Fire Hazard Risk Grading of Timber Architectural Complexes Based on Fire Spreading Characteristics

Abstract

Fire spread between buildings is the primary cause of extensive fire damage in traditional village timber structure clusters. Accurately assessing fire spread risk is crucial for the preservation of these architectural ensembles. During the development and conservation of traditional villages, fire risk dynamics may shift due to fire-resistant retrofits or layout modifications, necessitating repeated risk reevaluations. To address challenges such as the computational intensity of fire spread simulations, high costs, and data acquisition difficulties, this study proposes a directed graph-based method for fire spread risk analysis and risk level classification in timber structure clusters, accounting for their unique fire propagation characteristics. First, localized fire spread paths and propagation times between nodes (buildings) are determined through fire spread simulations, constructing an adjacency matrix for the directed graph of the building cluster. Path search algorithms then identify the spread range and velocity under specific fire scenarios. Subsequently, a zoned risk assessment model for individual buildings is developed based on critical fire spread loss and velocity, integrating each building’s fire resistance and its probability of exposure to different risk zones to determine the overall cluster’s fire spread risk level. The method is validated using a case study of a typical village in Yunnan Province. Results demonstrate that the approach efficiently computes fire spread characteristics across different scenarios and quantitatively evaluates risk levels, enabling targeted fire safety interventions based on village-specific spread patterns. Case analysis reveals significant variations in fire spread behavior: Village 1, Village 2, and Village 3 exhibit fire resistance indices of 0.59, 0.757, and 0.493, corresponding to high, moderate, and high fire spread risk levels, respectively.

1. Introduction

In China, a large number of famous historical and cultural cities (towns, villages) and traditional villages that need to be protected urgently, with various architectural styles, are the treasury of Chinese traditional residential buildings, possessing significant conservation value. By 2022, only in Yunnan Province, there were 14 historical and cultural cities, 25 historical and cultural towns, 37 historical and cultural villages, 19 historical and cultural streets, and 778 traditional villages. Most of these ancient towns and villages are timber architectural complexes built conjointly, characterized by low fire resistance ratings, large fire load, multiple fire hazard sources, inadequate deployment of fire protection infrastructure, and difficult fire rescue [1], leading to frequent fire hazards and fire hazard spreading between buildings. Many fire accidents show that fire spreading between buildings is the major problem of timber architectural complexes. For example, 107 civil houses were burned in the 3.11 [2] fire in Lijiang Dayan Ancient Town in 2013, 343 houses were burned in the 1.11 [3] fire in Dukezong Ancient Town in 2014, and 101 traditional residential buildings were burned in the 2.14 [4] fire in Wengding Old Village in 2021. Different building clusters exhibit significant variations in fire hazards and fire spread risks due to factors such as their distribution, architectural forms, fire resistance ratings, potential ignition sources, fire separation distances, and fire protection facilities. Effective fire prevention and control can only be achieved by considering these differences and implementing tailored fire safety retrofit strategies. Therefore, based on the fire spread characteristics of distinct building clusters, a rational assessment of fire spread risks and their severity levels is crucial for fire prevention and management in traditional villages and towns.

Currently, research on fire risks of timber architectural complexes mainly focuses on identifying fire hazards [5,6], evaluating zone fire hazard risks by considering risks of single buildings [7,8,9,10], fire hazard spreading modeling of architectural complexes [11], and risk calculation of fire hazard spreading ([11,12] et al.), while there is rarely research on the determination of fire hazard spreading risk grades of timber architectural complexes. To effectively differentiate the fire spread risks among various building clusters, a quantitative analysis incorporating both the characteristics of fire propagation during development and the resulting consequences is essential for risk assessment. In the fire hazard spreading modeling of architectural complexes, the empirical model [13,14], probability model [15,16], cellular automaton model [17,18,19], and physical model [20,21,22] have been developed worldwide. The physical model is established on the basis of fire dynamics. Because it can establish the relationship between fire spreading, building physical parameters, and environmental parameters, and accurately reflect changes in losses and spreading speeds, the physical model has received wide attention in recent years. Himoto and Tanaka [20] conducted extensive research in this field, establishing theoretical formulas for indoor fire development and spread, as well as theoretical models for thermal radiation and fire plume spread between buildings. Their proposed spread model has been continuously refined and validated, achieving high accuracy and widespread recognition. Regarding fire spread risk assessment, some scholars [23,24] applied the fundamental principles of directed graphs to describe fire spread in building clusters. They emphasized that fire, as a disaster, not only follows the laws of fire dynamics but also exhibits propagation phenomena within networks. Leveraging this characteristic enables highly accurate and efficient fire spread risk assessments and the formulation of mitigation strategies. However, in the process of traditional village development and preservation, challenges such as building fire safety modifications and layout changes often alter the fire risk dynamics of building clusters, necessitating repeated reassessments. This inevitably introduces difficulties, including extensive simulation workloads, high costs, and challenges in obtaining foundational data. To address these issues, this paper proposes a directed graph-based network model for fire spread risk analysis and quantitative risk level assessment in building clusters. First, a physical model is employed to simulate fire spread relationships between adjacent buildings, constructing a directed graph model of fire spread. A path search algorithm [24] is then used to calculate spread losses and velocities under different fire scenarios. Based on critical fire spread losses and velocities, a fire spread risk zoning model is established, determining risk zones and distribution probabilities for individual buildings. Additionally, a fire resistance capability index is introduced to evaluate fire spread risks across different timber structure building clusters. The proposed method, grounded in determining fire spread relationships between adjacent buildings, enables rapid computation of ignition sequences, spread losses, and velocities for various fire scenarios via the directed graph model. For issues such as fire safety modifications or layout changes during routine management, a network sensitivity analysis—by adding or removing nodes—can quickly assess post-modification risk variations. Furthermore, differences in fire spread risk characteristics and changes across building clusters can inform research on fire risk control, management, and architectural planning in traditional villages.

2. Materials and Methods

2.1. Fire Hazard Spreading Risk Characteristics of Architectural Complexes

During fire propagation, the physical parameters of individual buildings within a building cluster-such as dimensions, architectural style, spatial arrangement, quantity of combustible materials, and flammability characteristics, as well as environmental factors like terrain features and wind conditions, may lead to three distinct scenarios between adjacent structures: bidirectional spread, unidirectional spread, or no propagation. Consequently, when ignition occurs in different buildings, the resulting range of ignited structures and propagation speeds varies, thereby forming diverse fire spread scenarios, as illustrated in Figure 1. A directed graph consisting of five buildings was constructed, where all scenarios share the same node set V = {v₁, v₂, v₃, v₄, v₅} but differ in their edge configurations. Therefore, this paper models single buildings into nodes with reference to the basic idea of graph theory. Nodes are represented by physical parameters that are related to time t, such as the heat release rate Q_i. On this basis, physical models are used to analyze ignition processes between nodes to confirm their spreading relationship (edge), thus constructing the fire hazard spreading directed graph models of architectural complexes. The directed graph is defined as the set of nodes and edges G = {V, E}, where V = {v₁, v₂,…, v_M} is the set of nodes, and E = {e₁, e₂,…, e_N} is the set of edges. M and N are the number of nodes and the number of edges, respectively, corresponding to the number of single buildings and the number of spreading paths in architectural complexes. The direction of the edge represents the spreading path relationship between nodes, and the weight of the edge denotes the spreading time between nodes.

2.1.1. Fire Spread Process in Building Clusters

Fire Spread Development Process

Under uncontrolled conditions, building cluster fires typically undergo multiple developmental stages, including smoldering, open flame emergence, fire growth, flashover, fire spread from the initial room to adjacent rooms, inter-building fire propagation, and eventual extinguishment. These stages can be broadly categorized into three phases: (1) indoor fire development within a single building, (2) intra-building fire spread between rooms, and (3) inter-building fire propagation. The temporal evolution of fire intensity can be characterized by the heat release rate–time Q(t) curve, as illustrated in Figure 2a.

The fire development and spread process in a single building is illustrated in Figure 2a,b. When indoor combustibles are ignited, the fire enters the initial growth stage, during which it can be described by the t² [25] fire growth model. In this phase, the fire intensity increases gradually with accelerating growth rate. Upon reaching a critical stage, flashover occurs, resulting in the simultaneous ignition of most combustibles within the enclosure. The heat release rate continues to rise, and the fire temperature rapidly peaks, marking the transition to the fully developed stage. When wooden doors, windows, walls, floors, and other structural components exceed their fire resistance limits, the fire spreads horizontally through pathways such as wooden doors, windows, partitions, and corridors, while vertical propagation occurs via wooden floors, exterior wall openings, and stairwells. The fire development process in buildings can be analyzed through field modeling or zone modeling. Field modeling [7,10] divides the structure into discrete control volumes and applies computational fluid dynamics (CFD) principles to solve the Navier–Stokes equations, simulating spatial and temporal distributions of velocity, temperature, and concentration fields to determine the heat release rate (Q_i) at different combustion stages—as exemplified by tools like FDS. Zone modeling [7,10] partitions the building into interconnected compartments, solving conservation equations for mass and energy within each zone to derive Q_i. In this study, the fire dynamics simulator (FDS), developed by the National Institute of Standards and Technology (NIST), was employed to conduct field simulations for calculating the heat release rate of single-building fires.

The fire spread and development process in building clusters primarily involves the fire breaking through architectural constraints and propagating to adjacent structures, as illustrated in Figure 2c. The fire hazard spreading paths between buildings are mainly thermal radiation and fire plume. The node where fire breaks out is set as the independent ignition source in fire hazard spreading analysis. For the node j that is not on fire, when the thermal radiation flux q_jr(t) it received from adjacent combustible content is larger than the critical thermal flux of wood ignition q_cr, the node j is considered ignited, where q_cr is generally set to 12.5 kW/m² [26]. q_jr(t) is the thermal flux received by the exterior wooden walls or holes of the node j, which can be obtained by Equation (1).

$$q_{jr}(t)=\epsilon \left[\sigma \left(T_E^4-T_0^4\right)-{\displaystyle \sum _{i=1}^{N_i}{\phi }_i\sigma T_E^4+{\displaystyle \sum _{i=1}^{N_i}{\phi }_i{q}_i(t)}}\right]+h_w(T_E-T_0)$$

(1)

where ε is the wall emissivity, and the value is set as 0.8. σ is the Stefan–Boltzman constant, and the value is set as 5.67 × 10⁻⁸ W/(m².K). N_i is the number of nodes on fire. φ_i is the radiation angle coefficient of the wooden exterior wall of the i-th fire source node relative to node j. q_i(t) is the thermal radiation power of node i. By drawing on the calculation method of ignition sources in NFPA92B [27], it can be approximately calculated by formula (2). h_w is the convective heat transfer coefficient of walls, which can be calculated by the correlation formula of large space natural convection heat transfer experiment [10]. This paper takes the approximate value as 7.6 W/(m².K) [20]. T₀ is the wall temperature (K) of node j. T_E is the equivalent superimposed temperature of the fire plume of fire nodes of N_i and can be calculated by Equation (3) [20].

$$q_i(t)=\alpha {\chi }_R{Q}_i(t)$$

(2)

where α is the opening rate of the architectural exterior wall. χ_R is the proportion of the heat release energy released in the form of thermal radiation in fire hazards, and the value is generally set as 1/3.

$$T_E=273+{\left[{\displaystyle \sum _{i=1}^{N_i}{\left(\Delta T_i\right)}^{3/2}}\right]}^{2/3}$$

(3)

In the equation, ΔT_i represents the temperature increment at node j on the wall surface caused by the fire plume from ignition node i. Under the influence of ambient wind, the resulting thermal plume tilts, leading to increased temperatures on the leeward side, as illustrated in Figure 3. The temperature variation along the plume axis depends on the heat release rate and height of the fire, which can be calculated using Equation (4):

$$\Delta T_i=\left\{\begin{array}{l}900,\\ 60{(z/Q_i^{0.4})}^{-1},\\ 24{(z/Q_i^{0.4})}^{-5/3},\end{array}\right.\begin{array}{c}z/Q_i^{0.4}<0.08\\ 0.08\le z/Q_i^{0.4}<0.2\\ 0.2\le z/Q_i^{0.4}\end{array}$$

(4)

In the equation, z represents the height (m) of the projection from building j to the axis of the fire plume originating from building i. The inclination of the plume is primarily influenced by environmental conditions such as wind speed, wind direction, and ambient temperature. The angle between the plume axis and the horizontal plane can be estimated using the following formula:

$$\tan {\theta }_i=0.1{[{\displaystyle \frac{U_{\infty }}{{(Q_{i}g/c_{\mathrm{p}}{\rho }_{\infty }{T}_{\infty }\sqrt{A_i})}^{1/3}}}]}^{-3/4}$$

(5)

In the equation, θ_i represents the angle between the plume axis of fire source i and the horizontal plane; U_∞ denotes the ambient wind speed (m/s); C_p is the specific heat of hot smoke (kJ/kg·k); ρ_∞ indicates the air density (kg/m³); T_∞ refers to the ambient temperature (K); A_i is the floor area of fire source i (m²); and g represents gravitational acceleration, taken as 9.81 m/s². The temperature rise ΔT_ij at the exterior wall of building j, induced by the plume from fire source i, can be calculated as follows:

$$\Delta T_{ij}=e^{-{(r_{ij}/0.1z)}^2}•\Delta T_i$$

(6)

In the equation, r_ij denotes the distance (m) from building j to the fire plume axis of the ignited building i.

Simulation of Fire Spread Process in Building Clusters

The field-network or zone-network coupled simulation technique is a widely used numerical method for analyzing fire spread in building clusters. This approach employs a network-based concept, where individual buildings are modeled as nodes within the network. Each node is characterized by a set of uniform parameters representing physical quantities such as temperature and heat release rate. The ignition processes between different nodes are then analyzed to determine the connecting arcs, as illustrated in Figure 4.

In Figure 4, each individual building within the building cluster is treated as a node. At time t, the physical parameters of each node (including temperature and heat release rate) are represented by a set of state parameters Si(t, t_0i, Q_i, T_i). Here, t_0i denotes the ignition time of node i. For the initial fire source, t_0i = 0, while for unignited nodes, t_0i is assigned a sufficiently large value. Q_i and T_i represent the heat release rate (HRR) and average temperature (T) of node i, respectively, both being functions of t and t_0i. When t < t_0i, node i remains unignited, and both Q_i and T_i are zero. When t ≥ t_0i, node i is in a burning state, with both parameters becoming functions of the burning duration Δt_i (Δt_i = t − t_0i). For fire spread simulation, the propagation process can be modeled by examining and updating the state Si(t, t_0i, Q_i, T_i) of each node at time t. The workflow for simulating fire spread between buildings is illustrated in Figure 5.

The specific simulation process can be carried out according to the following steps:

(1)

Single-building fire simulation: Based on the building characteristics, analyze the fire development process in a single building to determine the state of the single building at different time nodes, denoted as Si(t, t_0i, Q_i, T_i).

(2)

Determine the initial conditions for fire spread simulation, mainly including environmental conditions such as wind speed and ambient temperature, simulation conditions such as the number of nodes in the building cluster, simulation time step dt, and total simulation steps N_t, as well as the initial conditions for the nodes. For the initially ignited node, its ignition time is set as t_0i = 0, and its initial state is set as S_i = S_i(0, 0, 0, T_∞). For non-ignited nodes, their ignition time is assigned a large value, which can be taken as t_0i = (N_t + 1)dt during calculation, and their initial state is set as S_i = S_i(0, (N_t + 1)dt, 0, T_∞).

(3)

Update the nodal states at different simulation times t_k = kdt, (k = 1, 2, …, N_t) to determine the ignition status of different nodes. The nodal state update can be performed as follows: ① For all ignited nodes (satisfying t_0i ≤ t_k), interpolate their heat release rate Q_i and temperature T_i at time t_k using the HRR and temperature interpolation curves of individual buildings. ② Calculate the total heat flux q_jr(t_k) exerted by all ignited nodes on each non-ignited node j (satisfyingt_0i = (N_t + 1)d_t) at time t_k based on the inter-building fire spread relationship determination method. ③ Determine whether node j is ignited. If node j is ignited, set t_0j = t_k and update its state to S_j = S_j(0, t_k, 0, T_∞). ④ Define a 1 × M row vector g as the ignition time vector during the simulation to record the temporal process of fire spread among buildings. The i-th element of vector g records the ignition time of node i.

2.1.2. Directed Graph Model

Based on the above calculation principle of fire spreading, the relationship and time of spreading between adjacent buildings are determined, and the adjacency matrix A_M×M is established to store the data of the connection relationship of network nodes, which corresponds to the direct ignition relationship (edge) between different nodes in architectural complexes. The adjacency vector of the directed graph is marked as a (i, j) (i = 1, 2, …, M; j = 1, 2, …, M). When there is an edge that the node v_i pointing to the neighbor node v_j, then a (i, j) =t_ij (t_ij is the time when the node v_i ignites the node v_j). The adjacency matrix A_T considering the weight value of time is determined. When A_T is known, the fire spreading matrix P_T can be calculated by the path-searching algorithm of the directed graph [28] to describe the direct or indirect connection relationship between network nodes. The fire spreading vector is marked as p (i, j) (i = 1, 2, …, M; j = 1, 2, …, M). When there is a direct or indirect edge connecting the nodes v_i and v_j, p (i, j) = T_ij, indicating that the node v_i passes through T_ij to ignite the node v_j.

In the directed graph network, the path with the minimum weighted sum of edges passed from node v_i to node v_j along directed edges, represents the shortest time for fire to spread from the building i to the building j. At present, a variety of shortest path algorithms have been developed, of which commonly used ones including Dijksra algorithm [29,30], A algorithm [31], Bellman–Ford algorithm [32], Floyd–Washall algorithm [33], etc. The Dijksra algorithm is a typical single-source shortest path method, which is used to calculate the shortest path from a node to other nodes. Its main feature is centering around the starting point to expand outward layer by layer until to the end point. The algorithm uses the breadth-first search algorithm to determine the shortest path between nodes v_i and v_j. Considering the weights of directed edges, the shortest path reflects the necessary time for the fire to spread from the igniting node v_i to the node v_j. When the weights of directed edges are not considered, the shortest path reflects the number of intermediate nodes the igniting node v_i passes through when spreading to the node v_j. The calculation steps are as follows:

Step 1: Set the set S to store accessed nodes. S∈V. Define t_ij as the time spent from the node v_i to the adjacent node v_j. If there is an edge connecting v_i and v_j, then t_ij is the weight of the edge (t_ii = 0). If there is no connecting edge between v_i and v_j, then t_ij = inf. Set an auxiliary matrix T of M × M, let t_ii = 0, and the initial values of other elements as inf.

Step 2: Make S= {v_i}, select the node v_k with the minimum weight value of the connection between the node v_i and the adjacent nodes from the set V-S. If it exists, put v_k into the set S, update the auxiliary matrix T according to Equation (7), and go to step 3. Otherwise, the algorithm ends and outputs the set S.

$$T_{ik}=\min \left(t_{ik}\right)$$

(7)

Step 3: Set the node v_k as the mediation point. Continue to select the node v_j from the set V-S with the smallest weight value of the connection between the node v_k and the adjacent node. If it exists, put v_j into the set S, update the auxiliary matrix T according to Equation (8), and go to step 4. Otherwise, end the algorithm and output the set S.When the same subscript “ik” appears on both sides of the equation, min(t_ik) denotes the minimization operation, where t_ik represents the propagation time parameter from node i to node k.

$$T_{ij}=\min (t_{ij},t_{ik}+t_{kj})$$

(8)

Step 4: Repeat step 3 until all nodes are traversed, that is, V-S = Φ. End the algorithm, output the set S and auxiliary matrix T. The auxiliary matrix T is the fire hazard spreading matrix P_T considering time weights. The number of columns and their values corresponding to the non-inf elements in the i-th row of the matrix P_T represent the number of nodes directly or indirectly ignited and the shortest time they spend after the node v_i on fire.

2.1.3. Fire Hazard Spreading Characteristics

The fire hazard spreading scenario loss is the number or area of buildings ignited by the building on fire, which can be expressed as the summation of the number or area of buildings ignited and calculated by the architectural complex fire hazard spreading matrix. Set the matrix P_f as the spreading matrix without considering time weights. The values of the elements in the i-th row of the matrix are taken according to Equation (9).

$$p_f(i,j)=\left\{\begin{array}{c}1\\ 0\end{array}\begin{array}{c},\\ ,\end{array}\begin{array}{c}\mathrm{if} p(i,j)\ne \inf \\ \mathrm{if} p(i,j)=\inf \end{array}\right.$$

(9)

The number of columns corresponding to elements whose values are 1 in row i of the matrix P_f represents the number of nodes that can be ignited after the node v_i on fire. The maximum fire hazard spreading loss L(i)_max caused by the igniting node i is calculated as follows

$$L(i)\max =P_{fi}S$$

(10)

where P_fi is the i-th row of the fire hazard spreading matrix P_f. S = [s₁…s_i…s_M]^T is the vector composed of the area of every single building of architectural complexes, where s_i is the area of the building i. If the area weight of every single building is not considered, S= [1, 1, …, 1]^T is the column vector with the element value of 1 in the row M.

The property risk after fire spread can be defined as the product of potential fire-induced property damage and its probability of occurrence. Under the assumption of a single fire incident, the resulting losses from fire propagation may vary depending on the initial burning building, introducing inherent uncertainty. Under these conditions, the property risk (expected loss) caused by fire spread in building clusters can be expressed as:

$$R={\displaystyle \sum _{i}L(i)\mathrm{Pr}(i)}$$

(11)

In the equation, Pr(i) represents the probability of fire spread scenario i occurring. Under the premise of a single fire incident, the probability of spread scenario i is generally considered proportional to the building area. If the influence of individual building area weights is disregarded, the probability of fire ignition in each building is equal, uniformly set as 1/M.

Fire hazard spreading speed is defined as the number or area of buildings ignited in unit time under the fire hazard spreading scenario i, calculated by Equation (11):

$$V\left(i\right)={L(i)}_{\max }/T\left(i\right)$$

(12)

where T(i) is the time needed to cause the maximum fire hazard spreading loss under the fire hazard scenario i, which can be obtained according to the fire hazard spreading matrix by Equation (12).

$$T\left(i\right)=\max ( P_T{)}_i$$

(13)

where (P_T)_i is the i-th row of the fire hazard spreading time matrix P_T.

2.1.4. Sensitivity Analysis Method for Fire Spread Networks

In building renovations or changes to architectural layouts, modifications to the directed graph of fire spread primarily involve the addition or deletion of nodes or edges. In practical engineering applications, the addition of nodes can describe the impact of newly constructed buildings, roadside vending, or the planting of trees between streets and buildings on fire spread paths within a building cluster. The deletion of nodes corresponds to the demolition of a specific building within the cluster. The addition of edges reflects changes in the ignition conditions between adjacent buildings due to alterations such as the installation of doors and windows, modifications to building materials, height adjustments, or changes in orientation during building use. The deletion of edges corresponds to fire safety measures implemented to enhance building fire protection, such as adding firewalls, fire-resistant doors and windows, sealing openings, or installing partition water curtain systems, which block fire spread paths to adjacent buildings. By adding or deleting nodes or edges, the directed adjacency matrix is adjusted to reflect the impact of these changes on fire spread relationships within the building cluster. Path search algorithms are then reapplied to determine the updated fire spread matrix.

If a specific building i within the cluster is demolished, the corresponding node v_i and its connected edges are removed from the network, and the i-th row and i-th column of the directed adjacency matrix must also be deleted. Depending on the actual fire protection modifications, edge deletions may occur in three scenarios: deleting the edge from node v_i to node v_j, deleting the edge from node v_j to node v_i, or simultaneously deleting both edges from v_i to v_j and from v_j to vᵢ. These cases can be corrected using Equations (14)–(16), respectively, where node v_j (j = 1, 2, …, M) represents an adjacent node to v_i.

$$a(i,j)=0$$

(14)

$$a(j,i)=0$$

(15)

$$a(i,j)=0,a(j,i)=0$$

(16)

When considering the impact of newly constructed buildings or trees i on the fire spread paths within a building cluster, the corresponding directed graph’s adjacency matrix is expanded by adding one row and one column, which are initialized to zero according to Equation (17). Here, M represents the total number of nodes after the addition. The fire spread relationship between the newly added node vᵢ and its adjacent nodes vⱼ is then evaluated, and the directed adjacency matrix is updated accordingly using Equations (18) and (19).

Similarly, if the structure or fire performance of building i is altered during use, the fire spread relationships between node vᵢ and its surrounding adjacent nodes vⱼ must be reassessed, and the directed adjacency matrix is revised again using Equations (15) and (16).

$$a(i,j)=0(j=1,2,....,M) , a(j,i)=0(j=1,2,....,M)$$

(17)

$$a(i,j)=\left\{\begin{array}{c}1,\hspace{1em}icannot ignitej\\ 0,\hspace{1em}icanignitej\end{array}\right.$$

(18)

$$a(j,i)=\left\{\begin{array}{c}1,\hspace{1em}jcan ignitei\\ 0,\hspace{1em}jcan not ignitei\end{array}\right.$$

(19)

The expected reduction rate or increase amplitude of fire spread loss in building clusters is introduced to quantify the change in fire spread risk after modification, as calculated by Equations (20) and (21).

$$\Delta R_{-i}=1-{\displaystyle \frac{R_{-i}}{R}}$$

(20)

$$\Delta R_{+i}={\displaystyle \frac{R_{+i}}{R}}-1$$

(21)

In the equation, R_−i represents the fire spread risk within the building cluster after removing node v_i or its connected edges; R_+i denotes the fire spread risk after adding node vi or its connected edges. The evaluation of changes in fire spread risk following the removal or addition of nodes or edges can be applied to research on fire risk control, management, and architectural planning layout in traditional village building clusters.

2.2. Fire Hazard Risk Partition Model

2.2.1. Fire Hazard Spreading Risk of Single Buildings

Timber structure building complexes exhibit characteristics such as extensive fire spread damage and rapid fire propagation. The fire spread damage reflects the scale of fire propagation caused by the initial building ignition; the fire spreading speed reflects the ability of the fire to expand (spread) outward and the difficulty of fire rescue in the process of fire development. Under given conditions, such as environment temperature, wind speed, etc., different settings of fire buildings will form different fire spreading development characteristics (fire spreading loss, spreading speed) due to different factors such as building scale, style, mutual location, and combustible quantity. Therefore, the fire risk of every single building in architectural complexes can be quantitatively described by the loss caused by different fire buildings and the fire spreading speed.

By modeling the fire spreading with every building in architectural complexes as the fire starting point, a series of corresponding relationships between fire spreading loss and fire speeding are obtained. The fire spread risk zoning model for individual buildings was constructed with fire spread loss as the vertical axis and fire spread velocity as the horizontal axis, as illustrated in Figure 6. When the fire of the igniting building i does not spread to other buildings, the building is considered no fire spreading risk, and its fire spreading speed is 0. When building i catches fire and inter-building fire spread occurs, the fire spread damage can be categorized into three levels based on the extent of damage (L_cr1, L_cr2): low damage, medium damage, and high damage. The speed of fire spread can be divided into three levels according to the magnitude of damage per unit time (V_cr1, V_cr2): relatively slow, moderate, and relatively fast. Based on the different positions of individual buildings in the risk zoning model, the fire safety characteristics of the building cluster are classified into 10 categories. According to these categories, the fire spread risk levels are divided into five tiers: no risk, low risk, medium risk, high risk, and extreme risk.

Traditional villages in the Southwest area are mainly inhabited by minority or local residents. The architectural layout is relatively compact, and the area of single buildings is mostly 90–130 m². The great majority of villages are located in remote mountainous areas, with small populations and a small scale of buildings of 50–100 structures. Fire spreading losses (measured by the number and area of buildings) accounting for 5% and 10% of the total number of buildings in a village can be set as the critical thresholds for low-to-medium and medium-to-high fire spreading loss, L_cr1 and L_cr2, respectively. L_cr1 can be determined as 500 m² or 5 buildings, and L_cr2 is 1000 m² or 10 buildings.

Fire rescue is the crucial factor in preventing fire from spreading. The intervention time of different fire rescue forces affect the size of the fire and the success probability of firefighting. Therefore, the time according to the specifications needed for the fire rescue force to arrive and carry out the rescue can be taken as the critical time T_cr1 for the fire spreading of the igniting building. The requirements for the arrival time of firefighting at fire stations or mini fire stations in the guidelines for firefighting design of cultural relics buildings [34] and the fire safety management of cultural relics buildings [35] in China can be effectively applied to the characteristics of rapid fire spreading of timber architectural complexes. However, the rescue abilities of most firefighting infrastructures and volunteer fire brigades in ancient towns and villages are poor. At present, active fire brigades are still the main rescue force. According to the regulations of the Standard for the Construction of Urban Fire Stations [36], fire stations need to carry out firefighting within 15 min, so the value of the first critical time T_cr1 can be set as 15 min. Studies found that timber buildings on fire usually come crashing down within 5 to 10 min. Obviously, the 15 min of firefighting time” stipulated cannot meet the firefighting requirements of traditional timber structure residential buildings. The time when the timber structure building collapses is set as the second critical time, set as T_cr2 = 8 min in this paper. Thus, the critical architecture fire spreading speeds, V_cr1 and V_cr2, are determined as 0.067 buildings/min and 0.125 buildings/min, respectively, as shown in Figure 6.

2.2.2. Fire Hazard Spreading Risk of Architectural Complexes

To quantitatively assess the fire spread resistance capability of individual buildings across different risk zones in Figure 6, this study draws upon the seismic capacity index proposed by Xie Lili [37] for evaluating building resilience against earthquake-induced losses. We introduce the Fire Resistance Capacity Index (k_i) to characterize a building’s ability to resist fire spread risks. A higher k_i value indicates stronger resistance to fire propagation, resulting in reduced fire damage and slower spread rates. The fire spread risk zoning model shown in Figure 6 divides the building into 10 zones, which also represent 10 grades (k₁, k₂, …, k₁₀) of the building’s resistance to fire spread. It quantitatively expresses the fire resistance capability index of individual buildings on a scale from 0 to 1, as illustrated in Figure 6 and

Table 1. Fire hazard spreading risk grades for single buildings.

Risk Grade	No Risk	Low Risk	MEDIUM RISK	High Risk	Extremely High Risk
Fire-resistance index	k1	k2	k3–k5	k6–k9	k10

.

As shown in Figure 6, due to the different characteristics of fire spreading loss and spreading speed, single buildings have different fire resistance abilities. Therefore, when evaluating fire spreading risks for timber architectural complexes, it is necessary to comprehensively consider fire resistance abilities and risk partition probabilities for single buildings. Similarly, the fire resistance index I of architectural complexes is introduced to represent the ability of architectural complexes to withstand the fire spreading risk, which is expressed as the product of the architectural fire resistance index matrix and its risk distribution probability. It can be calculated according to Equation (22).

$$I=K*P$$

(22)

where K is the architectural fire resistance ability grade matrix: [k₁, k₂, …, k_j, …, k₁₀]. P is the architectural fire hazard spreading risk probability matrix [p₁, p₂, …, p_j, …, p₁₀]^T, where p_j is the proportion of buildings in the area k_j, which can be calculated by Equation (23).

$$p_j=m_j/M$$

(23)

where m is the number of buildings in the area k_j. M is the total number of buildings in architectural complexes. The higher the architectural complexes’ fire resistance index I, the stronger the ability to withstand fire hazard risk, and the lower the fire hazard spreading risk grade for rural architectural complexes. According to the range of the architectural complexes’ fire resistance index, architectural complexes’ fire hazard spreading risk can be divided into five grades: extremely high risk, high risk, medium risk, low risk, and no risk, as shown in

Table 2. Fire hazard spreading risk grades for architectural complexes.

Fire Hazard Spreading Risk Grade of Architectural Complexes	I
Extremely high risk	[0.1, 0.3)
High risk	[0.3, 0.6)
Medium risk	[0.6, 0.9)
Low risk	[0.9, 1.0)
No risk	1

.

2.2.3. Fire Spread Prevention and Control Strategies

Based on the positioning of different building clusters within the fire risk zoning model, potential fire safety issues can be diagnosed. These primarily fall into three categories: excessive fire spread range; rapid fire spread that outpaces timely firefighting intervention; or the simultaneous occurrence of both scenarios. Building on this fire safety diagnosis, tailored fire spread prevention and control strategies can be formulated for individual buildings or clusters, focusing on two key aspects: mitigating fire spread damage and enhancing firefighting and rescue capabilities. For building clusters with high fire spread risk and potential losses, the primary strategy should emphasize controlling fire spread risks. This includes identifying critical structures, blocking fire propagation pathways, improving fire resistance performance, while also strengthening ignition source management and enhancing early-stage firefighting intervention capabilities. For building clusters where fire spreads rapidly, the strategy should prioritize measures such as installing alarm systems, deploying diverse fire rescue resources to improve early intervention capacity, or applying fire-retardant coatings and other fireproofing retrofits to slow the spread rate, thereby buying time for firefighting efforts.

3. Results

3.1. Analysis of Examples

This study selects three representative traditional timber structure building clusters in Yunnan Province as research objects, including two stilt-style residential complexes and one courtyard-style residential complex (see Figure 7). The geographical distribution and numbering of these buildings are illustrated in Figure 8, with individual structures shown in Figure 9. Village 1 comprises 106 residential buildings with a total floor area of 10,900 m². Each structure features a fully timber-framed, two-story design with elevated foundations, thatched roofs, and 2 cm wooden plank partition walls. Village 2 consists of 93 residential buildings covering a total area of 9486 m². While the roof material employs 10 mm thick calcium silicate boards, all other structural components—including beams, slabs, columns, exterior walls, and partitions—are constructed using timber or bamboo. Village 3 exhibits typical post-and-lintel timber structures, with 215 densely arranged buildings in contiguous blocks. The majority employ earth–timber or brick–timber hybrid construction, of which 142 buildings (approximately 66.05%) meet China’s Class III or IV fire resistance ratings.

3.2. Fire Spread Risk Level Assessment

The fire dynamics simulator (FDS) was employed to simulate the heat release rate curves Q(t) of various single-story buildings. The geometric model of a typical single-story building established in FDS is illustrated in Figure 10. Figure 11 shows the typical stilt-style single-story buildings in Village 1 and Village 2. The building measures 10.5 m in length and 5.2 m in width, with a total area of 109.5 m². Ventilation openings include two doorways (1.5 m × 0.7 m each), one vent (0.3 m × 5.35 m) between the wall and roof, two window openings (0.5 m × 0.5 m each) on the walls, and triangular openings (base: 2.5 m, height: 1 m) on both sides of the roof. The primary construction materials consist of grass, bamboo, and wood, typically fir or pine. The pyrolysis temperature range was set to 220 °C~380 °C, with a pyrolysis heat absorption of 5.0 × 10³ kJ/kg and a combustion heat release of 1.8 × 10⁴ kJ/kg. In Village 1, the roof was thatched with straw, having a pyrolysis temperature range of 220 °C~380 °C, a pyrolysis heat absorption of 1.7 × 10³ kJ/kg, and a combustion heat release of 1.8 × 10⁴ kJ/kg. To mitigate fire risks, Village 2 utilized flame-retardant asbestos tiles for roofing. The typical courtyard-style dwelling in Village 3 covers an area of 132 m² with a floor height of 3 m. The inter-window wall height between upper and lower floors is generally 2.0 m. For rooms without eaves, the fixed fire load is approximately 75 kg/m². Individual rooms measure 3.6 m × 6.0 m, with windows (1.0 m × 1.2 m) and doors (0.9 m × 2.0 m). Structural components such as partitions, doors, windows, and floors are constructed from wood, primarily local fir with a density of 640 kg/m³. The pyrolysis temperature range was set to 220 °C~400 °C, with a pyrolysis heat absorption of 2.2 × 10³ kJ/kg and a combustion heat release of 1.8 × 10⁴ kJ/kg. The simulated heat release rate curves Q(t) for these single-story buildings are presented in Figure 12.

The fire spread simulation technology was employed to model the fire propagation process between buildings, determining the ignition relationships and ignition times between nodes, and mapping the spread pathways among them, as illustrated in Figure 13, Figure 14 and Figure 15. The arrows in the figures indicate the direction of fire spread between nodes, while the ignition times between adjacent nodes are detailed in Figure 16, Figure 17 and Figure 18. The results reveal significant variations in ignition times between adjacent nodes across different rural building clusters due to differences in building types, materials, spatial layouts, and characteristic attributes. In Village 1, the fire spread time between adjacent buildings primarily ranged from 13 to 19 min, with a maximum ignition time of 20 min, a minimum of 5 min, and an average spread time of 16.4 min. Village 2 exhibited a maximum ignition time of 42.8 min, a minimum of 6.2 min, and an average spread time of 22.1 min. Village 3 displayed the most pronounced variation, with a maximum ignition time of 66 min, a minimum of 1 min, and an average spread time of 18.8 min. The gray buildings in Figure 15 are brick-concrete or frame structures with high fire resistance ratings, exhibiting no instances of fire spread between structures.

A directed graph model is constructed to simulate fire spread within the village building cluster, and the fire spread losses under different scenarios are calculated using the proposed method, as illustrated in Figure 19, Figure 20 and Figure 21. By applying a path search algorithm to the adjacency matrix of the directed graph, the maximum fire spread time for each scenario is computed, and the corresponding fire spread speeds are determined, as shown in Figure 22, Figure 23 and Figure 24.

As shown in Figure 19, Figure 20, Figure 21, Figure 22, Figure 23 and Figure 24, in Village 1, fire spread between buildings occurred in 75 structures, with a maximum fire spread loss of 21 buildings and an average fire loss of 6.34 buildings. In most fire scenarios, the spread speed ranged from 0.08 to 0.17 buildings/min, with a maximum spread speed of 0.2 buildings/min and an average spread speed of 0.125 buildings/min. In Village 2, fire spread occurred in 58 buildings, with a maximum loss of 11 buildings and an average loss of 3.57 buildings. Most fire scenarios exhibited a spread speed between 0.05 and 0.13 buildings/min, with a maximum speed of 0.325 buildings/min and an average speed of 0.061 buildings/min. In Village 3, fire spread occurred in 129 buildings, with a maximum loss of 68 buildings and an average loss of 30.82 buildings. Most fire scenarios had a spread speed ranging from 0.13 to 0.28 buildings/min, with a maximum speed of 0.331 buildings/min and an average speed of 0.169 buildings/min. The roofs in Village 1 were constructed with highly flammable thatch, resulting in a relatively faster fire spread compared to Village 2. In Village 3, the buildings were densely arranged, with adjacent streets mostly spaced at 2 m, leading to interconnected rows of structures, which contributed to greater fire spread losses and higher propagation speeds.

Based on the calculated fire spread speeds and losses under different scenarios, individual buildings in the villages were categorized according to the fire spread risk zoning model shown in Figure 4, resulting in fire spread risk zoning maps for different village building clusters, as illustrated in Figure 25, Figure 26 and Figure 27. Subsequently, the proportions of fire spread risk levels for individual buildings were statistically analyzed, as presented in

Table 3. Fire hazard spreading risk characteristics of architectural complexes of villages.

Risk Grade	No Risk		Low Risk		Medium Risk		High Risk		Extremely High Risk
	Amount	Proportion	Amount	Proportion	Amount	Proportion	Amount	Proportion	Amount	Proportion
Village 1	31	29.25%	0	0.00%	28	26.41%	35	33.02%	12	11.32%
Village 2	35	37.63%	8	8.60%	29	31.18%	21	22.58%	0	0.00%
Village 3	86	40.00%	4	1.86%	2	0.93%	22	10.23%	101	46.97%

. The results indicate that in Village 1, the majority of individual buildings (approximately 59.43%) exhibited medium-to-high fire spread risk, with a small proportion (11.32%) classified as extremely high-risk. In Village 2, most buildings (77.38%) fell under medium or lower risk levels, while high-risk buildings accounted for 22.58%. Village 3 was predominantly composed of high-risk buildings (46.97%) and no-risk buildings (40.00%), with the majority being highly fire-resistant structures where no inter-building fire spread occurred. The fire spread risk probability matrices for the building clusters were determined as follows: P₁ = [0.286, 0, 0.86, 0.01, 0.171, 0.124, 0, 0.105, 0.105, 0.114]^T, P₂ = [0.376, 0.086, 0.161, 0.043, 0.108, 0.065, 0.043, 0.065, 0.054, 0]^T, P₃ = [0.4, 0.018, 0.009, 0, 0, 0.009, 0, 0, 0.093, 0.469]^T. Using Equation (22), the fire risk resistance indices for the village building clusters were calculated as 0.59, 0.757, and 0.493, corresponding to high, medium, and high fire spread risk levels, respectively.

3.3. Preliminary Study on Daily Management and Prevention Strategies for Fire Spread Risk in Building Clusters

3.3.1. Daily Management of Fire Spread Risk in Building Clusters

In traditional villages and towns, activities such as new construction (or temporary structures), demolition, and renovation frequently occur during daily use. Taking Case 1 as an example, during normal usage, trees are planted or temporary wooden sheds are erected between buildings to enhance the surrounding environment and facilitate daily needs, as illustrated in Figure 28. Measurements from the 3D model show that the height of trees between buildings ranges from 3 to 6 m, slightly lower than the building height. These trees or wooden sheds reduce the fire separation distance between adjacent structures and act as intermediaries, potentially enabling fire spread between buildings that would otherwise remain unaffected due to continuous combustible materials. This study selects three locations, as shown in Figure 29, assuming that additional ignition nodes can ignite surrounding buildings. Equations (17)–(19) are then applied to modify the adjacency matrix, with the resulting fire spread paths illustrated in Figure 30. The losses under different fire spread scenarios after adding nodes are also presented in Figure 30. As can be seen in Figure 31, the introduction of additional nodes increases the connectivity of the directed graph representing fire spread among buildings, significantly raising the risk of fire propagation.

As shown in Figure 31, after adding new nodes, the maximum number of ignited buildings in the fire scenario reaches 53, accounting for approximately 50% of the total buildings, which is 2.52 times the maximum loss of the original building group. The expected fire spread loss of the building group is 18.76 buildings, 2.95 times that of the original group. The added nodes in this study are positioned between different connected subgraphs, functioning as “bridge nodes” that link these subgraphs, significantly increasing the overall fire spread risk of the building group. Therefore, in traditional village building clusters, the addition of new structures, trees, or other flammable materials should be avoided to mitigate their impact on fire risk. The on-site investigation of the Wengding Village fire (14 February 2021) [4] further confirmed that trees between buildings and surrounding the village accelerated both the spread and severity of the fire.

3.3.2. Preliminary Study on Fire Spread Prevention and Control Strategies for Building Clusters

Village 1 and Village 2 are located in remote mountainous areas, about 40 km away from the county seat, with winding mountain roads; it takes about 1 h for the active fire brigade to reach the fire site, and the local residents have not received professional fire rescue training, so they cannot respond promptly when a fire breaks out, which may easily result in missing the best opportunity for rescue. In addition, the configuration of fire-fighting facilities and equipment in the villages is insufficient; most buildings are only equipped with fire extinguishers, without fire-fighting facilities such as automatic alarm systems and automatic fire-extinguishing systems, and the fire water supply conditions are relatively poor. Village 3 is about 1.5 km away from an active fire brigade, with relatively good rescue conditions; the fire water is mainly supplied by the municipal pipe network, and the fire-fighting facilities and equipment are mainly fire extinguishers and automatic alarm systems, but the roads in the area are narrow, with many slopes and stairs, resulting in relatively slow movement. Combined with the FBIM model, the fire intervention time is 10.67 min; based on the statistics from 149 actual fire attendance data, under the 90% quantile, the fire intervention time in Village 1 is 10.54 min, and most buildings experienced fire spread between buildings when they caught fire. In addition, according to the location of different individual buildings in the fire spread risk zoning model of each village’s building group, the problems regarding the safety of the building group are diagnosed; for building groups with greater fire spread risk losses, the focus should be on controlling the fire spread risk of the building group; for building groups with faster fire spread speeds, fire mitigation measures such as adding alarm systems, setting up different types of fire rescue sevices to improve the ability of early intervention capabilities, or applying fire-resistant coatings, should be implemented to slow down the spread speed and gain time for fire intervention. Therefore, when carrying out fire mitigation measures or fire safety management in the above-mentioned villages, in addition to paying attention to the control and management of fire hazards such as regional use of fire, electricity, gas, and oil, and strengthening the management of unauthorized construction, new construction, reconstruction, and expansion projects, targeted fire renovation measures should also be formulated in combination with the characteristics of different villages, as shown in

Table 4. Transformation direction for different cases.

Case	Fire Safety Characteristics	Reconstruction Direction
Village 1	It is mainly characterized by high fire spread loss and high fire spread speed, and buildings with high or extremely high fire spread risk account for about 44.34% of the total number of buildings.	Remove continuous combustibles between buildings, install sprinkler systems, and prevent the spread of flying sparks; focus on fire protection reconstruction of buildings with extremely high fire spread risks to reduce the fire spread risks of building groups. Increase fire water supply, establish volunteer fire brigades, and shorten the fire-fighting intervention time.
Village 2	Medium fire spread loss and medium fire spread speed.	Focus on controlling the fire risks of individual buildings and strengthening fire safety education to prevent deaths from small fires. Increase fire water supply, establish volunteer fire brigades, and improve early fire-fighting and rescue capabilities.
Village 3	High fire spread loss and high fire spread speed. There are dense areas with relatively high fire spread risks.	For dense areas with relatively high fire spread risks, priority should be given to controlling the fire spread risks of building groups, identifying important buildings, cutting off spread paths, improving the fire resistance of buildings, and strengthening fire source control; add alarm systems, set up different types of fire rescue teams, and enhance the ability of early intervention in fire rescue.

.

In practical use, to improve building fire safety, fire prevention measures such as adding firewalls, fire doors, and windows, sealing openings, and installing automatic sprinkler systems are adopted to block the impact of fire spread paths with adjacent buildings. Taking Case 1 as an example, buildings No. 18, No. 30, No. 38, No. 40, and No. 61 with high fire spread risks (large spread losses and fast spread speed) can be selected for fire protection renovation to cut off their connections with surrounding adjacent buildings, so as to reduce fire spread losses. Equations (6) to (8) are used to process the above nodes, and the losses of different fire spread scenarios after renovating 5 high-risk buildings are calculated, as shown in Figure 32. For comparison, Monte Carlo simulation is used to randomly select five nodes from the building group fire spread network for fire safety renovation, so as to compare the renovation effects between the randomly selected renovation nodes and the renovation nodes given by the method in this paper, with a sample size of 100. The loss reduction rates of different fire spread scenarios after randomly sampling five nodes are given, as shown in Figure 33.

It can be seen from Figure 32 that fire protection renovation of five buildings with high fire spread risks can significantly reduce the fire spread risk of the building group, with the maximum fire spread loss being eight buildings and the expected reduction rate of fire spread loss being 49.36%. It can be seen from Figure 33 that when different numbers of nodes are randomly selected for fire safety renovation, the renovation effects vary greatly, and there are inefficient or ineffective renovated buildings in all cases. When 5 nodes are randomly selected for renovation, the average reduction rate of spread loss after renovation is 15.98%, with 57 groups of sequences having an average reduction rate lower than the expected loss reduction rate, among which 34 groups have a reduction rate of less than 10%, and only 31% of the renovation sequence groups have an expected loss reduction rate greater than 20%. This indicates that in engineering practice, blindly carrying out fire protection renovation on individual buildings in a building group may lead to inefficient or ineffective renovation effects.

4. Discussion

4.1. Work Performed

Based on multi-scenario fire spread simulation analysis, this study establishes a network model to characterize fire spread in building clusters. By integrating network node path search algorithms with node/edge addition-deletion algorithms, we developed risk analysis methods for fire spread scale and velocity, as well as sensitivity analysis methods for fire spread networks. This approach can evaluate the impact of new constructions, renovations, and expansions on fire risk management in traditional villages during daily use, while supporting targeted prevention strategies based on fire safety characteristics derived from different fire risk zoning models. Three village case studies were selected to validate the method and explore fire management and renovation strategies. The results demonstrate the following: (1) After determining inter-building fire spread relationships, changes in node information of directed graph adjacency matrices and matrix operations can efficiently calculate fire spread risk characteristics and assess the impact of individual building construction, renovation, expansion, or demolition activities on overall cluster fire spread. (2) Comparing risk variations caused by node additions at different locations enables analysis of how new combustibles (e.g., trees or additional buildings) affect fire spread risk. Varying reduction rates in expected fire losses after node deletions indicate significant differences in how individual nodes influence cluster-wide fire spread. (3) Traditional villages should avoid introducing new combustible structures or vegetation that may substantially increase fire risk during daily use. Randomly selecting buildings for fire safety upgrades proves significantly less efficient than prioritizing high-risk structures, demonstrating that blind retrofitting may yield ineffective results. Targeted modifications of buildings with greater influence on fire spread can reduce cluster-wide fire risk while minimizing impacts on traditional village landscapes.

4.2. Model Validation and Comparison

This study approaches the problem from a network system perspective, employing directed graph algorithms to calculate fire spread risk characteristics in building clusters. The accuracy of the results primarily depends on the determination of ignition relationships between adjacent buildings. Analytically, this paper adopts the same ignition process and judgment criteria for building cluster fire spread simulation as those established by Himoto and Ren Aizhu, all referencing the spread criteria of the Himoto model. The differences lie in the determination methods of key parameters such as heat release rate and temperature for individual buildings (or nodes). Himoto’s physical model uses zonal analysis to determine building fire parameters, while simplified physical models employ empirical formulas, whereas this study utilizes FDS-based field simulation analysis. These methods are relatively mature and widely applied, demonstrating reasonable reliability in judging inter-building fire spread relationships. Additionally, based on prior research, the authors proposed a simplified fire spread risk assessment method by combining the Hamada model with a physical fire spread model. This method establishes a regular grid layout inspired by the idealized building arrangement of the Hamada model [13], where all buildings within the grid share identical fire dynamics characteristics. By adjusting building forms, opening ratios, and spacing within the grid to represent different fire scenarios, the physical model analyzes fire spread under various conditions. The results were used to develop a fire spread risk classification table for different types of rural building clusters, which was successfully applied to courtyard-style, tufted-roof, stilted, and log-cabin dwellings in Yunnan Province. The current method analysis of three village building clusters aligns well with prior research findings. Comparisons with actual fire incidents—the 2013 Lijiang Dayan Ancient Town fire, the 2014 Dukezong Ancient Town fire, and the 2021 Wengding Village fire—show good agreement, except for a slight overestimation in the Wengding Village case. Field investigations revealed that severe fire spread damage was caused not only by thermal radiation, fire plumes, and flying embers but also by collapse-induced spread and tree-to-building ignition due to unique environmental and topographic conditions. In terms of computational efficiency, this study applies graph theory principles by modeling individual buildings as nodes and inter-building spread relationships as edges, significantly reducing the complexity of finite element modeling and improving efficiency. Furthermore, during the protection and renovation of traditional villages, changes in fire spread relationships due to building layout modifications can be updated simply by redefining adjacent edges, allowing real-time risk assessment updates. In contrast, the literature reports indicate that FDS analysis of a single building (11.6 m × 11.9 m × 7.5 m) requires approximately 74 h [38], making it impractical for large-scale building cluster fire spread analysis.

4.3. Future Perspectives

This study approaches the issue of fire spread risk and control methods in building clusters from a network systems perspective, employing systems engineering methodologies. It provides a novel viewpoint for researching fire prevention in traditional timber-structure village building clusters. However, existing uncertainties in fire spread processes lead to indeterminacy in the edges between adjacent nodes within network models—for instance, when adjacent buildings receive heat radiation not less than 12.5 kW/m². Extensive experimental studies indicate significant uncertainty in this ignition condition, further contributing to the unpredictability of edges describing ignition relationships. Therefore, future research could explore fire spread risk and mitigation strategies in building clusters based on probabilistic network models that account for such uncertainties. Additionally, the network formed by fire spread in building clusters exhibits the heterogeneous topological characteristics of complex networks. Removing certain critical buildings (nodes) or fire spread paths (edges) can disrupt the propagation network on a large scale, significantly reducing fire spread risk. Introducing complex network methods offers new insights into low-intervention fire spread control for timber-structure building clusters. Thus, subsequent research could integrate the risk characteristics of fire spread in building clusters to develop node importance analysis methods suitable for fire spread network models. This would help identify key buildings that significantly influence fire propagation, enabling targeted fire safety retrofits and the development of low-intervention fire spread control measures.