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Fracture mechanics is a relatively new field that combines the study of fractures and mechanical characteristics. It focuses on understanding damage, fractures, and related events. Fracture mechanics helps quantify material properties, stress distribution, crack length, and the processes of crack propagation. Many academics are currently applying fracture mechanics in their analyses. In this study, we have examined the recent research progress (2000–2023) using a scientometric approach to assess its contribution. Our findings indicate a recent slowdown in research growth within this area. There have been a considerable number of publications (620) and a significant body of available research papers (1564). Moreover, a large number of authors (3985) are actively working in this field. International collaboration accounts for nearly 19% of the research output. On average, each document receives about 18.2 citations, reflecting the notable impact in this growing domain. This study serves as a valuable resource for new researchers interested in undertaking research within this field.
Institute of Energy Infrastructure, Universiti Tenaga Nasional, Kajang, Malaysia
A. Nikhil Kumar
SR University, Warangal, Telangana, India
*Address all correspondence to: gobinathdpi@gmail.com
1. Introduction
Engineering material failure is an important concept engineers and designers look upon, material strength, if enhanced will give more durability and a quality product. Materials mostly fail due to loading (static, cyclic, fatigue) and avoiding failure through fracture is one of the key point we look upon. A fracture occurs when a body splits into two or more parts in response to a static stress applied at a temperature lower than the melting point of the material. There are two stages to a fracture: the crack starts, and then it spreads. There are two distinct fracture types which are brittle and ductile that varies according to the stress distribution in the member during loading.
1.1 Brittle failure occurs due to the following conditions that may occur in the material
Too much high energy absorption and plastic deformation close to the crack precede fracture. “The spread of cracks is sluggish due to the high amount of energy absorption and plastic deformation that occurs in the material near the crack. More energy is needed to generate ductile fissures.
In a tensile test, in general, failure comes after necking. Vacuum nucleation near the neck’s midline is often the initial trigger. In time, these gaps will join together as the deformation continues. When the outside rim of the crack can no longer bear the weight, it shears off suddenly. A cup and cone fracture describes this type of global failure.
Holes appear at inclusions when the inclusions themselves are brittle and/or the matrix’s inclusion cohesion is inadequate [1].
The broken surface is pitted with dimples. During the fracturing process, micro voids are generated and split in half, giving rise to the resulting dimples.
The ductility is measured in terms of the percentage of length change or area decrease.
Temperature, strain rate, and stress state all influence ductility. Propagation of cracks is stable [2].
1.2 Brittle failure in a material such as glass, rubber occurs due to the following reasons
Crack As a result of little to no plastic distortion during propagation, very little energy is lost [3].
Happens all of a sudden, with no prior notice. Cleavage is a possible mode of fracture (fracture on certain crystallographic planes by bond breaking). V-shaped chevron patterns or lines/ridges radiating from a crack are sometimes visible on a fracture’s surface. Hard materials can have a relatively smooth surface. A fracture at a grain border, also known as an intergranular fracture, can occur without significant plastic deformation, making it difficult to detect prior to failure. Toughness is grain size dependent. Toughness and ductility improve with reduced grain size.
Cracks spread in an unstable manner. A fracture can either be transgranular (between the grains) or intergranular (along the grain boundary) [4, 5, 6].
When a solid or structure has a geometrical discontinuity on the scale of the structure, its behavior can be described by the theories of fracture mechanics [2]. In two-dimensional media (such as plates and shells), the discontinuity features can take the shape of lines, whereas in three-dimensional media (such as spheres and cubes), the discontinuities can take the form of surfaces. Now a fully developed field of study, fracture mechanics has revolutionized our understanding of how engineering materials behave. Fracture mechanics has had a major influence by introducing a new design philosophy, damage tolerance design methodology, which is now the gold standard in aviation design.
Fracture mechanics is a new field that integrates fracture mechanics with the study of mechanical characteristics [7]. Mechanical properties study and fracture mechanics have recently been combined to form the emerging topic of fracture mechanics. Quantifying the connection between material qualities, stress, crack length, and crack propagation mechanisms is the goal of fracture mechanics [8]. The study of fractures and other phenomena associated with breaking is the focus of fracture mechanics. The advancement of fracture mechanics is inextricably tied to certain recent, high-profile disasters. It all started during World War II, when hundreds of ships bringing citizens to safety on the high seas were heavily damaged, the reason for the same being unknown at that time. During World War II, the construction of Liberty ships transitioned from riveted to welded construction. However, this change resulted in numerous failures caused by subpar weld quality, stress concentrations, and the use of brittle materials. As a result, approximately 400 of the 2700 Liberty ships constructed during the war were severely damaged due to these factors. The investigation of these failures kickstarted a new area of study called “fracture mechanics”, which aimed to understand the behavior of materials under stress and the mechanisms that lead to failure. The study of fracture mechanics has since become an important tool for identifying weaknesses and predicting the failure of materials in various applications, including soil strength identification. The Comet occurrences in 1954 led a thorough investigation into the causes, which greatly improved our understanding of fracture and fatigue. In July of 1962, the Kings Bridge in Melbourne suddenly collapsed after a car weighing 45 tons crossed one of the spans. Four girders failed because a crack extended from the bottom to the top of the girder, through the web and in some places the upper flange as well. Although no one was injured, the incident sparked a thorough investigation into the cause of the failure, which ultimately led to significant improvements in bridge safety and engineering practices. This kind of events become prelude for the initiation of Fracture mechanics study which progressed well and helped to avoid many disasters.
There are mainly two primary kinds of fracture mechanics approach: linear elastic fracture mechanics (LEFM) and elasto-plastic fracture mechanics (EPFM) (EPFM). LEFM excels at handling brittle-elastic materials such as high-strength steel, glass, ice, concrete, etc. In contrast, ductile materials, such as low-carbon steel, stainless steel, some aluminum alloys, and polymers, always exhibit plasticity before fracture. Linear fracture mechanics is still a good approximation to reality, but only for loads below a certain threshold. Hence it is evident that understanding the fracture properties of a material is necessary to produce a good quality product. In recent years, fracture mechanics has increasingly been applied in civil engineering to understand the properties and behavior of different materials. For example, stabilized soil and engineered soil are materials that have been extensively studied using fracture mechanics to analyze their cracking patterns and failure modes, among other factors.
2.1 Fracture mechanics approach towards soil strength
Soil always has some kind of defect, such as an inclusion, a vacuum, or a crack in any form. Environmental stress or mechanical strain could cause cracks to spread from these defects. Multi-layer pavement systems, buried pipes, and embankment dams use soil for sub-grade layers. Failure and fracture of this material can deform buildings and affect their long-term performance. Tensile type fracture (mode I fracture) of soil materials has been tested using several ways. Real-world loads can cause mixed mode tensile-shear deformations in clay materials. Among the failure pattern in soil, desiccation cracking [9, 10, 11] in cohesive soil, where cracks form due to volume changes with removal of water, has received a lot of attention from the scientific community. However, crack formation in the core of dams, the wall of tailings, and the liners of landfills, where the soil is saturated above the shrinkage limit, has received much less attention. Significant economic, environmental, and human losses have resulted from the collapse of these structures [12]. Over the course of the past three decades, linear elastic fracture mechanics (LEFM) has solidified its place as a key discipline within geotechnical engineering [13] Numerous geotechnical engineering literatures document the use of LEFM with great success in actual engineering projects. Because it is not possible to verify that failure criteria based on yield dominating failure of material, such as Tresca, Mises, or Coulomb, can be used to analyze the failure of brittle materials induced by fracture [14, 15] established that LEFM is a useful method for studying the fracture dominated failure or rupture of a wide variety of geomaterials, including stiff and over-consolidated soils, in particular those having cracks [16].
Correct knowledge of shear strength of the soil is necessary for the design of traditional geotechnical constructions including foundations, slopes, and retaining walls. But the void ratio, composition, friction angle, cohesion, stress history, temperature, strain, strain rate, and structure all have an impact on the shear strength of soil. When the tension exceeds the soil’s bearing capacity, failure is expected [17, 18]. Owing to these factors influence, analyzing soil failure become cumbersome. When there are no fractures present, a brittle failure that happens quickly and is guided by linear elastic fracture mechanics (LEFM) [19, 20]. When it comes to design, traditional soil mechanics criteria like cohesive strength (c) and angle of internal shearing resistance (phi) fall short. If one want to prevent failure in brittle and quasi-brittle materials by employing LEFM, you need to pay attention to the parameters, especially the critical stress intensity factor KIC [18, 21, 22, 23, 24]. At low saturation, cohesive soil starts to operate like a quasi-brittle material, failing mostly in ways described by linear elastic fracture mechanics. In the field of fracture mechanics, the KIC is a crucial mechanical characteristic that indicates a material’s resistance to fracture failure under mode I stress circumstances. Numerous studies have focused on the best way to calculate KIC and how it relates to other mechanical parameters like tensile strength t in geomaterials. Soil fracture toughness, defined as its resistance to crack initiation and propagation, is an important quality for determining the safe design limits of critical infrastructure including pipelines, bridges, and dams [25, 26]. Hence, it is found that fracture mechanics-based study on soil will help designers and engineers to develop better engineering soil [27]. In this work, we have tried to understand the real research works being undertaken in this domain.
Thus, research progress analysis is necessary to comprehend the research being done by different researchers and guide future research directions. This paper proposes quantitative visual representation and systematic analysis of existing studies to meet the requirements and provides a comprehensive and up-to-date review of fracture mechanics approach to engineered soil design. The scientometric analysis used here provides (a) a better understanding of the domain of knowledge encircling fracture mechanics approach towards engineered soil design, (b) more objectivity than prior reviews, and (c) a quantitative representation of the domain.
This study focuses on answering the following RQs:
How well-studied are Fracture mechanics methods?
What has changed in recent years?
How is this study and partnership distributed globally?
What areas are needed for these particular studies?
Where are researchers working?
This paper took a scientometric approach to answer the above-mentioned questions using most widely used bilbiometrics software for analysis. Scientometrics is widely used by many researchers to understand the research landscape and it can provide information related to important keywords, authors, affiliations, countries involved in research, organizations funding the research and other important information that can serve as a guideline for new researchers.
To understand the research progress, we have taken a scientometric approach using Scopus database which is one of the widely used database for this purpose. Scopus is the most comprehensive index of scholarly articles, books, and proceedings from scientific conferences and journals. Scopus provides a global overview of research in the areas of science, technology, medicine, the social sciences, and the arts and humanities, with useful capabilities for monitoring, analyzing, and visualizing this data. We ran a search with keywords during December 2022 which is adopted by using trial and error method as mentioned below. Keywords and selection of them influence the outcome of bibliometric research and care should be taken in arriving at keywords. The whole methodology is divided into keyword finalization, database search, outlier removal, bibliometric study, analysis and recommendations which is provided in the following sections.
3.1 Method
Scientometric analysis was used to rank the papers written about fracture mechanics during a specific period (2000–2023). Publication trends in academic works such as research articles, conference papers, and other scholarly documents can be analyzed quantitatively and statistically with the help of a technique called scientometric. On December 3, 2022, researchers went through the Scopus database (www.scopus.com). By conducting the search on a single day, we avoided the potential for bias caused by the databases being updated on a daily basis. For this study, researchers looked back at the papers indexed by Scopus between the years 2000 and 2023. There are other databases available for the same study including Web of Science, Dimensions, Lens etc. which are also widely used by researchers. Scopus is the go-to database for scientometric and bibliometric investigations due of its large data set and its widely adopted in bibliometrics study [28, 29, 30]. The scholarly community agrees that Scopus is the best and largest database of its kind. It is now widely used as a bibliometric data source by many researchers. The authors of this study set out to create a bird’s-eye view of the scientific landscape that has contributed to our knowledge of how fracture mechanics is used in engineered soil development. Both the intellectual (co-citation network) and social (collaboration network) structures of the gathered data were explored (co-occurrences of authors/keywords, theme progression).
3.2 Search query
To retrieve the scientometric data on finite element analysis and weak soil, the following search query was run in the main search interface of the Scopus database in the search field type:
(TITLE-ABS-KEY (fracture AND mechanics) AND TITLE-ABS-KEY (soil)) AND PUBYEAR >1999 AND PUBYEAR >1999
3.3 Inclusion/exclusion criteria
Authors ran the search using keywords in Scopus database and 1546 documents were found in the first search. A time frame of 2000–2023 is kept for publication only. Publications, conference papers, book chapters, reviews, and books were filtered out, leaving a total of 1558 results after narrowing the publication stage to “final.” The top ten nations for publishing articles in the topic of Fracture mechanics of soil were also considered. All materials must be written in English to be considered. The remaining 1558 entries were published between the years 2000 and 2023 and include articles (N = 1079), conference papers (N = 402), book chapters (N = 14), review articles (N = 25), and books (N = 4). This paper introduces a novel methodology for conducting a comprehensive literature evaluation on soil fracture mechanics by combining scientometric and complex network analyses. Figure depicts a description of the research procedure and the incorporation of analytical techniques. In order to ensure that the items selected were consistent and that the results were accurate, two authors of this research followed the identical procedures.
The 1558 documents that were returned were analyzed using a variety of bibliometric techniques to extract useful information. Microsoft Office Excel (Version 2209) was utilized for several fundamental tasks, such as gaining insight into publication and citation trends. The authors used a variety of programmes to assist with data visualization, including VOS viewer (version 1.6.15), Origin Pro 2022b (64-bit), and Biblioshiny (version 4.1.1). Relationships in citations, bibliographic coupling, co-citation, and co-authorship were also discovered with the help of these technologies.
3.3.1 Analysis of the overall growth trend
Figure 1 below summarizes the main results of the bibliometric analysis to describe the collection size in terms of number of documents, number of authors, number of sources, number of keywords, timespan, references, and average number of citations. Furthermore, many different co-authorship indices are shown.
Figure 1.
Summary of the main results of the bibliometric analysis.
Figure 2 shows the year-wise frequency of publications and citations of wave propagation through fracture mechanics literature from 2000 to 2023. The number of publications and citations have significantly increased over the years. The most successful publication year was 2021, in which the highest (130) number of articles were published. On the other hand, the highest number of citations (3607) were seen in the year 2022. More number of publications happening in an year is influenced by many factors including funding availability, increasing demand, increasing collaboration between authors, research tie up between institutions etc. It is found that the average publication in an year is well above many domains and it is showing the increasing awareness among authors.
Figure 2.
Publication and citation trend on fracture mechanics.
3.3.2 Top ten publishing countries
The top ten highly productive countries are shown in Figure 3, which shows the interest generated among the country research which is in turn attributed to many other parameters including applicability, funding available, policy decisions etc. It can be seen that the most productive country, China had produced 604 publications, the United State and United Kingdom produced 284 and95 publications followed by Australia and Canada with 84 and 76 publications during the period of the study. The results show that China has outstanding productivity with 604 publications and 7068 citations; followed by the United States with 284 publications and 5999 citations.
Figure 3.
Top ten highest- publishing countries and their corresponding citation.
3.3.3 Top ten high-research-producing institutions
The top 10 research-producing organizations are shown in Figure 4. The top 2 organizations had 80 and 78 publications, respectively. The Northwestern Polytechnic University emerged as the most productive organization with 80 publications, followed by the Not reported with 78 publications. The China University, Nanjing University and Tsinghua University produced 75, 57 and 55 articles, respectively.
Figure 4.
Top ten most highly productive organizations.
3.3.4 Most prolific authors
Results from the top ten most prolific scholars in the field of fracture mechanics application in soil strength analysis from 2000 to January 2023 is obtained. These scholars have shown consistency by contributing to the research in this field. The highest number of documents are produced with no author name provided until 2000 to 2023. The results revealed that Wang Y from China had produced 24 documents and earned the highest citation count of 619. He also has the highest h-index, which suggests that Liux remains the most impactful author in the field of finite element analysis and weak soil. Liux’s first article was published in 2011 with total citations per year of 6. Although our result shows that Liux has no publication in between 2012 and 2020, however, he has consistently published in this field between 2011 and 2021. The second most prolific scholar in this field is Zhang J from China. Zhang J has 15 publications. Zhang J began publishing in the field of finite element analysis and weak soil in 2010, where he had two publications and consistently published 1, 3, 2, and 2 papers in 2010, 2014, 2015, 2019, respectively, and yet to publish in the year 2022. Similarly, the results show that Shivashankar from India, Liu Y and Ylian S from China, have h-index of 6, 5, 4 and 4 respectively based on our dataset; hence, they have immensely impacted the field of finite element analysis. Other impactful scholars in this field may also be present but this work is confined to the database obtained during the study period only (Table 1).
Source
Impact measure (H – Index)
Yanshilixue Yu Gongcheng Xuebao/Chinese Journal of Rock Mechanics and Engineering
22
Journal of Rock Mechanics and Geotechnical Engineering
14
Computers and Geotechnics
13
Engineering Geology
12
Materials Science and Engineering A
11
Canadian Geotechnical Journal
10
Geotechnique
10
International Journal for Numerical and Analytical Methods in Geomechanics
10
International Journal of Geomechanics
10
Acta Geotechnica
9
Table 1.
Impact measure of the publications.
3.3.5 Three-factor analysis
3.3.5.1 Keywords, authors and countries
A more visualized representation of prolific scholars vis-à-vis their countries and the specific area of interest in the field of finite element analysis and weak soil is shown in Figure 5. This Figure is a three-field plot of article contributions by countries, authors, and themes within the field of fracture mechanics of soil. The right-most column represents active countries, the rightmost column shows scholars’ names contributing from those countries, and the middle column represents the most used keywords by the authors. The number of occurrences of these keywords forms what we refer to as ‘themes’ in this study. Note the height of the boxes and the thickness of the connecting lines. On the side of countries, China has more authors’ affiliations, with 1250 authors connected to the country, followed by Australia, United States and United Kingdom with 65, 49, and 12 connections. Observing the thickness of the line leading from the countries to authors, we can see that Wang Y and Li X remain the giant contributors from China. In India, Kodikara J remains the prolific writer.
Figure 5.
A three-field plot of countries, authors and themes.
The emphasis is placed on the height of each box and thickness of the connecting lines; the taller the box, the more significant; and the thicker the lines’ correlation, the more information or volume of work was produced.
3.3.5.2 Thematic evolution of keywords
Figure 6 demonstrates the evolution of keywords in two different stages (2000–2010 and 2011–2023). It is noticed that most of the research in the second stage relates to fracture, cracks and soil mechanics. This is supported by the height of the boxes and the thickness of the connecting lines during the period 2011–2023, which manifests that the research focus on these three terms is relatively more. Most of the research works will start with a keyword and will evolve into multiple other keywords and progress via other keywords, hence understanding keyword variation dynamics is important to understand the research progress in a domain. Concerned with this study, keywords such as “rocks”, “failure analysis”, “mathematical models”, “soil mechanics”, “compaction grouting” and “fracture mechanics” defines the research work being undertaken by researchers across the globe.
Figure 6.
Thematic evolution map of keywords from 2000 to 2023 with respect to fracture mechanics and soil.
3.3.6 Thematic map
Another analysis conducted in this study is the thematic map of fracture mechanics approach for engineered soil development. The aim of conducting a thematic map is to gain insight into the field’s current status and what its future sustainability holds. This analysis is useful in providing knowledge to researchers and stakeholders regarding the potential of future research development of thematic areas within a field.
Thematic analysis takes clusters of keywords plus and their interconnections to obtain themes. These themes are characterized by properties (density and centrality). The density is represented on the vertical axis, while centrality takes the horizontal axis. Centrality is the degree of correlation among different topics; density measures the cohesiveness among the nodes. These two properties measure whether certain topics are well developed or not, important, or not. The higher the number of relations a node has with others in the thematic network, the higher the centrality and importance, and it lies within the essential position in the network. Similarly, cohesiveness among a node, which represents the density of a research field, delineates its capability to develop and sustain itself. In Figure 7, we provide the thematic map of the field studied in this paper, which is divided into four quadrants (Q1 to Q4) and sustain itself. In Figure 7, we provide the thematic map of the field studied, which is divided into four quadrants (Q1 to Q4).
Figure 7.
Thematic map: Q1 contains the main theme, Q2 contains highly developed and specialized themes building ties with the leading theme, Q3 contains disappearing or emerging themes, Q4 consists of foundational and transversal themes.
The upper right quadrant (Q1) represents the driving themes, the lower right quadrant (Q4) denotes the underlying themes, the upper left quadrant (Q2) represents the very specialized themes, and the lower left quadrant (Q3) denotes emerging or disappearing themes. Notably from the figure, a theme such as “Fracture Mechanics,” placed in Q1, is well developed and capable of structuring the research field. In other words, fracture mechanics remains the leading theme within the field. Themes such as “soil mechanics,” “soil mechanics”, “soil testing” and “soils compressive strength” seen in Q4 are the basics and are critical for the field’s development. Themes in Q2 have developed internal bonds but still of marginal contribution to the development of the field of fracture mechanics. This finding suggests that themes in Q2 such as bending strength, silicon carbide and carbon fibers are potential topics that need to be more connected to fracture mechanics. Scholars in this field may explore these themes to provide twenty-first-century solutions in the field of finite element analysis.
The theme in Q3, “seepage”, “mechanical properties” and “fracture toughness” appears to be emerging but shows cohesiveness towards the themes of Q4, indicating that some of its components are basic and necessary for developing the field of Fracture Mechanics of soil. The thematic analysis suggests that more efforts are needed to develop themes deformation,” to establish more ties with “Fracture mechanics of soil.”
3.3.7 Thematic focus of the field of fracture mechanics of soil
3.3.7.1 Keywords analysis, co-occurrence network, and trend topics
This section investigates the themes that dominate the research landscape of fracture mechanics of soil and areas that scholars have focused on during the period 2000–2023.
Besides, the study also attempts to gain insight into whether there is a shift in the topic of discussion among scholars within the field. We first began by analyzing keywords plus and their frequency of occurrences. Next, we carried out an analysis of keywords dynamics, trending topics, co-occurrence network, and thematic areas of the field.
Analysis of keywords used by authors in publications is an essential tool for investigating trending topics and scholars focus on the field [7]. This analysis is so because publication keywords help us to identify the topic and focus of that publication quickly. The word-cloud in Figure 8 shows frequently used keywords in this work. Using this word cloud, one can understand the various keywords authors used to define their research related to fracture mechanics approach on soil development, thickness of the keywords is related to the high frequency of its usage among the articles analyzed in this research.
Figure 8.
A visualized word-cloud of frequently used keywords in the finite element analysis and weak soil, these are among the highest number of repetitive keywords within the field.
Specifically, Figure 9 shows the visualized word dynamics of the used keywords plus. Soils became one of the most used keywords from 2000 and grew quickly until 2023. This finding signified that fracture became the most discussed topic as an aspect of fracture mechanics among scholars within those years. However, frequently used keywords such as rock mechanics, cracks, soil testing, failure (mechanical) and finite element method are also continued to increase (see Figure 9). This finding suggests that the field of wave propagation will continue to be researched these prevailing aspects.
This study is done for a limited period between 2000 and 2023 owing to several attributes and hence careful understanding is solicited while interpreting results. Authors have considered only articles, conference papers, book chapters, reviews and books only and there may be other avenues where the research publications may happen which is not included in this study. Also, we have considered only publications in English language excluding other language publications. This studies primary focus is on engineering application of weak soil, finite element analysis and other applications was ignored in this work. We had used Scopus as the database, further studies using Web of Science, Lens, Dimensions and other databases also needed, each database has unique indexed content and the results may vary according to the database used.
In this work we have performed research trend analysis for Fracture mechanics applications in soil, through this study we have found the following important points that will give directions to future researchers.
Concerned with scientific output there is a negative growth of 0.22% in the study period which shows that the publication progress and in turn research outcome is reducing which may be owing to many attributes.
The main keywords surrounding which the work goes on includes “fracture mechanics”, “soil”, “finite element analysis”, “fracture” “clay”, “computer simulation”.
Concerned with this work done by countries, China has more authors’ affiliations, with 1250 authors connected to the country, followed by Australia, United States and United Kingdom with 65, 49, and 12 connections.
Some of the emerging topics include “seepage”, “fracture toughness”, “rock mechanics” and thus its evident that recent research revolves surrounding this topic.
Average citations per document in this domain is above average and its around 18 per paper, this shows that considerable interest exists among research fraternity.
Last five years had seen good number of publications done in these keywords and 2021 had maximum number of papers.
Hence, we suggest further study in this area using other databases and we are sure that this work will serve as a point of interest.
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Written By
Gobinath Ravindran, Vutukuru Mahesh, Herda Yati Binti Katman and A. Nikhil Kumar
Submitted: 10 February 2023Reviewed: 05 July 2023Published: 22 August 2023
Open access peer-reviewed chapter
