⚡ electrical engineering

Seismic Stability of Karst Sinkholes under high peak ground acceleration: a three dimensional numerical study in Barangay Dontogan, Baguio City, Philippines

This three-dimensional numerical study evaluates the seismic stability of 44 validated sinkholes in Barangay Dontogan, Baguio City, under high peak ground accelerations, revealing that while shallow cavities remain stable at 0.40 g, the 0.80 g design demand triggers a bifurcation into collapse and critical states for cavities with height-to-diameter ratios of 1.00 or less, leading to the proposal of a four-tier stability threshold matrix for foundation safety assessments.

Original authors: Deryl Jhon Lucas

Published 2026-09-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Deryl Jhon Lucas

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the rugged highlands of the Philippines, the ground beneath our feet is not always solid. In places where ancient rainwater has slowly dissolved limestone over millennia, a hidden network of caves and voids forms underground. When the roof of one of these voids becomes too thin to support the weight of the earth above it, the ground suddenly gives way, creating a sinkhole. These are not just deep pits; they are sudden, catastrophic failures that can swallow homes and roads without warning. The danger is amplified when the earth shakes. An earthquake does not just shake a building; it jolts the ground itself, adding a powerful, rhythmic force that can push a barely stable rock roof over the edge into collapse. For engineers and city planners, the challenge has long been knowing exactly when that roof is safe and when it is about to fail, especially in regions where the ground is already known to be unstable.

In the city of Baguio, a mountain resort known for its cool climate and steep terrain, this problem is acute. The city sits on a formation of fractured limestone, and a specific neighborhood, Barangay Dontogan, holds the highest concentration of documented sinkholes in the region. The local building code provides strict rules for designing structures to withstand earthquakes, but it offers no specific guidance for buildings sitting directly above these hidden underground cavities. To fill this gap, a researcher from the University of the Cordilleras turned to advanced computer modeling to simulate what happens when a sinkhole cavity is subjected to the intense shaking of a major earthquake. Their goal was not just to see if the ground would crack, but to determine the precise tipping point where a stable roof becomes a collapsing one, and to translate those findings into a practical tool for protecting the community.

The researcher focused on the geometry of the voids, specifically the relationship between the thickness of the soil and rock covering the cavity and the width of the cavity itself. They created a three-dimensional digital model of a spherical hole buried beneath a layer of soil and a layer of jointed limestone, mimicking the actual conditions found in Dontogan. They then subjected this model to simulated earthquake forces, scaling the shaking intensity to match the high seismic demands of the region, which can reach levels as high as 0.80 g. This is a measure of ground acceleration, representing a force nearly equal to the pull of gravity itself. By running the simulation across a range of different cavity sizes and cover thicknesses, the researcher could observe how the rock and soil responded to the stress of the shaking.

The results revealed a clear and somewhat alarming pattern. When the shaking was moderate, the ground remained stable regardless of the size of the hole. However, as the intensity of the simulated earthquake increased, the stability of the roof dropped sharply. The most critical finding occurred at the highest design level of shaking, where the researcher identified a specific geometric threshold. If the cover of rock and soil above the cavity was less than the width of the cavity itself, the system became critically unstable. In these scenarios, the computer models showed that the rock roof could not sustain the load, leading to a collapse. The simulations indicated that for the specific conditions in Barangay Dontogan, a roof that is thinner than the hole it covers is likely to fail under a major seismic event, while a roof that is significantly thicker than the hole remains safe.

To make these complex findings useful for everyday decision-making, the researcher developed a simple classification system. They divided the risk into four categories based on the calculated safety margin: stable, marginal, critical, and collapse. A "stable" rating means a conventional foundation, like a standard concrete slab or a single pile, is sufficient. A "marginal" rating suggests that the ground is shaky enough to require stronger support, such as grouted micro-piles that anchor the building deep into the solid rock below the cavity. A "critical" rating indicates that the risk is high enough to demand a specialized solution, like a raft of interconnected piles that bridges the void entirely. Finally, a "collapse" rating means the ground is too dangerous to build on at all, and the only safe option is to avoid the site or transfer the building's weight through the hole to the solid rock far beneath.

This new framework was applied to the forty-four validated sinkholes currently mapped in Barangay Dontogan. The analysis showed that the safety of a building cannot be assumed based on the stability of the surrounding neighborhood; every single footprint must be evaluated individually. A site that appears safe today could be on the verge of failure if a major earthquake strikes, particularly if the geometry of the underlying void places it in the critical or collapse zones. The study confirms that the traditional approach of relying on static stability is insufficient for this region; the dynamic force of an earthquake is the deciding factor. By providing a clear, quantitative method to assess these risks, the research offers city officials and engineers a vital tool to prevent future disasters, ensuring that new structures are built only where the ground can truly hold them.

Technical Summary: Seismic Stability of Karst Sinkholes under High Peak Ground Acceleration

Problem Statement
Barangay Dontogan in Baguio City, Philippines, faces a high risk of karst subsidence, hosting 44 validated sinkholes (the largest concentration in a regional inventory of 129). These sinkholes, with apertures ranging from 1.0 to 50.0 meters, overlay the jointed Kennon Limestone formation. While the National Structural Code of the Philippines (NSCP) provides seismic design provisions for Zone 4 (with a near-source design demand of approximately 0.80 g to 0.83 g), it lacks specific criteria for evaluating the stability of subsurface cavities under seismic loading. Existing rock-mass classification systems and deterministic analytical methods fail to account for the three-dimensional nonlinear behavior of jointed rock masses containing voids, leaving a regulatory gap in permit-level decision-making for residential development in this high-susceptibility area.

Methodology
The study employs a three-dimensional finite-element method (FEM) using PLAXIS 3D to model the seismic response of spherical karst cavities.

Model Geometry: A two-layer stratigraphic profile was constructed: a Mohr–Coulomb sandy/gravelly silt-clay overburden overlying a Generalized Hoek–Brown jointed Kennon Limestone. A spherical cavity was embedded such that the limestone-overburden interface passed through the cavity's mid-height.
Parametric Sweep: A 15-scenario matrix was generated by crossing five height-to-diameter (H/D) ratios (0.50, 0.75, 1.00, 1.50, 2.25) with three Peak Ground Acceleration (PGA) tiers (0.40 g, 0.60 g, and 0.80 g). The 0.80 g tier represents the NSCP 2015 design demand for the site.
Seismic Input: The analysis utilized a time-history accelerogram of the 1990 Mw 7.8 Luzon Earthquake, scaled to the target PGAs. The study acknowledges the limitation of using a single record rather than the ASCE 7-22 minimum of 11, noting the results are record-specific.
Analysis Procedure: The simulation followed a four-phase pipeline: (1) staged construction and static equilibrium; (2) dynamic time-history loading; (3) post-shaking residual re-equilibration; and (4) extraction of the Dynamic Factor of Safety ( $\Sigma M_{sf}$ ) using the Strength Reduction Method (SRM) at the residual limit-equilibrium state.
Verification: The model was verified for mesh independence and benchmarked against existing 3D limit analysis studies. Discrete-event verification runs at intermediate PGAs (0.55 g, 0.65 g, 0.75 g) were conducted to bracket the stability-to-collapse transition.

Key Results
The study quantified the stability of the sinkhole configurations under varying seismic demands:

0.40 g Tier: All five H/D configurations remained Stable ( $\Sigma M_{sf}$ range: 1.642–1.683). The stability margin was weakly sensitive to geometry.
0.60 g Tier: Stability degraded significantly. The $\Sigma M_{sf}$ band collapsed to 1.007–1.210, representing a 4.95-fold increase in the cross-H/D spread compared to the 0.40 g tier. Most configurations entered the Marginal (1.10–1.30) or Critical (1.00–1.10) zones.
0.80 g Tier (Design Basis): The sweep bifurcated into two distinct branches:
- Collapse Branch: Two configurations failed. H/D = 0.50 resulted in dynamic collapse ( $\Sigma M_{sf}$ = 0.9313). H/D = 1.00 failed during the static Phase 1 (pre-empted collapse, $\Sigma M_{sf}$ = 0.9092), confirmed as mesh-independent.
- Critical Branch: Three configurations (H/D = 0.75, 1.50, 2.25) remained marginally stable but critical, with $\Sigma M_{sf}$ values between 1.001 and 1.006.
Thresholds Identified: The study identifies a mechanical threshold of $\Sigma M_{sf}$ = 1.00 and a critical geometric range of H/D $\le$ 1.00 at the 0.80 g design demand. The transition from stability to collapse occurs between 0.75 g and 0.80 g.

Contributions and Outputs
The primary contribution is the development of a Stability Threshold Matrix tailored for Barangay Dontogan. This tool translates the abstract thresholds ( $\Sigma M_{sf}$ = 1.00 and H/D = 1.00) into four actionable verdicts mapped to foundation recommendations:

Stable ( $\Sigma M_{sf} \ge$ 1.30): Conventional shallow foundations or single piles.
Marginal (1.10 $\le$ $\Sigma M_{sf}$ < 1.30): Grouted micro-pile foundations.
Critical (1.00 $\le$ $\Sigma M_{sf}$ < 1.10): Micro-pile array rafts or avoidance.
Collapse ( $\Sigma M_{sf}$ < 1.00): Avoidance of construction or engineered load transfer through the void to competent rock.

The matrix was applied to the 44 validated sinkholes in the inventory, providing a site-specific, per-footprint screening instrument that moves beyond qualitative zoning.

Significance and Claims
The paper claims to fill a critical regulatory gap by providing the first quantitative, seismic-specific decision-support instrument for karst sinkholes in the Philippines. It demonstrates that seismic demand, rather than static overburden, governs the stability of shallow karst roofs in this region; configurations that appear stable under static conditions can fail under high PGA. The study emphasizes that stability margins at the design demand (0.80 g) are thin, necessitating individual numerical screening for every proposed building footprint rather than relying on the historical stability of surrounding ground. The author positions the Stability Threshold Matrix as a potential module for future editions of the NSCP, offering a bridge between the MGB-CAR's qualitative susceptibility maps and the quantitative requirements of structural engineers and building officials. The author maintains modesty regarding the generalizability of the results, noting that the thresholds are record-specific and calibrated to the specific geology of Barangay Dontogan, requiring re-calibration for other karst settings.

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