Geomechanical modeling of ground surface deformation related to thrust and reverse fault earthquakes

Abstract

Thrust and reverse fault earthquakes show complex patterns of surface fault rupture that pose substantial hazards to critical infrastructure, including buildings, energy production and transmission facilities, telecommunication systems, and other facilities. These scarps are often highly variable along-strike, with a range of geomorphic expressions from smooth monoclinal profiles to pop-up structures and even highly localized direct fault displacements. To properly design and protect our critical infrastructure, we need the ability to forecast specific ground deformation characteristics, which has proven a challenge given the wide range of possible fault scarp morphologies. There is a paucity of historical earthquakes with surface rupture measurements, limiting our ability to make accurate forecasts based simply on empirical approaches. Thus, this dissertation develops a physics-based approach to model this phenomenon that evaluates a range of geological site conditions – including fault and sediment properties – using numerical modeling techniques to develop a statistical suite of potential ground surface deformation characteristics associated with thrust and reverse fault earthquakes. We use the distinct element method (DEM) to model the near-surface coseismic deformation observed in thrust and reverse fault earthquakes. DEM is a deterministic modeling approach that is highly effective at reproducing the behavior of fault systems and the granular mechanics of soils and sediments in the shallow subsurface, making it especially well-suited for simulating geologic processes associated with ground surface rupture during large earthquakes. DEM treats aggregate materials as collections of circular disks (in 2D) or spheres (in 3D) that can move independently, with mechanical interactions governed by elastic and frictional contact laws that allow for complex elastic or pseudoplastic behavior. The particles can be bonded together using various contact bond models (we use the parallel-bond contact model) to impart cohesion, tensile strength, and other mechanical micro-properties which approximate natural soil and sediment mechanics. The models deform based on the displacement of boundary conditions at a prescribed velocity and timestep. This approach enables DEM to capture the emergence and evolution of structures like fractures, secondary faults, flexural slip surfaces, folds, and to realistically model sediment deposition, compaction, dilation, and deformation. By varying input parameters such as particle packing density and strength, DEM simulations can evaluate a wide range of natural geologic and soil properties, providing valuable insight into both faulting processes and granular mechanics in sediments and soils. Chapter 1 explores an initial suite of 2D DEM experiment across a select group of fault dips and sediment strengths to evaluate a range of surface deformation characteristics observed in thrust and reverse fault earthquakes. We calibrated the 2D DEM models to analog sandbox fault models in Cole & Lade (1984) as well as the 3D DEM models from Garcia & Bray (2018a,b). We performed 45 total models which explore shallow (20º), moderate (40º), and steep (60º) fault dips in weak, moderate, and strong sediment that is 5 m deep above bedrock. The key findings of this initial suite of 2D DEM models reveal that numerical models can replicate the natural, geomorphic characteristics of fault scarps. Additionally, we propose a classification of fault scarp morphologies for the 3 main geometries observed in the models: 1, monoclinal scarps; 2, pressure ridge scarps; and 3, simple scarps. Monoclinal scarps form a single, inclined dip panel at the surface. Pressure ridge scarps form backthrusts that contribute to additional uplift above the flat surface of the hanging wall block in a “pop-up” structure. Simple scarps represent a direct fault displacement that is indicative of the fault dip at depth, generating a scarp overhang. Each of these scarp morphologies were represented by unique geomorphic characteristics that could be subsequently modified via hanging wall collapse. Collapse modified features include tensile fracturing at the crest of the scarp that forms blocks of colluvium that gravitationally collapse down the scarp face. The surface deformation characteristics of the scarp height, deformation zone width, and scarp dip were measured every 0.5 m of slip up to 5.0 m of total displacement in the models. This dataset revealed that each of the scarp classes have quantifiable geomorphic characteristics that could improve seismic hazard assessments based on geological site conditions. Chapter 2 explores the same initial suite of 45 2D DEM models to train a machine learning script that measures the model results with higher accuracy and resolution than the previous 0.5 m of slip. This machine learning script was based on computer vision (CV) script packages and used object detection to identify the key geomorphic characteristics of fault scarps and automatically differentiate between scarp classes. From this classification system, measurements of the surface deformation characteristics (SDC) such as the scarp height (Us), uplift above the flat surface of the hanging wall (Us – Ud), deformation zone width (DZW), and scarp dip were obtained every 0.05 m of slip. We applied this machine learning script to significantly increase the number of SDC measurements by an order of magnitude, yielding 100 measurements per DEM model. Chapter 3 expands the initial suite of 2D DEM models to examine the influence of additional model parameters and support statistical analyses of ground surface deformation characteristics and geomorphic expressions of fault scarps in thrust and reverse fault earthquakes based on local geological site information. Specifically, we tested 2,459 experiments of homogeneous sediment strengths and 975 experiments of heterogeneous sediment strengths in dense, medium-dense, and loose sediment for depths of 3, 5, and 10 m above a planar fault that dips between 20º and 70º. The hanging wall of the fault in these models displaces up to 5.0 m at a continuous rate of 0.3 m/s. For homogeneous sediment strengths, we evaluated a range from weak to strong sediment in 5 increments that vary the cohesive and tensile strengths of the contact bonds. We also varied the cohesion and tensile strength relative to one another for a total of 13 options. For the heterogeneous sediment strengths, we assessed vertical strength gradients where the base is stronger than the uppermost layers in uniform increments, vertically randomized sediment strengths, and a cohesive top unit above moderate strength sediment. This resulted in a total of 3,434 2D DEM experiments and 346,834 SDC measurements taken every 0.05 m of slip using the same machine learning model as described in Chapter 2. We performed a statistical analysis of ground surface deformation patterns in conjunction with model input parameters to correlate geological site conditions with resultant fault scarp morphologies. We found that the most influential parameters on the patterns of ground surface deformation are the accumulation of slip on a fault, fault dip, sediment depth, and sediment strength. We directly compare these measurements of SDC to historic earthquake ruptures from established fault rupture databases – such as the Fault Displacement Hazards Initiative (FDHI) – as well as the 1952 M7.8 Kern County, California earthquake (Buwalda & St. Amand, 1955). The DEM results effectively describe the range of historic surface rupture observations in these datasets, with improved fits obtained by incorporating additional information about the earthquake size (slip), fault geometry, and surface deformation style. Based on these results, we propose that this dataset can supplement the surface rupture measurements in FDHI and help forecast potential patterns of future surface rupture hazards given specific site characteristics. Chapter 4 extends the modeling to three-dimensions and examines along-strike variability of fault scarps in thrust and reverse fault earthquakes. Thrust and reverse fault earthquakes are inherently complex and often show significant along-strike variability in the geomorphic expression of the fault scarp, although the geological conditions that yield this variability are largely unknown. Thus, we developed 18 3D DEM models to investigate the influence of fault dip and sediment strength on the along-strike variability of fault scarps. We tested fault dips of 20º, 40º, and 60º for weak and strong sediment and a case where the fault dip varied along-strike from 20º to 70º in 1º increments. Additionally, we performed a case study of randomized sediment strength heterogeneities. These 3D models successfully reproduce main fault scarp types – monoclinal, pressure ridge, and simple – aligning with surface rupture characteristics previously identified in 2D modeling. Our key results showed that the fault dip primarily determined the scarp class whereas variations in the sediment strength, specifically the randomized heterogeneities, influenced the geomorphic characteristics of scarps within that scarp class. Overall, the 3D models support the relationships of ground surface deformation characteristics (scarp class, width, height) established in previous 2D DEM results and replicate measurements of historical earthquake scarps from the Fault Displacement Hazards Initiative (FDHI) and SUrface Ruptures due to Earthquakes (SURE) datasets. These 3D DEM models provide insights into how fault dip and sediment strength govern along-strike transitions in fault scarp morphology. We propose that the combination of 2D and 3D DEM model results can aid Fault Displacement Hazard Assessments (FDHA) and infer patterns of surface ruptures based on local geological site conditions. Chapter 5 extends the initial suite of 3D DEM models to evaluate the influence of faulting and sediment parameters on the along-strike geomorphic variability of fault scarps observed during thrust and reverse fault earthquakes. We performed 81 3D DEM experiments which explored 4 main model cases: 1, a planar, cylindrical dipping fault at depth; 2, variable fault dip along-strike from 20º to 70º; 3, variable fault seed length along-strike of a planar, dipping fault; and 4, rotating the fault relative to the slip orientation to induce slip obliquity by 30º, 45º, and 60º. We evaluated both homogenous and heterogeneous sediment strengths in a dense sediment assemblage that is 3 m deep. The homogeneous sediment strengths considered weak, moderate, and strong sediment while the heterogeneous sediment assemblages tested randomized heterogeneities and a cohesive top unit. These experiments revealed that uniform, planar faults in homogeneous sediment produce cylindrical (or symmetrical) fault scarp morphologies with little to no variability along-strike. In contrast, variability in the fault dip yielded significant changes in the scarp class along-strike from pressure ridges to monoclinal scarps and simple scarps. This reinforces the conclusion that fault dip plays a primary role in determining scarp class, while the sediment strength influences the style of geomorphic characteristics within the given scarp class. The increasing slip obliquity models converge on the geomorphic expressions of strike slip style faults with increasingly smaller deformation zone widths. We compared the SDC measurements from the 2D and 3D DEM models to measurements of natural surface ruptures in historical earthquakes in the FDHI and SURE datasets. We find that the DEM models effectively capture the range of observed scarp heights and deformation zone widths from historical ruptures and fill the gaps in our understanding from limited historical earthquake events. Furthermore, the geomorphic features of distributed fracturing, splays, backthrusts, and blocks of colluvium that vary along-strike in natural surface ruptures (such as the 1999 Chi-Chi, Taiwan, 2008 Wenchuan, China, and 2013 Bohol, Philippines earthquakes) are replicated in these 3D DEM models such that individual geological site conditions can effectively be modeled in the DEM space. Therefore, we can forecast the potential patterns of future ground surface deformation using local geological site conditions. Ultimately, we propose that these 2D and 3D DEM models can supplement current FDHA datasets to better inform forecasts of anticipated ground surface deformation for given geological site and faulting conditions using both deterministic and probabilistic approaches. This capacity to forecast future surface rupture characteristics significantly improves available seismic hazard assessments and aid efforts to mitigate the loss of critical resources and sensitive infrastructure systems.