Geology topics

Andrew James Makdisi

Publications and source records attributed to Andrew James Makdisi.

16 recordsLinked to original sources

USGS2026

Development of liquefaction-targeted design basis in U.S. seismic provisions

Seismic design criteria for new buildings in the United States have historically focused on life safety performance objectives through minimizing the potential for structural collapse. Development of design criteria to meet this performance objective has evolved over time, leading to the current, risk-targeted maximum considered earthquake (MCE R ) design basis. Corresponding MCE R seismic design loads incorporate the full range of probabilistic ground motion hazard information available from U.S. Geological Survey National Seismic Hazard Models, as well as a representation of the uncertainty in structural collapse capacity. Despite these considerable advances in structural design criteria, guidelines for geotechnical hazards such as liquefaction-induced damage, which continue to be based on uniform ground-shaking hazard (i.e., MCE ground motions), are not well-connected with risk-based, collapse prevention performance objectives. This study, undertaken as part of Building Seismic Safety Council efforts to update recommended seismic provisions through the National Earthquake Hazards Reduction Program, presents probabilistic, liquefaction-targeted design objectives and corresponding ground motion parameters, with a focus on improving consistency in first-level screening criteria for liquefaction hazard assessment. This study identifies a potential maximum acceptable annualized probability of liquefaction triggering ( P L,max ) of 2.5% in 50 years, above which liquefaction consequences and potential mitigation measures would be considered. The P L,max -based design basis is calibrated to effective probabilistic liquefaction hazard levels obtained in practice using current MCE peak ground accelerations, and could be implemented via a new liquefaction-targeted maximum considered earthquake (MCE L ) peak ground acceleration ( PGA L ). The proposed PGA L is derived from probabilistic liquefaction hazard curves and includes uncertainties inherent to liquefaction hazard modeling. The potential design effects of the proposed PGA L are demonstrated via comparison with current MCE PGA levels, effects on first-level liquefaction screening analyses, and improvements in the consistency of P L,max levels across the United States, and for a wide range of site conditions.

conterminous United States↗

USGS2025

Preface to the focus section on earthquake-induced ground deformation

Ground failure due to earthquake-induced liquefaction, surface fault rupture, and landsliding has caused substantial damage in the past and continues to pose risks to critical infrastructure in the future. The consideration of ground failure is central to engineering analysis and design, ranging from site-specific engineering assessments of ground failure potential to broader regional-scale ground failure assessments of near-real-time earthquake impacts or longer-term portfolio risk. Uncertainties in all aspects of the problem complicate the prediction of earthquake-induced ground failure, including the identification of hazard-susceptible geomaterials, characterizing their spatial extent and physical properties, spatio-temporal variability in groundwater conditions, characterization of earthquake ground motions, assessing ground failure severity, and linking ground failure severity to infrastructure damage and loss.

Seismological Research Letters↗

USGS2025

Engineering and risk research—A strategic vision for extending USGS earthquake science to risk assessment and mitigation

As a part of the U.S. Geological Survey (USGS) Natural Hazards Mission Area, the Engineering and Risk Project (ERP) of the Geologic Hazards Science Center conducts civil engineering research to extend natural hazards science to risk assessments. The ERP includes predominantly, but not exclusively, staff funded by the USGS Earthquake Hazards Program. A major focus of the ERP is to deliver actionable information to decisionmakers that helps promote the safety, security, and economic well-being of the Nation. The report discusses briefly the ERP’s evolution and scope, its organization structure, describes key products and deliverables, their efforts to engage with external partners, and its strategy and vision in conducting range of engineering and risk research. The research topics outlined in this report, as developed by the ERP, may be used to facilitate project planning activities during the next 10 years and serve as a longer-term planning resource for the USGS Earthquake Hazards Program and Geologic Hazards Science Center.

Circular↗

USGS2025

Implications of physics-based M9 ground motions on liquefaction-induced damage in the Cascadia Subduction Zone: Looking forward and backward

Given the likelihood of future M9 Cascadia Subduction Zone (CSZ) earthquakes, various estimates of the resulting, regional ground motions have been made, including a suite of 30 physics-based simulations that reflect key modeling uncertainties. However, because the last CSZ interface rupture occurred in 1700 CE, the shaking expected in such an event is especially uncertain, as are the impacts to the built and living environments. Like other coseismic impacts, soil liquefaction poses a significant threat and must be considered by any scenario study used to inform planning and response, or to focus mitigation resources. Liquefaction is also notable for its potential to “ground truth” ground-motion estimates, given that its presence or absence in the geologic record can provide constraint on the intensities of shaking in past events. It is thus an important phenomenon looking both forward and backward. Accordingly, using recent physics-based simulations, this study (1) predicts liquefaction in M9 CSZ ruptures at 400 locations in Oregon, Washington, and British Columbia (BC) using an array of cone-penetration-test based models and (2) uses paleoliquefaction evidence at ten sites spanning from Southern Oregon to Vancouver, BC to constrain possible ground-motion intensities experienced in the 1700 CE earthquake. The forward predictions indicate that liquefaction in M9 events could be pervasive in the region and affect numerous population hubs, with the potential for damage across hundreds of square kilometers. The backward analyses suggest that 1700 CE ground-motion intensities may have been less than expected from M9 simulations in some northern portions of the CSZ (e.g. Seattle), given the paucity of 1700 CE liquefaction evidence in these areas. Ultimately, further discovery and analysis of CSZ paleoliquefaction, or lack thereof, will confirm or modify this possibility and the conclusions drawn herein.

Oregon, Washington↗

USGS2024

Effective site coefficients for the 2024 International Building Code (IBC)

The U.S. National Seismic Hazard Models (NSHMs), developed by the U.S. Geological Survey (USGS), have long been the scientific foundation of seismic design guidelines and have been used to compute design ground motions for construction of new buildings and retrofit of existing buildings in the United States and its territories. The 2018 NSHM is adopted by the 2024 International Building Code (IBC). Prior to the 2018 NSHM update, hazard calculations were required only at one reference site condition defined by V S30 =760 m/s (where V S30 is the time-averaged shear wave velocity from the surface to a depth of 30 m) and three periods (peak ground acceleration, PGA, and pseudo spectral accelerations at periods of 0.2 and 1 s, S s and S 1 ). Site coefficients, F PGA , F a , and F v , were then defined by the Building Seismic Safety Council (BSSC) Provisions Update Committee (PUC) in the site-specific procedures of National Earthquake Hazard Reduction Program (NEHRP) Recommended Seismic Provisions to calculate ground motions for other site classes with different V S30 values at the given periods. The design ground motions at other periods were then estimated using a generic spectral shape that was also defined by the BSSC PUC in NEHRP provisions. In recent years, the engineering community has realized there were deficiencies with the F a and F v site coefficients and the generic spectral shape. To avoid potentially dangerous underestimations of design ground motions for long period structures on soft site conditions in high seismicity regions, the BSSC PUC recommended the use of multi-period response spectra (MPRS) in 2017. As a result, the USGS produced multi-period and multi-V S30 response spectral values in the 2018 NSHM for calculations of design ground motions and the site coefficients F a and F v were eliminated from the 2020 NEHRP Provisions. As these site coefficients were widely used inside and outside of the United States, in this study we back-calculate the “effective” site coefficients F a,eff , and F v,eff by comparing MPRS for various site classes with the MPRS for the reference site condition, and discuss the changes that are observed in the 2024 IBC compared to its previous version in 2021. The effective site coefficients are presented for test site locations and their dependence on various factors including period, ground motion intensity, and regional models are discussed. Ratio maps between the new effective site coefficients and the old ones are then presented for soft site classes and for short and long periods. For soft site classes at short periods, the new effective site coefficients are lower than the old site coefficients for high seismicity regions and higher for low seismicity regions. As it was expected, for soft site classes at long periods and high seismicity regions, the new effective site coefficients are much larger than the old site coefficients without imposing the 50% increase as a penalty that was suggested in the 2021 IBC, whereas they could be much smaller if the 50% increase would have been imposed particularly around New Madrid and Charleston high seismicity regions. For low seismicity regions, the long period effective site coefficients can be smaller or larger by 20% compared to the 2021 IBC coefficients.

Conference Paper↗

USGS2024

Effects of stochastically-simulated near-fault ground motions on soil liquefaction

The scarcity of historically recorded near-fault ground motions poses a challenge to systematically understanding the influence of near-fault effects on various types of seismic demands for engineering purposes. In particular, the current state of knowledge of the influence of ground-shaking intensity on soil liquefaction and its consequences does not specifically account for the effects of near-fault ground motion characteristics. In this study, the influence of near-fault ground motions on liquefaction triggering and lateral spreading are investigated using non-linear modeling of a hypothetical liquefiable soil column in the finite-element computational platform OpenSees subjected to simulated ground motion time series that represent strong earthquake shaking in the near field. The simulated ground motion time series and resulting datasets are based on a parametric stochastic model and are developed for a range of source and path parameters to represent a realistic variability of ground motion characteristics. Dependencies between ground motion intensity measures (IMs) and liquefaction demand parameters are investigated for near-fault pulse and nonpulse-like ground motion sets. Evolutionary IMs, such as cumulative absolute velocity (CAV) and the time-varying magnitude-adjusted peak ground acceleration (PGAM), are considered in developing liquefaction triggering probability density functions. Post-liquefaction triggering responses such as lateral spreading displacements are examined in relation to PGA M and CAV. The ground motion simulations are validated by comparing their liquefaction-capacity PGA M fragilities and post-triggering CAV vulnerability relationships to historical records from the 1994 Northridge earthquake in California, USA. Finally, a path forward for future studies that includes finding systematic differences in the IM-liquefaction demand relationships between near-fault and far-field stochastic ground motion sets is outlined.

Conference Paper↗

USGS2024

Improved computational methods for probabilistic liquefaction hazard analysis

Current procedures for analysis of and design against liquefaction hazards focus primarily on the use of probabilistic ground motions at a single ground-shaking hazard level, with the cyclic loading represented by a peak ground acceleration ( PGA ) corresponding to a target return period and a single representative moment magnitude M w . These parameters are typically used in conjunction with deterministic simplified procedures for estimating liquefaction triggering and consequences that largely neglect the considerable uncertainties inherent to liquefaction problems. Motivated by these limitations and the resulting inconsistencies in liquefaction design levels, early methods for probabilistic liquefaction hazard analysis (PLHA) were proposed that incorporate the full ground motion hazard space, integrated with probabilistic liquefaction triggering models. Such methods provide liquefaction factor of safety ( FS L ) hazard curves for standard penetration test (SPT) data. Recognizing the increased use of higher-resolution cone penetrometer test (CPT) data in engineering analysis and design and the potential computational challenges it presents, an expanded suite of probabilistic triggering models, and wider availability of more detailed seismic hazard data, an improved PLHA computational methodology is presented in this study. The methods described utilize the U.S. Geological Survey National Seismic Hazard Model directly through web services to obtain PGA hazard and disaggregation calculations for any site and average shear wave velocity in the upper 30 m of the site ( V s 30 ) in the conterminous United States, to reconstruct the PGA hazard space for use in PLHA calculations, and to employ array calculations for efficient liquefaction hazard curve estimates for the thousands of CPT measurements in a given profile. The framework presented here is modular in nature, and discussion on the use of alternative models and extension to probabilistic liquefaction consequence evaluation is presented. The importance of appropriate representation of probabilistic liquefaction model uncertainties is also highlighted, along with the impacts of different levels of uncertainty on the PLHA calculation. Finally, a potential roadmap for incorporation of the PLHA framework in seismic provisions is presented, with an illustration of how it can address current limitations and impacts in liquefaction hazard analysis and design.

Soil Dynamics and Earthquake Engineering↗

USGS2024

Liquefaction timing and post-triggering seismic energy: A comparison of crustal and subduction zone earthquakes

The objective of the study is to assess when liquefaction is triggered in a suite of ground motions following simplified approaches and measure the remaining post-triggering energy content of those ground motions. For liquefaction-induced deformations, current simplified analysis procedures do not directly incorporate temporal effects and rely on peak transient intensity measurements. Liquefaction hazard from short-duration, small to moderate-magnitude (M) earthquakes (M4.5–7.5) is adequately expressed using transient intensity measurements. However, subduction-zone interface earthquakes can have magnitudes greater than 9.0, with ground-motion durations exceeding 300 s. Using 525 ground motions from the NGA-Subduction (NGA-Sub) database for subduction-zone earthquakes with M8.25–9.25, the timing of liquefaction was calculated using cyclic counting procedures by assuming a reference stress condition and incorporating cyclic strengths from laboratory element testing. A complementary analysis was completed using 514 crustal ground motion records from the NGA-West2 database for M6.75–7.75. Several trends were identified during this study. First, liquefaction will likely trigger during the first half of the ground motion duration, independent of the earthquake source type. However, subduction-zone motions have larger post-triggering energy content compared to crustal earthquakes. The findings from this work indicate that accurately predicting liquefaction-induced deformations from subduction-zone earthquakes may be substantially improved by using robust time-based liquefaction analysis procedures.

Conference Paper↗

USGS2024

Framework for mapping liquefaction hazard–Targeted design ground motions

Liquefaction-induced ground failure poses substantial challenges to geotechnical earthquake engineering design. Current approaches for designing against liquefaction hazards, as specified in most seismic provisions, focus on estimating a liquefaction factor of safety ( 𝐹⁢𝑆𝐿 ) and typically characterize earthquake loading using design parameters based on probabilistic or deterministic ground motion levels. Because 𝐹⁢𝑆𝐿 is estimated deterministically, this basis of design neglects considerable uncertainties for estimating liquefaction triggering and its consequences and results in a lack of liquefaction-specific design criteria, particularly as structural design has advanced toward risk-targeted performance objectives. This study presents a framework for developing liquefaction-targeted design criteria based on a minimum acceptable return period of liquefaction, informed by probabilistic liquefaction hazard analysis (PLHA). PLHA quantifies annualized rates of liquefaction by considering contributions from (1) the full ground-motion probability space, and (2) uncertainties in liquefaction triggering using probabilistic models. PLHA is used in this study to characterize the current, effective return periods of 𝐹⁢𝑆𝐿 ( 𝑇𝑅,𝐹⁢𝑆 ) obtained from conventional liquefaction hazard analysis (CLHA) using uniform-hazard ground motions. 𝑇𝑅,𝐹⁢𝑆 is evaluated in a parametric study of nearly 100 sites throughout the conterminous United States. The results indicate large geographic variations in acceptable liquefaction hazard levels, with implied 𝑇𝑅,𝐹⁢𝑆 ranging between approximately 1,000 to 3,000 years. To address these inconsistencies without the computational demands of full PLHA, a framework is proposed for developing a liquefaction-targeted design peak ground acceleration, 𝑃⁢𝐺⁢𝐴𝐿 , for use in liquefaction models that result in consistent liquefaction design levels across all geographic locations. The mapped 𝑃⁢𝐺⁢𝐴𝐿 is shown to be somewhat sensitive to site-specific properties, and adjustment factors are developed and presented. The proposed 𝑃⁢𝐺⁢𝐴𝐿 mapping procedure produces 𝐹⁢𝑆𝐿 estimates that are consistent with those obtained from full PLHA at a target 𝑇𝑅,𝐹⁢𝑆 , providing a promising roadmap to incorporating PLHA concepts into current liquefaction design methods.

Journal of Geotechnical and Geoenvironmental Engin↗

USGS2024

Challenges in developing vertical hazard for seismic analysis of concrete dams

The seismic response of concrete dams depends on both the horizontal (H) and vertical (V) components of ground motion (GM), and excluding the V components when conducting response history analyses (RHAs) may underestimate the seismic fragility. Although V components of GM time series could be selected to be consistent with the hazard, hazard curves for the V component (or for short, V hazard curves) are rarely available for evaluating such hazard consistency. One of the challenges in developing V hazard curves in the U.S. Geological Survey (USGS) National Seismic Hazard Model (NSHM) is the lack of ground motion models (GMMs) that directly estimate intensity measures (IMs) for the V component of GM. In this study, we compare alternative approaches of developing V hazard curves. Using a case study in California, we compare V hazard curves computed from GMMs for the V component of GM against those from applying GMMs for the V/H ratios and those from selecting multicomponent time series that are consistent with the H hazard. We discuss and invite feedback on issues such as availability of GMMs, applicability of GMMs, and choice of inputs for ground motion selection and modification (GMSM).

Conference Paper↗

USGS2024

Framework for implementing damping scaling factors in U.S. Geological Survey National Seismic Hazard Models

Traditionally, probabilistic seismic hazard analysis (PSHA) has focused on calculating ground motion hazard curves for elastic, 5%-damped pseudo spectral accelerations, Sa(T,5%), which are used as the basis for engineering design parameters and targets for ground motion selection and modification. However, structures and geotechnical systems can exhibit a wide range of damping ratios both above and below the 5% level, depending on the construction material, structural system, nonstructural elements, or subsurface soil properties. When spectral parameters at such damping levels are required for certain applications, 5%-damped accelerations have traditionally been extracted from PSHA-based hazard curves and adjusted outside of the hazard integral using damping scaling factors (DSF) such as those from Newmark & Hall (1982). Recent advances in the development of more rigorous and comprehensive damping scaling models (e.g., Rezaeian et al., 2014; Rezaeian et al., 2021) have allowed for the modeling of means and standard deviations of DSFs as functions of earthquake source and path properties for crustal, intraslab, and subduction interface tectonic environments. These DSF models can be applied to ground motion model (GMM) estimates of Sa(T,5%) for a given earthquake rupture scenario to produce a corresponding mean and standard deviation Sa at a specified damping ratio β, Sa(T,β). In this study, the DSF models of Rezaeian et al. (2014) and Rezaeian et al. (2021) are implemented within the U.S. Geological Survey National Seismic Hazard Model (NSHM) PSHA framework to calculate probabilistic hazard curves for spectral accelerations at damping ratios from 0.5% to 30%. The DSF models are applied directly to the mean and standard deviation of Sa(T,5%) predictions from each GMM in the NSHM logic tree. Resulting hazard curves and uniform hazard and risk spectra for Sa(T,β) are presented for several geographic locations and compared with corresponding spectra estimated using current design practices by applying the same DSFs outside of the PSHA calculation. Key differences between the two methods for estimating Sa(T,β) are discussed, and potential strategies are presented for the implementation and usage of the hazard-consistent Sa(T,β) in building codes. Comparing the results to those from DSFs used in current design practices that are mainly based on Newmark & Hall (1982) is not explored in this study.

Conference Paper↗

USGS2023

The 2023 US 50-State National Seismic Hazard Model: Overview and implications

The US National Seismic Hazard Model (NSHM) was updated in 2023 for all 50 states using new science on seismicity, fault ruptures, ground motions, and probabilistic techniques to produce a standard of practice for public policy and other engineering applications (defined for return periods greater than ∼475 or less than ∼10,000 years). Changes in 2023 time-independent seismic hazard (both increases and decreases compared to previous NSHMs) are substantial because the new model considers more data and updated earthquake rupture forecasts and ground-motion components. In developing the 2023 model, we tried to apply best available or applicable science based on advice of co-authors, more than 50 reviewers, and hundreds of hazard scientists and end-users, who attended public workshops and provided technical inputs. The hazard assessment incorporates new catalogs, declustering algorithms, gridded seismicity models, magnitude-scaling equations, fault-based structural and deformation models, multi-fault earthquake rupture forecast models, semi-empirical and simulation-based ground-motion models, and site amplification models conditioned on shear-wave velocities of the upper 30 m of soil and deeper sedimentary basin structures. Seismic hazard calculations yield hazard curves at hundreds of thousands of sites, ground-motion maps, uniform-hazard response spectra, and disaggregations developed for pseudo-spectral accelerations at 21 oscillator periods and two peak parameters, Modified Mercalli Intensity, and 8 site classes required by building codes and other public policy applications. Tests show the new model is consistent with past ShakeMap intensity observations. Sensitivity and uncertainty assessments ensure resulting ground motions are compatible with known hazard information and highlight the range and causes of variability in ground motions. We produce several impact products including building seismic design criteria, intensity maps, planning scenarios, and engineering risk assessments showing the potential physical and social impacts. These applications provide a basis for assessing, planning, and mitigating the effects of future earthquakes.

Earthquake Spectra↗

USGS2023

Incorporating uncertainty in susceptibility criteria into probabilistic liquefaction hazard analysis

Most conventional approaches for assessing liquefaction triggering hazards generally rely on simplified procedures that involve identifying liquefaction susceptible layers and calculating a factor of safety against liquefaction (FSL) in each layer. Such procedures utilize deterministic semi-empirical models for standard penetration test (SPT), cone penetrometer test (CPT), or shear wave velocity (Vs)-based subsurface data. This general approach largely neglects considerable uncertainties in ground shaking, as well as aleatory variabilities and epistemic uncertainties inherent to liquefaction susceptibility and triggering prediction. A more robust methodology introduced by Kramer and Mayfield (2007) is known as probabilistic liquefaction hazard analysis (PLHA), which integrates the full ground motion hazard space with probabilistic forms of liquefaction triggering models (e.g., Boulanger and Idriss 2014), resulting in the computation of FSL profiles with consistent return periods. Multiple PLHA computational platforms have been developed over the years, with the computational framework from Makdisi (2021) serving as the basis for a new Liquefaction Hazard Tool under development at the U.S. Geologic Survey (USGS). Despite significant improvements in recent years to the availability of seismic hazard data and probabilistic triggering and effects models, the issue of incorporating uncertainty in characterizing liquefaction susceptibility remains a challenge. Most compositional susceptibility criteria (i.e., whether or not the soil exhibits sand-like behavior) currently in use are presented as deterministic bounds based on in-situ or laboratory test data; similarly, determination of soil saturation is often based on a single groundwater level from in-situ testing. As a result, the same types of binary decisions must be made in PLHA as in more conventional methods. With the expansion and availability of field and laboratory data pertaining to liquefaction through resources such as the Next Generation Liquefaction (NGL) project, there exists the potential for an improved set of susceptibility models for CPT, SPT, and Vs-based applications. Presented here is a brief discussion on how probabilistic susceptibility modeling can be accommodated in PLHA calculations, as well as how the use of multiple models can be leveraged within a logic tree to improve the representation of epistemic uncertainty in liquefaction hazard analysis.

Conference Paper↗

USGS2023

Towards improved code-based performance objectives for liquefaction hazard analysis

Ground failure due to liquefaction in loose sand deposits poses substantial risks to the built environment, and has caused significant damage in past earthquakes to a wide range of infrastructure. Advances in liquefaction hazard analysis in practice have largely stagnated in recent years; the state of practice remains rooted in simplified procedure s that ignore considerable uncertainties in liquefaction phenomena, and are largely conditional on single-return period ground motions. As a result, they lack any sort of liquefaction-specific design criteria or performance objective. Presented herein is a roadmap for using probabilistic liquefaction hazard analysis (PLHA) to address many of these limitations and improve liquefaction design guidelines. PLHA incorporates hazard contributions from the full ground motion hazard space in conjunction with probabilistic liquefaction models, to produce hazard curves for various types of liquefaction-related demands. In this study, PLHA is utilized to assess the current, implied liquefaction design levels at 76 study sites throughout the U.S. using ASCE 7 guidelines, by computing effective return periods of liquefaction factor of safety FSL, and liquefaction potential index LPI. The results indicate broad inconsistencies in these design levels across different parts of the U.S, with return periods varying from about 300 years in deterministically-capped parts of California, to nearly 3,000 years on the Pacific Northwest coast and in the Charleston Fault zone region. These results are also used to inform potential strategies for establishing consistent, liquefaction-specific design objectives in the future, based on return period averaging methods that weight the importance of a study site according to both the population and relative liquefaction hazard level.

Conference Paper↗

USGS2022

Evolution of design ground motions in California: NEHRP 2009 to 2020

The U.S. Geological Survey (USGS) National Seismic Hazard Model (NSHM) is used in construction codes, such as the National Earthquake Hazard Reduction Program (NEHRP) Provisions, to develop ground motions for structural and geotechnical design. When the NSHM is updated (e.g. changes to its earthquake rupture forecast or ground motion models), or the manner in which it is implemented in construction codes changes, design ground motion values can increase or decrease at a given location. This study presents an analysis of 21 sites in California to characterize how design ground motion values (SS, S1, SMS, SM1) have changed from the 2009 to 2015 to 2020 NEHRP Provisions. Four sites are presented in greater detail: two in Southern California and two in Northern California. The results show that significant changes in design ground motion values between NEHRP releases are explained by major changes in the NSHM science (e.g., inclusion of basin effects) and its use (e.g., for a broader range of site classes), but in ways that are difficult to ascertain beforehand. It is therefore likely that design ground motion values may continue to evolve between NSHM and construction code updates as the earthquake science and engineering field's understanding continues to advance.

California↗

USGS2021

Hazard characterization for alternative intensity measures using the total probability theorem

Since their inception in the 1980s, simplified procedures for the analysis of liquefaction hazards have typically characterized seismic loading using a combination of peak ground acceleration and earthquake magnitude. However, more recent studies suggest that certain evolutionary intensity measures (IMs) such as Arias intensity or cumulative absolute velocity may be more efficient and sufficient predictors of liquefaction triggering and its consequences. Despite this advantage, widespread hazard characterizations for evolutionary IMs are not yet feasible due to a relatively incomplete representation of the ground motion models (GMMs) needed for probabilistic seismic hazard analysis (PSHA). Without widely available hazard curves for evolutionary IMs, current design codes often rely on spectral targets for ground motion selection and scaling, which are shown in this study to indirectly result in low precision of evolutionary IMs often associated with liquefaction hazards. This study presents a method to calculate hazard curves for arbitrary intensity measures, such as evolutionary IMs for liquefaction hazard analyses, without requiring an existing GMM. The method involves the conversion of a known IM hazard curve into an alternative IM hazard curve using the total probability theorem. The effectiveness of the method is illustrated by comparing hazard curves calculated using the total probability theorem to the results of a PSHA to demonstrate that the proposed method does not result in additional uncertainty under idealized conditions and provides a range of possible hazard values under most practical conditions. The total probability theorem method can be utilized by practitioners and researchers to select ground motion time series that target alternative IMs for liquefaction hazard analyses or other geotechnical applications. This method also allows researchers to investigate the efficiency, sufficiency, and predictability of new, alternative IMs without necessarily requiring GMMs.

Earthquake Spectra↗