintenance strategies, ensuring more accurate assessments of track conditions and more effective maintenance interventions.

In conclusion, this study underscores the significant impact of sand fouling on track stiffness and settlement, with findings that can guide more effective railway maintenance practices and enhance track performance under varying environmental conditions.

4.4. Recommendations for Research Development

Building on the findings of this study, the following recommendations for future research are proposed to further enhance our understanding of track stiffness and settlement behavior under different fouling conditions:

Expanded Fouling Conditions in Laboratory Tests: Conduct additional laboratory tests to investigate a wider range of fouling levels, including finer gradations between the currently tested percentages (e.g., 5%, 15%, 35%, etc.). This will help refine the correlation between fouling levels and track stiffness/settlement.

Longer Testing Durations: Extend the duration of load cycles beyond the current 3500 cycles to observe long-term behavior and potential fatigue effects on track stiffness and settlement. This can provide insights into the durability and resilience of the track under prolonged usage.

Variation in Loading Conditions: Introduce varied loading conditions, such as higher and lower load magnitudes and different loading frequencies, to simulate diverse operational scenarios. This will help understand how different loading conditions impact track performance under fouling.

Enhanced Measurement Techniques: Improve measurement techniques by integrating more advanced and precise instrumentation, such as high-resolution laser displacement sensors and strain gauges, to capture more detailed data on deflection and settlement.

Economic Analysis: Incorporate an economic analysis into the laboratory tests to evaluate the cost-effectiveness of various fouling levels and maintenance strategies. This analysis should consider the costs associated with track maintenance, repair, and downtime, providing a comprehensive assessment of financial implications.

Real-World Validation: Conduct field tests to validate laboratory findings using similar fouling conditions and loading scenarios. This will help confirm the applicability of laboratory results to real-world track conditions and enhance the reliability of the conclusions drawn.

Investigation of Settlement Patterns: Further analyze settlement patterns by conducting tests with different initial ballast conditions (e.g., pre-compacted vs. loose ballast) to understand how the initial ballast state affects settlement under fouling.

Impact of Ballast Type and Size: Explore the impact of different ballast types and sizes on track stiffness and settlement under various fouling conditions. This will help determine the most effective ballast configurations for mitigating fouling impacts.

By pursuing these recommendations, future research can deepen our understanding of how different fouling conditions affect railway track performance and contribute to developing more effective maintenance strategies. This, in turn, will enhance the longevity, safety, and cost-efficiency of railway infrastructure.