a review of case study method in operations management research

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International Journal of Operations & Production Management

ISSN : 0144-3577

Article publication date: 1 February 2002

This paper reviews the use of case study research in operations management for theory development and testing. It draws on the literature on case research in a number of disciplines and uses examples drawn from operations management research. It provides guidelines and a roadmap for operations management researchers wishing to design, develop and conduct case‐based research.

• Operations management
• Methodology
• Case studies

Voss, C. , Tsikriktsis, N. and Frohlich, M. (2002), "Case research in operations management", International Journal of Operations & Production Management , Vol. 22 No. 2, pp. 195-219. https://doi.org/10.1108/01443570210414329

Copyright © 2002, MCB UP Limited

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A Review of Case Study Method in Operations Management Research

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"A Review of Case Study Method in Op..." refers background in this paper

... At the core of theory building is data analysis (Eisenhardt, 1989; Glaser & Strauss, 1967; Yin, 2017). ...

... …is to replicate or extend the emergent theory by identifying extremes, polar types (opposite situations along some dimension), or candidates for niche situations. to help discover categories, properties, and interrelationships that will extend the theory (Glaser & Strauss, 1967; Yin, 2017). ...

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"A Review of Case Study Method in Op..." refers background or methods or result in this paper

... Using multiple data sources provides increased data reliability and more robust substantiation of constructs and propositions (Eisenhardt, 1989; Voss et al., 2002). ...

... In the case of research, we often build a sample of cases by selecting them according to different criteria (Eisenhardt, 1989). ...

... As a result, there is no easy answer to how many cases; Eisenhardt (1989) specifically suggested that in the range of 4–10 cases “usually works well.” ...

... These findings support the claims of Eisenhardt (1989), Yin (2017), and Barratt et al. (2011) that multiple case studies are used in theoretical research because of the validity, robust and testability of the theory. ...

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Approaches combining methods of Operational Research with Business Process Model and Notation: A systematic review

Hana tomaskova.

1 University of Hradec Kralove, Faculty of Informatics and Management, Hradec Kralove, Czech Republic

Gerhard-Wilhelm Weber

2 Faculty of Engineering Management, Poznan University of Technology, Poznan, Poland

3 Institute of Applied Mathematics, Middle East Technical University, Ankara, Turkey

Associated Data

The following information was supplied regarding data availability:

This article does not contain data or code because it is a literature review.

Business process modelling is increasingly used not only by the companies’ management but also by scientists dealing with process models. Process modeling is seldom done without decision-making nodes, which is why operational research methods are increasingly included in the process analyses.

This systematic literature review aimed to provide a detailed and comprehensive description of the relevant aspects of used operational research techniques in Business Process Model and Notation (BPMN) model.

The Web Of Science of Clarivate Analytics was searched for 128 studies of that used operation research techniques and business process model and notation, published in English between 1 January 2004 and 18 May 2020. The inclusion criteria were as follows: Use of Operational Research methods in conjunction with the BPMN, and is available in full-text format. Articles were not excluded based on methodological quality. The background information of the included studies, as well as specific information on the used approaches, were extracted.

In this research, thirty-six studies were included and considered. A total of 11 specific methods falling into the field of Operations Research have been identified, and their use in connection with the process model was described.

Operational research methods are a useful complement to BPMN process analysis. It serves not only to analyze the probability of the process, its economic and personnel demands but also for process reengineering.

Introduction

It has been more than 15 years since ‘Business Process Model and Notation’ or ‘Business Process Modelling Notation’ (BPMN) became the official notation for process modelling. During its lifetime, this notation has gained many users and, thanks to its user-friendliness, it is used in many areas. This wide usage has led to the interconnection and use of other technologies and methods. The fundamental problem of any complex process is decision making. Operational Research as a popular scientific approach is so often associated with procedural issues, making its connection to BPMN is more than natural. This article focuses on the analysis of the relationship between the Business Process Model and Notation (BPMN) process modelling and specific methods of Operational Research.

Business Process Modelling Notation was created by the Business Process Management Initiative (BPMI) as an open standards. It is very similar to flowcharts and Petri nets but offers much more sophisticated tools to describe and simulate behaviour. Silver (2009) stated that this approach is an ‘event-triggered behaviour,’ a description of the ‘something happened’ mode. Business Process Modelling is used to describe, recognize, re-engineer, or improve processes or practices, Tomaskova (2017) . Business Process Model and Notation (BPMN) is the language that is used to model business process steps from start to end. The notation was explicitly designed for wide-ranging use in process analysis, The Object Management Group (2011) . BPMN is both intelligible to non-specialists and allows a complicated processes between different participants to be represented. Another, very significant feature of BPMN is its ‘business-friendly’ orientation, which is essential for the company’s business and knowledge.

Operational Research (OR) is concerned with formulating, modelling, and solving a variety of decision-making situations to find the optimal solutions. The company’s philosophy and decide over business data are the most crucial management actions. The task of the manager is to select in the real system the problem to be analyzed and to formulate it precisely. The standard way of doing this involves the expression of the economic model and then the formulation of a mathematical model. It is necessary to build a simplified model of the real financial systems that only includes the essential elements that describe the formulated problem. The manager has to set the goal of the analysis and subsequent optimization. It is important to define all operations and processes that influence this goal, to describe all the factors, and to verbally express the relationships between the stated purpose and the mentioned processes and factors.

The article is divided into the following parts. The “Related works and background” section lists research articles that are relevant to a given combination of BPMN and OR areas and briefly. That part briefly provides essential information regarding the approaches that are fundamental to this systematic review. The “Research methodology” section describes a systematic search, i.e. entry conditions, exclusion criteria and limitations. The “Results” section presents the results of the analysis of articles fulfilling the requirements of the systematic review. We analyzed publications according to when they were published, their citations, the scientific areas covered, the cooperation of the authors and their keywords. Subsequently, we examined selected articles in terms of methodology, approach and research areas. In the “Discussion”, we focus on scientific gaps and future research. We present a research area where we expect an increase in publications, including their specific components. We also discuss the future development of applied methods and approaches. Finally, the “Conclusion” section summarizes the results and benefits of this study.

Related Works and Background

The background information and related works are listed in the paragraphs below. We first focused on process modelling and BPMN and then on OR and its essential methods and approaches.

Organizational processes and decision support can be captured in many ways, and for many areas, we can mention, for example: strategic management by: Maltz & Kohli (1996) , Certo (2003) , Tomaskova (2009) , Maresova (2010) , Tsakalidis et al. (2019) ; product development research and innovation implementation, see Repenning, 2002 , Garcia (2005) ; IT and economic analyzes see Shane & Cable (2002) , Dedrick, Gurbaxani & Kraemer (2003) , Krenek et al. (2014) , Tomaskova, Kuhnova & Kuca (2015) , Maresova, Tomaskova & Kuca (2016) , Tomaskova et al. (2016) , Maresova, Sobeslav & Krejcar (2017) , Cheng et al. (2019) , Tomaskova, Kopecky & Maresova (2019) , Tomaskova et al. (2019) , Kopecky & Tomaskova (2019) , Kopecky & Tomaskova (2020) ; different simulation approaches analysis, see Sterman (1994) , Kozlowski et al. (2013) , Cimler et al. (2018) or non-standard optimization techniques by: Gavalec & Tomaskova (2010) , Bacovsky, Gavalec & Tomaskova (2013) , Tomaskova & Gavalec (2013 , 2014 ), Gavalec, Plavka & Tomaskova (2014) , Gavalec, Mls & Tomaskova (2015) , Cimler et al. (2017) , Oudah, Jabeen & Dixon (2018) .

Some authors have attempted to provide a solution for process model analysis. For example Melao & Pidd (2000) discussed the strengths and limitations of the various modelling approaches used in business process transformation. The article by Glassey (2008) compares three process modelling processes used in case studies. The article by Sadiq & Orlowska (2000) analyze process models using graph reduction techniques. Other authors like Van der Aalst et al. (2007) , Krogstie, Sindre & Jorgensen (2006) use specific tools, frameworks and methods for process analysis and modelling.

Business process modelling

Today, process modelling and business process management (BPMN) have a significant impact. Process modelling is currently a mainly graphical representation of processes, e.g. in what order particular activities should be implemented and what inputs and outputs the processes require for proper functioning. The primary goal of process modelling is to increase the efficiency and effectiveness of the entire process as well as partial activities. Many business process modelling techniques have been proposed over the last decades, so the article Recker et al. (2009) comparatively assesses representational analyses of 12 popular process modelling techniques to provide insights into the extent to which they differ from each other. The review business process modelling literature and describe the leading process modelling techniques falling to and before 2004 are published in the articl Aguilar-Saven (2004) . The topic of visualization of business process model has been investigated in publication Dani, Freitas & Thom (2019) , where the authors performed a systematic literature review of the topic “visualization of business process models”. Kalogirou (2003) is a particularly fascinating article that illustrates how AI techniques might play an essential role in the modelling and prediction of the performance and control of the combustion process. Although BPM initially focused mainly on the industrial, service and business sectors, it has also appeared in other sectors in recent years. The popularity of BPMN has been confirmed by articles such as Zarour et al. (2019) , which presents the current state-of-the-art of BPN extensions. Publication De Ramon Fernandez, Ruiz Fernandez & Sabuco Garcia (2019) deals with the optimization of clinical processes.

Business process model and notation

Business process model and notation is a language for creating business process models Silver (2009) . Under the auspices of the Object Management Group (OMG), the Business Process Management Initiative (BPMI) created the BPMN as an open standard in 2004 by the first version 1.0. In 2005, BPMI merged with the Object Management Group (OMG), and the following year, the latter issued the BPMN specification document. In 2010, BPMN version 2.0 was developed, and the current version of BPMN 2.0.2 was released in December 2013. History of BPMN and notation development is a frequent topic of BPMN publications, we can mention Nisler & Tomaskova (2017) , Kocbek et al. (2015) , Chinosi & Trombetta (2012) , White (2008) , Van der Aalst, Adriansyah & Van Dongen (2012) and Recker (2012) . BPMN is similar to flowcharts and is based on the concept of Petri nets, but it is a more sophisticated and user-friendly language. The graphic form of BPMN makes it understandable even for non-experts. In BPMN, we distinguish several types of elements that we can use in modelling. The specific standards link these elements. In the base classification, we define four groups of items. These are Flow Objects, Connecting Objects, Swimlanes and Artifacts, see The Object Management Group (2011) .

Operational Reserach

Operational Research (OR) is the well-known approach of using analytical and advanced methods to help make the best possible decisions. As early as 1980, Article by authors Shannon, Long & Buckles (1980) presented the results of a survey of the perception of the usefulness and knowledge of the 12 OR methodologies commonly used in the practice of industrial engineering. The article by Dubey (2010) defines the relationship between OR and another branch of sciences. The article Gu, Goetschalckx & McGinnis (2010) presents a detailed survey of the research on warehouse design, performance evaluation, practical case studies, and computational support tools. The article Negahban & Smith (2014) provided a review of discrete event simulation publications with a particular focus on applications in manufacturing.

OR methods are often associated with new technologies. In article Sarac, Absi & Dauzère-Pérès (2010) , a state-of-the-art on RFID technology deployments in supply chains was given to analyze the impact on the supply chain performance. Xu, Wang & Newman (2011) , in their article, tries to identify future trends of computer-aided process planning (CAPP). Dynamic ride-share systems is investigated in the article Agatz et al. (2012) .

Linear programming

One of the most popular areas of OR in practice is linear programming (LP). The mathematical model of linear programming tasks contains a single linear purpose function, and the actual constraints of the problem are described only by linear equations and inequalities. These tasks are most often encountered in economic practices. Linear programming has been described in several books: Dantzig (1998) , Schrijver (1998) , Dorfman, Samuelson & Solow (1987) .

Multicriterial decision making

The solving of multi-criteria decision-making (MCDM) tasks comprises the search for optimal values of the unknowns, which are simultaneously assessed according to several often contradictory criteria. Thus, the mathematical model of multi-criteria decision problems contains several purpose functions. Depending on how the sets of decision variants are defined, we are talking about the tasks of multi-criteria linear programming or multi-criteria evaluation of options. A review of applications of Analytic Hierarchy Process in operational management is inverstigated in Subramanian & Ramanathan (2012) . The article Velasquez & Hester (2013) performs a literature review of common Multi-Criteria Decision Making methods. The authors present the results of a bibliometric-based survey on AHP and TOPSIS techniques in publication Zyoud & Fuchs-Hanusch (2017) .

Project planning

Project management tasks consist of several separate activities that are interdependent and may be run simultaneously. The most commonly used method is the so-called network analysis, where a network graph is created from the left chronologically arranged project activities representing the project life cycle. The longest possible path from the beginning to the end of the project is recorded by “the critical path”. The non-observance of this path will lead to a slowing down of the whole project, whose time duration is to be optimized. The optimistic, pessimistic, and most probable estimate of the implementation of the entire project is determined. The article Nutt (1983) relates the project planning process and implementation. Critical Path Method (CPM) is found in the article Jaafari (1984) , to be equally useful as a planning tool for linear or repetitive projects.

The Resource-Constrained Project Scheduling Problem (RCPSP) is a general problem in scheduling. The article Pellerin, Perrier & Berthaut (2020) examines the general tendency of moving from pure metaheuristic methods to solving the RCPSP to hybrid methods that rely on different metaheuristic strategies ( Cimr, Cimler & Tomaskova, 2018 ).

Nonlinear programming

Nonlinear programming is the case when the purpose function is not linear. Tasks then often have a large number of local extremes and often also have great difficulty finding them.

Dynamic programming

If constraints are functions of some parameter, which is most often time, we are talking about dynamic programming. This approach deals with the modelling of more complex multi-stage optimization problems divisible into related sub-problems. Depending on the time parameter, the system is always in one of the acceptable states during the process. At certain times it is necessary to choose from a set of possible decisions, which again results in the transition to the next state. We call the strategy a sequence of these states of the system and choices, looking for the course with the best valuation. Simulations are often used to model and analyze the operation of complex systems without realization and in less than real-time.

• Queuing theory is a type of dynamic programming task. It deals with streamlining the functioning of systems in which it is necessary to gradually serve all units whose requirements are continuously met on so-called service lines. The challenge is to find the most effective way to handle these requirements.
• Inventory management models address the issue of optimizing the supply process and the volume of inventory stored. Costs associated with ordering, issuing, and keeping stocks in stock should be minimized.

Stochastic programming

Stochastic programming deals with optimization problems in which they act as parameters of their constraints of random variables. Probabilistic calculus methods solve these problems, and their results have the character of random variables. Stochastic processes can also be ranked among tasks with the input data uncertainties. This approach is used to describe the behavior of systems evolving. We are talking about stochastic processes, a special case is the so-called Markov chains and Markov processes. Basic books on this topic are, for example: Kall, Wallace & Kall (1994) , Birge & Louveaux (2011) , Shapiro, Dentcheva & Ruszczyński (2014) .

Research Methodology

Kitchenham & Charters (2007) highlighted three essential elements for a systematic literary review: the determination of the research question(s), the organisation of an unbiased and extensive analysis of related publications, and the determination of precise criteria of inclusion and exclusion.

We identified three research questions:

• Research question 1 (R1): Greater adaptability of BPMN elements causes greater application of this notation in publications.
• Research question 2 (R2): The connection between BPMN and OR methods is most often applied to the business and economics areas.
• Research question 3 (R3): The queue theory is the most widely used method in BPMN processes.

The analysis process and criteria are given in the following relevant subsections.

Eligibility criteria

This study included publications listed in the Web Of Science (WOS) database of Clarivate Analytics that were published between 1 January 2004 and 18 May 2020. The year 2004 was selected as this is when BPMN was created by BPMI.

Exclusion criteria (EC) are:

• EC1 = The publication was published in a language other than English.
• EC2 = The full text of the publications was not available.
• EC3 = The publication did not coincide with the topic of systematic research.
• EC4 = BPMN was used only as a presentation tool and not as part of the research.

Information sources and search

The primary source of information for the study was the database Web Of Science (WOS) of Clarivate Analytics. An advanced search was performed for the search query mentiones below. The search was performed in the Topics (TS) section.

Especially, the CORE database with the indexes listed in Table 1 was selected. The search was performed for ‘All document types,’ ‘All languages’ and the years 2004–2020.

Study selection

The first step of the review process involved title and abstract screening, followed by a full-text review of the remaining articles. Two independent assessors verified the results of the title and abstract screening and the full-text review. One assessed the suitability of the results from the perspective of OR and the other from an IT perspective, i.e. whether it was BPMN notation and its use. Articles were included if they met all the following criteria: (i) they used an OR method, (ii) a BPMN model was used and (iii) the complete text was available in English (abstracts, commentaries, letters and unpublished data were excluded). Studies were not excluded based on their methodological quality.

The selected publications were examined from many perspectives, and each contribution was coded according to different criteria. This study aimed to enhance the discipline’s fundamental progress in understanding the link between OR methods and BPMN. The results of this study could encourage scientists to use OR methods for process analysis.

A limitation of this review was restricting the included articles to English-language publications that looked at process analysis using OR and BPMN published between 1 January 2004 and 18 May 2020. Relevant studies in other languages or published after 18 May 2020 may have been omitted.

Data collection process

Data was collected based on keywords selected from the article Lane, Mansour & Harpell (1993) , which analyzed the quantitative techniques of Operation Research. From this document, the 18 Operation Research methods were selected and listed in the Table 2 .

The results were further categorized as to whether they corresponded to the given keywords and their meaning. The main results of the systematic literature review were obtained by analyzing by the two main guidelines of PRISMA: Moher et al. (2009) and MECIR: Higgins et al. (2018) .

Synthesis of results

The individual studies were subjected to bibliometric analysis and then the studies were assessed according to the content and methods used. The bibliometric analysis describes and analyses up to date research. It aims at summarizing the latest progress in the field by quantitatively investigating the literature. This method provides a vast canvas of knowledge from the micro-level (institutes, researchers, and campuses) to the macro-level (countries and continents) Mryglod et al. (2013) . Frequency analysis was used to find the most common scientific areas, the countries with the most publications and the most common keywords. Science mapping was performing using the VOS viewer, Venn diagrams and bar and bubble graphs, Van Eck et al. (2010) , Cobo et al. (2011) .

The Venn/Euler diagram graphically represents the relationships of the largest set of keywords. Euler diagrams are considered to be an effective means of visualizing containment, intersection, and exclusion. The goal of this type of graph is to communicate scientific results visually. Leonhard Euler first popularized the principle of labeled closed curves in the article Euler (1775) Alternative names for Euler diagrams include ‘Euler circles.’ They can also be incorrectly called Venn diagrams. Venn diagrams require all possible curve intersections to be present, so can be seen as a subset of Euler diagrams, that is, every Venn diagram is a Euler diagram, but not every Euler diagram is a Venn diagram. John Venn introduced Venn diagrams a hundred years after Euler in the article Venn (1880) . Venn diagram is a schematic graph used in logic theory to depict collections of sets and represent their relationships.

The initial search resulted in 128 articles. After removing duplicates, 107 were left that underwent title and abstract screening. After screening, 61 articles remained that underwent full-text review. The final number of included articles for information abstraction was 36. Overview of the number of publications according to exclusion criteria is shown in Fig. 1 .

Eighteen keywords selected from the article by Lane, Mansour & Harpell (1993) were involved in the study. These keywords have been classified according to whether a publication meeting a study condition has been found for them. Only for 13 keywords were found a publication suitable for this study, as can be seen in Table 2

Categorization of publications based on the clarivate analytics

Journals and books covered by the Web of Science Core Collection were assigned to at least one Web of Science category. Each Web of Science category was mapped to one research area Clarivate Analytics (2019) . The research areas for the selected publications were:

• COMPUTER SCIENCE (CS)
• ENGINEERING (En)
• OPERATIONAL RESEARCH MANAGEMENT SCIENCE (OR)
• BUSINESS ECONOMICS (BE)
• ROBOTICS (Ro)
• AUTOMATION CONTROL SYSTEMS (ACS)
• TELECOMMUNICATIONS (Te)
• TRANSPORTATION (Tr)

We selected four main groups, for which we compiled a bar graph and a Venn diagram after analysis. We chose the number of four research areas for representation in the Venn diagram; four sets are still well arranged. Another argument was the number of publications in other areas, where the set "ROBOTICS" contains two documents and the sets ‘AUTOMATION CONTROL SYSTEMS,’ ‘TELECOMMUNICATIONS’ and ‘TRANSPORTATION’ each one document.

Bar graph on Fig. 2 is based on frequency analysis and contains the total number of publications in a given research area, their average number of citations, and the corresponding average number of pages per article. The graph shows the results by type of purpose. The first part shows the frequency of documents for each research areas. The second part focuses on the average number of citations, and the third shows the average number of pages per article.

The Venn diagram, in Fig. 3 , shows selected four research areas as sets, including their intersection areas. In a specific area, we also stated the relevant number of documents and their average number of citations.

This part of the bibliometric analysis showed us the answer to the research question R2. Although BPMN was explicitly designed for corporate analysis and economic analysis, and Operational Research focuses primarily on addressing managerial decisions, most publications were not in the field of business economics (BE). Surprisingly, this area actually has the fewest publications. The field of computer science had the most papers, and papers in the field of OR had the most citations. The field of BE had the most extended publications, however, i.e. the average number of pages per paper.

Result1: Research question R2—not confirmed.

Year of publication

Figure 4 illustrates the distribution over time of the selected publications with BPMN milestones. The BPMN versions adoption dates, taken from OMG.org (2018) , complements this figure.

The different BPMN versions brought more or fewer changes in notation. While the changes between BPMN 1.0 and BPMN 1.2 were rather consmetics, e.g. renaming ‘Rule’ elements to ‘Conditional’ or slight increasing the number of elements from 48 to 55. The arrival of BPMN 2.0 was a major breakthrough and represented the largest revision of BPMN since its inception. In this version, it is possible to create a new ‘Choreography model,’ ‘Collaborations model’ and ‘Conversation model’ in BPMN in addition to collaborative processes and internal (private) business processes. Events are now divided into ‘interrupted’ and ‘non-interrupted’ and ‘catching’ and ‘throwing.’ The message type is newly introduced, and the data object has three specifications. BPMN 2.0 contains 116 elements. BPMN 2.0.2 included only minor modifications in terms of typos.

Given the magnitude of changes between the different versions of the BPMN notation, the sharp increase in publications following the introduction of the BPMN 2.0 notation can be considered a confirmation of research question R1. It is very interesting that publications in the field of BE did not appear until 2017.

Result: Research question R1—confirmed.

The average number of citations of the analysed documents was 2.22. The first quartile was 0, and the third quartile was 3.75. The median was equal to 1 and data variability above the third quartile was limited to seven citations. We identified two outliers values: 12 citations for Hasic, De Smedt & Vanthienen (2018) and 15 citations for article Wu et al. (2015) .

Author analyses

Bibliometric analysis cannot be done without review by the authors. We focused on illustrating co-authorship. The total number of authors of publications selected for this study was 84: al achhab, m (1), aouina, zk (1), ayani, r (1), aysolmaz, b (1), bahaweres, rb (1), batoulis, k (1), ben ayed, ne (1), ben said, l (1), ben-abdallah, h (3), bisogno, s (1), bocciarelli, p (1), boukadi, k (1), braghetto, kr (1), burattin, a (1), calabrese, a (1), ceballos, hg (2), chien, cf (1), cho, sy (1), creese, s (1), cunha, p (1), d’ambrogio, a (1), d’ambrogio, sa (1), de lara, j (1), de smedt, j (2), demirors, o (1), duran, f (2), el hichami, o (1), el mohajir, b (1), ferreira, je (1), figl, k (1), fitriyah, a (1), flores-solorio, v (2), fookes, c (1), garcia-vazquez, jp (1), ghiron, nl (1), ghlala, r (1), gomez-martinez, e (1), hansen, z (1), hansen, znl (3), happa, j (1), hasic, f (2), herbert, lt (8), holm, g (1), iren, d (1), jacobsen, p (3), jobczyk, k (1), kamrani, f (1), khlif, w (2), kluza, k (1), ligeza, a (1), manuel vara, j (1), marcos, e (1), mazhar, s (1), mendling, j (1), mendoza morales, le (1), mengersen, k (1), monsalve, c (1), moradi, f (1), naoum, m (1), onggo, bss (1), pablo garcia, j (1), perez-blanco, f (1), pitchforth, j (1), proudlove, nc (1), rekik, m (1), rocha, c (2), rosemann, m (1), rozy, nf (1), salaun, g (2), sharp, r (4), sperduti, a (1), suchenia, a (1), tang, rz (1), tokdemir, g (1), tomaskova, h (1), vanden broucke, sklm (1), vanthienen, j (3), veluscek, m (1), villavicencio, m (1), vincent, jm (1), weske, m (1), wisniewski, p (1), wu, ppy (2), xie, y (1).

These authors formed different sized groups, as can be seen in Fig. 5 . We grouped the authors according to their co-authors’ collaborations with a curve connecting the co-authors. The size of the node of this connection corresponds to the number of documents by the given author. The colours used to distinguish the authors were created using the average years of the publication of their papers.

For the authors’ average publication years, the first quartile was 2015, the third quartile was 2018.5 and the median was 2017. The variability outside the lower and upper quartiles was given by 2011 and 2020. We identified one outlier value corresponding to the year 2009.

The most prominent groups were around the authors listed in Fig. 6 . This figure also contains the number of documents by the authors, their total number of citations and their average value.

According to this analysis Wu, P. Y. had the highest number of citations (7.5), followed by De Smedt, J. (7) and Hasic, F. (7). Herbert, L.T. had the most documents (8) and Tomaskova, H. had no co-author connections.

The authors were also analyzed in terms of their country or region affiliations. A total of 25 countries were identified and their location, including the number of relevant publications, are shown in Fig. 7 . The countries with the highest number of affiliated publications were Denmark (8) and Tunisia (4), followed by Belgium, France, Saudi Arabia, Italy and Spain, who all had three.

Keywords analysis

The keywords were categorized according to those identified by the published authors and the keywords PLUS assigned by Clarivate Analytics databases. The data in KeyWords Plus are words or phrases that frequently appear in the titles of an article’s references but do not appear in the title of the item itself. Based upon a special algorithm that is unique to Clarivate Analytics databases, KeyWords Plus enhances the power of cited-reference searching by searching across disciplines for all the articles that have cited references in common, more information is on the web link Clarivate Analytics (2018) . A total of 130 unique keywords and 46 unique KeyWords Plus keywords were found for selected publications.

A total of 130 author keywords were mentioned in the publications and a general view of their interconnection can be seen in Fig. 8 .

Below is a list of all author keywords with the number of the weight-link to other keywords: activity theory (4), affiliation (6), agent based model (4), agent-based systems engineering (3), airport passenger facilitation (8), atl (5), automated verification (4), bayesian network (4), bayesian networks (4), bpm (6), bpmn (60), bpmn business processes (4), bpmn extension (3), bpmn model restructuring (5), business process (18), business process automation (3), business process management (13), business process model (5), business process model measures (3), business process modelling notation (4), business process optimisation (5), business process outsourcing (3), business processes (3), cloud computing (3), clustering (5), communication theory (11), configurable reference model (8), consequence modelling and management (10), contextual factors (8), cycle time (4), decision making (15), decision mining (3), decision model and notation (3), decision modeling (4), decision modelling (5), dikw (11), discrete-event simulation (4), dmn (15), effort prediction model (3), engineering agent-based systems (3), engineering systems (6), enterprise risk management (4), eqn (5), evolutionary algorithm (2), evolutionary algorithms (5), facilitated modelling (4), fault tree analysis (6), fault tree generation (6), flow (8), formal risk analysis (6), genetic algorithm (3), healthcare (4), hierarchical clustering (6), incident response (11), integrated modelling (5), interviews (11), jeqn (5), knowledge discovery (6), knowledge management (11), knowledge rediscovery (6), licenses (11), maude (7), mc-dmn (5), mcdm (5), mda (5), metrics (5), model checking (4), model transformations (5), model-driven architecture (4), model-driven engineering (5), modelling (4), object modeling (4), optimisation (6), organizational mining (3), performance (5), performance evaluation (3), petri nets (5), pproduction optimisation (2), preference to criteria (5), prism (8), probability (2), process configuration (8), process enhancement (3), process chain network (5), process merging (8), process mining (6), process modeling (4), process modelling (5), project management (3), qualitative analysis (4), quantitative model checking (10), quantitative service analysis (6), quantitative workflow analysis (4), queues (3), queuing theory (4), reliability analysis and risk assessment methods (4), resource allocation (4), restructuring (6), rewriting logic (7), rules (5), safety assessment software tools (4), safety management and decision making (4), security (11), security operation center (11), sense-making (11), separation of concerns (5), service engineering (6), scheduling (4), simulation (4), simulations (3), social network (5), social network analysis (3), social network model (6), socio-technical systems (sts) (4), soundness (4), space-sensitive process model (8), statistical model checking (4), stocastic bpmn (2), stochastic automata network (3), stochastic bpmn (11), stochastic model checking (13), stochastic modeling and analysis (4), structural and semantic aspects (5), tacit knowledge (11), task analysis (11), task assignment (4), task model (4), timed automata (4), topsis (5), verification (2).

As you can see in the figure, most of the author’s keywords are directly or indirectly linked with the term ‘BPMN’, but there are also isolated groups. In the following text, we’ve listed separate keyword groups. We’ve added a year of publication, a number of citations, and a specific document to which the keywords belong.

• 2013; citations; (business process automation; business process model measures; effort prediction model; project management) Aysolmaz, Iren & Demirors (2013) .
• 2014; citation; (evolutionary algorithm; pproduction optimisation; stocastic bpmn) Herbert et al. (2014) ,
• 2015; citations; (agent based model; bayesian network; business process modelling notation; modelling; socio-technical systems (sts)) Wu et al. (2015) ,
• 2015; citation; (affiliation; bpm; hierarchical clustering; knowledge discovery; knowledge rediscovery; restructuring; social network model) Khlif & Ben-Abdallah (2015) ,
• 2016; citations; (bpmn extension; business process outsourcing; cloud computing; genetic algorithm) Rekik, Boukadi & Ben-Abdallah (2016) .
• 2017; citations; (bpmn model restructuring; clustering; metrics; rules; social network; structural and semantic aspects) Khlif, Ben-Abdallah & Ben Ayed (2017) .
• 2019; citations; (atl; business process model; model transformations; model-driven engineering; petri nets; process chain network) Gómez-Martnez et al. (2019) .

As mentioned above, there were only 46 KeyWords Plus keywords (the number of links to other keywords is given in parentheses after the keyword): accuracy (6), ambiguity (6), automation (3), bpmn (20), business process models (6), checking (6), cognitive effectiveness (7), communities (2), complex (0), confidence (6), context (9), critical path (9), decision-making (7), design (7), dimensions (7), distributed simulation (1), framework (8), functional size (2), group creativity (6), identification (9), implementation (5), information (6), integration (2), model (7), neural-network (7), organizational knowledge (1), patterns (6), performance (9), process execution (9), process models (9), productivity (2), quality (2), reality (2), reference models (2), resources (9), risk (6), science research (2), semantics (9), sensemaking (1), simulation (9), strategy (0), systems (6), tables (7), verification (15), web (1), workflow (9).

As can be seen in Fig. 9 , these keywords are far more separate from each other compared to the author’s keywords.

Classification of articles by methodology

Based on the expert assessment, we examined the documents regarding the methods and approaches used. We created seven groups corresponding to a method or approach that was an essential part of the publication: probabilistic models, Decision Model and Notation (DMN), dynamic task assignment problem, evolutionary and genetics algorithms, queuing theory, social networks and others. These groups were also based on keyword analysis, as some separate groups of copyright keywords belong to highly unique articles. We assigned each document to just one group. That is in contradiction to research areas, where one article can be attributed to more than one research area. The individual documents and their division between research areas and methodological groups can be seen in Table 3 . We further analyzed the documents regarding their years of publication and plotted a bubble graph ( Fig. 10 ) with the publication years on the x .axis and the methodological groups on the y -axis. The appropriate number of publications corresponding to the given year and the group is indicated in the respective bubble. This quantity is also graphically represented by the size of the given bubble.

The largest group consisted of 10 publications on DMN and BPMN. Given the initiate year of DMN, this is the most significant approach serving with BPMN. DMN 1.0 was made available to the public in September 2015, the OMG group released DMN 1.1 in June 2016, DMN 1.2 was released in January 2019 and the latest version of DMN 1.3 was released in March 2020. The latest version did not affect this systematic search; however, the growth of publications since 2017 (see Fig. 10 , for example, was undoubtedly be affected by the DMN update.

We only assigned four documents to the methodological group focused on queue theory (See Table 3 and Fig. 10 ). The specific articles are listed in the following section under the appropriate heading. As the largest group was the DMN and BPMN group, we can thus rule out research question R3.

Result: Research question R3—not confirmed.

The methods, techniques and approaches used in the included publications are listed in the following section.

Probabilistic models

The probabilistic model can be used to make decisions when the activity reaches an exclusive splitting gateway and the activity’s subject must decide between alternative actions. They can be used for predicting or deciding between alternative works based on desirable outcomes. Probabilistic models were presented in the following publications:

• Herbert & Sharp (2012) : Quantitative analysis of probabilistic BPMN workflows;
• Herbert & Sharp (2013) : Precise quantitative analysis of probabilistic business process model and notation workflows;
• Ceballos, Flores-Solorio & Garcia-Vazquez (2015) : Towards Probabilistic Decision Making on Human Activities modeled with Business Process Diagrams;
• Ceballos, Flores-Solorio & Pablo Garcia (2015) : A Probabilistic BPMN Normal Form to Model and Advise Human Activities;
• Naoum et al. (2016) : A probabilistic method for business process verification: Reachability, Liveness and deadlock detection,

there the (Causal) Bayesian Network or Markov Decision processes were used.

DMN and decision analysis

Decision Model and Notation (DMN) is an industry standard for modeling and executing decisions that are determined by business rules. The association of DMN and BPMN is now common practice:

• Batoulis & Weske (2017) : Soundness of decision-aware business processes,
• De Smedt et al. (2019) : Holistic discovery of decision models from process execution data,
• Durán, Rocha & Salaün (2019) : A rewriting logic approach to resource allocation analysis in business process models,
• Figl et al. (2018) : What we know and what we do not know about DMN,
• Ghlala, Aouina & Ben Said (2017) : MC-DMN: Meeting MCDM with DMN Involving Multi-criteria Decision-Making in Business Process
• Hasic, De Smedt & Vanthienen (2018) : Augmenting processes with decision intelligence: Principles for integrated modelling
• Cho, Happa & Creese (2020) : Capturing Tacit Knowledge in Security Operation Centers,
• Mazhar, Wu & Rosemann (2018) : Designing complex socio-technical process systems - the airport example,
• Suchenia et al. (2019) : Towards knowledge interoperability between the UML, DMN, BPMN and CMMN models
• Tomaskova (2018) : Modeling Business Processes for Decision-Making.

Both standards fall under OMG.

Dynamic task assignment approach

The study : A dynamic task assignment approach based on individual worklists for minimizing the cycle time of business processes by Xie, Chien & Tang (2016) develop a dynamic task assignment approach for minimizing the cycle time of business processes. The contribution of this article lies in developing a dynamic task assignment approach based on queuing theory, individual worklist model, and stochastic theory.

Evolutionary and genetic algorithms

The evolutionary algorithm was applied in the following publications:

• Herbert & Sharp (2014b) : Optimisation of BPMN business models via model checking;
• Herbert et al. (2014) : Evolutionary optimization of production materials workflow processes;
• Herbert, Hansen & Jacobsen (2015) : Using quantitative stochastic model checking tool to increase safety and improve efficiency in production processes;
• Herbert & Hansen (2016) : Restructuring of workflows to minimise errors via stochastic model checking: An automated evolutionary approach;

to optimize the BP diagram, thus looking for a more efficient process. Especially the publication: Specifying business process outsourcing requirements, Rekik, Boukadi & Ben-Abdallah (2016) , presented a genetic algorithm to identify most appropriate activities of a business process that should be outsourced.

Queuing theory

In the article: Comparative analysis of business process litigation using queue theory and simulation (case study: Religious courts of South Jakarta) Bahaweres, Fitriyah & Rozy (2017) , Onggo et al. (2018) . A BPMN extension to support discrete-event simulation for healthcare applications: an explicit representation of queues, attributes and data-driven decision points Onggo et al. (2018) and Gómez-Martnez et al. (2019) . Formal Support of Process Chain Networks using Model-driven Engineering and Petri nets Gómez-Martnez et al. (2019) , the authors use queuing theory and simulation to compare processes modeled in BPMN. In the article: Automated performance analysis of business processes Bocciarelli & D’Ambrogio (2012) , authors presented a BP performance model of EQN (Extended Queueing Network) type.

Social network

The publications below focus on the application of social network analysis metrics (SNA) to studies of biological interaction networks in informatics.

• Khlif & Ben-Abdallah (2015) : Semantic and structural performer clustering in BPMN models transformed into social network models;
• Khlif, Ben-Abdallah & Ben Ayed (2017) : A methodology for the semantic and structural restructuring of BPMN models.

Other approaches

The following publications were unique in their approaches. We can mention for example: Workflow fault tree generation through model checking by Herbert & Sharp (2014a) with FMEA analysis. An effort prediction model based on BPM measures for process by Aysolmaz, Iren & Demirors (2013) with Linear multiple regression analysis. Performance evaluation of business processes through a formal transformation to SAN by Braghetto, Ferreira & Vincent (2011) using Stochastic Automata Network. Estimating performance of a business process model by Kamrani et al. (2009) using a Task assignment approach. Formal verification of business processes as timed automata by Mendoza Morales, Monsalve & Villavicencio (2017) convert BPMN to Timed Automata and then perform standard Queuing analysis. Business models enhancement through discovery of roles by Burattin, Sperduti & Veluscek (2013) , there the authors have extended the process model to roles, specifically designed role-sharing algorithm. Stochastic analysis of BPMN with time in rewriting logic by Duran, Rocha & Salaun (2018) presents a rewriting logic executable specification of BPMN with time and extended with probabilities. SBAT: A STOCHASTIC BPMN ANALYSIS TOOL by Herbert, Hansen & Jacobsen (2014) presents SBAT, a tool framework for the modelling and analysis of complex business workflows and A framework for model integration and holistic modelling of socio-technical systems by Wu et al. (2015) presents a layered framework for the purposes of integrating different socio-technical systems (STS) models and perspectives into a whole-of-systems model.

We have identified several gaps in the research and issues that need to be addressed in future research. The main gaps concern the research area of business economics. We assumed that this area would be the main and most frequent for the combination of BPMN and OR methods. However, we found that this area could be affected by the absence of specific notation. The relevant publications were written only after the release of version DMN 1.1. The effect of DMN notation will be addressed in future research.

An unexpected gap was a solution to finance and human resources management through OR. We would like to introduce publications Savku & Weber (2018) and Graczyk-Kucharska et al. (2020) as the pioneering works. The first article added the problem of optimal consumption problem from cash flow with delay and regimes. The authors developed the general analytic model setting and methods for the solution by studying a stochastic optimal control problem using the tools of the maximum principle. They proved the necessary and sufficient maximum principles for a delayed jump-diffusion with regimes under full and partial information. The second publication focused on transversal competencies, which are sets of knowledge, skills and attitudes required for different positions and in different professions. The authors used the method of multivariate additive regression spline together with artificial neural networks to create a model describing the influence of various variables on the acceleration of the acquisition of transverse competencies.

We assume that future research will be influenced by simulation and prediction methods. This study showed the use of Agent-based modelling methods and discrete-event simulations, or probabilistic models and social networks, but neural networks or artificial intelligence methods appeared in any publication. Based on this study, we further expect the use of more sophisticated approaches and the effect of new techniques. At the same time, it is possible to extend process modelling to inaccurate data using Fuzzy methods.

This paper presented a systematic overview of publications using BPMN and OR methods in process analysis. We analyzed 108 articles, that were selected using the appropriate strings in the advanced search option of in the WOS database. The papers that met the conditions of the study were subjected to various analyzes and were briefly described.

The review showed that the processes modelled by BPMN can be extended or analyzed as probabilistic processes, queue theory, or role and task assignments. Alternatively, processes can be optimized using evolutionary or genetic algorithms. The research also highlighted the need to identify keywords in publications correctly. For example, less than two-thirds of the selected articles contained the keyword BPMN, even though all the documents used this notation. Most of the articles were so-called one-off publications. Only a small number of author teams developed their topic in further continuing publications. Due to this, the average number of citations is relatively low. Due to the average number of citations to the total number of publications in all research areas, documents falling into the field of Operational Research are outstanding; there is an average of seven citations per article.

We analyzed the publications by research area and found that there is great potential for the research area of business economics (BE). Only a few papers were associated with this area (five in total) but all of them had a higher than average number of citations. The first document we included in this research area was published in 2017, that is only in the last quarter of the examined publication years. This focus on BE may have been initiated by the introduction of DMN notation.

Among the authors, smaller collaborating groups around the world were been identified. That groups co-work within the framework of co-authorship and co-citations. We only identified one single-author publication.

The analysis of keywords showed a significant difference between the keywords assigned by the authors and the so-called KeyWords Plus keywords. While the former were almost completely connected across publications, the latter were significantly diversified.

We have pointed out that the introduction of BPMN 2.0 led to an increase in publications using this notation.

Acknowledgments

The authors thank the student M. Kopecký for support in the field of BPMN modeling.

Funding Statement

The research has been supported by a GACR 18-01246S and by the Faculty of Informatics and Management UHK Specific Research Project. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Additional Information and Declarations

The author declares that they have no competing interests.

Hana Tomaskova conceived and designed the experiments, performed the experiments, analyzed the data, performed the computation work, prepared figures and/or tables, authored or reviewed drafts of the paper, and approved the final draft.

Gerhard-Wilhelm Weber analyzed the data, authored or reviewed drafts of the paper, and approved the final draft.

Gangue grouting filling in subsequent space of coal green mining: methodology and case study

• Original Article
• Open access
• Published: 27 March 2024
• Volume 83 , article number  217 , ( 2024 )

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• Kunpeng Yu 1 ,
• Liqiang Ma 1 , 2 ,
• Ichhuy Ngo 1 ,
• Jiangtao Zhai 1 ,
• Yujun Xu 3 ,
• Zhiyang Zhao 1 ,
• Hui Wang 1 &
• Dangliang Wang 2  

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Underground backfilling stands out as a crucial technological strategy for the eco-friendly and effective management of solid waste in mining operations. However, existing backfilling techniques have led to increased production processes at the working face, resulting in a reduction in coal extraction efficiency. Addressing the temporal and spatial interference between mine solid waste backfilling and coal mining is essential. To overcome this challenge, this study introduces a novel post-mining spatial gangue slurry backfilling method. Radar detection was employed to ascertain the typical characteristics of the subsequent space collapse roof shape. Stress monitoring and compaction experiments were conducted to establish the relationship between stress and the bulking coefficient of the overlying rock mass, identifying subsequent spatial void structure characteristics. The development of a CO 2 mineralized coal-based solid waste filling material, utilizing conventional low-calcium fly ash under normal temperature and pressure conditions, was presented. This paper provides a comprehensive understanding of the post-mining spatial gangue slurry backfilling method, outlines the spatial layout approach for the corresponding system, and analyzes research challenges associated with gangue slurry backfilling materials and the technology of slurry injection borehole layout. The research aims to innovate an efficient underground disposal model for gangue, contributing to the refinement of the technical system for the comprehensive disposal and utilization of gangue.

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Introduction

Coal is one of the primary sources of energy worldwide and plays a significant role in economic development (Zhang et al. 2019a , b , c ; Gao et al. 2018 ). The healthy development of the coal industry is crucial for energy security and sustainable economic growth (Chen et al. 2020a , b ; Xu et al. 2020 ). While coal has made tremendous contributions to industrial development, it has also brought a series of environmental damage issues, significantly impacting surface ecology and groundwater environments, particularly in ecologically vulnerable areas (Singh and Guha 2018 ; Li et al. 2019 ). The contradiction between large-scale coal extraction and environmental protection is particularly pronounced in areas characterized by coalfields with thick coal seams, shallow burial, limited water resources, and fragile ecosystems (Wang et al. 2018a , b , c ; Chen et al. 2020a , b , 2021 ; Zhong et al. 2019 ). In response to the ecological damage caused by large-scale mechanized mining methods, the current scientific development strategy for coal resources needs to shift from “passive restoration” to “active protection” and from “intensive mining” to “harmonious coordination” (Zeng et al. 2019 ; Liu et al. 2020 ).

Due to the limited conditions for coal occurrence, around 90% of coal in China is primarily extracted through underground mining (Wang et al. 2019 ; Huang et al. 2022 ; Qi et al. 2019 ). In accordance with the overall requirements of ecological civilization construction and prioritizing environmental protection, as well as emphasizing natural restoration, efforts should be made to minimize and control the ecological damage caused by mining operations underground. Currently, the main methods used to prevent ground ecosystem disruption resulting from coal mine strata collapse are pillar extraction and backfill mining (Zhu et al. 2018 ; Zhang et al. 2017a , b ; Wang et al. 2018a , b , c ). However, the pillar extraction method leads to resource wastage and reduces the service life of mines. It also affects production layout and efficient coal recovery (Bai et al. 2022b ; Li et al. 2016 ). On the other hand, traditional backfill mining incurs high costs and poor economic viability, making it unsuitable for large-scale promotion and implementation by coal mining enterprises (Wang et al. 2018a , b , c ; Yu et al. 2020a , b ; Shao et al. 2020 ). Therefore, it is crucial to explore a comprehensive, scientifically sound, and efficient coal mining technique that minimizes subsidence and ensures water preservation, which is a vital and practical requirement for green and efficient mining at the current stage (Meng et al. 2021 ; Hou et al. 2021 ; Yuan et al. 2021 ).

In underground mining, longwall mining method, compared to other mining methods, enables continuous coal extraction and possesses advantages such as high productivity, efficiency, recovery rate, and strong applicability (Zhang et al. 2017a , b ; Liu et al. 2023 ). Consequently, it has been widely applied and developed. However, the damage caused by longwall mining to the surface and groundwater in mining areas should not be underestimated (Doulati et al. 2022 ; Bai et al. 2022a ). Since most longwall mining methods primarily adopt the full caving method to manage the roof, the roof collapse area is extensive, resulting in significant displacement and deformation of overlying rock layers from the coal seam to the surface (He et al. 2015 ; Bai and Tu 2019 ). In cases where the coal seam is close to aquifers or surface water bodies, mining-induced fractures may penetrate the aquifer sealing layers, leading to water resource loss and sudden inrush of water in working areas, thereby triggering a series of ecological, environmental, and production safety issues (Gao et al. 2019 ; Yu et al. 2020a , b ; Hu et al. 2018 ). The various environmental and safety problems caused by underground coal mining essentially revolve around the loss of water resources induced by mining operations (Li et al. 2020 ; Xu et al. 2019 ).

Backfill mining is an effective method that limits the impact on water, soil resources, and infrastructure within the tolerable range of ecological tolerance for mining activities (Liu et al. 2018 ; Hu et al. 2017a , b ; Chen et al. 2019 ; Zhang et al. 2020a , b ). Promoting advanced technologies such as efficient backfill mining in an adaptable manner and conducting feasibility studies on coal mine backfill mining are among the key tasks for comprehensive management of mining subsidence areas (Zhao et al. 2019 ; Ma et al. 2018 ; Zhang et al. 2019a , b , c ; Wang et al. 2020 ). Backfilling the goaf is currently one of the most effective approaches to water conservation in coal mining (Liu et al. 2019 ; Zhang et al. 2020a , b ; Xie et al. 2016 ; Xu et al. 2017 ). However, traditional goaf backfilling encounters challenges such as insufficient time and space for timely backfilling before the roof collapses after coal extraction (Chen et al. 2018 ; Yang et al. 2017 ; Wu et al. 2016 ; Zhao et al. 2020 ). Additionally, mining and backfilling operations occur within the same limited space, making it difficult to coordinate parallel operations and causing backfilling to affect mining progress (Zhang et al. 2019a , b , c ; Shi et al. 2019 ; Hu et al. 2017a , b ; Wang et al. 2021a , b ). In coal mining environments characterized by complex geological conditions, a specialized approach to backfill mining has been implemented. This practice entails utilizing materials like gangue, sand, and crushed stone to fill the goaf, with the primary objective of minimizing subsidence associated with the mining process (Yang et al. 2019 ; Jiang et al. 2018 ; Liu et al. 2021 ). However, whether using coal gangue backfilling, cementitious backfilling, partial substitution of fly ash for cement in backfilling, or concrete backfilling, the unit cost is generally high. The relatively high investment cost significantly impacts the economic benefits of enterprises and objectively limits the widespread application of this method.

Regarding this particular situation, the authors propose a delayed backfilling approach for goaf filling. The backfilling operation is delayed compared to the mining operation, allowing for the natural collapse of the goaf roof. This results in a completely or nearly completely filled goaf area formed by the natural collapse of the goaf roof after coal mining. The authors utilize the fragmentation and expansion properties of the collapsed rocks. On the side close to the working face, a designated delayed filling zone is determined. Through directional drilling or upper-level roadways near the working face, the voids in the collapsed zone are grouted before compaction, consolidating the collapsed zone to form a load-bearing structure with certain strength, as depicted in Fig.  1 . Radar detection was utilized to characterize the typical shape of the roof collapse in the subsequent space. Stress monitoring and compaction experiments were carried out to establish the correlation between stress and the bulking coefficient of the overlying rock mass, revealing the characteristics of the subsequent spatial void structure. The paper introduced the development of a CO 2 mineralized coal-based solid waste filling material, employing conventional low-calcium fly ash under normal temperature and pressure conditions. It systematically elaborated on the concept of the subsequent space gangue grouting filling method and provided the spatial layout approach for the subsequent space gangue grouting filling system. The challenges in the development of gangue grouting filling materials and the technology for grouting borehole layout were thoroughly examined. The backfilling volume and range only cover a portion of the mined-out space. After reinforcing the collapsed rock mass with backfill material, it supports the overlying strata and achieves the objectives of controlling strata movement and water conservation while mining proceeds parallelly. The advantage of this method is that it separates the mining and backfilling processes, avoiding interference between them. Based on field investigations, the authors provide a detailed analysis of the characteristics of the collapsed goaf roof and the height of the collapsed zone, establishing the boundaries for grout filling. By monitoring the stress of the goaf in real-time, a stress distribution model for the delayed filling zone of the collapsed rock mass is established. This provides theoretical support for determining the timing of delayed grout filling in the collapsed goaf and understanding the development patterns of overlying strata fractures in the delayed filling zone.

Idea of subsequent space gangue grouting filling technology

Study area and hydrogeological conditions

The Yushen mining area is located in the arid inland region of central and western China, characterized by scarce water resources, making it a typical ecologically fragile mining area (Fig.  2 ). Groundwater in this region mainly relies on atmospheric precipitation, with an annual average precipitation ranging from 248.7 to 724.9 mm and a long-term average precipitation of 471.5 mm. Due to the terrain and landform, most of the precipitation forms surface runoff and is lost, with less than 15% infiltrating into the rock and soil layers. Moreover, the area experiences a high average annual evaporation of 1611 mm, leading to severe water shortage (Ma et al. 2022 ). In the early twenty-first century, the Yushen mining area began adopting modern coal mining technologies such as large working faces and one-time full-height mining. Due to the shallow burial of coal seams, thin overlying bedrock, and thick wind-blown sand cover on the surface, this high-intensity, integrated mining leads to deformation and fracture zones known as “double zones.” The structural damage to the aquifers results in the infiltration of water from the bedrock aquifer and the loose water-bearing layers of the Quaternary system into the goaf. This has caused a series of mining environmental geological effects, including leakage of underground water resources, sudden inrush of water and sand underground, groundwater level decline, and degradation of the ecological environment. The original fragile ecological environment of the mining area has become even more difficult to restore. For example, on July 13, 2003, when the 1310 working face in the Dalitata mine advanced to a position 16.7 m away from the cutting eye, the roof collapsed completely, leading to a geological disaster of water inrush and sand outburst, with a maximum water inflow of 510 m 3 /h (Ma et al. 2022 ). According to the statistics of water inflow in the Yushen mining area in recent years, the average water inflow of the Dalitata, Bulianta, and Shigetai mines exceeds 13,000 m 3 /d. The maximum water inflow is 16,853 m 3 /d (Shigetai). The average flow rate of the Mother River Spring Domain in the Dalitata mining field was 5961 m 3 /d before coal mining, with a maximum average flow rate of 106,273 m 3 /d (Fan et al. 2018 ). However, in recent years, due to the damage and drainage of the Quaternary water-bearing layer caused by coal mining, the flow rate of the Mother River Spring Domain has decreased to only 1680 m 3 /d, a reduction of 72% (Song et al. 2021 ). Protecting and utilizing groundwater resources in coal mining has become an urgent issue in the scientific development of coal resources in ecologically fragile areas of central and western China.

Location of Yu-Shen mining area

The project proposes the technique of delayed backfilling for low-carbon water-conserving mining in goaf areas. It determines the space for delayed backfilling in goaf areas, the layout of grouting holes for backfilling, and parameters for delayed grouting and backfilling. The main contents include the fragmentation characteristics of collapsed rock blocks in goaf areas, the initial distance for delayed backfilling, the ultimate distance for delayed backfilling, the stratigraphic position for delayed backfilling, the arrangement of surface grouting holes and underground grouting holes, hole spacing, hole structure, and grouting volume.

The typical comprehensive stratigraphic column of the Yu-Shen coal area and the lithological characteristics are shown in Fig.  3 . The surface is primarily covered by Quaternary strata, and bedrock outcrops are sporadically distributed in valleys. The mining area is defined within the coal field, and it comprises six mineable coal seams at various depths. The total estimated coal resources amount to 1.24 billion tons, with a remaining reserve of 1.19 billion tons. The designed production capacity of the mine is 8 million tons per year, and the expected mine service life is 67.9 years. As of October 2021, the mining operation has completed the extraction in the 301 panel area, including ten working faces (30,101–30,110), and the extraction is ongoing in the 302 panel area, specifically in the 30,201 working face. In the next three years, the mine plans to extract from the 30,201 and 30,202 working faces. The 301 panel area adopts a multi-slice longwall (MSL) method with a mining height of 5 m, while the 302 panel area plans to use a single pass longwall (SPL) method with a mining height of 7.2 m.

Comprehensive geological histogram of the Yu-Shen coal area

Based on the groundwater occurrence conditions and hydraulic characteristics, they are divided into two types: the Quaternary loose rock porous confined aquifer and the Jurassic Middle System Zhijialu Formation and Yan'an Formation sandstone fractured confined aquifer. From top to bottom, it can be divided into five aquifer layers (formations): the Quaternary Holocene alluvial layer porous confined aquifer, the Upper Pleistocene lacustrine layer porous confined aquifer, the Quaternary Middle Pleistocene loess layer porous fractured confined aquifer, the Jurassic clastic rock weathered crust fractured aquifer, and the clastic rock fractured confined aquifer. The aquitards mainly consist of Quaternary Middle Pleistocene relative aquitard and the mudstone and sandy mudstone aquitard between the Jurassic sandstone layers (Table  1 ).

Upon analyzing the distribution characteristics of aquifers in the mining area, two main types of aquifers were identified: the loose rock mass aquifer with pore and fissure water in the Quaternary system, and the fractured rock aquifer in the Jurassic clastic rocks. As for the distribution characteristics of aquitards in the mining area, two major aquitards were identified: the relative aquitard composed of middle-lower Quaternary loess in the Quaternary system and the interbedded aquitard in the Jurassic bedrock. Current research indicates that the focus of water hazard prevention and control lies in ensuring safe mining operations by minimizing the inflow of water from the roof during the mining process. Properly controlling the position of the interface between the water-conductive fractured zone and the aquifers based on the hydrogeological conditions of the mined coal seam and preventing damage to the aquitards caused by mining activities are essential approaches to achieve water-conserving mining practices.

Field detection of collapsed roof form

The detection area is the goaf of the No. 3 coal seam in the 301 panel area. The ZTR12 series geological radar (GR) utilizes shielded antennas to emit high-frequency electromagnetic waves ranging from 1 MHz to 2.5 GHz, while the receiving antennas collect the corresponding signals, which are then stored and displayed by a computer. The ZTR12 series GR has a central antenna frequency of 100 MHz, a length of less than 1 m for each individual antenna, a step size smaller than 2 × 10 –12  s, an output signal of 10 × 10 –9  s, and a voltage of 90 V. Additionally, when generating a 100 MHz transmission pulse, the amplitude ratio between the pulse and ripple increases significantly to over 30 dB, allowing the effective mapping depth of the GR to reach within a range of 30 m below the No. 3 coal seam, making it fully applicable in underground mining environments. The ZTR12 series GR was employed to detect the roof strata of the goaf in the No. 3 coal seam. The GR has a detection depth of 30 m and a detection distance of 70 m. The detection area is illustrated in Fig.  4 , and the GR system conducted tests at 1024 sampling points.

Location of GR detection

The GR detection data collected were processed through zero-point calibration, denoising, filtering, and gain adjustment to obtain the GR detection images. These images clearly reflect the collapse status of the roof strata after coal seam extraction in the detection area, as shown in Fig.  5 . From Fig.  5 , it can be observed that within a distance of 30 to 70 m from the detection starting point, there are four distinct alternating strong and weak reflection zones. Specifically, a weak reflection zone appears in the 60 to 70 m position, and its phase is generally consistent with the surrounding medium reflection image. Therefore, the black dashed-line area represents a mildly damaged region where the roof exhibits minor fragmentation and relatively high integrity. On the other hand, a strong reflection zone appears in the 50 to 60 m positions, and its phase differs from the surrounding medium reflection image. Hence, the white dashed-line area represents a severely damaged region where the roof exhibits significant fragmentation and poor integrity. This cyclic pattern of alternating reflection zones follows the advancing direction of the working face and is in basic agreement with the results obtained from on-site borehole observations. Based on the aforementioned detection results, the collapsed morphology of the roof in the goaf of the No. 3 coal seam was reconstructed, as shown in Fig.  6 .

Processed detection results of GR data

Inversion map of breaking structure form with GR of coal seam mining

From Fig.  6 , it can be observed that after the extraction of the No. 3 coal seam, the immediate roof (carbonaceous mudstone) and the overlying roof (siltstone) exhibit well-developed fractures, and the fracture development has extended into the mudstone layer. However, the upper portion of the siltstone layer is minimally affected by the extraction of the No. 3 coal seam, with a collapse zone height of 25 m.

Collapse rock mass expansion characteristics

Based on the theory of overlying stress in collapsed rock blocks within goaf areas, the stress variation and dilatancy coefficient of the collapsed rock blocks within the goaf are divided into different zones. By analyzing the stress variation patterns and dilatancy characteristics of the collapsed rock blocks within the goaf, the initial lag filling distance is determined.

Zoning of stress in collapsed rock blocks

After the collapse of the roof in the goaf area, the overlying load is transferred and redistributed, resulting in the formation of supporting pressure. Based on the principles of limit equilibrium and conservation of overlying load, the calculation methods for the range of coal wall support influence and stress recovery zone are studied. The deformation zoning of the lag filling zone is analyzed, and the corresponding stress paths during mining are determined based on the longitudinal and transverse stress variation patterns of the overlying strata. A stress-distance distribution model for the collapsed rock blocks in the lag-filling zone is established. Combining the theories of cantilever beams and elastic foundation beams, the stress variation patterns of collapsed rock blocks in the goaf area are analyzed. Based on the subsidence of the underlying rock layer in the 302 panel area, the stress zones of the collapsed rock blocks in the goaf area are classified as follows: low stress zone (LSZ), stress-increasing zone (SIZ), and stress-stable zone (SSZ), as shown in Fig.  7 .

Schematic diagram of stress distribution in goaf

The relationship between stress \(\sigma_{I}\) in low-stress zone of collapsed rock mass and the position l of coal wall in the working face satisfies:

In the equation: \(\sigma_{I}\) represents the stress in the low-stress zone of the collapsed rock mass in MPa; l represents the distance from the coal wall in meters; \(\Delta C\) represents the compensation parameter; a and b are coordination parameters determined through stress measurement experiments on the collapsed rock mass.

Distribution of fragmentation and swelling characteristics of collapsed rock blocks

Based on the relationship between rock swelling coefficient and axial pressure, the distribution characteristics of fragmentation and swelling of collapsed rock blocks are analyzed. Since the rock swelling coefficient is not a constant value but a function of stress variation, the rock swelling coefficient and the characteristics of swelling can only be obtained when the regression coefficients are determined. In the field of the 302 panel area, random samples of collapsed rock blocks were collected, crushed, and placed in rigid cylinders for compaction experiments. By using a Multi-functional Mechanical Test Loading System (MMTLS), as shown in Fig.  6 , the rock swelling coefficient under compression was calculated (Table  2 ), and the relationship curve between the swelling coefficient and stress was plotted (Fig.  8 ).

Collapse rock mass compaction experiment

At the initial filling stage, the fragmentation coefficient is relatively large, and at this time, the initial delayed filling position is located in the low-stress zone. According to Eq. ( 1 ), the relationship between the fragmentation coefficient ( k p ) of the collapsed rock block and the distance ( l ) from the working face to the coal wall is given by:

In the equation, \(\alpha\) and \(\beta\) represent the regression coefficients related to the overlying rock stress in the goaf area, while c and d are the coordinating parameters for overlying rock stress determination. ΔE represents the compensatory parameter. It should be noted that the distance between the coal mining face and the backfill body needs to be greater than the initial collapse step distance of the roof. The calculation formula for the roof's ultimate collapse step distance is as follows:

Here, L represents the collapse step distance of the roof. Q denotes the load borne by the strata beam of the overlying roof. R T is the ultimate tensile strength of the strata at that location. H represents the thickness of the overlying roof strata. k is the coefficient that accounts for the influence of the support stress generated by the mining face advancement and the production technical conditions.

Analyzing the stress distribution of the collapsed rock mass in the goaf, the stress in the collapsed rock mass is mainly derived from the overlying strata pressure. The overlying strata above the adjacent coal seam form a cantilever beam structure, which restricts the stress exerted by the overlying strata on the collapsed rock mass. According to the principle of limited stress distribution in the overlying strata near the coal seam (Wang et al. 2021a ; b ), the relationship between the stress in the collapsed rock mass ( σ ) and the position of the mining face relative to the coal seam ( l ) can be expressed as follows:

In the equation, σ represents the stress in the collapsed rock mass, MPa. l represents the distance from the coal seam, m. ΔC represents the compensation parameter. a and b are coordination parameters determined through experimental measurements of the stress in the collapsed rock mass.

After coal extraction, VSP530 vibrating wire rock stress meters were installed on the mining floor, along with the GT204A vibrating wire readout instrument, to measure the overburden stress of the collapsed rock blocks (Fig.  9 ). Based on the measured stress data of the collapsed rock mass in the goaf, an approximate exponential relationship curve was fitted, which showed good agreement with the established mathematical model (Fig.  10 ). It was observed that the closer the distance to the coal wall, the smaller the stress exerted by the overlying strata on the collapsed rock mass, with the corresponding parameters of ΔC  = − 0.02, a  = 7, and b  = 0.03.

Testing of overlying strata stress on the collapsed rock mass

Stress-position relationship of the collapsed rock mass

Determination of the delayed backfilling zone in the goaf area

Considering the natural caving state of the roof after coal mining operations in the 302-panel area, the technique of delayed backfilling with low-carbon water-retaining mining was proposed. A precise slurry system was established on the ground to produce a slurry of coal gangue, water, and additives with a certain mass fraction. Then, the gangue slurry was transported through a pipeline system and high-pressure injection to fill the space behind the working face, thereby achieving the disposal of coal gangue in an environmentally friendly manner without affecting normal production (Fig.  11 ).

Schematic diagram of delayed backfilling in the goaf area

To support the overlying strata and control the development of water-conducting fractures, delayed backfilling plays a crucial role in preventing the connection with aquifers. Therefore, before determining the backfilling area, it is necessary to identify the layers for groundwater protection. Based on the distances between the 3# coal roof and major aquifers within the scope of the 302-panel area, as shown in Table  1 , it is observed that the Zhenwu Cave Sandstone is located at a distance of 0.99 to 18.38 m from the coal seam, which is too close to be protected through goaf backfilling. On the other hand, the Qili Town Sandstone is situated at a distance of 40.97 to 99.05 m from the coal seam, which is sufficiently far to be protected through delayed backfilling. Consequently, the groundwater protection layers are identified as the Qili Town Sandstone aquifer and the overlying Fourth Series Sandstone aquifer.

The distance for delayed backfilling in the goaf

Based on the geological data of the 302-panel area, the initial collapse step distance of the roof is estimated to be 41.6 m. Through the rock fragmentation compaction experiments, the initial filling coefficient of the collapsed rock blocks in the 302-panel area is determined to be 1.5. By applying Eq.  3 , the distance from the mining face to the coal wall is calculated to be 46 m, which exceeds the roof collapse step distance. Combining surface observations in the Yushen mining area and surface subsidence monitoring of the 30,201 working faces in the Hanglaiwan coal mine, it is observed that the initiation phase of the surface movement for the 30,201 working face lasts for 6 days, with a starting distance of 59 m. With an average daily mining progress of 10.38 m, the underground mining distance during the initiation phase is determined to be 62 m. Therefore, the final determined distance for the initially delayed backfilling is 62 m.

The further the distance from the working face, the more compact the collapsed rock blocks in the goaf become, leading to a decrease in the void ratio between the rock blocks. When the residual fragmentation coefficient is less than 1.03, it is not feasible to carry out delayed backfilling work. Based on the fitted relationship between the fragmentation coefficient and the overlying rock stress, according to Eq.  3 , the distance to the mining face is calculated to be 706 m in this case. Combining surface observations in the Yushen mining area and surface subsidence monitoring of the 30,201 working faces in the Hanglaiwan coal mine, it is observed that the surface movement duration is 220 days, with an average active phase of 71 days. With an average daily mining progress of 10.38 m, the underground mining distance at this stage is determined to be 737 m. Therefore, the final determined distance for the maximum delayed backfilling is 737 m.

The stratigraphic position for delayed backfilling in the goaf

The stratigraphic position for delayed backfilling in the goaf is determined by the sum of the collapsed rock layer thickness and the coal seam extraction thickness. By analyzing the hydrogeological data of the 302-panel area and considering the occurrence conditions and physical–mechanical properties of the overlying rock layers in the mining area, along with empirical calculations based on mining height, collapsed zones, and fracture zones, the relative position relationship between the overlying aquifer and the collapsed zones/fracture zones is determined to ensure that the collapse and fracture zones do not extend into the aquifer. In the 302-panel area, the coal seam extraction thickness is 7.2 m, and empirical formulas yield a collapsed zone height of 30 m and a fracture zone height of 154.8 m.

The thickness of the collapsed rock layer and the position for delayed backfilling are determined based on the accumulated height of the collapsed zone on the immediate roof and the gap height between the immediate roof and the old roof. If the collapse thickness of the immediate roof layer is \(\Sigma h\) , then the accumulated height after the collapse is \(k_{p} \Sigma h\) , and the gap left between the immediate roof and the old roof is denoted as \(\Delta\) :

In the equation, M represents the thickness of the extracted coal seam, and \(\Sigma h\) represents the thickness of the collapsed rock layer.

When \(M = \Sigma h(k_{p} - 1)\) , \(\Delta = 0\) , the collapsed rock layer fills the goaf completely. At this point, the bending and sinking of the immediate roof are usually negligible and can be disregarded. Therefore, the thickness of the collapsed rock layer \(\Sigma h{ = }h^{\prime}\frac{M}{{k_{p} - 1}}\) , where h’ represents the safety factor for caving, \(h^{\prime}{ = }5\sim 5.5\) .

The position of the backfill layer in the goaf is determined by the sum of the thickness of the collapsed rock layer and the thickness of the coal seam being mined. Different backfill regions correspond to different coefficients of rock fragmentation for the collapsed rock in the goaf, resulting in different positions for the backfill layer. In the initial stage of backfilling, when the coefficient of rock fragmentation for the collapsed rock in the goaf is 1.5 and a safety factor of 5.5 is chosen, the calculation yields a rock collapse thickness of 97.2 m. With a coal seam thickness of 7.2 m in the 302-panel area, the position of the backfill layer in the goaf is determined to be 86.4 m. In the ultimate stage of backfilling, when the coefficient of rock fragmentation for the collapsed rock in the goaf is 1.35 and a safety factor of 5 is chosen, the calculation yields a rock collapse thickness of 102.9 m. With a coal seam thickness of 7.2 m in the 302-panel area, the position of the backfill layer in the goaf is determined to be 110 m. Therefore, the position of the backfill layer in the goaf ranges from 86.4 m to 110 m.

Preparation of CO 2 mineralized fly ash backfill material

During coal mining operations, a significant amount of solid waste and CO 2 is generated. In the context of the peak carbon and carbon neutrality goals, the comprehensive utilization of solid waste and CO 2 is an important approach for achieving green and low-carbon development in the coal industry. Traditional CO 2 mineralization of fly ash typically requires high-temperature, high-pressure, and high-calcium conditions to enhance the reaction rate, mineralization conversion rate, and strength of the backfill material. However, in engineering practice, it is difficult to meet the requirements of high-temperature and high-pressure mineralization conditions, and there are safety risks involved.

To address this challenge, the development of CO 2 -mineralized fly ash backfill material under conventional low-calcium conditions at ambient temperature and pressure is pursued. The main raw material for the backfill material is the fly ash from a power plant in Zhengzhou, Henan Province, China, with Ordinary Portland Cement (OPC) procured from Zhucheng Yangchun Co., Ltd. as an additive and CO 2 as the mineralization gas supplemented with alkaline activator SA. The experimental process is outlined in Fig.  12 . The chemical properties of fly ash, the characteristics of OPC and details about the mixing procedure of the negative carbon filling material (NCFM) are the same as previous studies (Ngo et al. 2023 ). Mortar samples were prepared in accordance with the Chinese standard GB/T17671-2021. The Unconfined Compressive Strength (UCS) tests for NCFM samples were conducted following the identical procedures, utilizing the same equipment, and maintaining consistent parameter settings as described in previous studies (Ngo et al. 2023 ). The CO 2 -mineralized fly ash backfill material is filled into the goaf, achieving both water retention during coal mining and sequestration of CO 2 and fly ash.

Preparation of NCFM backfill material

The CO 2 mineralization reaction is conducted during the preparation of the backfill material, resulting in the development of mineralized backfill. The alkaline activator SA is added to tap water to prepare an activating agent solution, which is then added to the solid mixture at a water-to-ash ratio of 1:2. CO 2 is introduced into the mixture during the stirring process to initiate a mineralization reaction. The backfill slurry is prepared into cylindrical specimens measuring 50 mm × 100 mm and cured at constant temperature and humidity (humidity: 95 ± 1%, temperature: 20 ± 1 °C) for 3, 7, 14, 28, and 56 days. The composition ratios of the CO 2 mineralized fly ash backfill material are shown in Table  3 . The rheological parameters and fitting results of the slurry are presented in Table  4 . The influence of curing time and fly ash content on the unconfined compressive strength (UCS) of the negative carbon filling material (NCFM) specimens are illustrated in Fig.  13 .

UCS of NCFM backfill material

The yield stresses of FA50-FA80 are 36.01 Pa, 26.75 Pa, 16.76 Pa, and 15.99 Pa, respectively. The yield stress of the NCFM slurry decreases with an increase in the mass of fly ash. During the carbonation process, CO 2 reacts with the hydration products of cement to form C–S–H gel, consuming free water in the slurry and reducing its fluidity. Therefore, slurry with a lower fly ash content requires higher yield stress for pumping. However, when the fly ash content is increased to 90%, the yield stress increases to 17.09 Pa. This is due to the excessive fly ash content, which increases the specific surface area of particles in the slurry and adsorbs a large amount of free water.

To ensure the transportation of filling materials through pipelines, the yield stress of the slurry needs to be within 200 Pa, and thus the yield stress of NCFM meets the industrial application requirements. Regarding hydration and carbonation reactions, the adoption of ambient temperature and pressure CO 2 mineralization method produces silica-based gel and CaCO 3 , providing strength to high fly ash filling materials and overcoming the disadvantage of low strength in conventional low-calcium fly ash in filling applications. The flowability and UCS of NCFM filling materials meet the requirements for underground filling. The UCS at 3 days and 28 days are 2.70 MPa and 5.12 MPa, respectively. The silica-based gel generated from the reaction of CO 2 with alkali activators compensates for the low binding property of high fly ash filling materials, exhibiting early strength characteristics and subsequently promoting the reaction of volcanic ash, thereby increasing the long-term strength of NCFM. Based on market prices, the direct cost of NCFM filling materials is approximately 131 RMB per ton. Compared to conventional fly ash filling materials and traditional filling materials, NCFM filling materials can save direct costs of 28 RMB per ton and 59 RMB per ton, respectively. For detailed cost analysis, refer to Table  5 .

The arrangement of drilling and grouting parameters

The arrangement of drilling involves a combination of surface drilling and underground directional drilling. Due to being unaffected by factors such as the coal seam dip angle, priority is given to surface drilling and grouting filling (Fig.  14 ). If surface conditions do not permit drilling, directional drilling is conducted in the vicinity of the mining area (Figs.  15 and 16 ).

Schematic diagram of surface grouting drilling hole arrangement

Arrangement of directional drilling for grouting (Option 1)

Arrangement of directional drilling for grouting (Option 2)

Drilling spacing

Referring to experimental measurements and empirical data, the diffusion radius of the backfill slurry is determined to be 100–150 m (Shi et al. 2021 ). Applying a safety factor of 1.5, the grouting hole spacing is set at 66–100 m. For the 302 panel area with a working face length of 300 m, the surface grouting drilling arrangement is shown in Fig.  14 . Three holes are arranged along the inclined direction of the working face with a spacing of 75 m. The underground directional drilling arrangement is shown in Figs.  13 and 14 . Based on the determined distance and stratigraphic position of delayed filling, directional drilling is conducted from the filling drifts on both sides towards the fractured zone above the goaf. Two directional drilling holes are arranged on each side of the filling drifts, and four directional drilling holes are arranged along the inclined direction of the working face. Two options are considered: Option 1, where the two directional drilling holes are located in the same vertical cross-section with a spacing of 75 m (Fig.  15 ); Option 2, where the two directional drilling holes are located at the same horizontal stratigraphic position but staggered, with a spacing of 37.5 m (Fig.  16 ).

Drilling parameters

Both the vertical and inclined sections of the borehole require permanent cement grouting to ensure water sealing and meet the requirements for drilling and grouting construction, thereby ensuring construction safety.

The borehole structure is determined based on factors such as the comprehensive treatment approach, geological conditions, and equipment capabilities. The surface borehole has a diameter of Ф311 mm, and a surface casing of Ф244.5 mm × 8.94 mm is inserted down to the bedrock and cemented for wellbore integrity.

The underground directional drilling borehole has a diameter of Ф135 mm, and the horizontal section is left unlined.

Maximum grouting volume

There is a certain relationship between the grouting volume of the collapsed zone with fragmented gangue and the rock mass dilation characteristics. The dilation coefficient ( k p ) of the rock mass in the study area is generally between 1.12 and 1.5, and the grout cannot completely fill the voids in the collapsed zone. Depending on the block size of the fragmented rock mass, the filling capacity under grout pressure can only reach 60–90% of the dilation volume, i.e., the filling degree (the ratio of grouting volume to rock mass volume) γ is between 0.6 and 0.9. The maximum grouting volume ( V g _) of the entire collapsed zone with backfill slurry is given by:

where V g is the grouting volume of the slurry, V m is the volume of coal extraction, V r is the original volume of the roof that collapses during coal extraction, k p is the rock mass dilation coefficient. By definition, when γ  =  V g /( k p V r ), we can obtain:

The maximum grouting volume of the entire backfilling space is influenced by the mining volume, the original volume of the collapsed roof, and the rock mass dilation coefficient. Since the mining volume and the original volume of the collapsed roof are constant, the maximum grouting volume can be obtained by integrating the dilation coefficient equation along the length in the mining direction and substituting it into Eq. ( 7 ).

Following the principle of initial dilution, subsequent concentration, and final dilution, grouting filling is carried out. The maximum grouting pressure is determined to be 6 MPa based on the water inflow from the goaf to the working face, the horizontal thrust of the collapsed rock blocks on the support, and the maximum compressive strength of the grouting pipe during grouting. The filling degree ranges from 68 to 80%, and the filling degree after water leakage is ensured to be above 50%.

Mining volume of the grouting section at the working face is as follows:

where L is the length of the grouting section at the working face, m. D is the width of the working face, taken as 300 m. M is the mining thickness, taken as 7.2 m. η is the recovery rate, taken as 100% (without considering the gangue content).

Volume of post-mining collapse at the working face is as follows:

where q o is the settlement coefficient of full extraction at the working face.

Volume of injected backfill material required for subsidence reduction ( n /%) is as follows:

where A is the backfill coefficient.

Grouting volume is as follows:

where x is the water-to-cement ratio, taken as 0.5. For the 302 panel, the calculated unit grouting volume is 1400 kg/m 3 .

Conclusions

Underground backfilling was essential for environmentally friendly waste disposal in mines. However, addressing temporal and spatial interference between mine waste backfilling and coal mining was crucial to overcome technical challenges. This paper proposed a post-mining gangue grouting filling method for goaf collapse blocks, utilizing post-mining space efficiently. Collapse roof morphology in the post-mining space was determined using radar detection. The intrinsic relationship between roof stress in collapse blocks and the swelling coefficient was established through stress monitoring and compaction experiments, revealing structural characteristics and spatiotemporal evolution of post-mining space voids. NCFM was developed under normal temperature, pressure, and conventional low-calcium fly ash conditions. Key parameters for grouting filling were meticulously designed.

The study identified two main aquifer types: Quaternary loose rock porous and fractured confined aquifers, and Jurassic clastic rock fractured confined aquifers. Two main aquitards were also recognized: the Quaternary middle and lower Pleistocene loess relative aquitard and the Jurassic interbedded aquitard rock group.

The stress variation law of collapse blocks in the goaf, the distribution characteristics of block swelling, and the observation of surface (roof) subsidence in the mining area are analyzed, determining the initial lag filling distance of 62 m and the ultimate lag filling distance of 737 m. The thickness of the collapsed rock layer that fills the goaf is determined based on the accumulated height of the directly collapsed roof and the void between the directly collapsed roof and the old roof, and the final lag filling stratum is determined to be 86.4 m to 110 m.

Under standard temperature and pressure conditions, and employing conventional low-calcium fly ash, NCFM was synthesized. Demonstrating suitable flowability, setting time, and UCS, NCFM met the stringent requirements for underground filling, exhibiting UCS values of 2.70 MPa at 3 days and 5.12 MPa at 28 days. The silica gel produced from the reaction between CO 2 and alkali activators compensated for the low binding capacity inherent in high fly ash filling materials. This phenomenon facilitated the formation of a dense structure in the early stages and enhanced the long-term strength of NCFM through volcanic ash reactions. The financial benefits of employing NCFM, in comparison to conventional fly ash and traditional filling materials, amounted to 28 yuan/ton and 59 yuan/ton, respectively.

The innovative slurry injection method for backfilling coal mine gob post-mining improved the technical system for comprehensive gob disposal. This approach, reducing emissions at the source and promoting on-site disposal, holds significant promise for efficient solid waste disposal and ecological protection in coal mining.

Data availability

Data available on request from the authors.

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The authors would like to make an appreciation to the Fundamental Research Funds for the Central Universities (2022QN1004) for financial support.

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School of Mines, China University of Mining and Technology, Xuzhou, 221116, China

Kunpeng Yu, Liqiang Ma, Ichhuy Ngo, Jiangtao Zhai, Zhiyang Zhao & Hui Wang

Key Laboratory of Xinjiang Coal Resources Green Mining (Xinjiang Institute of Engineering), Ministry of Education, Urumqi, 830023, China

Liqiang Ma & Dangliang Wang

State Key Laboratory of Mining Response and Disaster Prevention and Control in Deep Coal Mines, Anhui University of Science and Technology, Huainan, 232001, Anhui, China

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K. Y. and L. M. wrote the main manuscript text and Z. Z and H. W. prepared Figs. 1 , 2 , 3 , 4 . All authors reviewed the manuscript.

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Yu, K., Ma, L., Ngo, I. et al. Gangue grouting filling in subsequent space of coal green mining: methodology and case study. Environ Earth Sci 83 , 217 (2024). https://doi.org/10.1007/s12665-024-11514-4

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Received : 07 November 2023

Accepted : 16 February 2024

Published : 27 March 2024

DOI : https://doi.org/10.1007/s12665-024-11514-4

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