Next Article in Journal
A Comprehensive Study on the Challenges of Using Pure Water Jet as Post-Treatment of Abrasive Water Jet Milled Pockets in Titanium Alloy
Previous Article in Journal
Intelligent Healthcare Platform for Diagnosis of Scalp and Hair Disorders
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Applied Sciences
Volume 14
Issue 5
10.3390/app14051740
applsci-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Numerical Analysis of Differential Settlement in Road Due to Widening Considering Different Reinforcement Techniques

by
Shaista Jabeen Abbasi
1,*,
Xiaolin Weng
1 and
Muhammad Jawed Iqbal
2
1
School of Highway, Chang’an University, Xi’an 710064, China
2
National Institute of Transportation (NIT), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan
*
Author to whom correspondence should be addressed.
Appl. Sci. 2024, 14(5), 1740; https://doi.org/10.3390/app14051740
Submission received: 25 November 2023 / Revised: 13 February 2024 / Accepted: 17 February 2024 / Published: 21 February 2024
(This article belongs to the Section Civil Engineering)
Browse Figures
Versions Notes

Abstract

:
Embankment and pavement widening of an existing road is a viable option to cope with increased traffic volume. One of the common challenges in road expansion is the occurrence of differential settlement between the old and the new portions. This article pertains to the field case study of the National Highway-120, where pavement distresses developed in the weak sections of the highway following the operation of traffic within a few months. Field monitoring and geotechnical tests, including the requisite in situ as well as laboratory tests, were conducted on soil specimens from the study area, followed by the performance of a numerical analysis using the two-dimensional finite element software Abaqus CAE 2021 to investigate the weak section of the road. Different techniques such as geogrid reinforcement, installation of cement–fly-ash–gravel (CFG) piles, and lightweight foamed concrete (LWFC) embankment fill were used to analyze the reduction in differential settlement between the old and the widened portions. Among the applied reinforcement techniques, the use of LWFC as embankment fill in the widened portion was determined to be most effective in minimizing the differential settlement in the weak section of the highway.

1. Introduction

Green highways are a current trend in the construction of sustainable development projects [1]. The construction of a new road disturbs the lives of people and animals along the route of the road [2]. Historical data indicate that each additional mile of interstate highway reduces agricultural land [3]. However, the growth of highway transportation is necessary for the economic and social development of a country [4]. Therefore, the rehabilitation, widening, and addition of new carriageways in old roads are important to maintain the level of service (LOS). In road widening projects, most deformations in the embankments develop due to differential settlement between the old and widened portions [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. The impact of traffic load on the widened portion of the road is more dominant than the volume [23,24]. In road widening, the subgrade of the new road is more affected by the dynamic load than the old road subgrade [9]. Differential settlement ultimately develops due to expansion of the road [25], which increases and decreases later [26]. The differential settlement increases with increasing groundwater level and subgrade height [27]. The differential settlement creates a soil arching effect in the embankments [28], which is higher at the edge of the slope than at the centerline [29]. Aiming at the above-mentioned issue, this research is based on the road widening project of National Highway-120 (N-120), Sindh, Pakistan. In particular, the study is focused on the weak sections of N-120, where differential settlement developed and caused pavement failures.
The characteristics and progression of settlement because of road widening construction activities have been examined through small- and large-scale model tests [9,30], centrifuge tests [11,31], numerical modeling [12,14,17,27,32,33,34,35,36,37], and field tests [20]. As differential settlement develops in the middle of the embankment, transverse cracks simultaneously appear at the surface [38]. The self-weight of the widened embankment and pavement creates uneven settlement above weak road foundations, which consequently causes cracks in the pavement structure [21]. Failures appear in the pavement layers in the form of spalling, loose binders, changes in the horizontal slope of the road, and longitudinal cracks at the junction of the old and widened portions of the road constructed on weak soils [39]. Vehicle speed, traffic load area, and temperature contribute to the load rate on the asphalt layers [40]. It is pertinent to mention that the mid-pavement-layer strains are more significant than in the top layers [21]. Shear and transverse tensile strains are more sensitive to fluctuations in contact pressure than longitudinal tensile strains at the bottom of asphalt concrete [41]. For the maintenance and construction of weak sections in road widening projects, the study of the mechanism of differential settlement is necessary because the joint between the old and widened portions of the road needs to be strengthened by necessary remedial measures.
Several techniques are applied to enhance subgrade performance when it is necessary to construct over weak soils [9]. The research outcomes show that reinforcement is crucial at the junction of old and widened portions of roads for compaction and reduction of differential settlement [7,9,15,30,38]. Pile-supported embankments are now widely used in foundation treatments because of their cost, safety, and simple construction [42]. Several research projects have aimed to produce new sustainable construction materials, especially lightweight concrete, to move toward sustainable construction [43]. The effective use of geosynthetic products as soil reinforcement was identified in the 1970s [44]. Considering the features of the project, three reinforcement techniques are selected for analysis in this study. First, geogrid reinforcement is widely used, which increases the resilience modulus of the subgrade and reduces inhomogeneous deformation. The geogrid makes the stress and strain distributions uniform in the pavement under the effect of traffic loads [9]. The outcome is greatly improved when more layers of geogrid reinforcement are added [12,45,46]. Cement–fly-ash–gravel (CFG) piled embankments are another successful reinforcement technique for the construction of weak sections at road transitions [47,48]. Thirdly, the lightweight foamed concrete (LWFC) embankment fill technique can minimize differential settlement and provide connectivity between old and widened portions of the road [34,44,49]. The light filling materials are approximately one-third of the density of conventional soils [1], and they need more research before their extensive use [33]. National Highway-120 (N-120), Sindh, Pakistan, is a unique project due to the field conditions, soil types, traffic load variations, and increasing effects of climatic change. The key objectives of the study are (i) to conduct field monitoring to understand the project features, (ii) to conduct field and laboratory soil tests for the weak road sections for further analysis of differential settlement, (iii) to investigate the effect of load variations by numerical analysis using the Abaqus CAE 2021 software without and with reinforcement techniques.
The applicability of the numerical simulation is verified, as the settlement deformations calculated by both the model and numerical analysis are highly similar [20,50,51]. The findings of the centrifugal model tests and the numerical simulations coincide well, and the research can be used as a solid scientific basis for designing and optimizing highway widening projects [38,52]. Under the widening process in road projects, it is crucial to investigate post-construction differential settlement [27] and the mechanism of pavement deformations [32]. This study has the potential to draw the attention of a wider audience from academic and road construction project teams in terms of understanding the approach to the determination of software parameters in the field and laboratory and their use in numerical analysis applications. In general, this numerical technique can be helpful in many real-world contexts and quickly solve various related [53] issues. This is important when infrastructure development planning, design, and construction stages sometimes require extensive prediction techniques. In addition, the simulation of road widening projects using the Abaqus software will open new doors for future studies in similar regions.

2. Methodology

The methodology of this study is outlined below:
(a)
The literature related to the mechanism of differential settlement and treatment techniques was analyzed.
(b)
For this research, field surveys were conducted to study the settlement in the already-completed pavement. Subsequent site visits were conducted to investigate soil, topography, traffic patterns, and pavement distresses.
(c)
A geotechnical investigation of the soil was conducted. Samples were collected from test pits and boreholes; three main test pits for the foundation (natural ground), the old road, and the new road (widened portion) with loose clayey soils were identified. Moreover, the direct shear test was performed to calculate the shear strength properties of three identified soil samples.
(d)
Using the finite element software Abaqus CAE 2021, the interaction between the old and new road portions was established.
(e)
To explore the settlement features under various circumstances, several models for 2D simulation were established for analysis. For a detailed study, a weak section of the highway was selected for numerical model validation.
(f)
Reinforcement techniques in the embankment widening to control differential settlement in the pavement structure were used to evaluate the effect of the techniques, such as geogrid reinforcement and installation of CFG piles, separately and in combination. In addition, lightweight foamed concrete (LWFC) was used as a soil replacement in the widened portion of the road.

3. Brief Project Description

National Highway-120 (N-120) is one of the significant routes of the national high-way network of Pakistan; the location of the project is displayed in Figure 1. The N-120 was formerly a provincial highway that was federalized and handed over to the jurisdiction of the National Highway Authority (NHA), Pakistan. The traffic volume on the highway increased due to the commencement of the Thar Coal power plant initiated under the China–Pakistan Economic Corridor (CPEC) program. Therefore, rehabilitation and widening of N-120 were officially started to prevent traffic congestion. As per the widening plan, the width of the embankment and pavement was increased on both sides of the carriageway of N-120. The layout plan is shown in Figure 2.
When some completed road sections were opened for traffic movement, significant cracks and deformations appeared on the pavement surface due to the development of differential settlement in the embankment, as shown in Figure 3, Figure 4, Figure 5 and Figure 6. During the field inspection the deformations were investigated, and it was observed that many contributing factors may have caused the differential settlement. First, the route of the road passes through flat terrain, due to which rainwater accumulates along the road and gradually infiltrates into the embankment. Secondly, an unlined water channel flows parallel to some road sections, resulting in seepage in the embankment. Third, a more critical factor is uncontrolled, heavily loaded traffic using this road.

4. Geotechnical Investigation

The geotechnical investigation was carried out to evaluate the properties of the soil material in the foundations of the old and new roads. Considering the pavement problems, the road sections from Km 9+000 to Km 38+000 were selected for detailed field and laboratory investigations. Both undisturbed and disturbed soil samples were collected from eleven test pits and one borehole. Three main test pits were identified for the foundation, old, and new roads with loose soils. The bulk density, specific gravity, void ratio, and permeability of the collected samples were determined as per ASTM standards. In addition, the moisture content was noted using a speedy meter, and then, by laboratory testing.
Moreover, to calculate the shear strength properties, direct shear tests were performed as per ASTM D3080 [54]. The direct shear tests were carried out at varying normal stresses under controlled conditions. The test was performed by deforming a specimen at a controlled strain rate on or near a single shear plane determined by the configuration of the apparatus. At least three or more specimens were tested, each under a different normal load, to determine the effects upon shear resistance and displacement [54]. The bearing capacity values were also derived from the shear strength parameters using Terzaghi’s equation.
It was observed from the field observations and laboratory test results that the foundation soil consists of well-distributed gray-colored cohesive clayey soils up to twelve meters below the ground surface. The locations of the three primary samples of the soil from the pavement surface are shown in Figure 7, and the soil condition along the road is shown in Figure 8. Some of the soil testing results are shown in Table 1. The soil properties of the foundation were the same throughout the selected weak road sections. Also, the groundwater level was measured about two meters below the excavated ground surface, but some locations were waterlogged. It was further observed that natural ground and new subgrade showed a cohesion intercept. Strain hardening behavior was observed in all the soil tests, possibly due to high soil moisture content and a relatively loose state. Table 1 shows that the bearing capacities of the foundation and old road are higher than the bearing capacity of the new road.
The moisture content was measured at ten locations near Km 9+000, Km 16+200, Km 23+050, Km 28+200, Km 34+000, and Km 38+000, and the results are shown in Table 2. The type of soil is mainly clayey at all the locations. At Km 38+000, the moisture content is highest for the foundation soil on the left side. On the other hand, at Km 28+200, the moisture content is lowest for the foundation soil on the left side. At Km 38+000, the moisture content for the new road is lowest compared to the moisture content measured at the same location, and this is because the soil sample has been borrowed to use as subgrade material.
The direct shear test results are shown in Figure 9 and Figure 10. The shear stress, shear displacement, and vertical height curves are plotted for the foundation, new road, and old road in Figure 9. Three soil samples were tested at three normal stresses: 104 kPa, 212 kPa, and 300 kPa. It is shown in Figure 9a that in the soil specimen of the foundation soil, the shear stress attains a peak value of approximately 219 kPa at the normal stress of 300 kPa. With further increases in normal stress the shear stress becomes constant. In contrast, the shear stress attains peak values of 92 kPa and 167 kPa at normal stresses of 104 kPa and 212 kPa, respectively. The maximum stress increases by 70% when the normal stress is increased from 104 kPa to 300 kPa. Figure 9a also shows the shear stress and shear displacement behavior of the soil sample at three normal stresses: 104 kPa, 212 kPa, and 300 kPa. Figure 9a shows that for the foundation, at the maximum vertical height of 9.1 mm, the maximum shear displacements are 0.37 mm, 0.72 mm, and 0.64 mm at 104 kPa, 212 kPa, and 300 kPa, respectively.
It is shown in Figure 9b that for the three soil specimens from the new road the shear stress attains a peak value of approximately 217 kPa at a normal stress of 300 kPa. With a further increase in normal stress, the shear stress is constant. In contrast, the shear stress attains peak values of 93 kPa and 164 kPa at normal stresses of 104 kPa and 212 kPa, respectively. The maximum stress increases by 57% when the normal stress is increased from 104 kPa to 300 kPa. Figure 9b shows that for a new road at 104 kPa the vertical height is 0.063 at a shear displacement of 2.7 mm. After that, the vertical height is constant. Figure 9b shows that for a new road at 212 kPa normal stress, 0.69 mm is the vertical height and the shear displacement is 8.5 mm. The trend in the curve shows that the vertical height is directly proportional to the shear displacement. Figure 9b shows that for a new road at 300 kPa normal stress, 0.525 mm is the vertical height at a shear displacement of 6.9 mm. After 6.9 mm, the vertical height is constant.
It is shown in Figure 9c that for the three soil specimens from the old road the shear stress attains a peak value of approximately 119 kPa at a normal stress of 300 kPa. With further increases in the normal stress the shear stress is constant. In contrast, the shear stress attains peak values of 56 kPa and 122 kPa at normal stresses of 104 kPa and 212 kPa, respectively. The maximum stress increases by 70% when the normal stress is increased from 104 kPa to 300 kPa. Figure 9c shows the old road at 104 kPa normal stress, with 0.49 mm as the vertical height at a shear displacement of 9.1 mm. The trend in the curve shows that the vertical height is directly proportional to the shear displacement. Figure 9c shows that for the old road at 212 kPa normal stress, 0.63 mm is the vertical height and the shear displacement is 9.1 mm. The trend in the curve shows that the vertical height is directly proportional to the shear displacement. Figure 9c shows that for the old road at 300 kPa normal stress, 0.56 is the vertical height and the shear displacement is 9.1 mm. The trend in the curve shows that the vertical height is directly proportional to the shear displacement.
The shear strength is a linear function of the normal stress. Figure 10 shows the shear stress and normal stress values of the foundation, as well as the old and new subgrade specimens. Figure 10 shows that the angles of internal friction of the foundation and old road specimens are similar. The cohesion of the foundation and the new road is 20 kPa and 25 kPa, respectively. However, cohesion for the old road is zero, and its friction angle is 28.8 degrees.

5. Numerical Analysis

In this study, numerical analysis was carried out for both reinforced and unreinforced models integrated into Abaqus CAE version 2021. The main objective of this parametric study was to examine the development of differential settlement and to evaluate the traffic load transfer mechanisms between soil and different reinforcement techniques.

5.1. Geometry of the Numerical Model

The cross-section and dimensions for the numerical model used for this parametric study are presented in Figure 11. The centerline of the old road is considered to be one-half of the roadway because of the symmetry of the finite element model. The height of the foundation used in this model is 4 m. The pavement thickness is 0.45 m; therefore, the thickness used for the embankment soil layers is also 0.45 m, with a slope of 1:2 for step excavation. Step excavation in the model geometry is helpful for smooth software analysis and meshing with the least number of errors.

5.2. Modeling Procedure

Numerous geotechnical issues are addressed with the Mohr–Coulomb model (MC model) as it only needs a small number of input parameters that may be obtained by laboratory experiments [55]. The Mohr–Coulomb (MC) model is widely used in the numerical modeling of embankments [56]. The MC model is suitable for sand as well as clay [57]. Therefore, the Mohr–Coulomb model, a perfect plastic model for analyzing such soils, was employed here for subgrade, and foundation. The material properties are shown in Table 3.
In this study, the numerical analysis was carried out for the road section at Km 38+000 using the Abaqus CAE 2021 software using reinforced and unreinforced cases. In this analysis, the vertical deformations were calculated for the new road during one year of construction and nine years of operation. The construction phases of the new and old roads were not considered, and it was assumed that consolidation of the old road had already been completed. The finite element model was set so as to make it an actual representation of N-120. In the numerical analysis, the old road plus the foundation was considered part 1 and the new road part 2 in the Abaqus software environment. The overall analysis progress was divided into three steps. The old road was set to be active since the geostatic phase, and the widened part was set to be active since the first year of operation. The boundary conditions and traffic loads are shown in Figure 12. The bottom of the model was constrained for horizontal and vertical displacement. The horizontal displacement was limited for the left and right vertical sides of the model. Geostatic stresses were created in the geostatic step. The gravity load was applied on the new road, and the traffic load was applied since the geostatic step on the old road surface and in the second step on the new road surface.
The numerical analysis used a 4-node plane strain quadrilateral, bilinear displacement, and bilinear pore pressure (CPE4P) for parts 1 and 2, as described above. The mesh size of the element used was 0.2 for both parts having quad and structured shapes. The mesh density for part 1 was 2252 elements with 0% errors. The mesh density for the new road was 197 elements, with 0% errors and 10% warnings. The unreinforced model was the basis; therefore, geogrid was considered part 3 and CFG piles as part 4 in the remaining cases for parametric study. The geogrid was modeled in a 4-node bilinear plane strain quadrilateral, reduced integration unit in Abaqus (CPE4R). The CFG piles with a diameter of 0.5 m [18] were modeled in a 4-node bilinear plane stress quadrilateral, reduced integration (CPS4R). The mesh element shape was quad and structured, and the element size used was 0.2 units for both geogrid and CFG piles. Mesh density analysis was carried out, according to which geogrid and CFG piles have 86 and 60 elements, respectively, with 0% analysis errors. The interaction of geogrid and CFG with the soil was set to be active in step 3. For numerical analysis, the surface-to-surface interaction property was used between part 1 and part 2 with hard contact type and friction, as shown in Figure 13. The geogrid and CFG piles were embedded as constraints in the modeling process. Further case settings are displayed in Figure 14.

6. Results and Discussion

6.1. Untreated Road Section

Various approaches and load magnitudes are used in different parts of the world to codify traffic loads. In China, 20 kPa and 40 kPa are used for light and heavy traffic, respectively [58]. The same are used in this study to simulate the traffic loading. The final settlements are shown in Figure 15, Figure 16 and Figure 17 at the unique nodes at traffic loadings of 20 kPa, 40 kPa, and 80 kPa, respectively; the settlement progressed in the first year and continued to increase to 3600 days with a slowing rate. Figure 15 depicts the final settlement after nine years of operation. The maximum value of the settlement at 20 kPa is approximately 1 mm, 2 mm, and 4.5 mm at the center, 1.2 m, and 2.4 m away from the center, respectively. Figure 16 shows the maximum value of the settlement in the road at 40 kPa, which is approximately 1.5 mm and 4.5 mm at the center of the existing road surface and 2.4 m away from the center, respectively. But, on the same load at the toe of the old road, the maximum settlement is 83% higher than the top center of the road, which shows that the subgrade settlement increases in the soil layer with increasing depth due to the location of the settlement point. Figure 17 illustrates that at the traffic load of 80 kPa, the final settlement on the surface of the road is 4.5 mm and 20 mm at the center and 4.7 m away from the center, respectively. It is evident that the maximum settlement increases by 77% when the traffic load increases from 20 kPa to 80 kPa.
Figure 18 shows changes in the vertical displacement at the pavement surface at traffic loads of 20 kPa, 40 kPa, and 80 kPa. The graph shows that the widened portion of the road, under increasing traffic load, has exerted additional stresses on the foundation, which has increased the deformation characteristics of the road. It can also be noticed that the traffic load variations have a high effect on existing road settlement. It can be noticed that the final settlement is higher on the new road pavement surface than on the old road pavement surface. Also, the settlement of new roads has increased more rapidly at the junction of the old and new road pavement surfaces, and this is because of the fresh stresses developed at the joint due to the disturbance of the soil envelope at this location. Figure 18 shows that at 20 kPa, the maximum settlement is 10 mm, and at 40 kPa, the maximum settlement percentage increase is 23%. On the other hand, the maximum settlement at 80 kPa is 18.5 mm, which is 45% more than the maximum settlement at 20 kPa. It can be noticed that at 20 kPa, the settlement at the old road centerline is about 1.8 mm, and at the shoulder of the new road is about 8.5 mm, showing an uneven or differential settlement of 6.7 mm.
Figure 19 shows the variation in differential settlement on the foundation surface at traffic loads of 20 kPa, 40 kPa, and 80 kPa. The trend in the settlement curves is like a trench, which shows that the settlement at the old road foundation is less than at the new road foundation. The settlement gradually increases until it attains a maximum value at the edge of the new shoulder. At 20 kPa, the final settlement on the surface of the foundation is approximately 6.5 mm, and with a 73% increase, the minimum settlement is 1.5 mm. At the traffic loads of 40 kPa and 80 kPa, the maximum settlement on the foundation of the existing embankment increases by 72% and 71%, respectively. There is an increase of 53% in the settlement developed under the loadings of 20 kPa and 80 kPa. It can be noticed that the differential settlement is 4.7 mm, 6 mm, and 8.5 mm at 20 kPa, 40 kPa, and 80 kPa traffic loads, respectively. The results show that the differential settlement is directly proportional to the magnitude of the traffic loading. The settlements in Figure 18 and Figure 19 show that the foundation and pavement settlements are directly proportional. Therefore, controlling differential settlement at the foundation surface in the weak road section can prevent pavement deformations.

6.2. Calibration of Numerical Model

The settlement developed in the section under study, as shown in Figure 19, was measured during field monitoring at Km 38+000. The measured settlement was closer to the estimated settlement at a traffic load of 40 kPa. The analysis shows that the increase in traffic load is directly proportional to the differential settlement. Further numerical analysis was carried out in this study, in which the reinforcement techniques were applied at the subgrade and foundation of weak road sections.

6.3. Parametric Study

For further analysis, 20 kPa traffic load was considered as the base value for the soil reinforcement techniques. Figure 20 and Figure 21 show the settlement on untreated and treated foundation surfaces under the 20 kPa traffic load application. It is observed that there is a 2% decrease in the maximum settlement in case A, case B, and case C as compared to the untreated foundation. However, in case D, it can be observed that due to LWFC embankment fill material, the final settlement has decreased by 35%. It can be noted that the locations of the points with the maximum settlements change with the treatment techniques. For further analysis, traffic load variations of 5 kPa, 10 kPa, 20 kPa, and 40 kPa were applied on the roadway for case D. Figure 22 shows the effects of the LWFC under traffic load variation. It is noted that the increasing traffic loads have a significant effect on the maximum settlement. It increases by 58% when the load is increased from 5 kPa to 40 kPa.

7. Discussion

Simulation of the actual road cross-section of the project was a challenging task. Several other critical features of the project need to be analyzed. For example, a water canal flows parallel to some road sections. Potential hazards of overflowing the water channel due to heavy rain flooding could also be considered for further numerical analysis. The speed of the vehicles, pavement type, and roadway width are essential parameters that need to be considered for detailed research in the analysis of differential settlement in road widening projects. This article provides a reference for further research on the diverse aspects of road widening construction. This work could help further explore this research using the latest machine learning tools.

8. Conclusions

The importance of road widening has increased as the construction of entirely new roads causes disturbance in the lives of humans and disruption of land and environment. However, differential settlement develops due to the widening of old embankments over weak sections of roads. Such problems have not previously been presented in detail in terms of a geotechnical investigation and the prediction of differential settlement under load variations. This research study has presented an insight into the N-120 project in the Sindh province of Pakistan as a case study. In this work, input parameters for numerical analysis in the Abaqus software are calculated by geotechnical investigation. In this study, two-dimensional finite element software is used to investigate the mechanism of differential settlement in widened embankments with and without the application of different treatment techniques. Traffic loading highly influences the differential settlement; therefore, the final settlements are studied under the traffic load conditions of 20 kPa, 40 kPa, and 80 kPa. Some conclusions can be drawn as follows:
i.
It is evident that the maximum settlement increases, without applying the reinforcement, by 77% when the traffic load increases from 20 kPa to 80 kPa.
ii.
The foundation and pavement settlements are directly proportional. Therefore, controlling differential settlement of the foundation surface in the weak road section can prevent pavement deformations.
iii.
Application of geogrid and cement–fly-ash–gravel (CFG) pile reinforcement can reduce inhomogeneous deformation of the subgrade.
iv.
The differential settlement due to road widening is considerably reduced by the use of lightweight foamed concrete (LWFC) as embankment fill in the widened portion. The final settlement decreased by 35% due to the use of lightweight foamed concrete (LWFC) as embankment fill in the widened portion at a 20 kPa load.

Author Contributions

Conceptualization, S.J.A. and X.W.; data curation, S.J.A.; formal analysis, S.J.A.; investigation, S.J.A., X.W. and M.J.I.; methodology, S.J.A. and X.W.; project administration, S.J.A., X.W. and M.J.I.; resources, X.W.; software, S.J.A. and X.W.; supervision, X.W. and M.J.I.; validation, S.J.A.; visualization, S.J.A.; writing—original draft, S.J.A.; writing—review and editing, X.W. and M.J.I. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data will be available with Shaista Jabeen Abbasi at 2019021903@chd.edu.cn. Content related details will be provided on request.

Acknowledgments

We appreciate the support, input, and motivation from our teachers and friends from China and Pakistan. We acknowledge Highway Research and Training Institute (HRTC), Burhan, Pakistan; Research Institute of Highway, Ministry of Transport, China; China Road and Bridge Cooperation (CRBC), Beijing, China; Chang’an University, Xi’an, China; National University of Sciences and Technology (NUST), Islamabad; National Highway Authority (NHA), Pakistan; Laboratory of Quaid e Awam University of Engineering Sciences and Technology (QUEST), Nawabshah, Sindh, Pakistan to facilitate execution of this research.

Conflicts of Interest

The authors declare no conflicts of interest.

References

  1. Zhang, H.; Ning, X.; Wang, F.; Zhong, L. Application analysis of green highway design in highway reconstruction and expansion project. “Resid.” Issue 2023, 5, 82–84. Available online: https://www.cnki.com.cn/Article/CJFDTOTAL-SJCZ202305028.htm (accessed on 1 September 2022).
  2. Spellerberg, I.F.; Morrison, T. The Ecological Effects of New Roads: A Literature Review. Available online: https://researcharchive.lincoln.ac.nz/handle/10182/1837 (accessed on 1 September 2022).
  3. Mothorpe, C.; Hanson, A.; Schnier, K. The impact of interstate highways on land use conversion. Ann. Reg. Sci. 2013, 51, 833–870. [Google Scholar] [CrossRef]
  4. Sha, A.; Ma, B.; Wang, H.; Hu, L.; Mao, X.; Zhi, X.; Chen, H.; Liu, Y.; Ma, F.; Liu, Z.; et al. Highway constructions on the Qinghai-Tibet Plateau: Challenge, research and practice. J. Road Eng. 2022, 2, 1–60. [Google Scholar] [CrossRef]
  5. Weng, X.; Nie, Y.; Lu, J. Strain Monitoring of Widening Cement Concrete Pavement Subjected to Differential Settlement of Foundation. J. Sens. 2015, 2015, 679549. [Google Scholar] [CrossRef]
  6. Huang, X.; Wang, H. Comparison between responses of reinforced and unreinforced embankments due to road widening. J. Cent. South Univ. Technol. 2009, 16, 857–864. [Google Scholar] [CrossRef]
  7. Hu, Y.; Li, H.; Wang, X.; Wang, Q.A.; Zhang, X. Application of Geogrid in Widening Highway Embankment. In ICCTP 2011: Towards Sustainable Transportation Systems, Proceedings of the 11th International Conference of Chinese Transportation Professionals (ICCTP), Nanjing, China, 14–17 August 2011; ASCE Library: Reston, VA, USA, 2011. [Google Scholar] [CrossRef]
  8. Wang, Y.M.; Yi, H.; Li, Q.Z. Model Tests on Working Performance of Geogrid Reinforcement Influenced by Differential Settlement. Adv. Mater. Res. 2011, 255–260, 3376–3381. [Google Scholar] [CrossRef]
  9. Weng, X.; Wang, W. Influence of differential settlement on pavement structure of widened roads based on large-scale model test. J. Rock Mech. Geotech. Eng. 2011, 3, 90–96. [Google Scholar] [CrossRef]
  10. Weng, X.L.; Zhang, L.J.; Wang, W. Research on the Treatment for Water Damage to Widened Subgrade of Collapsible Loess Based on Centrifuge. Appl. Mech. Mater. 2011, 99–100, 821–825. [Google Scholar] [CrossRef]
  11. Zhang, J.; Zheng, J.; Huang, X. Centrifuge Model Test and Numerical Analysis of Geosynthetic-Reinforced Embankments for a Road Widening. In Road Pavement and Material Characterization, Modeling, and Maintenance, Proceedings of the GeoHunan International Conference 2011, Hunan, China, 9–11 June 2011; ASCE Library: Reston, VA, USA, 2011. [Google Scholar] [CrossRef]
  12. Chen, M.Y.; Liu, Y.; Shi, H.L.; Chen, R.; Yuan, B.X. Numerical Analysis of Widened Embankments with Geogrid Reinforcement. Appl. Mech. Mater. 2013, 256–259, 2004–2008. [Google Scholar] [CrossRef]
  13. Liu, J.L.; Wang, D.L. Influence of Width of Widened Part in Road Engineering. Appl. Mech. Mater. 2013, 341–342, 1445–1448. [Google Scholar] [CrossRef]
  14. Yang, L.; Zheng, L. Numerical Analysis for Steps Excavation Schemes of Old Embankment in Highway Widening Engineering. In ICTE 2013: Safety, Speediness, Intelligence, Low-Carbon, Innovation, Proceedings of the Fourth International Conference on Transportation Engineering, Chengdu, China, 19–20 October 2013; ASCE Library: Reston, VA, USA, 2013. [Google Scholar] [CrossRef]
  15. Miao, L.; Wang, F.; Han, J.; Lv, W. Benefits of geosynthetic reinforcement in widening of embankments subjected to foundation differential settlement. Geosynth. Int. 2014, 21, 321–332. [Google Scholar] [CrossRef]
  16. Weng, X.; Zhu, H.-H.; Chen, J.; Liang, D.; Shi, B.; Zhang, C.-C. Experimental investigation of pavement behavior after embankment widening using a fiber optic sensor network. Struct. Health Monit. 2014, 14, 46–56. [Google Scholar] [CrossRef]
  17. Tang, L. Numerical Analysis of Uncoordinated Deformation in Highway Subgrade Widening. IOP Conf. Ser. Earth Environ. Sci. 2020, 474, 072027. [Google Scholar] [CrossRef]
  18. Yu, H.; Wang, Y.; Zou, C.; Wang, P.; Yan, C. Study on Subgrade Settlement Characteristics after Widening Project of Highway Built on Weak Foundation. Arab. J. Sci. Eng. 2017, 42, 3723–3732. [Google Scholar] [CrossRef]
  19. Lan, T.; Wang, J. Settlement Prediction and Differential Settlement Criterion for Heightening and Thickening Levee. Appl. Sci. 2018, 8, 2392. [Google Scholar] [CrossRef]
  20. Wei, J.; Song, Z.; Bai, Y.; Liu, J.; Kanungo, D.P.; Sun, S. Field Test and Numerical Simulation for Coordinated Deformation of New Subgrade and Old Embankment Adjacent to River. Appl. Sci. 2018, 8, 2334. [Google Scholar] [CrossRef]
  21. Yu, H.; Wang, Y.; Chen, Y. Causes of cracking of an existing pavement after highway widening in an area of soft soil. Proc. Inst. Civ. Eng.-Transp. 2022, 175, 168–177. [Google Scholar] [CrossRef]
  22. Lu, L.; Ma, S.; Wang, Z.; Zhang, Y. Experimental study of the performance of geosynthetics-reinforced soil walls under differential settlements. Geotext. Geomembr. 2021, 49, 97–108. [Google Scholar] [CrossRef]
  23. Wang, C.; Chang, J.; Cai, G.; He, H.; Liu, S.; Wang, M.; Wu, M. Numerical simulation of the subgrade settlement of highway expansion based on CPTU data. Int. J. Geotech. Eng. 2023, 17, 541–552. [Google Scholar] [CrossRef]
  24. Wu, T.; Jin, H.; Guo, L.; Sun, H.; Tong, J.; Jiang, Y.; Wei, P. Predicting method on settlement of soft subgrade soil caused by traffic loading involving principal stress rotation and loading frequency. Soil Dyn. Earthq. Eng. 2022, 152, 107023. [Google Scholar] [CrossRef]
  25. Yuan, K.; Wang, S.; Niu, F.; Chen, J.; Li, J. Analysis of differential settlement characteristics of permafrost widening subgrade. China J. Highw. Transp. 2016, 29, 21–28. Available online: https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL201609002.htm (accessed on 1 September 2022).
  26. Li, K.; Xu, W.; Yang, L. Deformation Characteristics of Raising, Widening of Old Roadway on Soft Soil Foundation. Symmetry 2021, 13, 2117. [Google Scholar] [CrossRef]
  27. Lin, Q.; Zhang, Y.; Yang, C.; Wang, X.; Lei, T.; Ju, C.; Yao, Z.; Yao, K. Evaluation of Differential Settlement of Subgrade for Highway-Widening Projects. Sustainability 2023, 15, 2950. [Google Scholar] [CrossRef]
  28. Gu, S.; Liu, W.; Ge, M. Failure and Remediation of an Embankment on Rigid Column-Improved Soft Soil: Case Study. Adv. Civ. Eng. 2020, 2020, 2637651. [Google Scholar] [CrossRef]
  29. Jiang, X.; Chen, X.; Fu, Y.; Gu, H.; Hu, J.; Qiu, X.; Qiu, Y. Analysis of Settlement Behaviour of Soft Ground Under Wide Embankment. Balt. J. Road Bridg. Eng. 2021, 16, 153–175. [Google Scholar] [CrossRef]
  30. Weng, X.; Li, L.; Zhang, L. Model Experimental Research on Wetting Damage Mechanism of Widening Loess Roadbed. Chin. J. Rock Mech. Eng. 2010, 29, 1075–1081. Available online: https://www.cnki.com.cn/Article/CJFDTOTAL-YSLX201005031.htm (accessed on 1 September 2022).
  31. Xie, M.; Li, L.; Cao, W.; Zheng, J.; Dong, X. Centrifugal and numerical modeling of embankment widening over soft soils treated by pile-supported geosynthetic-reinforced soil wall. Acta Geotech. 2023, 18, 829–841. [Google Scholar] [CrossRef]
  32. Yang, L.; Xu, W.; Li, K.; Han, P.; Wu, Y. Analysis of the Effects of Different Filling Materials on the Deformation of a Widened Subgrade. Int. J. Civ. Eng. 2023, 21, 1679–1695. [Google Scholar] [CrossRef]
  33. Shi, X.; Huang, J.; Su, Q. Experimental and numerical analyses of lightweight foamed concrete as filler for widening embankment. Constr. Build. Mater. 2020, 250, 118897. [Google Scholar] [CrossRef]
  34. Jiang, X.; Jiang, Y.; Wu, C.-Y.; Wang, W.-Q.; Geng, J.-Y.; Qiu, Y.-J. Numerical analysis for widening embankments over soft soils treated by PVD and DJM columns. Int. J. Pavement Eng. 2020, 21, 267–279. [Google Scholar] [CrossRef]
  35. Gao, S.; Tang, B.; Zhang, J.; Zhao, G. Numerical Simulation of Reinforced Soil Slope in Subgrade Widening of Expressway. IOP Conf. Ser. Earth Environ. Sci. 2020, 565, 012105. [Google Scholar] [CrossRef]
  36. Chen, M.; Liu, Y.; Chen, R.; Yuan, B.; Shi, H. Numerical Analysis of Fluid-solid Interaction for Widening Subgrade Deformation. Subgrade Eng. 2013, 4, 39–42. Available online: http://www.cqvip.com/qk/98281x/201304/46770520.html (accessed on 1 September 2022).
  37. Wei, J.; Wang, Z.; Zheng, J.; Zhao, W. The Finite Element Analysis of Highway Unilateral Widened Deformation Characteristics on Soft Soil Ground. Adv. Sci. Lett. 2012, 6, 337–341. [Google Scholar] [CrossRef]
  38. Shen, Z.; Li, H.; Wei, Y.; Fang, L. Centrifugal model test of embankment widening with geogrid treatment technique. Arab. J. Geosci. 2021, 14, 2484. [Google Scholar] [CrossRef]
  39. Ling, J.; Qian, J.; Huang, Q. Failure Mechanism and Design Criterion for Low-Volume Roads Subgrade Widening. Transp. Res. Rec. 2007, 1989-2, 135–141. [Google Scholar] [CrossRef]
  40. Cheng, H.; Sun, L.; Wang, Y.; Liu, L.; Chen, X. Fatigue test setups and analysis methods for asphalt mixture: A state-of-the-art review. J. Road Eng. 2022, 2, 279–308. [Google Scholar] [CrossRef]
  41. Baghel, R.S.; Kasu, S.R.; Chandrappa, A.K. Effect of dual and new generation wide-base tire assembly on inverted pavements. J. Road Eng. 2022, 2, 124–136. [Google Scholar] [CrossRef]
  42. Wang, K.; Ye, J.; Wang, X.; Qiu, Z. The Soil-Arching Effect in Pile-Supported Embankments: A Review. Buildings 2024, 14, 126. [Google Scholar] [CrossRef]
  43. Ebid, A.M.; Deifalla, A.F.; Mahdi, H.A. Evaluating Shear Strength of Light-Weight and Normal-Weight Concretes through Artificial Intelligence. Sustainability 2022, 14, 14010. [Google Scholar] [CrossRef]
  44. Vibhoosha, M.P.; Bhasi, A.; Nayak, S. A Review on the Design, Applications and Numerical Modeling of Geocell Reinforced Soil. Geotech. Geol. Eng. 2021, 39, 4035–4057. [Google Scholar] [CrossRef]
  45. Fan, L. Analysis of reinforcement effect of widening geogrid of highway subgrade. Transp. World 2023, 13, 94–96. [Google Scholar] [CrossRef]
  46. Wang, Y. Research on differential settlement control technology of new and old subgrade of expressway. West. Transp. Sci. Technol. 2023, 3, 20–23. [Google Scholar]
  47. Uge, B.U.; Guo, Y.-C. CFG Pile Composite Foundation: Its Engineering Applications and Research Advances. J. Eng. 2020, 2020, 5343472. [Google Scholar] [CrossRef]
  48. Lv, G.H.; Cui, W.; Zhang, Q.Q.; Wu, S.Q.; Wang, S.J. Experimental Study on Embankment Failure Law and Reinforcement Technology for Highway Widening Project over Silt Soils. J. Test. Eval. 2021, 49, 4248–4260. [Google Scholar] [CrossRef]
  49. Sui, X. Application of Foam Lightweight Soil in Highway Reconstruction and Expansion Project. Fujian Transp. Sci. Technol. 2023, 5, 19–21. Available online: https://www.cnki.com.cn/Article/CJFDTOTAL-FJJT202305005.htm (accessed on 1 September 2022).
  50. Tanoli, A.Y.; Yan, B.; Xiong, Y.; Ye, G.; Khalid, U.; Xu, Z. Numerical analysis on zone-divided deep excavation in soft clays using a new small strain elasto–plastic constitutive model. Undergr. Space 2022, 7, 19–36. [Google Scholar] [CrossRef]
  51. Yadav, S.K.; Ye, G.; Xiong, Y.; Khalid, U. Unified numerical study of shallow foundation on structured soft clay under unconsolidated and consolidated-undrained loadings. Mar. Georesour. Geotechnol. 2020, 38, 400–416. [Google Scholar] [CrossRef]
  52. Yadav, S.K.; Ye, G.; Khalid, U.; Fukuda, M. Numerical and centrifugal physical modelling on soft clay improved with floating and fixed sand compaction piles. Comput. Geotech. 2019, 115, 103160. [Google Scholar] [CrossRef]
  53. Khalid, U.; ur Rehman, Z.; Mujtaba, H.; Farooq, K. 3D response surface modeling based in-situ assessment of physico-mechanical characteristics of alluvial soils using dynamic cone penetrometer. Transp. Geotech. 2022, 36, 100781. [Google Scholar] [CrossRef]
  54. ASTM D3080-04; Standard Test Method for Direct Shear Test of Soils Under Consolidated Drained Conditions. ASTM: West Conshohocken, PA, USA, 2012. Available online: https://www.astm.org/d3080-04.html (accessed on 1 September 2022).
  55. Shah, S.R.A.; Kumar, A.; Zardari, M.A.; Ali, T.H.; Bhanbhro, R. Numerical Analysis of Settlement of a Piled Raft Foundation on Coastal Soil. Civ. Eng. J. 2023, 9, 319–333. [Google Scholar] [CrossRef]
  56. Pham, T.A.; Dias, D. 3D numerical study of the performance of geosynthetic-reinforced and pile-supported embankments. Soils Found. 2021, 61, 1319–1342. [Google Scholar] [CrossRef]
  57. EDS. Available online: https://edstechnologies.com/blog/how-to-perform-geotechnical-analysis-of-soil-using-abaqus/ (accessed on 1 September 2022).
  58. Topolnicki, M.; Holding, K. Technical Paper: Road Traffic Loads for Geotechnical Analyses of Embankments. Available online: https://www.geplus.co.uk/technical-paper/technical-paper-road-traffic-loads-for-geotechnical-analyses-of-embankments-04-06-2020/ (accessed on 1 September 2022).
Applsci 14 01740 g001
Figure 1. Location of N-120 on map of Sindh province of Pakistan.
Figure 1. Location of N-120 on map of Sindh province of Pakistan.
Applsci 14 01740 g001
Applsci 14 01740 g002
Figure 2. Layout plan for traffic movement and lane marking (units in mm).
Figure 2. Layout plan for traffic movement and lane marking (units in mm).
Applsci 14 01740 g002
Applsci 14 01740 g003
Figure 3. Fatigue cracks in the widened part of the pavement of N-120.
Figure 3. Fatigue cracks in the widened part of the pavement of N-120.
Applsci 14 01740 g003
Applsci 14 01740 g004
Figure 4. Alligator cracks in the widened part of the pavement of N-120.
Figure 4. Alligator cracks in the widened part of the pavement of N-120.
Applsci 14 01740 g004
Applsci 14 01740 g005
Figure 5. Cracks in the widened part of the pavement of N-120.
Figure 5. Cracks in the widened part of the pavement of N-120.
Applsci 14 01740 g005
Applsci 14 01740 g006
Figure 6. Pavement distresses in N-120 in the widened part of the pavement.
Figure 6. Pavement distresses in N-120 in the widened part of the pavement.
Applsci 14 01740 g006
Applsci 14 01740 g007
Figure 7. Locations of soil samples.
Figure 7. Locations of soil samples.
Applsci 14 01740 g007
Applsci 14 01740 g008
Figure 8. Road section before widening.
Figure 8. Road section before widening.
Applsci 14 01740 g008
Applsci 14 01740 g009aApplsci 14 01740 g009b
Figure 9. Shear test results at 300 kPa, 104 kPa, and 212 kPa. (a) Foundation. (b) New road. (c) Old road.
Figure 9. Shear test results at 300 kPa, 104 kPa, and 212 kPa. (a) Foundation. (b) New road. (c) Old road.
Applsci 14 01740 g009aApplsci 14 01740 g009b
Applsci 14 01740 g010
Figure 10. Shear test results (normal stress vs. shear stress diagram).
Figure 10. Shear test results (normal stress vs. shear stress diagram).
Applsci 14 01740 g010
Applsci 14 01740 g011
Figure 11. Geometry of the model (units in mm).
Figure 11. Geometry of the model (units in mm).
Applsci 14 01740 g011
Applsci 14 01740 g012
Figure 12. Schematic of boundary conditions and applied loads.
Figure 12. Schematic of boundary conditions and applied loads.
Applsci 14 01740 g012
Applsci 14 01740 g013
Figure 13. Schematic for interaction.
Figure 13. Schematic for interaction.
Applsci 14 01740 g013
Applsci 14 01740 g014
Figure 14. Case setting (treatment strategies). (a) Case A: Geogrid at the base. (b) Case B: Geogrid at the base and CFG piles under new road embankment. (c) Case C: CFG piles under new road embankment and the joint. (d) Case D: Lightweight filling material as soil replacement.
Figure 14. Case setting (treatment strategies). (a) Case A: Geogrid at the base. (b) Case B: Geogrid at the base and CFG piles under new road embankment. (c) Case C: CFG piles under new road embankment and the joint. (d) Case D: Lightweight filling material as soil replacement.
Applsci 14 01740 g014
Applsci 14 01740 g015
Figure 15. Settlement on the pavement surface for untreated embankment at 20 kPa.
Figure 15. Settlement on the pavement surface for untreated embankment at 20 kPa.
Applsci 14 01740 g015
Applsci 14 01740 g016
Figure 16. Settlement on the pavement surface and toe for untreated embankment at 40 kPa.
Figure 16. Settlement on the pavement surface and toe for untreated embankment at 40 kPa.
Applsci 14 01740 g016
Applsci 14 01740 g017
Figure 17. Settlement on the pavement surface for untreated embankment at 80 kPa.
Figure 17. Settlement on the pavement surface for untreated embankment at 80 kPa.
Applsci 14 01740 g017
Applsci 14 01740 g018
Figure 18. Settlement profile at the pavement surface.
Figure 18. Settlement profile at the pavement surface.
Applsci 14 01740 g018
Applsci 14 01740 g019
Figure 19. Settlement profile at the foundation surface.
Figure 19. Settlement profile at the foundation surface.
Applsci 14 01740 g019
Applsci 14 01740 g020
Figure 20. Settlement profile comparison at the foundation surface.
Figure 20. Settlement profile comparison at the foundation surface.
Applsci 14 01740 g020
Applsci 14 01740 g021aApplsci 14 01740 g021b
Figure 21. Settlement cloud diagrams. (a) Without reinforcement. (b) Case A. (c) Case B. (d) Case C. (e) Case D.
Figure 21. Settlement cloud diagrams. (a) Without reinforcement. (b) Case A. (c) Case B. (d) Case C. (e) Case D.
Applsci 14 01740 g021aApplsci 14 01740 g021b
Applsci 14 01740 g022
Figure 22. Settlements under load variation.
Figure 22. Settlements under load variation.
Applsci 14 01740 g022
Table 1. Soil testing results.
Table 1. Soil testing results.
Chainage (Km)LocationSpecific GravityBulk Density (g/cc)Void RatioBearing Capacity (kPa)
16+200Foundation2.542.140.43346.42
38+000New road2.472.060.44112.61
38+000Old road2.532.210.39342.13
Table 2. Soil moisture content.
Table 2. Soil moisture content.
Pit No.Chainage (Km)LocationDirectionMoisture Content (%)
19+000FoundationRight side17.00
216+200FoundationLeft side18.00
323+050FoundationRight side17.00
428+200FoundationLeft side16.40
534+000FoundationRight side18.00
638+000FoundationRight side18.00
738+000FoundationLeft side18.80
838+000New RoadRight side16.00
938+000New RoadLeft side18.30
1038+000Old RoadRight and left sides18.00
Table 3. Material properties.
Table 3. Material properties.
LocationDensity (kg/m3)Modulus of
Elasticity
(MPA)		Poisson RatioCohesion (kPa)Dilation Angle (°)Friction Angle (°)Permeability (m/s)Void Ratio
Natural Ground214016.30.32201311 × 10−90.43
New Road206020.40.3225030.11 × 10−90.44
Old Road221013.60.320028.81 × 10−90.39
Pavement1900
[36]		1400
[36]		0.4 1 × 10−200.3
Geogrid_38,700
[18]		0.25
[18]
CFG2447
[18]		150
[18]		0.15
[18]
Lightweight foamed concrete699
[33]		285
[33]		0.10
[33]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Abbasi, S.J.; Weng, X.; Iqbal, M.J. Numerical Analysis of Differential Settlement in Road Due to Widening Considering Different Reinforcement Techniques. Appl. Sci. 2024, 14, 1740. https://doi.org/10.3390/app14051740

AMA Style

Abbasi SJ, Weng X, Iqbal MJ. Numerical Analysis of Differential Settlement in Road Due to Widening Considering Different Reinforcement Techniques. Applied Sciences. 2024; 14(5):1740. https://doi.org/10.3390/app14051740

Chicago/Turabian Style

Abbasi, Shaista Jabeen, Xiaolin Weng, and Muhammad Jawed Iqbal. 2024. "Numerical Analysis of Differential Settlement in Road Due to Widening Considering Different Reinforcement Techniques" Applied Sciences 14, no. 5: 1740. https://doi.org/10.3390/app14051740

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop