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Dynamic response analysis and comprehensive evaluation of cement-improved aeolian sand roadbed

  • Yonggang Wang , Hui Wang , Guangying Yuan , Kexin Ren EMAIL logo , Xunchang Li and Wei Yang
Published/Copyright: October 9, 2025
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Open Geosciences
From the journal Open Geosciences Volume 17 Issue 1

Abstract

Long-term stability of high-speed railway roadbeds is a complex multi-criteria decision-making problem. The stability of cement-improved sandy roadbeds is investigated and evaluated in order to efficiently identify and control risk, assure train safety, and optimize resource allocation. This study relies on bibliometric analysis to filter out roadbed assessment indexes and create an evaluation index system. The Analytic Hierarchy Process-Technique for Order Preference by Similarity to Ideal Solution evaluation model is established, and finite element software is used to simulate the actual project, allowing for dynamic stability analysis of the roadbed and lateral comparison of each scheme. The roadbed’s dynamic stability analysis and lateral comparison are completed, as well as the analysis and optimization of the roadbed parameters. The results reveal that a 3:7 pulverized soil ratio and 6% cement mixing improve roadbed stability by 5%. The effect of cement was larger than that of silt. The proposed model’s evaluation results were similar to the field test, demonstrating its dependability, and the research findings can be used to construct a cement-improved aeolian sand high-speed train foundation.

Keywords: cement aeolian sand; dynamic response; railway subgrade; evaluation

1 Introduction

The roadbed of a high-speed rail (HSR) is impacted by both train load and environmental conditions throughout long-term service. Stability of the roadbed affects the HSR’s long-term performance and train safety. For example, the high-speed railway roadbed of the Daxi Passenger Dedicated Line may cause dynamic instability due to differential settlement of strata on both sides of ground cracks, and freight train derailment accidents have occurred on the Dazheng Line due to train vibration, insufficient roadbed stability, and line maintenance issues. Therefore, in order to screen the influencing factors of roadbed disease, screen the risk, and reduce the potential loss, it is especially important to establish the roadbed risk evaluation, which can better understand the behavior of roadbed under different geological conditions, environmental factors, and loads, and provide a scientific basis for the design of the roadbed to reduce the occurrence of accidents.

Because of the scarcity of excellent fillers in the western desert region, the use of improved soil of aeolian sand as roadbed fill for high-speed railroads is an economic and practical measure [1], which can adapt to large temperature changes and a dry environment, as well as solve environmental problems in the desert region while lowering project costs. However, aeolian sand has tiny particles and a loose structure [2] and is classified as a Group C filler, which has a negative impact on the stability and bearing capacity of railroad roadbeds. The project improves the overall quality of the high-speed train roadbed by managing important admixtures such as cement admixture, pulverized soil ratio, fly ash, and water content [3,4,5,6,7], ensuring the roadbed’s stability and reliability. Some experts have conducted research on the suitability and durability of aeolian sand enhanced soil as a high-speed railroad base. Through on-site tests, Liu et al. [8] showed that the vibration damping capacity of reinforced aeolian sand roadbed is superior to that of gravel soil roadbed, establishing the foundation for desert roadbed construction. California bearing ratio is also commonly utilized in road engineering and foundation design to quantify the material’s performance improvement [9,10,11]. Dapeng et al. [12] created a 1:1 full-scale model of a low embankment, tested it under various loading conditions, and compared the stress attenuation rate and diffusion capacity of different embankments to study the dynamic response law of the aeolian sand roadbed. Mengqian et al. [13] investigated the change rule of dynamic response under various operating conditions using on-site monitoring and evaluated the deformation of aeolian sand roadbed to fulfill specification criteria using the critical dynamic stress formula. Yang et al. [14] and Zhang et al. [15] conducted a triaxial test with material proportioning to investigate the change in shear strength and the strength change rule of improved aeolian sand. They discovered that the shear strength increased with the incorporation of pulverized soil and additives, and elaborated on the trend and feasibility of the incorporation for improving the performance of aeolian sand-improved soil. Cabalar and Karabash [16] investigated the effects of five different sample preparation techniques, including different curing pressures, times, and stress conditions on mechanical response, and used electron microscopy to explain the mechanism of their effects, providing data support for roadbed construction. Chuxuan et al. [17] and Yang [18] discussed the effects of various conditions such as roadbed thickness and reinforcement improvement on the dynamic response of aeolian sandy roadbeds by establishing computational models. The study of different working conditions showed that with the increasing depth of the roadbed layer, the amplitude of dynamic velocity, dynamic acceleration amplitude, and dynamic stress amplitude showed a gradual attenuation; and the treatment approach has a stronger effect on the dynamic response curve’s volatility.

In conclusion, researchers investigated the dynamic response, shear strength change, and other properties of aeolian sand enhanced soil using field tests and numerical simulations. However, the majority of available research focuses on the examination of a single element and does not provide a full evaluation of roadbed stability when numerous factors are coupled. As illustrated in Table 1, a variety of models and approaches are currently being used to analyze roadbed assessment, including the fuzzy comprehensive evaluation method, the approximation ideal solution ranking method, the entropy value method, and others.

Table 1

Research methods and contents

Method Research
Game theory – Toppable models Zhu et al. [19] constructed a new type of stability assessment model for perennial permafrost highway subgrade, which evaluates the four aspects of permafrost type, climatic conditions, geological environment, and engineering conditions, and provides a decision-making basis for the maintenance of perennial permafrost subgrade
Gray correlation analysis Zhang et al. [20] used gray correlation to investigate the effect of pore structure factors on compressive strength in order to develop a model for predicting concrete strength
In the research, Liyang et al. [21] used the gray correlation degree method to investigate, selecting the internal friction angle and compression modulus, among other evaluation indexes, and determining the integrated water content acceptable for fly ash roadbed construction
Analytic Hierarchy Process (AHP)-extended Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) Zheng and Bao [22] evaluated the safety of permafrost roadbeds by the AHP-extended TOPSIS method, and the combination of the two created conditions for the accuracy of roadbed safety evaluation
Machine learning algorithms Bai et al. [23] used machine learning techniques to quantify the form evaluation metrics of longitudinal flatness, edges, and roughness of stacked stone materials for roadbeds, in order to examine the effect of stacked stone particles on roadbed fill settling
To determine the optimal ratio for soft soil roadbeds, Li et al. [24] created a strength database of modified fill based on the physical parameters and mechanical properties of the reinforced soft soil, then used machine learning for evaluation and prediction to improve testing efficiency
Entropy Xin et al. [25] utilized the entropy value method based on the principle of acoustic wave transmission test to assess the quality of roadbed filling and proposed the minimum standard for evaluating the qualified roadbed, which proved the reasonableness of the bubble mixed lightweight filler roadbed

At the moment, roadbed evaluation is primarily concerned with converting the qualitative description of each indicator into a quantitative expression [26], so addressing the uncertainty in the evaluation process, which necessitates a significant number of expert judgments. Furthermore, the current evaluation indexes are primarily used to evaluate and analyze the stability and filling quality of roadbeds based on material strength and external environment, with an even greater lack of relevant dynamic response indexes, particularly for aeolian sand improved soil research.

To solve the problems listed above, this study uses the evaluation approach to solve the problem of aeolian sand rationing, and the article’s structure is as follows: Section 3 illustrates the construction of the evaluation model, Section 4 introduces engineering and simulation, Section 5 analyzes the evaluation of the dynamic stability of the roadbed and the effect of the improvement, Section 6 discusses the effect of the impacts and the validation of the model, and Section 7 draws the conclusion.

2 Significance of the study

To meet the high standards of high-speed railway roadbed and solve the problem of railroad construction in the western desert area, materials with dynamic stability and low cost are required. In this study, the optimal proportioning scheme is derived using a combination of refined finite element numerical simulation and a comprehensive evaluation model, which reveals the intrinsic law of material proportioning improvement affecting the dynamic response, but it also effectively solves the problem of index selection and scheme preferential selection in multi-criteria decision-making. More importantly, it effectively addresses index selection and program preference issues in multi-criteria decision-making, as well as improving the scientific, comprehensive, and practicality of decision-making. The roadbed analysis provides an effective evaluation approach for roadbed design, as well as data support for material selection and design of cement-improved sandy roadbed, which is critical technical support for railroad construction in the western desert area. However, in the actual project, the climatic and geological circumstances of different places vary widely, and a single material ratio may not be sufficient to suit all technical requirements. In the future, the specific environmental conditions of different regions can be used to further refine the prediction of the proportioning and design of aeolian sand-improved materials to improve their adaptability and engineering performance, resulting in more projects promoting aeolian sand-improved technology.

3 Establishment of evaluation model

3.1 Data collection

Bibliometrics is a quantitative way of studying scientific literature that looks for patterns and trends in scientific activities by counting and analyzing a range of data in the literature, such as authors, keywords, and citation counts. Knowledge mapping is a way of portraying knowledge in the form of a graph that displays the fundamental connectedness and structure of knowledge by creating a network of entities and inter-entity links. The steps are as follows:

  1. Data collection: Identify the research topic and gather relevant literature data, such as academic articles, specifications, and accident reports.

  2. Data organization and statistics: Categorize, code, and format the acquired literature, and analyze the data using statistical methods such as frequency analysis, co-occurrence analysis, and citation analysis.

  3. Data analysis: It includes integrating and storing knowledge, resolving ambiguities and conflicts between entities, applying graph algorithms to reason about the knowledge graph, and discovering new knowledge and relationships.

  4. Visualization: Use visualization tools to display the knowledge graph and reveal the research object’s development pattern.

3.2 AHP evaluation method

The AHP technique is an assignment method that uses expert weights to determine the relevance of the indicator evaluation. The computation steps are as follows. First, the hierarchical analysis model is created, which includes the goal, criterion, and program layers. The program layer’s indicators are used to create the n × n judgment matrix A.

A = a 11 a 12 ⋯ a 1 n a 21 a 22 ⋯ a 2 n ⋮ a n 1 ⋮ a n 2 ⋱ ⋯ ⋮ a n n ,

where a ij is the quantitative value of the relative importance of criterion i and criterion j. The importance scaling methods are shown in Table 2, and values are usually taken according to the Saaty 1–9 scale method table.

Table 2

Scale value method

Scale Meaning (i compared to j)
1 Both are equally important
3 The former is slightly more important than the latter
5 The former is obviously more important than the latter
7 The former is more important than the latter
9 The former is strongly more important than the latter
2, 4, 6, 8 The median value in the adjacency judgment above

Formula (1) identifies the eigenvector ω for the criterion layer.

(1) ω =   ∑ j = 1 n c 1 j n   ∑ j = 1 n c 2 j n   ∑ j = 1 n c 3 j n T .

The consistency test evaluates whether the results of several tests for the same research item are consistent (where n is the number of indicators at the criterion level). The consistency test index (C R ) is defined as

(2) C R = C I R I ,

(3) C I = ω max − n n − 1 .

When C R < 0.1, then the judgment matrix passes the consistency test.

3.3 TOPSIS evaluation method

The TOPSIS [27] evaluation approach sorts evaluation items by calculating the distance between the ideal solution and the negative ideal solution in order to evaluate the advantages and disadvantages of each evaluation object. TOPSIS, as a multi-objective decision analysis and assessment method, can fully utilize index data and has high objectivity. It is commonly used for objectively evaluating engineering designs. The calculations are as follows:

  1. Create a decision matrix Y = (y ij ) m×n using the indicator data from each evaluation program.

    Y = y 11 y 12 ⋯ y 1 n y 21 y 22 ⋯ y 2 n ⋮ y m 1 ⋮ y m 2 ⋱ ⋯ ⋮ y m n ,

    where y ij represents the value of program i in relation to evaluation indication j, m is the number of evaluated programs, and n is the number of evaluation indicators.

  2. Data standardization processing:

    The lower the value of the indicator, the better the indicator, using formula (4) for positive processing

    (4) y i j ' = q i j − min q i j max q i j − min q i j .

    The larger the value of the indicator, the better the indicator, using formula (5) for negative processing

    (5) y i j ' = max q i j − q i j max q i j − min q i j .

    In order to eliminate the influence of different scales of the evaluation indicators, the positive decision matrix Y′ is standardized, and the standardized decision matrix Z = (y ij ) m×n is obtained

  3. Determine the positive and negative ideal solutions

    The ideal solution Z + = {z 1+, z 2+, …, z n+}is the set of maximum values corresponding to each index in the weighted gauge matrix, and the negative ideal solution Z − = {z 1−, z 2−, …, z n−} is the set of minimum values corresponding to each index in the weighted gauge matrix.

  4. Calculate the score

    The distance from scheme i to the positive ideal solution is defined as d i + , and the distance from scheme i to the negative ideal solution is defined as d i − . The calculation formula is as follows:

    (6) d i + = ∑ j = 1 n w j ( z j + − z i j ) 2 , i   = 1 ,   2 ,    m ,

    (7) d i − = ∑ j = 1 n w j ( z j − − z i j ) 2 , i   =   1 ,   2 ,    m .

The larger the relative sticking point C i is, the closer the sample point is to the positive ideal solution, and the better the result of the comprehensive evaluation.

(8) C i = d i − d i + + d i −   .

3.4 AHP-TOPSIS method model

To evaluate and analyze cement upgraded aeolian sand high railway foundations, a complete assessment model based on AHP-TOPSIS was developed. Figure 1 illustrates the specific technique.

Figure 1 The flowchart of the evaluation model.
Figure 1

The flowchart of the evaluation model.

4 Example analysis

4.1 Project example

Baoyin Railway starts from Baotou, which is an important railroad trunk line connecting Baotou City of Inner Mongolia Autonomous Region and Yinchuan City of Ningxia Hui Autonomous Region, with a total line length of 519 km and a design speed of 250 km/h. The railroad is located on the edge of the Ulan Buh Desert, which is a dry area with little annual precipitation and high evaporation. The region where it is located is the edge of Ulan Buh Desert, which has an arid climate, scanty annual precipitation, high evaporation, and a significant temperature difference between day and night, and this special geographic and climatic condition poses a serious challenge to railroad construction, due to the lack of qualified AB group filler required for railroad subgrade filling around the area, and in order to save costs, the wind-deposited sand in the desert. Figure 2 depicts the geographic position of Baoyin Railway.

Figure 2 Geographical location information of Baoyin Railway.
Figure 2

Geographical location information of Baoyin Railway.

This study uses the Baoyin Railway as a backdrop to build a finite element model to investigate the effect of the proportion of aeolian sandy improved soil below the sub-base layer on roadbed stability, and chooses 20–40% of pulverized soil and 4–6% of cement to create nine programs for evaluation and comparison based on the requirements of the design code for high-speed railway, as shown in Table 3.

Table 3

Simulation scheme

The scheme Cement content Silt ratio Degree of compaction E (MPa) Ψ (°)
1 4% 2:8 0.98 26 36.5
2 4% 3:7 46 37
3 4% 4:6 49 40
4 5% 2:8 46 37.5
5 5% 3:7 55 38
6 5% 4:6 59 39
7 6% 2:8 73 38.5
8 6% 3:7 83 39
9 6% 4:6 83 39.5
Symbol Meaning
E Elastic modulus
μ Poisson’s ratio
Ψ Friction Angle

4.2 Engineering simulation

Based on GTS-NS, we design ballasted track-roadbed finite dynamic model. According to the actual roadbed, the model consists of railroad track, graded gravel, AB filler, sub-bed, sub-bed and foundation, in which the railroad track consists of rails, sleepers, roadbed, sub-bed, and sub-bed are made of cement-improved airborne sand. The length, width, and height of the model are 100 m × 200 m × 35 m, and the heights of graded gravel, AB filler, the bottom layer of the bedrock, below the bottom layer of the bedrock and foundation level are 0.7, 0.8, 1.5, 2.5, and 30 m, respectively, and the slopes are 1:1.5, which are shown in Figures 3 and 4.

Figure 3 Model profile.
Figure 3

Model profile.

Figure 4 Schematic diagram of the model.
Figure 4

Schematic diagram of the model.

The rails, sleepers, and roadbeds are configured as linear elastic models, while the rail fasteners are simulated using spring-damping units. Mohr-Coulomb models are used for the bed’s surface and bottom layers, as well as stratums 1 and 2. The elastic-viscous boundary is established at the foundation’s edge, considering the boundary vibration at the chosen foundation boundary. Table 4 displays the simulation parameters of the fill materials in each stratum of the roadbed based on the test data and the investigation report [28].

Table 4

Material parameters

Properties
Name Materials E (MPa) μ Unit weight (kN/m3) Cohesive force (kPa) Ψ (°)
Rail / 2.1 × 105 0.3 78.3 / /
Sleeper / 1.8 × 104 0.3 25 / /
Track bed / 710 0.17 27 / /
Subgrade surface layer Graded gravel 150 0.27 23 75 27
Above ground floor AB packing 110 0.33 21 55 20
Subbed Aeolian sand improved soil 87 0.33 21 55 20
Formation 1 Fine sand 3.46 0.32 17.6 30 32
Formation 2 Sandy soil 3.5 0.33 18.6 30 25

In this study, the train is a CRH2A type train set, with a speed of 250 km/h and a length of 201.4 m. The precise train data are provided in Table 5. The simulation uses the real train speed, the vibration time is 3 s, and the train load curve is illustrated in Figure 5.

Table 5

Train data

Train parameter Train data
Axle load (t) 15
Gauge (m) 1.435
Vehicle distance (m) 17.5
Wheelbase between two cars (m) 5.6
Bogie fixed wheelbase (m) 2.5
Figure 5 Load time history curve.
Figure 5

Load time history curve.

5 Comprehensive study of the dynamic stability of the roadbed

5.1 Screening for roadbed stability evaluation indicators

Because cement enhanced sandy roadbed is a complex integrated system, its dynamic stability is influenced by a variety of index parameters. The Baoyin Railway is used as a background for the research.

This study employs the bibliometric analysis approach [29], utilizing Citespace software and picking the Web of Science core database and China Academic Journal Database (CNKI) as data sources for visualization. The advanced search with “roadbed” as the keyword obtained 1,000 pieces of literature, and the keyword analysis is shown in Figure 6. Summarizing the research hotspots of high-speed railroad roadbeds in the past years and the evaluation indexes mentioned in the relevant standards and specifications, the focus of the research on roadbeds and the indexes of the study mainly focus on the static and dynamic characteristics, among which, the resilience modulus, the quality of compaction, the moisture content and the unconfined compressive strength belong to the static and dynamic characteristics, which are the most important. Static characteristics include rebound modulus, compaction quality, moisture content, and unconfined compressive strength, whereas dynamic response refers to the mechanical behavior of a structure or material under dynamic loading, which describes changes in physical quantities such as displacement, velocity, acceleration, and stress.

Figure 6 Analysis of knowledge graph.
Figure 6

Analysis of knowledge graph.

At the same time, this study combines the specifications for railway roadbed design [30], technical regulations for observation and evaluation of settlement and deformation of railway engineering [31], and technical regulations for the construction of high-speed railway roadbed engineering [32] with the main research directions and contents of the current literature summarized in the knowledge graph, and establishes the evaluation indexes as shown in Figure 7. Among them, insufficient unconfined compressive strength may result in insufficient bearing capacity of the roadbed, causing settlement, deformation, or even collapse of the roadbed, which is the primary indicator used to test the bearing capacity of materials. Excessive dynamic stress caused by train dynamic load fatigues roadbed material, and long-term accumulation can cause cracking, settling, and other disorders. Surface settlement, lateral displacement, and vertical displacement that are too large may cause track unevenness, trigger bumps, and vibration of the train operation, and, in severe cases, lead to derailment accidents. It is an important index to test the roadbed disease. The specification is also commonly used in the surface displacement to monitor that the design of the roadbed is qualified. Excessive dynamic acceleration may cause fatigue damage to the roadbed material, while long-term buildup may cause cracking, loosening, and other roadbed disorders. Since the modulus of elasticity, angle of internal friction, and cohesion are used as input parameters in the simulation experiment, the unconfined compressive strength, surface settlement, lateral displacement, vertical displacement, lateral acceleration, vertical acceleration, and effective stress are chosen as evaluation indexes to ensure evaluation independence.

Figure 7 Evaluation index system of aeolian sand subgrade.
Figure 7

Evaluation index system of aeolian sand subgrade.

5.2 Calculation of indicator weights

In the real project, the assessment indicators are rated using the expert evaluation method [33], and the scale score between [0, 10] is calculated based on their importance to the variables considered in the roadbed design, and this is considered the data of the relevant indicators. Based on equation (2), the importance of the indicators is calculated as surface settlement, unconfined compressive strength, lateral displacement, lateral acceleration, vertical displacement, vertical acceleration, and effective stress, with the final weights being [0.281719, 0.281710, 0.047030, 0.033966, 0.136198, 0.083162, 0.136198] T . Equation (3) yields C R = 0.0419 < 0.1, indicating the model passes the required conditions (Figure 8).

Figure 8 Weight of evaluation indicators.
Figure 8

Weight of evaluation indicators.

5.3 Initial data of the test

The simulation test is carried out according to different sections of the roadbed, and the simulation results of the evaluation indexes are shown in Table 6.

Table 6

Simulated initial data

Experimental sequence number Evaluation index
Surface displacement (mm) Unconfined compressive strength (kPa) Lateral displacement (mm) Lateral acceleration (m/s2) Vertical displacement (mm) Vertical acceleration (m/s2) Dynamic stress (kPa)
1 0.038254 0.56 0.184738 0.027003 0.034650 0.099544 3.517328
2 0.034788 0.79 0.105767 0.029713 0.032896 0.103286 3.932547
3 0.034593 0.85 0.105773 0.030437 0.032751 0.103565 3.981740
4 0.034788 0.78 0.105767 0.029713 0.032896 0.103286 3.932547
5 0.034254 0.92 0.105422 0.031382 0.032493 0.103889 4.077386
6 0.034057 1.09 0.104986 0.031709 0.032342 0.103975 4.137598
7 0.034203 0.97 0.105326 0.031484 0.032454 0.103919 4.092687
8 0.033484 1.26 0.102691 0.031567 0.031892 0.103829 4.331942
9 0.033176 1.42 0.100081 0.030820 0.031783 0.103583 4.447083

5.4 Comprehensive evaluation of dynamic stability

Data are evaluated and processed by combining multiple data indications. Based on the baseline data from the simulation in Table 5, the judgment matrix X can be calculated statistically.

X =   0.038254 0.56 0.184738 0.034788 0.79 0.105767 0.034593 0.85 0.105773 0.027003 0.034650 0.099544 0.029713 0.032896 0.103286 0.030437 0.030437 0.103565 3.517328 3.932547 3.981740 0.034788 0.78 0.105767 0.034254 0.92 0.105422 0.034057 1.09 0.104986 0.029713 0.032896 0.103286 0.031382 0.032493 0.103889 0.031709 0.032342 0.103975 3.932547 4.077386 4.137598 0.034203 0.97 0.105326 0.033484 1.26 0.102691 0.033176 1.42 0.100081 0.031484 0.032454 0.103919 0.031567 0.031892 0.103829 0.030820 0.031783 0.103583 4.092687 4.331942 4.447083  

The acceleration index, dynamic displacement index, and dynamic stress index are all negative, while the unconfined compressive strength is positive. Using the TOPSIS method, the matrix X is normalized using equations (4) and (5), yielding the normalized matrix X 1.

X 1 = 0.000000 0.000000 0.000000 0.682599 0.267442 0.941731 0.721019 0.337209 0.941657 1.000000 0.000000 1.000000 0.424136 0.611711 0.155648 0.270156 0.662616 0.092536 1.000000 0.553410 0.500501 0.682599 0.255814 0.941731 0.787717 0.418605 0.945840 0.826493 0.616279 0.951050 0.424136 0.611711 0.155648 0.069419 0.752344 0.019405 0.000000 0.805259 0.000000 0.553410 0.397628 0.332867 0.797777 0.476744 0.946989 0.939369 0.813951 0.978410 1.000000 1.000000 1.000000 0.047789 0.766024 0.012704 0.030139 0.962007 0.033034 0.188775 1.000000 0.088519 0.381171 0.123840 0.000000

Determine the positive ideal solution Z + = {1, 1, 1, 1, 1, 1, 1, 1}, the negative ideal solution Z − = {0, 0, 0, 0, 0, 0, 0}, and then calculate the C i of each evaluation scheme to the ideal solution according to equation (8). The larger the C i , the better the ratio. The results are shown in Table 7.

Table 7

Program evaluation

Option Positive ideal solution distance Negative ideal solution distance Distance from solution to ideal solution Ranking Evaluation zone
1 0.864093 0.503316 0.368080 9 Poor stability
2 0.545865 0.542148 0.498292 7 Poor stability
3 0.530942 0.563294 0.514783 6 Good stability
4 0.550278 0.540565 0.495548 8 Poor stability
5 0.524604 0.604205 0.535259 5 Good stability
6 0.482684 0.667367 0.580293 3 Good stability
7 0.510154 0.620728 0.548888 4 Good stability
8 0.474623 0.780070 0.621722 2 Excellent stability
9 0.477118 0.865170 0.644549 1 Excellent stability

This study defines C i ∈ [0.6, 1] as outstanding roadbed stability. C i ∈ [0.5, 0.6] represents strong roadbed stability, while C i ∈ [0, 0.5] denotes poor roadbed stability. In conclusion, the 4:6 pulverized soil ratio and 6% cement dosing have the best overall stability, while the 3:7 pulverized soil ratio and 6% cement dosing are second best, but the stability is satisfactory.

5.5 Site selection

Traditionally, there are two primary objectives when building roadbeds: fulfilling mechanical criteria and minimizing construction costs. The design of the roadbed must meet the specification requirement that the bearing capacity of the part of the roadbed below the foundation bed be 250 kPa, whereas in the actual project, considering the local freezing and thawing environment, the unconfined compressive strength should be greater than 350 kPa to ensure sufficient stability. Furthermore, water content and compactness have a considerable impact on freezing rate; the lower the water content or the higher the compactness, the lower the freezing rate. Therefore, when designing material proportioning, it is vital to select the ideal water content to assure compaction while decreasing frost expansion rate in order to meet engineering performance and durability criteria. Figure 9 depicts the field monitoring of water content and unconfined compressive strength. After a thorough analysis and comparison, the optimal strategy is scheme 5> scheme 6> scheme 7> scheme 8> scheme 9> scheme 1, 2, 3, 4. As a result, in the building process of DK254+962- DK255+262, the subgrade of the foundation bed uses a cement mixing quantity of 5.4–5.9% and a pulverized soil proportion of 3:7 [34].

Figure 9 Tests of strength and moisture content in the field.
Figure 9

Tests of strength and moisture content in the field.

The image depicts a comparative examination of field preference, evaluation preference, and the field excitation test [35,36]. In comparison to other researchers’ studies, the simulated dynamic stress curve and the actual dynamic stress curve at the bottom layer of the roadbed are nearly identical [37], demonstrating the validity of this numerical simulation follow-up research effort. The settlement of scheme 8 is clearly smaller than that of scheme 5 chosen from the field test, and the gap is larger as the depth of the roadbed declines. The evaluation results presented in this research have a higher resistance to dynamic load damage than the field selection (Figures 10 and 11).

Figure 10 Comparison of settlement in situ and optimal ratio.
Figure 10

Comparison of settlement in situ and optimal ratio.

Figure 11 Rationality verification.
Figure 11

Rationality verification.

The full on-site examination is based on subjective expert judgment and combines with actual technical requirements, and the evaluation results are useful. In contrast, the quantitative examination examines the roadbed’s strength, deformation, shear resistance, and other critical indices under dynamic loading using dynamic stability and mechanical properties. Special emphasis is placed on dynamic loading performance, which is more in line with the actual operating conditions of high-speed rails with high mechanical property requirements. Experimental data are used to support the evaluation outcomes, ensuring their comprehensiveness and dependability.

5.6 Comparison of improvement effect

The effects of complete settlement and dynamic stress under train load on the roadbed as a whole are investigated, and the results are contrasted as follows.

Figures 12 and 13 depict the simulated horizontal profile cloud at Y = 30 m (0 ≤ Y ≤ 200) and longitudinal profile cloud at X = 50 m (0 ≤ X ≤ 100) with train load. The maximum cumulative vertical deformation value is located in the center of the dynamic load, the settlement amplitude gradually decreases with increasing distance, the lateral dynamic displacement along the roadbed is V-shaped, and the vertical deformation maps show a semi-elliptic distribution decreasing outward from the center. The dynamic stress distribution along the direction of train movement fluctuates periodically as a result of the action of the moving train load. As the depth of the roadbed increases, the settlement decreases and eventually reaches zero. With the direction of train movement, the front part of the roadbed is the first to absorb the impact and vibration of the wheels, and because the front section of the roadbed is concentrated in stress and subjected to vibration for an extended period of time, the settlement at the front end is more visible. From scenario 1 to scenario 9, the settlement of the roadbed beneath the train track varies dramatically, and the dynamic displacement effect range and amplitude rapidly decrease. Figure 14 depicts the specific distribution. In this roadbed cross-section, the highest settlement value of the roadbed fell from 2.0728 mm to 1.72913 mm, while the surface settlement induced by the train load was lowered by 0.35 mm. When the roadbed was selected at 1.6 mm, Scheme 1’s vertical deformation was 1.3 and 1.8 times that of Schemes 5 and 9, respectively.

Figure 12 Cloud map of displacement changes.
Figure 12 Cloud map of displacement changes.
Figure 12

Cloud map of displacement changes.

Figure 13 Dynamic stress cloud map.
Figure 13 Dynamic stress cloud map.
Figure 13

Dynamic stress cloud map.

Figure 14 Statistics of dynamic stress and dynamic displacement.
Figure 14

Statistics of dynamic stress and dynamic displacement.

The longitudinal profile of the roadbed at X = 50 m (0 ≤ X ≤ 100) shows that the largest dynamic stress is located in the railroad track below the railroad roadbed. The dynamic stress distribution under the action of the dynamic load was periodic fluctuations, with stress contours being wide and slow “bowl-shaped” distribution. The high stress area is focused in the graded gravel layer, and the stress diffusion speed varies in the roadbed’s bottom layer due to material ratio differences. As the roadbed depth increases, the dynamic stress approaches zero.

The statistics of the above cloud map reveal that the percentage of 1.5–2 mm settlement has decreased from 12.8 to 3.2%. The dynamic stress change range tends to be stable. To summarize, the improved system efficiently reduces the impact of vibration on the roadbed as a whole.

6 Discussion

6.1 Analysis of dynamic stability of roadbed and discussion of improvement scheme

The lateral displacement changes little as the cement admixture increases, and scheme 1 has a substantially bigger lateral displacement than the other schemes because the unconfined compressive strength does not fulfill the requirements. And when the cement concentration increases, both vertical and surface displacement decrease equally, indicating that cement doping aids in the reduction in roadbed settlement and stability. Figure 15 shows that the vertical displacement diminishes with increasing depth. As the proportion of pulverized soil increases, the trend of lateral displacement and vertical displacement is similar to that of cement incorporation, but the magnitude of change is smaller, indicating that pulverized soil incorporation has a smaller effect on dynamic displacement than cement incorporation. When comparing the effect of cement and pulverized soil on dynamic displacement, the best ratio is 6% cement and 4:6 silt.

Figure 15 Changes in dynamic displacement.
Figure 15

Changes in dynamic displacement.

As shown in Figure 16, the lateral and vertical accelerations of the roadbed subgrade under train loading change significantly, with the lateral acceleration being much smaller than the vertical acceleration, implying that the harm caused by the lateral movement of coarse particles under train loading will be less than the vertical acceleration. The dynamic acceleration response below the roadbed subgrade improves with the addition of pulverized soil at 4 and 5% cement dosage, but not at 6% cement dosage. The dynamic acceleration response decreases as the fraction of pulverized soil increases in 6% cement dosage. It demonstrates that different proportions have varied impacts on dynamic acceleration, i.e., dynamic acceleration is influenced by the material proportion, and dynamic acceleration is greatest when the material strength reaches a specific level.

Figure 16 Change in acceleration effect.
Figure 16

Change in acceleration effect.

Figure 17 depicts the trend of dynamic stresses below the roadbed’s subgrade with various ratios, and the dynamic stress response increases with the increase in pulverized soil and cement, indicating that both cement and pulverized soil admixture are incompatible with the stabilization of the dynamic stress response and the decay rate of the dynamic stresses. Cross-sectional comparisons revealed that the magnitude of change gradually increased with cement incorporation and was greater than the magnitude of change with the addition of pulverized soil, with a rate of change of 10.2% when the cement incorporation was changed and 5% when the pulverized soil ratio was changed.

Figure 17 Changes in dynamic stress below subgrade.
Figure 17

Changes in dynamic stress below subgrade.

In conclusion, the change rule of dynamic response of cement-improved sandy roadbed under train load is as follows: pulverized soil and cement have a reinforcing effect on dynamic displacement, which is unfavorable to the dynamic stress response of the roadbed sublayer, and the dynamic acceleration response is related to the strength of the roadbed material. Furthermore, the degree of influence of cement is greater than that of pulverized soil, and it is advised that the amount of crushed soil mixed be adjusted suitably to improve material performance.

According to the full evaluation and one-factor analysis of dynamic response, both are ideal at 6% cement and a 4:6 pulverized soil ratio. Yanjun and Wenhua [38] and Cui et al. [39] demonstrated that when cement doping reaches 6%, the surface structure becomes smoother and shows an obvious surface cementation stage, and increasing the proportion of cement doping significantly improves the cohesion and internal friction angle of the improved aeolian sand, as well as void filling, which improves the strength of the improved sand and the dynamic stability of the roadbed. The findings of this examination and research are consistent with the statements of various scholars, all of whom see 6% cement doping as an improved remedy for aeolian sand. Liu et al. [40] proposed that 20% powdered soil dosing is easy to compress using static triaxial testing, and electron scanning microscopy demonstrated that filling the holes between sand grains at 20% can improve cohesiveness and make compaction easier under compaction. However, excessive pulverized dirt might generate a too fine particle skeleton, increasing the soil’s compression deformation. Furthermore, an excessive amount of silt can adsorb a considerable amount of water, preventing the hydration reaction of cement, which is detrimental to the enhancement of material qualities. The sensitivity of the mix to water increases dramatically as the dosage of crushed soil increases, resulting in an increase in the specimen’s water content, greater free water lubrication between the particles, and increased elastic strain [41]. At the same time, controlling water content during construction is extremely challenging and will undoubtedly affect the project’s quality and progress [42]. The above Baoyin HSR site test, considering the local climate, frost expansion, and norms and standards, chose a 3:7 powder soil ratio. To summarize, the additional powder dirt increased the roadbed’s stability while negatively impacting field construction and elastic strain. Comprehensive on-site construction, on the basis of superior roadbed stability, the choice of 3:7 powdered soil is advantageous to the completion of on-site compaction, which should be more stable and convenient for option 8.

6.2 Comparison of existing assessment models

Figure 18 depicts a schematic diagram of the indicators covered by the bibliometric technique and the coding criteria, demonstrating that the indicators and statistical weights for both are nearly equivalent. The indications for detecting roadbed stability in the railroad design specification include the physical, mechanical, and environmental features of the roadbed. These indicators can be used to qualitatively examine the safety and longevity of railroad projects. The indicators screened using the bibliometric technique primarily investigate the stability of the roadbed from dynamics and material characteristics, which satisfies the specification criteria and provides a more accurate judgment on the dynamic stability of the roadbed under train loads. The bibliometric method has the advantages of objectivity, comprehensiveness, and visualization in screening evaluation indexes, with data-driven objectivity and relevance, which has strategic guiding significance for the construction of the evaluation index system of dynamic stability of roadbed in line with the design of high-speed railroad roadbed, and knowledge mapping has been widely used in index selection [43,44]. It indicates that this method can take into account multiple factors, and the rating index system is of guiding significance.

Figure 18 Comparison of evaluation indicators. (a) Specification requirement. (b) Literature research.
Figure 18

Comparison of evaluation indicators. (a) Specification requirement. (b) Literature research.

The reported progress ranking values were linearly fitted, and the slope value was used to explain the overall resolution level of the ranking findings, as shown in Figure [45]. It shows the evaluation findings and ranking fitting curves for each evaluation model. A comparative examination of the stability of aeolian roadbeds was conducted using the entropy value approach, the AHP-TOPSIS model, and gray connection theory, all of which are extensively utilized in contemporary roadbed evaluation and are suited for small samples and systems with limited information. The results show that the AHP-TOPSIS model has a high correlation with the ranking results of the entropy value method and gray relationship theory, and the evaluation results are highly consistent with each other, with both indicating that scenarios 8 and 9 are more stable roadbeds, indicating the proposed model’s reliability. The slope values of the linear fit of the evaluation model results are 0.028, 0.028, and 0.022, respectively, indicating that the mathematical evaluation model used in this study outperforms other mathematical evaluation models at the evaluation and resolution levels, making it more conducive to decision-making and judgment. Compared to other machine learning assessment approaches, its optimal model prediction is more accurate [46]. However, for small samples, machine learning introduces the issue of data bias, and there is an engineering risk of data distribution sensitivity, making it impossible to estimate the priority (Figure 19).

Figure 19 Correlation proximity fitting comparison.
Figure 19

Correlation proximity fitting comparison.

In summary, the method presented in this work integrates theories and methods from various disciplines into a comprehensive evaluation to become a development trend, which can improve the scientific nature of the method, meet the advantages of comprehensiveness, foresight, and high resolution, and is applicable to the quantitative analysis of roadbeds. It aids in resource optimization, error reduction, and result credibility, and the assessment results can be used to construct a cement-improved aeolian sand high-speed railway roadbed.

7 Conclusion

Based on existing evaluation indexes for aeolian sand roadbeds, this study proposes a strategy for optimizing the proportioning of cement-improved aeolian sand roadbeds. The model is used to assess the proportioning scheme for cement-improved sandy roadbed and optimize the proportioning parameters. The primary conclusions are as follows:

  1. A three-level index system for sandy roadbed stability was developed using the hierarchical analysis method and knowledge mapping principles. The evaluation indexes impacting roadbed stability are divided into two categories: mechanical indexes and dynamic reaction indexes, with surface settlement and unconfined compressive strength having the largest weight and serving as the project’s primary monitoring indices.

  2. Using a finite element model, this study examines the impact of cement and pulverized soil on improved soil roadbeds and concludes that pulverized soil and cement have a reinforcing effect on dynamic displacement, which is not conducive to the dynamic stress response, and that the dynamic acceleration response is related to the strength of roadbed material. Cement exerts a greater impact than pulverized earth does.

  3. A comprehensive evaluation of the roadbed using the AHP-TOPSIS method is proposed by synthesizing the various indexes above, and it is concluded that 4:6 pulverized soil ratio and 5% cement mixing are the best for comprehensive stability, with a 5% improvement in stability, but 3:7 pulverized soil ratio and 6% cement mixing are favorable for both field construction and stability. The suggested model’s evaluation findings are consistent with the real project, demonstrating the model’s reliability and the stability of the project roadbed. The research results provide data support for the simulation of aeolian sand and the design of aeolian sand improved soil, offering new ideas for subgrade evaluation

  1. Funding information: This work was supported by Major project of China Railway Beijing Engineering Group Co., Ltd (Grant No.2023A-Major project-005)，National Natural Science Foundation of China (Grant No. 42277187), and the Basic Research Program of Natural Sciences of Shaanxi Province (Grants No. 2022JM-280).

  2. Author contributions: The order of authors of this article is: Yonggang Wang, Hui Wang, Guangying Yuan, Kexin Ren, Xunchang Li, and Wei Yang. Yonggang Wang and Hui Wang Guangying processed the data and wrote the article. Yuan completed the experiment. Kexin Ren conducted experiments and data processing, and revised the article. Xunchang Li helped complete the experiment and revise the article. Wei Yang proposed the idea of the experiment and revised the article.

  3. Conflict of interest: The authors state no conflict of interest.

  4. Data availability statement: The data underlying this article will be shared on reasonable request to the corresponding author.

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Received: 2025-05-28
Revised: 2025-07-15
Accepted: 2025-08-18
Published Online: 2025-10-09

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/geo-2025-0884
Keywords for this article
cement aeolian sand; dynamic response; railway subgrade; evaluation
Creative Commons
BY 4.0

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