Identifying Key Factors for the Collapse Range of Cover-Collapse Sinkholes

Abstract

Cover-collapse sinkholes are one of the most hazardous geohazards, causing severe damage to civil infrastructure, roadway networks, and substantial economic disruptions. In the United States alone, the economic loss caused by cover-collapse sinkholes exceed USD 300 million annually. Despite extensive research on the causes and formation mechanisms of cover-collapse sinkholes, reliable prediction of the collapse range remains a significant challenge because the development of cover-collapse sinkholes occurs underground and is generally undetectable at the ground surface until collapse occurs. This study presents a comprehensive review of 162 peer-reviewed journal articles, technical reports, and case studies to systematically identify the key factors governing the collapse range of cover-collapse sinkholes. This paper covers several influencing factors for collapse range of cover-collapse sinkholes, including soil properties, geometric characteristics of cavities and soil cover, hydraulic conditions, and the presence of buried structures. Among these factors, soil cohesion, friction angles, void ratio, soil cover thickness, and cavity geometry are identified as the key influencing factors for the collapse range of cover-collapse sinkholes. In addition, existing prediction methods were also summarized, which are predominantly empirical and have limited capability to capture the influence of multiple factors on the collapse range. Based on the literature review, this study finally identifies current research gaps and suggests future directions for developing more accurate and integrated models to predict collapse range of cover-collapse sinkholes.

1. Introduction

Sinkholes pose a severe risk to civil infrastructures due to their sudden and severe consequences to people and properties [1,2,3,4,5]. Sinkholes are generally classified into three main types, including dissolution sinkholes, cover-subsidence sinkholes, and cover-collapse sinkholes [6]. In particular, cover-collapse sinkholes are the most destructive type of sinkholes which lead to abrupt ground failure and may cause extensive damage to civil infrastructures and loss of life [7,8,9,10,11,12,13]. The economic losses caused by sinkholes in karst terrains in the United States exceed USD 300 million annually [14]. For example, insurance records show that more than 24,600 sinkhole claims were filed between 2006 and 2010 in Florida alone with a total amount of approximately USD 1.4 billion [14]. Sinkholes could also induce significant environmental risks, particularly to groundwater quality by introducing contaminants into aquifers [14]. Additionally, one of the most catastrophic cover-collapse sinkholes occurred in Land O’Lakes, Florida, in 2017, where sudden collapse formed a 70 to 80 m wide and 15 m deep sinkhole that destroyed multiple homes [15]. Another recent event in 2025 in Bangkok, Thailand, created a 30 m wide and 50 m deep cover-collapse sinkhole, shallowing a heavy tow truck and severely disrupting urban traffic [16]. Sinkholes have increased over the past few decades which can also be caused by human activities specifically groundwater pumping, underground construction, and deterioration of buried structures [17].

Previous studies on sinkhole susceptibility and hazard mapping use GIS, statistical methods, machine learning, and remote sensing tools to estimate the spatial probability of sinkhole occurrence [18,19,20,21,22,23,24,25,26,27,28,29]. Geo-mechanical studies investigate the mechanisms of subsurface cavity formation, while geo-physical monitoring of sinkholes using ground penetrating radar (GPR), electrical resistivity tomography (ERT), and Interferometric Synthetic Aperture Radar (InSAR) detects signs of maximum deformation before collapse [30,31,32,33,34,35,36,37]. In addition, studies on trigger mechanisms, including extreme precipitation, groundwater table fluctuation, and seismic events, effectively identify conditions that initiate cover-collapse sinkholes [38,39,40,41,42]. These studies can only identify where sinkholes are likely to occur, their formation mechanisms, early warning signs, and what triggers them. Although advanced studies on different karst regions in North America, Europe, and China have improved sinkhole mapping, monitoring, and modeling, there is still no reliable method to predict the collapse range accurately, as the transition from stable soil arch to abrupt failure is controlled by multiple interacting factors, including soil properties, subsurface cavity geometry, groundwater changes, and buried utilities. Additionally, the prediction of sinkhole collapse in terms of range and timing remains a challenge since the development of sinkholes is hidden in the ground and cannot be observed from the ground surface until sinkhole collapses. The objective of this paper is to document the advancement of cover-collapse sinkhole research in recent years, including empirical equations, laboratory experiments, physical modeling, and especially coupled hydro-mechanical numerical models, to identify key influencing factors for collapse range of cover-collapse sinkholes and thus to prevent and mitigate cover-collapse sinkholes more effectively and efficiently.

2. Methodology

This review collected 162 research articles, government reports, and non-governmental documents from academic databases, including Google Scholar, Web of Science, and ScienceDirect, spanning publications from 1936 to 2026, to systematically examine collapse sinkholes and their implications for engineering practice. The literature search was conducted using a comprehensive set of keywords such as cover-collapse sinkholes, sinkhole formation mechanisms, karst terrain, soil cover collapse, cavity development, soil arching, collapse range and timing, sinkhole hazard assessment, and sinkhole risk mitigation and preventive strategies.

A screening process was applied to identify relevant publications based on two criteria: (1) publications that specifically examined the cover-collapse sinkhole formation mechanisms, including the influence of soil properties, cover thickness, and sinkhole geometry on collapse behaviors, arching, and propagation of failure; (2) articles discussing experimental, numerical, and analytical methods for assessing stability of sinkholes. Publications were excluded based on two criteria: (1) publications that focused exclusively on dissolution or subsidence sinkholes without relevance to cover-collapse mechanisms; (2) articles lacked sufficient methodological detail for reproducibility assessment.

Among the 162 documents reviewed, approximately 118 were peer-reviewed journal articles, 5 were government or institutional reports, 19 were conference proceedings, and the remaining 20 were other sources including books, news articles and web resources. Geographically, the reviewed literature is concentrated primarily in North America, particularly in the United States, where well-documented cases in Florida and Kentucky are commonly associated with cover-collapse sinkholes driven by groundwater fluctuations, rainfall events, and groundwater pumping. In China, site-specific investigations from regions such as Guangxi, Guangzhou, Wuhan, Hunan, and Shanghai predominantly focus on sinkhole formation linked to tunnel and metro excavations, as well as leakage-induced internal erosion in sandy soil layers. In Europe, especially in Spain, Belgium, Italy, and Croatia, extensive research has been conducted on sinkhole hazards in karst terrains. In contrast, comparatively fewer studies have been reported from the Middle East (notably the Dead Sea region), Southeast Asia (including the Philippines and Thailand), and Africa (such as South Africa), where sinkhole occurrences are mainly related to evaporite or carbonate dissolution, and groundwater level fluctuations.

3. Classifications of Sinkholes

A sinkhole is a localized surface depression or collapse feature of the ground surface caused by the downward movement of soils or rocks into subsurface voids due to dissolution, internal erosion, and mechanical failure in the ground [43]. Sinkholes, which are also called “dolines” in Europe, are natural features in carbonate regions which are underlain by soluble rocks such as limestone, dolomite, and marble. These rocks dissolve over time and create voids and lead to sinkholes. Human activities such as underground construction, groundwater withdrawal, and defective buried structures can also cause sinkholes. The sinkholes due to human activities are also known as induced sinkholes that are more severe compared to the ones caused by rock resolutions [44,45].

Collapse refers to when the roof of a cavity in the soil or rock subsides and eventually fails, causing a sudden dropout at the ground surface. The collapse event is known as catastrophic failure that produced steep side openings near vertical walls and deep depressions. Such collapses happen rapidly without early warning that distinguishes from slow subsidence processes. Sinkhole collapse occurs when the shear stress in the soil roof above an underground cavity exceeds the shear strength of the soil [46]. Terzaghi discussed brittle roof rupture, progressive cavity enlargement, loss of soil arching capacity in overlying materials, sudden dropout, and funnel shaped sinkholes [47]. On the other hand, subsidence is termed as progressive ground movement, which takes place due to ground loss or removal of fluids in the ground. Slow internal soil erosion, consolidation or gradual deformation of soil, and rock masses are the causes of subsidence. Subsidence-related sinkholes generally develop gradually over time and exhibit shallow and broad depression. The rate of subsidence development is low (i.e., 0.5 mm/day initially but later increase to 0.1 mm/day), which indicates subsidence sinkholes can be monitored to avoid severe damage [48].

Waltham presented the basic genetic classification of sinkholes of six main types based on their formation process and material properties, including solution, collapse, caprock, dropout, suffusion, and buried sinkholes [49,50]. Later, Gutiérrez refined the classification of sinkholes by focusing on the interaction between materials (cover, bedrock, and caprock) and process interactions (sagging, suffusion, and collapse) [51]. However, the United States Geological Survey (USGS) classifies sinkholes into three main types: dissolution sinkholes, cover-subsidence sinkholes, and cover-collapse sinkholes based on the geological conditions of Florida, as shown in Figure 1 [2]. Among them, cover-collapse sinkholes are more predominant, more dangerous, and unpredictable [5,52,53]. Cover-collapse sinkholes occur when soil arching over a cavity progressively loses strength due to saturation, groundwater erosion, loading, and human activities, eventually failing suddenly [54,55,56,57].

4. Cover-Collapse Sinkhole Formation Process

Baryakh and Fedoseev described the cover-collapse sinkhole formation mechanism as a five-stage process [58]:

Stage 1: Formation of the Cavity

An underground cavity can develop due to both natural processes and human activities. Natural processes include dissolution of soluble bedrock [59,60], internal soil erosion caused by groundwater seepage [61,62,63], groundwater fluctuations [64], heavy rainfall or flooding [65,66,67], and seismic shaking or earthquake [68]. Human-induced causes include pumping induced groundwater extraction [69], the breakage or leakage of sewer pipes [70], mining [71], tunneling [72], and abandoned underground excavations [73].

Stage 2: Growth of the Cavity

The cavity enlarges due to continued internal erosion in ground, stress redistribution in soil, groundwater fluctuations, progressive weakening of soils, external loading, or vibration. During the stage, soil arching develops above the cavity roof, which allows the cavity to remain hidden and does not show any immediate distress on the ground surface.

Stage 3: Reaching Critical Dimension of the Cavity

When the cavity width reaches a critical dimension, a tensile-stress zone develops on the roof of the cavity. Then, the rocks start to deform permanently due to the growth of plastic strain, and the roof will eventually collapse.

Stage 4: Collapse of Overlying Soils into the Cavity

Roof collapse occurs when the plastic-strain zone propagates rapidly through the overlying soils. The corresponding dynamic failure condition of the overlying soils is given by:

$$V_a+V_b\ge k_{frag}{V}_a$$

(1)

where $V_a$ is the space created by collapsed rock, $V_b$is the existing void space, and $k_{frag}={\displaystyle \frac{VolumeafterFragmentation}{InitialVolume}},$ which denotes fragmentation coefficient of the collapsed rocks.

$k_{frag}>1$ denotes highly fragmented soil that undergoes bulking and occupies more volume, $k_{frag}=1$ indicates no bulking which means no volume change, and $k_{frag}<1$ indicates the material has been washed out, compacted, or consolidated.

In Equation (1), the total amount of fallen material into the cavity is $V_a$; after fragmentation, this volume effectively becomes to $\left(k_{frag}{V}_a\right)$. If the total cavity space, $(V_a+V_b)$ is greater or equal to volume after fragmentation $\left(k_{frag}{V}_a\right)$, collapse will happen. This means the total cavity space is sufficient to accommodate the volume of fragmented material. Therefore, the collapse height, $\left(h\right)$ is obtained by dividing the available cavity space $\left(V_a+V_b-k_{frag}{V}_a\right)$ with the maximum width of the plastic-strain failure zone, $\left(r\right)$.

$$h={\displaystyle \frac{\left(V_a+V_b-k_{frag}{V}_a\right)}{r}}$$

(2)

Stage 5: Formation of Cover-Collapse Sinkhole

The cavity keeps moving upward and propagates through overburden soil layer(s) and cover-collapse sinkhole forms at the surface. Therefore, sinkhole depth at the ground surface, $h_{sink}$

$$h_{sink}=\left(h+H_{ov}\right)-k_{ovf}{H}_{ov}$$

(3)

where $H_{ov}$ and $k_{ovf}$ are the thickness of overburden layer(s) and overburden fragmentation coefficient, respectively.

From Equation (3), the condition for cover-collapse sinkhole formation can be derived as follows:

$$h_{sink}>0🡺\left(h+H_{ov}\right)-k_{ovf}{H}_{ov}>0🡺h>(k_{ovf}{H}_{ov}-H_{ov})🡺h>{(k}_{ovf}-1)H_{ov}$$

(4)

In Equation (4), when the collapse height $h>{(k}_{ovf}-1)H_{ov}$, the collapse reaches the ground surface, and a cover-collapse sinkhole forms.

5. Influencing Factors of Collapse Range of Cover-Collapse Sinkhole

The interaction of several key factors, including soil strength parameters, cavity geometry, hydraulic conditions, and buried structures, collectively influences stress redistribution, soil arch development and stability, and failure propagation, thereby controlling the collapse range of cover-collapse sinkholes.

5.1. Effects of Soil Properties on Collapse Range

Soil arching controls the collapse range by redistributing overburden loads around a subsurface cavity. Strong soil arching transfers overburden loads laterally to surrounding stable soil, allowing the subsurface cavity to grow progressively and delaying collapse [74]. However, once the soil arch breaks, it produces a wider collapse range. In contrast, when soil arching is weak or absent, overburden loads act directly downward, which leads to early failure and produces a narrower collapse range. Soil properties influence the development of soil arching and thereby control the collapse range, as described in

Table 1. Soil properties controlling collapse range with corresponding sources.

Soil Properties	Effects on Collapse Range	Significance	Sources
Cohesion	Higher soil cohesion → stronger soil arching → wider collapse range	High	[75,76,77,78]
Friction Angle	Poorly graded, non-cohesive soils → lower friction angle → wider collapse range	High	[79,80,81,82]
Void Ratio	Higher Void Ratio → wider collapse range	High	[83,84,85,86,87,88,89,90,91,92,93]
Tensile Strength	Higher tensile strength → wider collapse range	Moderate	[82]
Modulus of Elasticity	Stiff soils (low compressibility) → wider collapse range	High	[85,94,95]
Over Consolidation Ratio (OCR)	High OCR → wider collapse range	Moderate	[78]
Plasticity Index (PI)	Higher PI → wider collapse range	Moderate	[96]
Viscosity	Higher viscosity → wider collapse range	Low	[97]

.

Table 1 summarizes the significance of influence of soil strength parameters on collapse range. Cohesive soil covers rely more on cohesion, whereas granular material covers depend more on friction angle [98]. Differences in the literature arise from variations in soil types, loading conditions, and scale effects, highlighting the need for a unified framework that incorporates the most significant parameters simultaneously.

Luu et al. introduced a dimensionless particle cohesion number ($Coh)$ for 2D models [99] in their study as shown below:

$$Coh={\displaystyle \frac{C}{{(\rho }_s-{\rho }_f)gS}}$$

(5)

where $C,{\rho }_s,{\rho }_f$ and $S$ are the soil particle bond strength, the density of the soil, the density of the fluid and the soil particle surface area per unit thickness, respectively. A high cohesion number $\left(Coh\right)$ indicates that soil particle bond strength exceeds the submerged weight per unit thickness of the soil, allowing overburden loads to be transferred laterally and forming a stable soil arch. In contrast, a low cohesion number $\left(Coh\right)$ indicates gravity-dominated behavior, leading to particle raveling and the development of a weak soil arch.

The collapse index $\left(I_s\right)$ combines both collapse sensitivity (collapse magnitude) and the collapse rate (time required for 90% settlement). Soil with a higher collapse index, such as loess or saturated wad, loses volume quickly, shrinks, and collapses upon wetting, resulting in a wider range of cover-collapse sinkholes [100,101].

5.2. Effects of Soil Cover Thickness and Subsurface Cavity Size on Collapse Range

Both soil cover thickness and subsurface cavity size influence the collapse range which is primarily governed by the ratio of cavity diameter to soil cover thickness $\left(DR\right)$.

$$DR={\displaystyle \frac{H}{D}}$$

(6)

where $H$ is thickness of the soil cover; and $D$ is the diameter of subsurface cavity. Rather than treating subsurface cavity size and soil cover thickness as independent parameters, the $DR$ captures their interaction as a single dimensionless factor.

As the soil cover thickness $\left(H\right)$ increases, stability increases, soil arching enhances, surface fails abruptly, and collapse range tends to increase. Thick soil cover collapses along a single dominant failure surface, whereas thin soil cover produces more than one failure surface [87,91,102,103,104,105]. Additionally, the collapse range increases with the diameter of the subsurface cavity, such that larger cavities tend to produce wider cover-collapse sinkholes and require higher support pressure to maintain ground stability [106]. Moreover, previous studies have shown a linear relationship between soil cover thickness and the range of cover-collapse sinkholes, indicating predicted collapse range is often approximately equal to soil cover thickness or two-thirds of it [46,99]. In addition, Jacobsz demonstrated that the effect of the cavity diameter on the collapse range is more significant than that of the soil cover thickness [107].

Shiau introduced Pressure Ratio $\left(PR\right)$ as a new approach to find the stability number, which depends on the ratio of cavity diameter to soil cover thickness $\left(DR\right)$ that eventually affects the collapse range [108]. As $DR$increases, Pressure Ratio $\left(PR\right)$ increases nonlinearly that means more surface pressure ${(\sigma }_s)$ is required to cause collapse [109,110]. Thin soil cover over subsurface cavities ($DR\le 1.3$) becomes highly unstable, the failure surface can easily propagate to the ground surface and create a narrower collapse range [111,112]. Thick soil cover ($DR\ge 3to5$) increases stability, improves the potential for soil arching, and transfers the load to the side walls, delaying surface collapse but fails abruptly and produces a wider range of cover-collapse sinkholes [82,83,113,114,115,116,117,118,119,120,121]. Furthermore, factor of safety is proportional to soil cover thickness to cavity diameter ratio, showing thicker soil cover provides greater stability and thinner soil cover leads to collapse early [122,123].

Table 2. Stability evaluation methods for soil cover above sinkholes.

Equations Related to Soil Cover and Subsurface Cavity Size	Sources
Stability ratio $\left(N\right)$ for tunnels $$N={\displaystyle \frac{{\sigma }_s-{\sigma }_t+\gamma (H+\frac{D}{2})}{S_u}}$$ where ${\sigma }_s,$${\sigma }_t,$$\gamma$ and $S_u$ represent surface surcharge, internal supporting pressure required to prevent collapse, unit weight and undrained shear strength, respectively.	[106]
Collapse solution for shallow cover ratios ($DR\le 1.3$). $$N_c=1.956{\displaystyle \frac{H}{D}}$$	[112]
Pressure ratio $\left(PR\right)$ for circular tunnels $$PR={\displaystyle \frac{{\sigma }_s}{c^{\prime }}}=f({\phi }^{\prime },{\displaystyle \frac{\gamma D}{c^{\prime }}},DR,{\displaystyle \frac{S}{D}})$$ where ${\sigma }_s,$${\sigma }_t,$$\gamma ,$ where S is center to center distance. and $c^{\prime }$ represent surface surcharge, internal supporting pressure required to prevent collapse, unit weight and undrained shear strength.	[110]
Stability number, ($N_c$) $$N_c={\displaystyle \frac{\gamma H}{S_u}}$$	[124]
Strength ratio, $\left(SR\right)$ $$SR={\displaystyle \frac{\gamma D}{S_u}}$$ Pressure ratio $\left(PR\right)$ controls collapse stability $$PR={\displaystyle \frac{{\sigma }_s-{\sigma }_t}{S_u}}=f(DR,SR)$$	[108]

summarizes the evaluation methods for the stability of soil cover above sinkholes.

An increase in the volume of the subsurface cavities leads to a corresponding increase in the range of cover-collapse sinkholes. Caudron demonstrated that settlement trough volume is directly proportional to the cavity volume which determines the equivalent collapse range [125].

$$V_{trough}={\displaystyle \frac{1}{1+K}}{V}_{cavity}$$

(7)

where $V_{trough}$_, $V_{cavity}$ and $K$ are the volume of settlement trough, the volume of subsurface cavity, and the expansion coefficient, respectively; $K$ is typically taken as an empirical value of 0.5.

5.3. Effects of Hydraulic Conditions on Collapse Range

Hydraulic loading, including seepage, exfiltration, and groundwater fluctuations, controls soil arching through poromechanical processes between pore fluid and soil skeleton as described by Biot’s consolidation theory, in which changes in pore water pressure alter effective stresses in soil, thereby influencing soil deformation, stiffness, and strength [126,127,128]. Groundwater rise increases pore water pressure within the soil cover, reducing effective stress and load bearing capacity of soil, resulting in a weak or unstable soil arch [129,130]. In contrast, groundwater drawdown decreases pore water pressure and increases effective stress, stiffening the soil through enhanced interparticle contact forces and volumetric compression under drained conditions, thereby forming a stable soil arch with wider collapse range [82,128,130]. However, rapid groundwater drawdown induces transient seepage forces and excess pore water pressures under undrained conditions, disrupting stress redistribution and preventing stable arch development [131,132]. Additionally, groundwater fluctuations or cyclic infiltration and exfiltration induce pore water pressure variations, alternating between drained and undrained poromechanical responses, driving stress redistribution and shear band evolution, resulting in temporary arch formation and accelerated subsurface cavity growth [133,134,135]. Moreover, high hydraulic gradients generate seepage forces that may exceed interparticle contact forces, promoting particle detachment and internal erosion, thereby further weakening the soil arch [128,135,136,137]. However, existing studies treat hydraulic effects in a simplified manner, neglecting the poromechanical processes governing soil arching behavior.

5.4. Effects of Existing Buried Structures on Collapse Range

Existing buried structures, such as pipes, tunnels, and underground structures, can reinforce the soil cover by promoting soil arching, leading to a narrower collapse range [138,139,140,141]. In tunnel–soil–pipe interaction studies, pipes and similar buried elements act as stiff inclusions that transfer the load laterally [142]. Field case studies, including Qingdao Metro Line 1 and Shanghai Metro Line 4, show that seepage-induced water–sand inrush caused internal erosion, leading to stable soil arch formation, resulting in a relatively localized zone [143,144], as shown in Figure 2.

CFD-DEM studies further confirmed that buried pipes act as boundaries for cavity growth and form temporary soil arches. This soil arching effect reinforces the soil cover initially, but leakage-driven hydraulic erosion or mechanical degradation reduces soil arch strength, and the soil arch fails abruptly, leading to a wider collapse range [145,146]. For both reduced scale tunnel leakage and buried drainage pipe leakage tests, CFD-DEM simulations indicate temporary soil arch formation can reinforce the soil cover above the subsurface cavity, but hydraulic or mechanical weakening causing sudden collapse over a wider range [147,148,149,150,151,152,153,154,155,156,157]. Therefore, buried structures modify soil arching behavior; they can reinforce the ground and, in some cases, increase instability.

6. Current Methods to Determine Collapse Range

The geometry of cover-collapse sinkholes such as range, depth, and shape is critical to understanding the risk and severity of cover-collapse sinkholes. According to Williams, cover-collapse sinkholes can range from 10 to 100 m [158].

Table 3. Summary of existing methods for predicting collapse range.

Formulas	Sources
The correlation between soil cover thickness $\left(H\right)$ and collapse range $\left(d_{sink}\right)$ based on empirical mining derived formula is given by $$d_{sink}=2.53H^{0.27}$$	[159]
The Sachs–Zakolski–Skinderowicz method estimates the collapse range ($d_{sink})$ using shallow mining-based equations as follows $$d_{sink}=2r_i\sqrt{{\displaystyle \frac{ln\frac{a}{z-H}}{ln\frac{a}{r_i}}}}$$ where $r_i$and $a$ are radius of initial underground cavity and vertical extent of void propagation, respectively.	[160]
Whittaker and Reddish method is used to collapse range ($d_{sink}$) at the ground surface, $$d_{sink}=2\sqrt{{\displaystyle \frac{Lg(2gcot\alpha +L)}{\pi h(k-1)}}}$$ where $L,g,\alpha ,h$ and $k$ are length of the excavation, height of the excavation, slope angle of collapse debris (angle of repose of the collapsed rock), height of the collapse zone and rock loosening coefficient, respectively.	[161]
The Clostermann method is used to find out the collapse range ${(d}_{sink})$ $$d_{sink}=\sqrt{{\displaystyle \frac{V_b}{\pi \times h\times (k-1)}}}$$ where $V_b,h$ and $k$ are volume of primary void, height of the collapse zone, and rock loosening coefficient, respectively.	[162]

summarizes existing empirical formulas for predicting collapse range.

Existing stability equations in Table 2 and prediction models for collapse range in Table 3 are based on classical empirical formulations with simplified assumptions, largely derived from mining subsidence theories, and small-scale trapdoor experiments. In contrast, recent research trends have shifted toward three-dimensional advanced numerical analysis, time-dependent simulations, and coupled hydro-mechanical approaches for natural karst settings that can capture non-linear behavior of soils, transient groundwater effects, and the time-dependent development of subsurface cavities, but do not yield simple closed form solutions.

7. Research Gaps and Future Research Directions

Existing methods for predicting collapse range of cover-collapse sinkholes are mostly empirical or highly site-specific and ignore most of the influencing factors. Based on the review, the following research gaps were identified: (1) soil properties of the soil cover were not included in the collapse range equations as shown in Table 3. Presented in Table 1, soil properties could influence collapse range significantly which should be included in the prediction method; (2) the growth of underground cavities with time is typically ignored. With the growth of underground cavities, the soil cover roof may fail with time, which could result in the reduction in soil cover thickness and thus influence the stability of soil cover; (3) the hydraulic conditions are not considered in existing methods, such as groundwater level fluctuations and extreme flooding events. The seepage force caused by the groundwater level change and/or extreme floods could influence the stability of the soil cover above underground cavities; and (4) the effects of existing buried structures or superstructures on the collapse range are not considered. However, these existing structures could reinforce the ground and reduce the collapse range. Once hydraulic or mechanical weakening of pipes degrades soil arch strength, failure becomes more sudden, producing a wider collapse range.

To address these research gaps, we would like to suggest the following directions: (1) incorporating key properties of soil cover into the collapse range prediction; (2) integrating cavity growth with time and considering the time-dependent behaviors of soil covers above underground cavities; (3) incorporating the groundwater level fluctuations and flooding hydraulic dynamics into the stability analysis of soil cover and including seepage forces in the prediction method for the collapse range; and (4) investigating the influence of existing structures on the collapse range of cover-collapse sinkholes considering the dimension, burial depth, and stiffness of these structures. Therefore, a multi-factor predictive framework can be developed by considering collapse range as a function of key influencing factors, including soil properties, cavity geometry, hydraulic conditions, and the influence of buried structures, enabling integrated assessment of cover-collapse sinkholes.

8. Conclusions

Cover-collapse sinkholes are highly destructive and remain difficult to predict due to their hidden subsurface cavity development which causes USD 300 million economic loss annually in the United States alone. The formation mechanism of cover-collapse sinkholes has been investigated extensively; however, the collapse range of cover-collapse sinkholes still cannot be predicted accurately, which means that it is important to propose effective mitigation measures. In this paper, 162 publications were reviewed and the influencing factors on the collapse range of cover-collapse sinkholes were summarized and the key factors were identified. In addition, the existing methods for the collapse range were also examined. Based on the literature review, the following conclusions can be drawn:

(1) Soil arching is the most critical mechanism dominating the collapse of cover-collapse sinkholes. A stronger soil arch leads to a wider collapse range. Soil properties such as cohesion, friction angle, void ratio, and stiffness are key influencing factors for the collapse range.

(2) Cavity geometry and soil cover thickness affect the collapse range. Larger subsurface cavities and thicker soil covers would cause wider collapse range. Hydraulic conditions such as groundwater fluctuations and extreme flooding events could accelerate subsurface cavity development and result in a wider collapse range. The existence of superstructures and underground structures could reinforce the ground and induce a narrower collapse range. Once hydraulic or mechanical deterioration of pipes weakens soil arch strength, failure may become more abrupt, resulting in a wider collapse range.

(3) Existing prediction methods are mostly empirical and fail to capture multiple influencing factors, the growth of underground cavities, change in hydraulic conditions, and existing buried structures.

(4) Future directions were suggested to address the current research gaps including the multi-factors, time-dependent behaviors of underground cavities and soil cover, seepage force caused by hydraulic dynamics, and the influence of existing structures should be incorporated into the prediction method for the collapse range of cover-collapse sinkholes.

For engineering practice and hazard zoning, engineers and practitioners can consider the combined effects of the identified key influencing factors for site assessment in karst areas, develop early warning indicators, and design mitigation measures including controlled drainage, ground reinforcement, and subsurface void filling to reduce cover-collapse sinkhole risk.