Engineering Social Stability: An Innovation-Driven Approach to Risk Management in Major Construction Projects

Abstract

This study introduces a novel risk detection and control system to enhance social stability in major construction projects. Utilizing a heterogeneous cellular automaton model, the system simulates complex interactions among project stakeholders to identify and mitigate Social Stability Risks (SSR). Integrating the Ignorant–Latent–Malcontent–Recovered (ILMR) framework, the model applies principles from epidemiology to predict and manage the spread of social stability risks. Simulation results demonstrate the model’s effectiveness in reducing the number of malcontent and ignorant individuals while increasing the recovered category, stabilizing the social environment around large projects. This approach helps manage immediate risks and improves long-term social acceptance and sustainability of engineering projects. By bridging risk management with advanced simulation techniques, this research contributes to major construction projects by providing a robust framework for managing complex social dynamics, thereby enhancing project success and stakeholder satisfaction. The findings underscore the potential of integrating innovative technological tools with traditional risk management strategies to address the socio-technical challenges of large-scale engineering projects.

1. Introduction

Major engineering projects are fundamental drivers of economic growth and societal advancement. However, their large-scale, complex nature and extended lifespans inherently introduce social stability risks (SSR). These projects, often funded partially or entirely by governments, encompass various sectors and can significantly impact regions’ political, economic, cultural, and environmental landscapes. Substantial investments, lengthy construction periods, and the involvement of multiple stakeholders with often conflicting interests create a breeding ground for social discontent [1].

This complex social system acts as a breeding ground for SSR. At its core lie the inherent conflicts of interest among project stakeholders [2]. When individual grievances escalate into collective action, these conflicts become contagious, amplifying and potentially mutating through social transmission mechanisms fueled by social media platforms. Negative events or information can rapidly spread and coalesce, exceeding the social system’s risk tolerance threshold and culminating in collective action and potential social unrest. Social risk research has gained significant traction in recent decades, with a growing body of literature dedicated to understanding and mitigating SSR in major engineering projects [3]. Pioneering scholars such as Ulrich Beck and Anthony Giddens laid the groundwork by exploring the concept of “risk society” and classifying social risk factors within internal and external environments. Luhmann’s complex systems theory and Kasperson’s social amplification of risk framework provide valuable insights into how social risks propagate and influence public risk perception, potentially leading to risky behaviors [4]. Beyond these foundational theories, the “Triple Bottom Line” (TBL) emphasizes the interconnectedness of economic, social, and environmental considerations in achieving sustainable development. Economic factors encompass issues related to land acquisition, resettlement, and potential livelihood disruptions, all of which can expose residents to economic hardships [5]. Social factors include project safety concerns, community disintegration, and the integration challenges relocated populations face. Environmental considerations encompass potential air, water, and soil pollution and the destruction of natural habitats, which can trigger public opposition.

Internal factors also play a critical role in SSR. Policy risks arise from insufficient public participation, limited information disclosure, and incomplete project planning, all of which can erode public trust and exacerbate social tensions. The public risk stems from low social satisfaction with project processes and outcomes, potentially leading to opposition and collective action. Social media and public opinion amplify public risk sentiment. With China’s emphasis on SSR management, research on SSR in significant construction projects has become a prominent field of study. Most existing research focuses on risk identification and assessment, with scholars developing various models to evaluate SSR and establish comprehensive social risk management frameworks [6,7]. Recognizing the interconnected nature of SSR factors, some scholars have constructed coupling evaluation models to capture the complex relationships between these factors. Additionally, research has explored the role of internet user sentiment and risk perception about SSR.

Although existing studies have explored the formation and impact of social stability risks (SSR) from multiple perspectives, systematic characterization of their dynamic diffusion mechanisms and behavior-driving processes remains lacking. Current models predominantly rely on homogeneity assumptions, which limits their ability to capture the heterogeneous behaviors of individual agents and the spatial clustering patterns inherent in risk propagation [8,9]. Accordingly, this study develops an SSR diffusion model that integrates the ILMR behavioral state chain with a heterogeneous cellular automaton, grounded in individual behavioral evolution and spatial interaction mechanisms. The model captures, at the individual level, behavioral transitions such as risk perception, awakening, dissatisfaction, and recovery, while incorporating heterogeneity in individual transmission and resistance capacities within the spatial neighborhood structure. This framework reveals typical features of SSR, including cluster aggregation, path dependence, and time-lagged diffusion, arising from the interplay of individual heterogeneity and local interactions. Building on this, the study further analyzes how varying intensities and combinations of interventions structurally influence risk evolution paths, thereby mechanistically explaining the differential effects of risk management measures at different stages.

2. Literature Review

Theoretical frameworks such as Risk Society Theory, the Social Amplification of Risk Framework, Complex Systems Theory, and the Triple Bottom Line Theory provide valuable insights into understanding the complexities of Social Stability Risks (SSR) within major construction projects. These theories highlight the interconnectedness of various factors contributing to SSR. Stakeholder conflicts emerge as a primary catalyst for SSR, driven by diverse interests and perspectives among stakeholders involved in these projects. However, a notable gap exists in understanding how these risks diffuse and evolve within diverse project contexts. Understanding SSR diffusion patterns is essential for anticipating and effectively addressing emerging risks, enhancing construction projects’ resilience, and fostering sustainable socio-economic development.

2.1. Theoretical Underpinning

Risk Society Theory, formulated by German sociologist Ulrich Beck [10], offers a profound lens to understand the contemporary landscape of social instability, particularly in the context of major construction projects. Central to Beck’s theory is that risks are no longer confined to localized or natural phenomena but are instead deeply intertwined with human activities, institutions, and systems [11]. These risks often transcend geographic, temporal, and sectoral boundaries, amplifying their impacts and complexities.

The Social Amplification of Risk Framework, pioneered by Roger Kasperson, offers valuable insights into the dynamics of SSR diffusion. This framework elucidates how individual grievances regarding a construction project can escalate into collective action and widespread social unrest through social media, public discourse, and interpersonal communication [12]. Central to the Social Amplification of Risk Framework is the recognition that individual perceptions of risk are shaped by a complex interplay of cognitive, affective, and social factors [4].

As articulated by Niklas Luhmann, Complex Systems Theory offers a comprehensive framework for understanding the intricate dynamics of Social Stability Risks (SSR) within the context of significant construction projects. At its core, this theory emphasizes the interconnectedness and interdependence of various factors shaping social systems [13]. Additionally, Complex Systems Theory underscores the importance of adaptability and resilience in navigating the complexities of modern risk landscapes [14].

The Triple Bottom Line (TBL) Theory offers a holistic framework for analyzing the multifaceted dimensions contributing to Social Stability Risks (SSR) within significant construction projects. Originating from sustainability, TBL emphasizes the interconnectedness of economic [15], social [16], and environmental [17] considerations in achieving sustainable development outcomes. By incorporating TBL principles, the literature review can elucidate how these social factors interact with economic and environmental considerations to shape the overall dynamics of SSR within construction projects.

2.2. Stakeholder Conflicts and Social Stability Risks

The intersection between large-scale construction projects and the emergence of Social Stability Risks (SSR) is a complex and crucial aspect that demands meticulous examination. Understanding the factors contributing to SSR is paramount for crafting effective mitigation strategies and fostering sustainable development [18]. Stakeholder conflicts loom large as a primary catalyst for SSR in the context of significant engineering projects. Disputes commonly arise over resource allocation, distribution of benefits, and decision-making authority, leading to simmering tensions that can escalate into open confrontation [19].

Environmental degradation emerges as a critical factor exacerbating SSR in the context of significant engineering projects. The pursuit of infrastructural development often entails exploiting natural resources, altering landscapes, and disrupting delicate ecosystems [20]. These activities can inflict irreversible environmental harm, compromising essential ecosystem services [17]. Inadequate governance and institutional capacity further exacerbate SSR in the context of significant engineering projects. Weak regulatory frameworks, ineffective enforcement mechanisms, and institutional corruption create fertile ground for malpractices, including land grabs, corruption, and human rights abuses [21]. Moreover, more institutional capacity is needed to improve project planning, implementation, and monitoring, increasing the likelihood of cost overruns, delays, and substandard outcomes [22].

2.3. Risk Diffusion Dynamics

From a complex systems perspective, risk diffusion is a non-linear process driven by multi-agent interactions, where Cellular Automata (CA) and agent-based modeling have proven effective. Liu et al. [23] constructed a heterogeneous CA model for mixed traffic flow (intelligent controlled vehicles and human-driven vehicles), integrating the Gipps safety distance rule to accurately capture dynamic traffic changes. Their refinement of heterogeneous agent interaction rules offers insights for analyzing risk transmission among diverse stakeholders (residents, enterprises, governments) in construction projects. Complementing this, Luo et al. [24] proposed a flexible symmetric two-lane CA model (F-STCA), demonstrating that optimizing behavioral rules (e.g., lane-changing strategies) enhances dynamic simulation accuracy—aligning with SSR stakeholders’ heterogeneous risk responses. Notably, Zhang et al. [25] developed a multi-layer innovation network resilience framework, finding that core network layer (e.g., knowledge networks) disruptions trigger cross-layer spillover effects. This insight applies to SSR research, highlighting the need to prioritize core stakeholder groups and key information channels in construction projects.

In spatiotemporal dynamic simulations, CA and hybrid models have shown strong potential across fields. Cao et al. [26] integrated CA with the Unity engine to develop a 3D urban fire spread platform, achieving a 16% simulation error in the 2025 Altadena wildfire case—providing a reference for SSR diffusion across heterogeneous project regions. Benhamza et al. [27] proposed a DNN-CA hybrid model, feeding deep learning-predicted ignition probabilities into CA as seed risks, establishing a seamless “prediction-simulation” framework for SSR early warning.

In ecological and land system research, Zarei [28] used the IMP-CA model to assess Iran’s drought susceptibility, while Krishan et al. [29] developed a CA-ANN model for land use change analysis in Almora, Uttarakhand, achieving 94.27% simulation accuracy. These studies confirm CA models’ efficacy in capturing non-linear diffusion in complex systems. Ivanov et al. [30] employed a CA–Markov model to predict landscape changes in drained peatlands, emphasizing temporal dynamics and external factor interactions—aligning with SSR’s evolution under policy adjustments and stakeholder interactions.

Multi-scale and adaptive CA models further enrich risk diffusion understanding. Perestrelo et al. [31] developed a two-scale network model integrating percolation theory and CA, identifying phase transitions between controllable and uncontrollable fire regimes—offering a reference for SSR diffusion across project regions. Syed et al. [32] integrated nighttime light data, land use data, and CA to assess sea-level rise impacts, demonstrating the value of combining socio-economic factors with spatial simulation for SSR models. Wu et al. [33] proposed a CA-based lane-changing optimization strategy for heterogeneous traffic flow in work zones, highlighting context-aware rule design’s importance for SSR management.

The integration of adaptive neighborhoods enhances CA performance in heterogeneous environments. The ASHN-GCA model [34], optimizing attenuation coefficients via genetic algorithms, improved simulation accuracy for core land use types (cropland, construction land) by 0.40–201.67% compared to homogeneous neighborhood models. This underscores the need to account for spatial heterogeneity in SSR modeling, where risk transmission intensity varies with social and spatial distances among stakeholders.

In summary, significant strides have been made in researching social stability risks (SSR) within construction projects, identifying risk factors, assessing impacts, and proposing mitigation strategies [35]. However, a notable gap persists in understanding how these risks spread and evolve within diverse project contexts. While existing studies have provided valuable insights into SSR dynamics, they often overlook the intricate diffusion processes that underpin social instability [36]. This oversight impedes our ability to grasp the full complexity of SSR within construction projects and hampers the development of targeted interventions for effective SSR management. Understanding the mechanisms through which SSR spreads is essential for promptly anticipating and addressing emerging risks. By exploring deeper into the diffusion process, researchers can uncover hidden patterns, feedback loops, and tipping points that shape the dynamics of social instability within construction projects.

3. Materials and Methods

3.1. Research Framework

The dynamics of Social Stability Risks (SSR) within major construction projects present a multifaceted challenge, encompassing loss, uncertainty, and contagion. The complexity of SSR propagation lies in its resemblance to infectious disease transmission, where even minor shifts in information availability can trigger sudden outbreaks. Recognizing the urgent need for effective risk management, a novel approach integrates advanced modeling techniques and simulation capabilities to address SSR proactively.

Central to this approach is the adoption of the Ignorant–Latent–Malcontent–Recovered (ILMR) epidemic framework, categorizing individuals into categories: Ignorant, Latent, Malcontent, and Recovered. However, while these models provide valuable insights into macro-level dynamics, they face limitations in capturing micro-level interactions and spatial variations. To address this, the study proposes advancements in traditional cellular automata models, incorporating heterogeneity and mobility to simulate SSR diffusion more accurately. The research idea of this paper is depicted in Figure 1.

3.2. ILMR Infectious Disease Model

At present, there are more research models about the diffusion process, such as the BASS model, independent cascade model, linear threshold model, thermodynamic-based diffusion model, etc. However, these models are not based on group states, do not classify the states of groups, and cannot reflect the quantitative changes of each group state. In contrast, the state of individuals’ exposure to social risks during the spread of SSR for significant engineering projects has a group nature, and the state of individuals needs to be classified so as to develop target control strategies for each group state. Indeed, the SEIR (Susceptible–Exposed–Infectious–Recovered) compartmental model stands as a classic framework for understanding the nuanced dynamics of population segmentation and transitions among at-risk individuals. This model enables the subdivision of at-risk individuals into four distinct groups, offering a more realistic depiction of numerical changes within each group throughout the transmission process. Leveraging the SEIR model in the context of Social Stability Risks (SSR) allows for a comprehensive simulation of SSR spread, given the similarities between SSR transmission and pathogen propagation. Both phenomena exhibit characteristics such as a source of infection, exposure, specificity, and contagiousness, resulting in the development of pathological features within population systems. Hence, this paper employs the SEIR epidemic theory to reclassify SSR subjects, constructs the Ignorant–Latent–Malcontent–Recovered (ILMR) epidemic model, and applies disease transmission principles to describe the SSR propagation process.

The classical models of infectious diseases are the SI, SIS, SIR, and SEIR models. The SI and SIS models divide the population into two categories, susceptible and infected, but the SIS model takes into account the reinfection of infectious diseases. The SIR model divides the population into three categories: susceptible, infected, and immune. In practice, susceptible and infected individuals do not show clinical symptoms immediately after exposure to the virus, but only after a period of latent period. Therefore, this paper considers the introduction of latent individuals to establish the ILMR infectious disease model. The ILMR model represents a modification of the SEIR epidemic model tailored to capture the dynamics of SSR transmission. Within this framework, individuals are classified into four distinct categories: Ignorant (I), representing the population unaware of the social risk; Latent (L), representing the latent population; Malcontent (M), representing the dissatisfied population capable of transmitting social risk; and Recovered (R), representing the immune population that refuses to transmit social risk. This model offers two key advantages in this study. First, at the macro level, it reconstructs the semantics of social stability risk (SSR) propagation through a stage-based framework, which helps depict the evolution path and the core logic of state transitions. Second, with parameterized settings, it can flexibly represent variations in the pace and propagation patterns under different social contexts. Notably, these models cannot adequately represent micro-level interactions between individuals or account for spatial variation across multiple dimensions, limiting their ability to fully capture the complexity of SSR transmission dynamics.

3.3. Theory of Cellular Automata

At the heart of social stability risk diffusion lies the intricate process of micro-level interaction between individuals, whether it involves actual harm or perceived threats. Cellular Automata (CA) offers a robust framework for capturing these interactions, spanning microscopic to macroscopic scales and localized to global contexts. Unlike traditional differential equations, which assume equal transmission probabilities between individuals and disregard heterogeneity and spatial variations, CA provides a dynamic and evolutionary perspective on complex systems’ evolution processes. It elucidates how micro-level decisions and mechanisms can give rise to dynamic macroscopic effects, offering a clearer understanding of these intricate processes. CA models can effectively describe unequal interaction probabilities between individuals and spatial variations, making them particularly suitable for modeling the complex dynamics of social stability risk propagation in major engineering projects. Therefore, the CA model not only overcomes the limitations of traditional methods in spatial representation and handling individual heterogeneity, but also provides a more interpretable and evolutionary mechanism for modeling the complex dynamics of SSR.

Cellular Automata (CA) serves as a lattice dynamics model characterized by discrete space, time, and state. Unlike models determined by strictly defined physical equations or functions, CA operates based on a set of rules constructed using various models. These models can be represented as $CA=(L_d,S,N,f)$, where CA denotes a cellular automata system, $L_d$ represents a d-dimensional cellular space, $d$ is a positive integer, S signifies the set of states of the automaton, N denotes the set of neighboring cells ($N\subset L$, $N=\left(s1, \mathrm{s}2,\cdots , \mathrm{s}\mathrm{n}\right)$, with $n$ being the number of neighboring cells), and f represents the evolution rule ($S_i^{i+1}=f(S_i^t,{ S}_N^t)$. This formula indicates that the state of a cell at time t + 1 is determined by the state of the same cell at time t and the states of its neighboring cells.

3.4. The Construction of SSR Control and Detection System for Major Engineering Projects

The integration of the ILMR infectious disease model with CA enables effective analysis of SSR in major engineering projects. In this study, the “transmission” process from the ILMR model is embedded into the state transitions of CA cells, allowing each cell to represent an individual at risk. In the integrated model, the ILMR component captures the dynamics of risk transmission between individuals, while the CA framework offers a spatial discretization platform to simulate the evolution of risk across different spatial units, as illustrated in Figure 2. This integration enables the dynamic representation of the spatial diffusion characteristics and clustering effects of social stability risk, thereby providing a more realistic simulation of risk event propagation during the implementation of major engineering projects.

3.4.1. The SSR Diffusion Process Based on the ILMR

During the implementation of major engineering projects, a series of risk factors accompany them, posing threats to the interests of groups related to the project. However, these objective risk factors alone do not generate social risks. Social risk events are formed when these factors stimulate interest-damaged groups, leading to feelings of threat and human intervention. These events arise from the combination of material and human factors. Initially, interest-damaged groups seek protection through legal channels, but when traditional avenues fail, they resort to non-traditional complaint channels, such as collective marches, leading to social risks. At the onset, only a few individuals, known as opinion leaders, defend their rights through unconventional channels, drawing media attention. As media coverage increases, bystanders who lack interest in the project join the event, becoming the dominant force driving SSR contagion. As the event escalates, the herd effect takes hold, reinforcing group consensus opinions and leading to infected herding behavior. The “spiral of silence” hypothesis explains this behavior, where individuals conform to mainstream views or choose silence when dissenting.

Given the similarities between SSR spread and infectious disease transmission, the idea of Ignorant–Latent–Malcontent–Recovered (ILMR) disease transmission describes SSR diffusion. This model captures the temporal evolution of behavior diffusion at the micro level and predicts behavior spread dynamics at the macro level. In the context of major engineering projects, SSR originates from losing interest due to productivity limitations, akin to the source of an infectious disease. If risks are not controlled, they accumulate and spread like a contagious period, eventually leading to an outbreak. Information is continuously exposed and modified as risks spread, leading to exponential amplification. Once affected parties receive reasonable protection, the risk subsides like an immune period. Additionally, SSR propagates within cyberspace, aligning with compartmental models, prompting the adoption of the ILMR model to classify SSR subjects. Categorizing subjects of SSR dissemination into four groups, this article delineates their roles in the diffusion process: Ignorant Individuals lack awareness but are susceptible, Latent Individuals are hesitant to participate, Malcontent Individuals actively engage in communication, and Recovered Individuals refrain from dissemination. The SSR diffusion process is illustrated through a model incorporating risk transmission, deterioration, dissipation, immunity, awakening, and forgetting rates, shedding light on the complex dynamics of SSR propagation within major engineering projects.

Figure 2 illustrates the intricate dynamics of Social Stability Risk (SSR) diffusion within major engineering projects. Following the interaction between Ignorant Individuals (I) and Malcontent Individuals (M), a majority of I transition into Latent Individuals (L) with varying probabilities, reflecting the heterogeneity and mobility inherent in social systems. Concurrently, a portion of I directly transforms into Recovered Individuals (R) due to their heightened risk perception capability. Once Latent Individuals become aware of risk information, they amplify the risk exponentially as the information spreads and evolves, with some transitioning into Malcontent Individuals with a certain probability. Strengthening network regulation and expanding information disclosure pathways can facilitate the direct transformation of Latent Individuals into Recovered Individuals. However, under the influence of group dynamics and pressure, coupled with the depersonalization effect of psychological priming, an increasing number of individuals transition into Malcontent Individuals, contributing to the widespread dissemination of SSR and reaching a peak in propagation. Without timely intervention, the broken window effect may emerge, exacerbating the spread of SSR.

As individual interests receive fair and equitable protection through intervention measures, the momentum of the societal risk event gradually subsides, with a significant portion of Malcontent Individuals transitioning into Recovered Individuals. However, the phenomenon of forgetting may lead to a subsequent transformation of Recovered Individuals back into Malcontent Individuals, perpetuating the cycle of risk propagation. This underscores the importance of sustained efforts to address underlying grievances and maintain social stability over the long term. By understanding and effectively managing the complex dynamics illustrated in Figure 3, stakeholders can develop targeted interventions to mitigate SSR and promote sustainable development within major engineering projects.

3.4.2. Propagation Model of SSR Based on Heterogeneous Cellular Automata

Differences among individuals, such as risk perception, cultural literacy, and levels of interest, influence their decision-making. Therefore, this article explores the propagation patterns of SSR from an individual interaction perspective and proposes a social risk control and detection system.

(1)

Individual Heterogeneity

Individual heterogeneity manifests in varying probabilities of infection between individuals, determined by individual resistance, infectivity of neighboring cells, and the distance between cells.

Let $N_{Ci,j}$ represent the set of neighbors of cell $C_{ij}$. The maximum value of the infection probability of cell $C_{ij}$, which is infected by all its neighboring cells, is taken as the probability of cell $C_{ij}$ being infected at a given time t:

$$P_{Cij\left(t\right)}=\underset{\left(k,l\right)\in NCi,j}{max}\left\{P_{C\left(i,j\right),C\left(k,l\right)}\right\}$$

(1)

$P_{C(i,j),C(k,l)}$ represents the probability of cell $C_{(i,j)}$ being infected by cell $C_{(k,l)}$ at time $t$. The distance determines the deterioration of SSR diffusion in major engineering projects. The shorter the cellular distance, the greater the deterioration of social risk diffusion. In this study, the distanced does not denote physical geographic distance, but rather social proximity, which reflects the closeness of social connections, communication frequency, and organizational relationships among stakeholders. Individuals who are socially closer (e.g., belonging to the same community, work group, or interest network) are more likely to influence each other’s risk perception and emotional state. To operationalize this concept within the cellular automata framework, social proximity is abstractly represented using a two-dimensional grid structure. The Euclidean distance between cells is therefore used as a topological approximation of social network distance, where shorter distances correspond to stronger potential interaction and influence. This abstraction enables the model to capture the localized clustering and gradual spread of SSR through socially connected groups rather than purely spatial neighborhoods.

Let $d$ be the Euclidean distance, represented as follows, between individual $C_{(i,j)}$ and $C_{(k,l)}$:

$$d_{C\left(i,j\right),C\left(k,l\right)}=\sqrt{(i-k{)}^2+(j-l{)}^2}$$

(2)

Generally, the closer the distance, the higher the probability of being infected by neighboring cells. Since the probability of an individual being infected is inversely proportional to their resistance and directly proportional to the infectivity of neighboring elements, it can be represented as follows:

$$P_{C\left(i,j\right),C\left(k,l\right)}\left(t\right)={\displaystyle \frac{1}{d_{C\left(i,j\right),C\left(k,l\right)}}}\sqrt{f_{C\left(i,j\right),C\left(k,l\right)}\left(1-R_{C\left(i,j\right)}\right)}$$

(3)

Let $f_{C\left(i,j\right),C\left(k,l\right)}$ represent the transmission of infection from individual $C_{(k,l)}$ to $C_{(i,j)}$, and $R_{C\left(i,j\right)}$ represents the resilience of individual $C_{(k,l)}$ against social stable risks. These variables follow a uniform distribution (0, 1) which indicates that individual heterogeneity depends on their ability to resist socially stable risks, the contagiousness of neighboring cells, and the distance between cells.

(2)

Individual Mobility

Since individuals move randomly throughout the propagation space, the thesis study considers the random walk of cells (social risk subjects). Therefore, the maximum step length $U$ is set for the random walk of each cell, and a random scan is performed on all cells within the spatial domain. Consequently, $M$ proportion of cells are randomly selected for the state evolution in the next time step. For the chosen cells, two independent random numbers, ${\mathrm{d}}_{\mathrm{i}}$ and ${\mathrm{d}}_{\mathrm{j}}$ ($\left|{\mathrm{d}}_{\mathrm{i}}\right|$, $\left|{\mathrm{d}}_{\mathrm{j}}\right|\le \mathrm{U}$|), were created. The cell at $(\mathrm{i},\mathrm{j})$ was then switched with the cell at $(\mathrm{i}+{\mathrm{d}}_{\mathrm{i}},\mathrm{j}+{\mathrm{d}}_{\mathrm{j}})$.

(3)

Cellular Space

$L=\mathit{nxn}$ represents a two-dimensional cellular space where $C_{(i,j)}$ represents a social risk-affected cell within $L$. The cellular space can be expressed by the following equation:

$$C=\left\{L(i,j)|1\le i\le n,1\le j\le n\right\}$$

(4)

In this case, $i$ and $j$ represent the coordinate values of the cellular space $C_{(i,j)}$.

(4)

Cellular Neighborhood

Neighborhood relations reflect the interaction between the victims of social risks and the spread of social risk. Von Neumann neighborhood (a) and Moore neighborhood (b) with a radius of 1, and extended Moore neighborhood (c) with a radius of r, where r is greater than 1, are illustrated in Figure 4 for a commonly used square grid cellular space. In this paper, the Moore-type neighborhood format is used.

(5)

Cellular State

Let $S_{\left(i,j\right)}\left(t\right)$ be the cell state variable, representing the state of the cell at time $t$ in row $i$ and column $j$. $S_{\left(i,j\right)}\left(t\right)=\left\{0,1,2,3\right\}$, each corresponding to a different cell state:

① When $S_{\left(i,j\right)}\left(t\right)=0$, cell $C_{i,j}$ represents $I$, which means that the individual is not aware of the social risk information and is susceptible to the interference of risk information.

② When $S_{\left(i,j\right)}\left(t\right)=1$, cell $C_{i,j}$ represents $L$, which means individuals have been exposed to and understand social risk information. However, due to a lack of active participation or personal interests being met to the expected satisfaction conditions, they remain in a hesitant state and will temporarily not propagate social risk.

③ When $S_{\left(i,j\right)}\left(t\right)=2$, cell $C_{i,j}$ represents $M$, which means the individual starts to propagate social stability risks. Cells in the $M$ state have the highest infectivity, and it is necessary to control the dissemination of these cells for societal stability.

④ When $S_{\left(i,j\right)}\left(t\right)=3$, cell $C_{i,j}$ represents $R$, which means individuals are immune to social stability risks. At this stage, individuals have a higher awareness of social stability risks and understand the risk information but have no intention to propagate it, or the interests of the affected parties are reasonably protected. However, due to forgetfulness and curiosity, over time or with the emergence of a new wave of social risks, some recovered individuals may once again transition back to malcontented individuals.

Introducing time parameters $t_a$, $t_b$, and $t_c$ for each cell, where $t_a$ represents the latency period, $t_b$ represents the unsatisfactory period, and $t_c$ represents the immunity period. $t_a\left(S_{\left(i,j\right)}\left(t\right)\right)$ denotes the latency time of an individual, $t_b\left(S_{\left(i,j\right)}\left(t\right)\right)$ denotes the duration of dissatisfaction of an individual, and $t_c\left(S_{\left(i,j\right)}\left(t\right)\right)$ denotes the duration of immunity of an individual.

(6)

Evolutionary Rules

① The initial state of all individuals for SSR is set to S = 0, and the state of the infected source individual is set to S = 2. Starting from time step 0, at each time step, scan all cells in the space and determine the individual state of each cell. The state update is performed based on the following rules:

② When $S_{\left(i,j\right)}\left(t\right)=0$, individual infection probability $P_{Cij\left(t\right)}$ is calculated, and then whether the individual will be transformed into $S_{\left(i,j\right)}\left(t+1\right)=1$ is determined with the probability $P_{Cij\left(t\right)}$. Otherwise, $S_{\left(i,j\right)}\left(t+1\right)=0$, $t_a\left(S_{\left(i,j\right)}\right(t\left)\right)=t_a\left(S_{\left(i,j\right)}\right(t\left)\right)+1$. Meanwhile, the individuals will transition to recovered individuals with a probability of $\theta$, and $S_{\left(i,j\right)}(t+1)=3$, $t_c\left(S_{\left(i,j\right)}\right(t\left)\right)=t_c\left(S_{\left(i,j\right)}\right(t\left)\right)+1$.

③ When $S_{\left(i,j\right)}\left(t\right)=1$, when $t_a\left(S_{\left(i,j\right)}\right(t\left)\right)>t_a$, $S_{\left(i,j\right)}(t+1)=2$, $t_b\left(S_{\left(i,j\right)}\right(t\left)\right)=t_b\left(S_{\left(i,j\right)}\right(t\left)\right)+1$. Otherwise $S_{\left(i,j\right)}(t+1)=1$, $t_a\left(S_{\left(i,j\right)}\right(t\left)\right)=t_a\left(S_{\left(i,j\right)}\right(t\left)\right)+1$. Meanwhile, the remaining latent individuals will transition to recovered individuals with a probability of $\mu$, and $S_{\left(i,j\right)}(t+1)=3$, $t_c\left(S_{\left(i,j\right)}\right(t\left)\right)=t_c\left(S_{\left(i,j\right)}\right(t\left)\right)+1$.

④ When $S_{\left(i,j\right)}\left(t\right)=2$ and $t_b\left(S_{\left(i,j\right)}\right(t\left)\right)>t_b$, $S_{\left(i,j\right)}\left(t+1\right)=3, { t}_c\left(S_{\left(i,j\right)}\right(t\left)\right)=t_c\left(S_{\left(i,j\right)}\right(t\left)\right)+1$. Otherwise, $S_{\left(i,j\right)}(t+1)=2$, $t_b\left(S_{\left(i,j\right)}\right(t\left)\right)=t_b\left(S_{\left(i,j\right)}\right(t\left)\right)+1$.

⑤ When $S_{\left(i,j\right)}\left(t\right)=3$ and $t_c\left(S_{\left(i,j\right)}\right(t\left)\right)>t_c$, the individual will revert to being a malcontent individual with a probability of $\delta$, and $S_{\left(i,j\right)}(t+1)=2$, with $t_b\left(S_{\left(i,j\right)}\right(t\left)\right)=t_b\left(S_{\left(i,j\right)}\right(t\left)\right)+1$. Otherwise, $S_{\left(i,j\right)}(t+1)=3$, $t_c\left(S_{\left(i,j\right)}\right(t\left)\right)=t_c\left(S_{\left(i,j\right)}\right(t\left)\right)+1$.

(7)

Algorithm Detail Design

Based on the above steps, this paper designs relevant algorithms to simulate the interaction behavior between units, shown below. Algorithm 1 describes the specific steps of transforming contact individuals into individuals of other states, through which the micro-behavioral interactions between individuals can be achieved. Steps 1–3 are used for cell traversal, steps 4–8 for threshold judgment, and steps 9–11 for updating the individual’s own infection rate and regenerating the counter. Algorithm 2 describes the infection behavior of neighbors, specifically referring to the infection behavior at the four corner positions as well as the upper, lower, left, and right positions.

Algorithm 1 Contact Individual Transformation Rules (Pseudocode)
1 2 3 4 5 6 7 8 9 10 11	for t = 1:simulate_time for i = 1:N for j = 1:N if Cell{i,j}(1) == 1 if Cell{i,j}(5) > Ta Cell{i,j}(1) = 2; infection_rate = A + (B-A).*rand(1,1); infection_rate = round(infection_rate,point); Cell{i,j}(4) = infection_rate; Cell{i,j}(5) = 0;

Algorithm 2 Neighborhood Infection Behavior (Pseudocode)

for i = 1:N for j = 1:N if Cell{i,j}(1)==0 if i==1 && j == 1 Cell = update_calculate_one(Cell,i,j); elseif i == 1 && j == N Cell = update_calculate_two(Cell,i,j); elseif i == N && j == 1 Cell = update_calculate_three(Cell,i,j); elseif i == N && j == N Cell = update_calculate_four(Cell,i,j);

4. Experiments and Simulation

The occurrence of SSR in major engineering projects is triggered by the socially rebellious behaviors of individuals or groups with vested interests in the projects. This demonstrates that humans, as carriers of social stability risks, can facilitate the escalation of these risks. Therefore, based on the diffusion patterns of SSR in major engineering projects, this paper proposes a control and detection system for SSR. According to the aforementioned evolution patterns, controlling the spread of SSR can be achieved by increasing recovered individuals and reducing ignorant individuals, latent individuals, and malcontent individuals. This research suggests four control mechanisms based on these evolution rules:

(1)

To raise the risk immunization rate and quicken the process of turning ignorant individuals into recovered individuals.

(2)

To enhance the risk awakening rate for latent persons to promote their conversion into recovered individuals.

(3)

To decrease the dissatisfaction cycle of individuals and quicken the process of turning the malcontent individuals into recovered individuals.

(4)

To reduce the risk forgetting rate for the recovered persons, decrease the number of malcontent individuals and enlarge the amount of recovered individuals.

4.1. The Process of Spreading SSR Without Any Intervention

The data collection process of this study is based on field investigations and expert interviews, combined with theoretical frameworks and previous research findings in relevant fields. Through interviews and questionnaire surveys, initial parameters were obtained from multiple engineering projects. Some other parameters were determined with reference to expert judgments and research findings in related fields [29,37,38]. In this study, a total of six experts related to SSR in major engineering projects were interviewed. The experts specialized in project management, risk management, and social governance. For specific expert information, please refer to Appendix A. In addition, multiple completed or ongoing major engineering projects were investigated, primarily encompassing transportation infrastructure and building construction projects. The survey focused on scenarios characterized by concentrated public demands, complex stakeholder relationships, and heightened social stability risks during the project implementation process.

The specific initial parameter information obtained is as follows: $\mathrm{N}$ = $50\times 50$, simulation duration $\mathrm{T}=40$, individual latent period $t_a$ = $3$, malcontent period ${\mathrm{t}}_{\mathrm{b}}$ = $3$, individual immunity duration ${\mathrm{t}}_{\mathrm{c}}$ = $10$, risk immunity rate $\mathsf{\theta }$ = $0.2$, risk awakening rate $\mathsf{\mu }$ = $0.2$, and δ = 0.3. The mapping relationships of the transition parameters among the four states are presented in

Table 1. Mapping of simulation parameters.

Model Parameter	Real-World Significance
θ	Control and guidance exerted by opinion leaders
μ	Authority and transparency of information dissemination
tb	Effectiveness of emergency management and mechanisms for safeguarding rights and interests
δ	Public cognitive resilience and immunity to rumors

. Assuming that the initial proportion of infected individuals in the population is 0.5%, the infectivity and resistance of cells follow a normal distribution with parameters (0, 1). It is important to emphasize that model parameter settings should be adjusted to specific sociocultural and governance contexts.

This article utilizes MATLAB (R2020b) to model the evolution of diffusion based on the parameters mentioned above, as seen in Figure 5. In Figure 5a, depicting the initial stage of diffusion, a predominant presence of ignorant individuals is observed, while malcontent, latent, and recovered individuals are relatively scarce and randomly distributed across the cellular space. However, in Figure 5b, a notable shift occurs as the number of ignorant individuals dramatically decreases, facilitating a concurrent increase in the numbers of latent, malcontent, and recovered individuals. By T = 15, illustrated in Figure 5c, a discernible evolution is evident: the proportion of ignorant and latent individuals dwindles while the ranks of malcontent individuals swell, reaching a peak of infection. Meanwhile, recovered individuals become more active participants, and red cells visibly aggregate into clustered formations, indicating the intensification of SSR propagation dynamics.

As the diffusion process progresses towards its culmination, Figure 5d portrays the final stage, wherein only recovered individuals and malcontent individuals persist throughout the entire space. This progression underscores the dynamic nature of SSR diffusion, characterized by shifting proportions of different individual states and the eventual convergence towards a state dominated by recovered individuals and a diminishing presence of malcontent individuals.

While the diffusion graph provides insights into the dynamics of state transitions, it does not comprehensively depict the quantities associated with each state within the population. Figure 6 illuminates this aspect, revealing a nuanced trajectory of state quantities over time, where the horizontal axis represents simulation time and the vertical axis represents the number of cells. Notably, the number of ignorant individuals undergoes a notable decline, nearly vanishing by the 20th time step. This trend can be approximated by a curve following the equation x = ky² (where k > 0 and y < 0), illustrating a rapid decrease in the population of ignorant individuals over time. The number of latent individuals exhibits a distinct pattern, initially rising to a peak before gradually declining. This trend is attributed to the transition of some ignorant individuals into the latent state, followed by subsequent conversions into recovered and malcontent individuals. Conversely, the number of malcontent individuals experiences a significant surge during the propagation period, followed by a sharp decline during the immune period, ultimately stabilizing at a relatively constant level. This fluctuation reflects the dynamic nature of SSR propagation, characterized by varying degrees of dissatisfaction and response intensity among affected individuals. In contrast, the number of recovered individuals shows a rapid increase during the initial stage, as ignorant, latent, and malcontent individuals transition into this state. However, the possibility of recovered individuals reverting to the malcontent state introduces fluctuations in this trend. Despite these fluctuations, the number of recovered individuals generally remains higher than the number of individuals in other states, underscoring the resilience of this state and its role in stabilizing the overall system.

4.2. Ignorant Individuals Control Strategy

When considering the pivotal role of ignorant individuals as the initiators of societal risk propagation in major engineering projects, it becomes imperative to bolster their transition to a recovered state, given that they serve as the primary source for other state individuals. Therefore, setting θ = 0.4 and θ = 0.8 and keeping the rest of the parameters constant yields Figure 7.

Compared with Figure 6, Figure 7 shows a rapid early decline in ignorant individuals, although the time required for this group to reach zero remains similar. Recovered individuals increase markedly in the initial stage due to the higher risk immunity rate. In addition, the peak values of both latent and malcontent individuals decrease noticeably. Malcontent and recovered populations subsequently exhibit alternating fluctuations, reflecting the dynamic transition between spreading and immune states.

During a risk outbreak, proactive management of opinion leaders becomes paramount, as they serve as conduits for spreading SSR contagion. It is essential to ensure that opinion leaders are cognizant of the impact of their words and actions on others. Identifying and controlling the information output of these individuals becomes imperative to prevent further distortion of risk-related information and mitigate the spread of SSR within the project environment.

4.3. Latent Individuals Control Strategy

The role of latent individuals in the propagation of Social Stability Risk (SSR) within major construction projects is nuanced. Unlike genuine beneficiaries with a proactive inclination to engage in risk-related dissemination, latent individuals typically adopt a wait-and-see attitude, refraining from actively participating in risk propagation. However, during this period of uncertainty, accurately discerning whether latent individuals have transitioned into malcontent individuals poses a challenge, potentially exacerbating the hazard. Furthermore, latent individuals serve as a direct source of malcontent individuals, underscoring the importance of expediting their transition to a recovered state. To achieve this, increasing the risk awakening rate (μ) becomes crucial. Therefore, setting μ = 0.4 and μ = 0.8 and keeping the rest of the parameters constant yields Figure 8.

In contrast to Figure 6, Figure 8 reveals the impact of increasing the risk awakening rate, with a notable decrease in the latent individual population and a corresponding increase in the recovered individual population. This shift reflects the accelerated transition of latent individuals to a recovered state, thereby diminishing their role as potential sources of SSR propagation. While the number of ignorant individuals remains stable, the proportions of latent and malcontent individuals change markedly. A higher risk awakening rate accelerates the transition from the latent to the immune state, increasing the share of immune individuals and limiting the growth of malcontent individuals.

During the developmental phase, risks associated with major construction projects undergo modification and amplification, often triggering heightened sensitivities among the populace and exacerbating social conflicts. To mitigate these tensions and prevent further escalation, it becomes imperative to disseminate accurate risk information through authoritative channels such as government websites, official social media platforms, and press conferences. Moreover, ensuring transparency and openness throughout major infrastructure projects, including those related to SSR, is essential.

4.4. Malcontent Individuals Control Strategy

Malcontent individuals play a pivotal role in the dissemination process of Social Stability Risk (SSR) within significant engineering projects. To this end, it becomes crucial to shorten social risk’s malcontent cycle (t_b), thereby accelerating its transformation into immune individuals. Therefore, setting t_b = 2 and t_b = 1 and keeping the rest of the parameters constant yields Figure 9.

In contrast to Figure 6, Figure 9 shows relatively stable trends for latent individuals, while the malcontent population declines rapidly and stabilizes at a lower level. This change is mainly due to the shortened duration of dissatisfaction, which accelerates the transition from the malcontent to the recovered state, thereby promoting a faster resolution of SSR within the project environment. The risk outbreak phase represents a critical juncture in the management of SSR, necessitating proactive governmental actions to establish a fair interest protection mechanism, implement consistent authority and responsibility, and enhance the government’s social stability risk management capabilities. Strengthening supervision of the online environment is also paramount to prevent the spread and proliferation of false information, which can exacerbate social tensions and amplify SSR propagation dynamics.

4.5. Recovered Individuals Control Strategy

To ensure sustained disinterest in Social Stability Risk (SSR) among individuals, efforts must focus on maintaining individuals in a state of recovery while minimizing the number of individuals who revert to malcontent status. Thus, reducing the risk of forgetting rates becomes imperative, setting δ = 0.2 and δ = 0.05 while keeping other parameters unchanged to derive Figure 10.

In contrast to Figure 6, Figure 10 shows that the number of ignorant individuals remains stable, while potential individuals exhibit only minor fluctuations with a slightly lower peak. The most pronounced change occurs in the malcontent group, whose peak and overall numbers decrease as the reduced risk forgetting rate limits reconversion into the malcontent state. Meanwhile, the growth of recovered individuals slows and eventually stabilizes at approximately 2433, indicating a more persistent recovery state with fewer relapses.

During immunization, the public must strengthen their awareness of rumor prevention regarding SSR in major projects. This entails enhancing beliefs, rational coping strategies, and judgment to avoid mindlessly following the crowd under group pressure, thereby minimizing the risk of individuals re-emerging as malcontent individuals.

4.6. Integrated Control Strategy

A comprehensive strategy combines both strong and weak intervention parameters from all the aforementioned control measures to form an integrated system of strong and weak interventions, as illustrated in Figure 11. Although the implementation of comprehensive strong intervention strategies significantly optimized system responses and reduced the propagation effects of unsafe behaviors, achieving this maximum control effect remains challenging in actual production processes. Therefore, the combination of control strategies for the aforementioned four state groups aims to explore and optimize the synergistic effects of control measures, thereby enhancing the system’s adaptability and performance across different environments.

5. Discussion

This research explored the intricate diffusion patterns of Social Stability Risks (SSR) within the context of major construction project. The investigation unearthed nuanced patterns of SSR propagation, shedding light on the interconnected factors that drive the emergence and escalation of social stability risks within major construction projects. The research elucidates the underlying mechanisms through which SSR unfolds and amplifies over time by dissecting the intricate interplay between various stakeholders, environmental factors, and policy considerations. To verify the theoretical rationality and effectiveness of the model, this study conducted strong and weak intervention analyses on key parameters. In addition, the simulation results of the model align with the general theoretical patterns of social stability risk diffusion at the macro-evolutionary level, preliminarily demonstrating the structural adaptability and explanatory power of the proposed model.

Moreover, the study’s findings hold significant implications for risk management practices within the construction industry and beyond. By discerning SSR diffusion’s key drivers and dynamics, stakeholders are empowered to proactively identify and address potential risk hotspots, enhancing project resilience and minimizing the likelihood of social unrest [39]. Additionally, the insights from this research inform the development of robust risk detection and monitoring systems, enabling early intervention and swift response to emerging SSR threats. As anticipated, the Integrated Ignorant–Latent–Malcontent–Recovered (ILMR) model, adeptly integrating these fundamental traits, effectively depicted the transitions of individuals across various risk states—Ignorant, Latent, Malcontent, and Recovered. This modeling framework’s capacity to simulate SSR propagation using real-world project data underscores its potential as a valuable risk assessment tool, offering practitioners a nuanced understanding of SSR dynamics and aiding in the formulation of targeted mitigation strategies. Although the ILMR framework is primarily developed to elucidate the diffusion mechanism of SSR, it can also serve as a complementary analytical tool within existing construction risk management systems. The modeled risk-state evolution supports social risk identification, dynamic assessment, and scenario-based intervention planning, thereby enhancing stakeholder risk awareness without requiring changes to established governance structures.

An unexpected revelation surfaced from the extensive heterogeneity observed in stakeholder risk profiles within the Heterogeneous Cellular Automata (HCA) simulations. This variance suggests that adopting a uniform communication and mitigation approach may prove suboptimal. Instead, tailoring interventions based on stakeholders’ distinct risk profiles, such as their level of information access and risk tolerance, could bolster mitigation endeavors. By recognizing and addressing stakeholders’ diverse needs and concerns, practitioners can devise more effective strategies to mitigate SSR and foster greater project resilience. Furthermore, the identification of such heterogeneity underscores the importance of adaptive risk management practices within the context of major construction projects. Embracing a flexible and iterative approach to risk assessment and mitigation allows for responsive adjustments to changing stakeholder dynamics and project conditions, thereby enhancing the overall effectiveness of risk management efforts [14]. Moreover, integrating stakeholder engagement mechanisms that facilitate ongoing dialogue and feedback exchange can foster greater transparency, trust, and collaboration, ultimately promoting a more inclusive and resilient project environment [40].

6. Conclusions and Future Work

This study significantly contributes to the understanding and management of social stability risks (SSR) in major construction projects. By developing the Integrated Ignorant–Latent–Malcontent–Recovered (ILMR) model and utilizing Heterogeneous Cellular Automata (HCA) simulations, we have provided a comprehensive framework for analyzing SSR dynamics. The research findings highlight the core characteristics of SSR, including loss aversion, uncertainty, and contagion, shedding light on the dynamic processes by which SSR propagates and evolves. Integrating the proposed control and detection system for Social Stability Risks (SSR) into existing risk management frameworks requires a strategic approach that ensures practical implementation and effectiveness. First, stakeholders should prioritize the adaptation of the Integrated Ignorant–Latent–Malcontent–Recovered (ILMR) model and Heterogeneous Cellular Automata (HCA) simulations into their risk assessment protocols. This entails training project teams to interpret and utilize SSR data generated by these models, enabling early identification of risk hotspots and trends. Second, establishing a proactive communication strategy tailored to stakeholder risk profiles is crucial. This involves regular engagement and feedback mechanisms that foster transparency and trust, mitigating potential SSR outbreaks by addressing concerns in real-time. Third, continuous refinement of the control and detection system through ongoing validation against real-world case studies ensures its predictive accuracy and relevance. This iterative process enhances the system’s adaptability to dynamic project conditions, reinforcing its role as a cornerstone of resilient risk management in major construction projects.

However, this study has not yet used real field data in simulating the diffusion process of social stability risk in large-scale and complex engineering projects, and the relevant parameters are mainly set based on the existing literature and the results of expert interviews. Although the parameter setting reflects the field knowledge and empirical judgment to a certain extent, there is still a certain deviation from the real situation. In future research, efforts will be made to incorporate more dynamic data based on real engineering cases, combining field surveys with multi-source data fusion techniques, in order to further enhance the representativeness of the model parameters. In addition, although individual heterogeneity and mobility mechanisms have been incorporated into the model to enhance its micro-level expressiveness, some complex social behaviors and multiple influencing factors (such as social media, individual emotions, etc.) have either been simplified or not yet included in the modeling framework. To further enhance the model’s real-world adaptability and mechanistic expressiveness, future research could consider coupling this approach with multi-agent systems to more comprehensively depict the dynamic evolution process of social stability risk driven by multiple sources. Expanding upon the ILMR model presents an exciting avenue for future research, particularly by integrating advanced sentiment analysis techniques. By exploring the intricate nuances of social sentiment, researchers can gain a more nuanced understanding of how emotions shape SSR dynamics.