Fragility Evaluation Research Articles

A novel approach to seismic fragility evaluation of underground structures considering hybrid epistemic uncertainties of both seismic demand and capacity

Precise seismic fragility analysis holds significant importance in the evaluation of seismic resilience for underground structures. However, the conventional seismic fragility analysis of underground structures usually ignores the hybrid epistemic uncertainties caused by the limited samples of both seismic demand and thresholds and deterministic boundaries between different limit states, which can inevitably cause errors in the seismic resilience evaluation of underground structures. Thus, focusing on the quantification of epistemic uncertainties, this paper aims to propose an approach to seismic fragility evaluation of underground structures considering hybrid epistemic uncertainties of both seismic demand and capacity. In this approach, the analytical formulation of seismic fragility considering the fuzziness of limit states is firstly derived via adopting the entropy equivalence method. Then, the non-parametric Bootstrap method and maximum entropy principle, as well as the Copula theory are combined to establish a probability model characterizing the statistical uncertainties of both seismic demand and capacity. On this basis, the variability of failure probability of underground structures is quantified, and the envelope fuzzy seismic fragility is obtained. Moreover, the influences of the coupling effect of statistical uncertainty and fuzziness on the seismic fragility of underground structures are also analyzed in this paper. The results show that the seismic fragility of underground structures based on limited samples of both seismic demand and thresholds and deterministic boundaries between different limit states has significant variability, and the variability degree of fragility is various under different ground motion intensities. Besides, the envelope fuzzy seismic fragility curves can effectively reflect the coupling effect of statistical uncertainty and fuzziness and adequately characterize the variability of estimated seismic fragility, which can provide a more accurate basis for seismic resilience evaluation of underground structures.

Rapid time-varying seismic fragility evaluation with bounded uncertainty for a novel prestressed cable-stayed steel frame based on multi-scale modeling

Rapid time-varying seismic fragility evaluation with bounded uncertainty for a novel prestressed cable-stayed steel frame based on multi-scale modeling

Mainshock–aftershock seismic fragility assessment of civil structures: A state‐of‐the‐art review

AbstractSequential seismic events occur worldwide, which impose significant threats to the safety and serviceability of Civil infrastructure, especially buildings and bridges. Fragility functions are imperative to support decision‐making tools for potential seismic risk identification and its impact on structural performance during sequential earthquakes. The increasing number of publications shows a notable increase in interest among researchers and the scientific community in this domain. This study presents a systematic review of available resources and techniques for structural performance and fragility evaluation subjected to mainshock–aftershock seismic loading. Efforts have been made to focus on the salient features of various approaches rather than criticizing the mathematical frameworks and associated analysis approaches. Existing knowledge related to the effect of sequential seismic loading on buildings and bridge infrastructures and their fragility estimates is presented concisely. The paper concludes by detailing the opportunities for future developments in the fragility analysis of Civil infrastructure under sequential seismic hazard. This would encourage stakeholders and decision‐makers to put into practice their applications for risk mitigation, recovery planning, and well‐informed decision‐making.

A framework for rapid seismic performance and fragility analysis of earth slopes considering uncertainties

It is acknowledged that various sources of uncertainties play a vital role in the seismic vulnerability of slope systems, while many studies ignore these sources in seismic assessments. This is because seismic performance and fragility evaluation of large soil-structure systems is challenging and computationally intensive by conventional nonlinear dynamic analysis methods, especially when the modeling uncertainties are considered. To address this challenge, this paper proposes a new framework for addressing uncertainties in the seismic evaluation of earth slopes using the Endurance Time Analysis (ETA) method. The ETA method is a dynamic pushover procedure in which the slope is subjected to a limited number of artificial intensifying records, and seismic responses are obtained over a continuous range of seismic intensities. For the purpose of this study, probabilistic two-dimensional numerical simulations of earth slopes are created using the FLAC software by considering the soil parameters uncertainty. Latine Hypercube Sampling is employed to generate random simulations. The models are then subjected to the intensifying prefabricated excitations based on the ETA method, and the fragility curves of the slope are obtained in three damage states by considering and not considering uncertainties. The results indicate that as the endurance time, which is a kind of intensity measure, increases, the uncertainties of seismic responses also increase. This shows that the effects of uncertainties become more significant when the slope is subjected to strong ground motions. Additionally, the influence of modeling uncertainty is negligible in the slight damage state, but significant in the extensive damage state. The proposed framework provides an effective and rapid way for performing the fragility and associated risk analysis of earth slopes considering uncertainties.

Clinical benefit and fragility evaluation of systemic therapy trials for advanced soft tissue sarcoma.

The clinical benefit of systemic anticancer therapies can be unclear despite positive trials, and outcomes may not translate to real-world practice. This study evaluated the benefit of soft tissue sarcoma (STS) treatments using the European Society of Medical Oncology Magnitude of Clinical Benefit Scale (MCBS) v1.1 and measured the robustness of STS trial results using Fragility Index (FI). Database searches for adult phase II or III trials in advanced STS (January 1998-December 2023) were performed. Therapies with trial outcomes that met the criteria for MCBS were scored 1-5 (≥4 represents substantial clinical benefit). For randomized clinical trials with positive time-to-event endpoints, the number of additional events that would render results nonsignificant, FI, was calculated and expressed as a proportion of the experimental arm size (fragility quotient [FQ]). Higher FI/FQ implies more robust results. Among 194 trials, 19 (9.8%) were phase III. Most phase II trials (146/175; 83.4%) had single-arm or non-comparative design. Trials that were eligible for MCBS scoring (n=78; 40.2%) evaluated 56 different agents/regimens. Median MCBS score was 2. Only three agents/regimens (all cytotoxic therapies) had an MCBS score ≥4. Among 47 randomized clinical trials, 16 (8 phase II; 8 phase III) trials had positive outcomes. Median FI was 7 (range, 2-52) and 10 trials (62.5%) had an FQ < 10%, with median of 7% (range, 1%-59%). Most systemic therapies in STS trials did not confer substantial clinical benefit per European Society of Medical Oncology-MCBS. Additionally, positive randomized trials were often fragile. Novel STS therapy trials should use clinically meaningful endpoints and real-world efficacy confirmation is essential, especially for less robust trials.

Seismic vulnerability and performance-based assessment of monopile offshore wind turbine considering turbine blades

This paper investigated the seismic vulnerability and performance-based assessment of offshore monopile wind turbine (OWT) considering turbine blades. A three-dimensional finite-element model of NREL 5-MW OWT was established with detailed consideration of the nonlinear-behavior of turbine, monopile, blades, pile-soil interactions and pile-water interaction etc. Subsequently, incremental dynamic analysis and fragility evaluation were conducted via a great number of nonlinear time history analysis involving far-field and near-fault records with and without pulse characteristics. It is found that the ignorance of turbine blades in conventional lumped mass (LM) model would significantly underestimate the vulnerability of OWT's acceleration responses, and more importantly, underestimates the stress level at turbine top, misleading the failure pattern of OWT which may be probably damaged at both top and middle part of OWT rather than solely the middle part as estimated by the LM model ignoring the effect of turbine blades. Finally, it can be concluded that the modeling of turbine blades should be consider in the numerical studies.

Failure criterion and seismic fragility evaluation of isolated nuclear power plant piping system using BP neural network

The pipeline connecting the isolated nuclear island and the non-isolated turbine building is prone to significant relative displacements during intensive earthquakes. Generally, elbows closest to the isolation layer are considered to be at particularly high risk of seismic damage. The failure criterion is the critical part in determining the damage state of elbows throughout the loading cycle. Therefore, in this study, a three-tier, four-category failure criterion was firstly proposed in response to the damage patterns of elbows. A BP neural network model was subsequently developed using extensive simulation data derived from a verified numerical model, accompanied by influence analysis of the three failure indices. Finally, a fragility evaluation was conducted based on the seismic response of the piping system, and a comparison is made between the new criterion and the existing ones. The results indicate that the new failure criterion demonstrates comprehensiveness and safety, enabling a more detailed division of damage before elbow failure and providing more conservative estimates upon failure occurrence. Additionally, the study finds that under the current design of nuclear power plants, elbows across isolation layers fail to meet the requirements for safe shutdown earthquakes in certain directions. By adjusting the elbow parameters, the resistance of the elbows to damage under seismic conditions can be improved to some extent.

Comprehensive evaluation of seismic fragility in base isolated buildings enhanced with supplemental dampers considering pounding phenomenon

Base isolation is a proven technology effective in minimizing earthquake-induced damage to both the structural and non-structural elements (especially freestanding contents) of buildings. Nevertheless, it has been shown that allowing the flexible isolation layer to endure substantial demand displacements might subject the isolated structure to failure. This vulnerability arises from potential superstructure yielding due to increased deformations and reduced stiffness, such as those occurring through pounding against a moat wall during intense earthquakes. One alternative to controlling these large deformations is to use supplementary dampers at the isolation plane of the building, creating a hybrid base isolation system (HIS), which adds damping to the isolation system. In this research, the seismic performance of base isolated structures with lead-rubber bearing (LRB) are studied in conjunction with linear viscous dampers (LVD). Due to this aim, a base-isolated steel frame with 2 story X-type braces and a surrounding moat wall is modeled with two various configurations: LRB, and LRB with LVD. Fragility curves are developed for an ensemble of near-field (NF) pulse-like ground motions and for the maximum inter-story drift ratio (MIDR) as an engineering demand parameter (EDP). The incremental dynamic analysis (IDA) is conducted to calculate the damage probability of the structure by assuming different threshold values for damage states. It was found that adding viscous dampers to the isolation system balanced the behavior of the structure under near field pulse-type records; resulting in reduced isolation displacement while its adverse effects are insignificant and can be ignored. Moreover, the median spectral acceleration, namely the spectral acceleration associated to a probability of exceedance (POE) equal to 50 %, at the specific limit state, in the hybrid base isolation system is higher compared to the conventional one.

Fragility evaluation of bridge shallow foundation piers under floods by coupling simulation in structural and hydraulic fields

The erosion of soil around bridge shallow foundation piers can substantially increase the fragility of bridges during flood events. The available research for assessing the fragility of shallow foundation piers under floods is predominantly qualitative, while ignoring the influence of coupling effects arising from complex hydrodynamic-soil-structure interactions. To fill these gaps, a numerical solver for coupled simulations accounting for hydrodynamic-soil-structure interaction is developed, facilitating boundary conversions for different physical fields and updating them over time. The numerical solver is validated in terms of subgrade reactions, pier displacements and scour extent based on the results of open-channel tests of a reference shallow foundation pier. The validation results show that the developed coupled solver has satisfactory accuracy in predicting the morphology of scour-hole and failure process of shallow foundation piers. Then all potential failure modes of shallow foundation piers under floods are analyzed within the framework of deterministic analysis. Finally, a probabilistic fragility analysis using the coupled solver accounting for uncertainties in hydraulic, structural, and geological parameters is performed through the Latin Hypercube Sampling method. The study concludes that the deterministic analysis without considering the uncertainties in model parameters leads to underestimating the risk due to overturning failure and vertical failure.

Impact of choice of fragility approaches on seismic risk quantification of nuclear power plants

Development and evaluation of seismic fragility of structures and components is crucial in seismic probabilistic risk assessment of nuclear power plants. Simulation-based fragility approaches are a prevailing trend in the literature, while industry-recommended methodologies rely heavily on engineering judgment and deterministic analysis. In this paper, four critical components are selected, modeled and analyzed as a case study. Their fragilities are evaluated using both state-of-the-art fragility methods and code-recommended methods with approximate models. The impact of the choice of fragility approaches on the fragilities of the components and conditional core damage probability of the plant are assessed. The findings reveal that the recommended approaches employed with approximate models have limitations in estimating the median capacity of complex equipment. While there is a notable variance in the treatment of uncertainty among fragility approaches, its influence on core damage probability remains limited unless the component is the primary contributor to core damage.

DXA evaluation of bone fragility 2 years after bariatric surgery in patients with obesity

PurposeThe primary objective was to evaluate bone fragility on dual X-ray absorptiometry (DXA) in patients with obesity before and 2 years after bariatric surgery. The secondary objective was to identify risk factors for the development of a bone mineral density ≤ −2 SD at 2 years. MethodsThis descriptive study included patients with obesity who underwent DXA before and 2 years (±6 months) after bariatric surgery. The BMD and the T-score were assessed at the lumbar spine, femoral neck and total hip. Data on body composition on DXA were also collected. The diagnosis of osteoporosis was retained for a T-score ≤ − 2.5 SD at any measured location. Osteopenia, or low bone mass, was defined by −2.5 SD < T-score ≤ −1 SD. ResultsAmong the 675 included patients, 77.8 % were women, with a mean age of 49.5 years (±11.1). After bariatric surgery, there were significantly more patients with osteoporosis: 3.6 % vs. 0.9 % (p = 0.0001). Multivariate analysis revealed that the risk factors for developing a bone mineral density ≤ −2 SD 2 years after bariatric surgery in patients with normal BMD before surgery were age and lower lean and fat mass before the surgery (OR = 1.07, 95%CI = [1.03–1.12], OR = 0.83, 95%CI = [0.77–0.91], OR = 1.08, 95%CI = [1.02–1.15], respectively). ConclusionThere was a significantly higher prevalence of osteoporosis and low bone mass 2 years after bariatric surgery. Older age and lower lean and fat mass at baseline were risk factors for the development of a BMD ≤ -2SD at 2 years.

High prevalence of morphometric vertebral fractures opportunistically detected on thoracic radiograms in patients with non-functioning pituitary adenoma.

Vertebral fractures (VFs), the hallmark of skeletal fragility, have been reported as an emerging complication in patients with pituitary diseases associated with hormonal excess and/or deficiency, independently from bone mineral density. Non-functioning pituitary adenoma (NFPA) is amongst the most frequent pituitary adenomas; however, skeletal health in this context has never been investigated. We aimed at assessing the prevalence and the determinants of morphometric VFs in patients with NFPA. We enrolled 156 patients (79M/77F, mean age 55.75 ± 12.94years) at admission in Neurosurgery Unit before trans-sphenoidal surgery and compared them with an age and sex-matched control group of subjects with neither history/risk factors for secondary osteoporosis nor pituitary disorders. We performed a vertebral morphometric evaluation of the thoracic spine on pre-operative X-ray images (MTRx) and collected biochemical, demographic, and clinical data from the entire cohort. The prevalence of thoracic VFs in patients with NFPA was significantly higher than the control group (26.3% vs. 10.3%; p < 0.001). In the NFPA group, 20 patients (48.8% of the fractured patients) showed multiple VFs, 14 (34.1% of them) showed moderate/severe VFs. Patients with VFs were significantly older and had lower serum free triiodothyronine (fT3) levels than non-fractured ones (p = 0.002 and p = 0.004; respectively). The prevalence of secondary male hypogonadism was higher among men with VFs as compared to those with no VFs (72% vs. 48.1%; p = 0.047). Consistently, total testosterone levels in males were significantly lower in fractured patients than in non-fractured ones (p = 0.02). The prevalence of gonadotroph adenomas was significantly higher among patients with VFs (p = 0.02). In multiple logistic regression analysis, older age and lower serum fT3 levels were independent factors predicting the risk for VFs. For the first time, we reported a high prevalence of thoracic radiological VFs in patients with NFPAs. Our data should prompt clinicians to proceed with a clinical bone fragility evaluation already during the diagnostic work-up, particularly in those with concomitant hypogonadism, or in those with older age and/or with lower fT3.

Estimation of wind pressure field on low-rise buildings based on a novel conditional neural network

The estimation of wind pressure on building envelopes is critical for accurate risk and resilience evaluation of coastal structures. It is possible and convenient sometimes to interpolate existing wind-tunnel tests for the estimation of untested buildings. However, the complex bluff-body aerodynamics pose a challenge for wind tunnel test interpolation. Specifically, the nonlinear interpolation needs to be conducted simultaneously on coordinate and wind and building condition, which cannot be accomplished using conventional interpolation methods. To address this issue, a novel machine learning approach called Conditional Neural Network (CondNN) is developed. In the CondNN, a two-level architecture is utilized to interpolate existing test data for a certain building (i.e., the lower level takes the coordinate on building envelope as input) and across different buildings (i.e., the upper level takes the wind and building condition as input). Wind tunnel measurements are further used for verifying the performance of the proposed conditional natural network for wind pressure estimation. The CondNN not only paves a path toward the fast fragility evaluation of a diverse set of buildings exposed to coastal wind hazards, but also illuminates the use of machine learning techniques in a broader spectrum of engineering applications.

Influence of frequency characteristics of seismic ground motion on the fragility of an RC frame structure

Ground-motion frequency characteristics have a significant impact on structural damage. A quantitative description of the impact of ground-motion spectral features on structures is an urgent topic that requires solutions. In this study, the ratio of peak displacement to peak acceleration (R d2a ) is used as a representative index of the ground-motion spectral characteristics. The seismic records collected from the Kik-net strong-motion array in Japan are grouped according to their R d2a values. By adopting the incremental dynamic analysis method, the seismic fragility curves of a six-story RC frame structure loaded by inputting seismic records with different R d2a values are calculated using the OpenSees platform. The influence of R d2a values on the structural fragility is analyzed. Ground-motion records of liquefied sites are collected, and the peak ratios of seismic records at the liquefied sites are analyzed to reveal the differences in the fragility of the six-story RC structures at liquefied and non-liquefied sites. The results of this study are expected to serve as a reference for the evaluation of structural fragility and to understand the effect of ground-motion frequency characteristics on the fragility of RC frame structures.

Bone health: Quality versus quantity

Healthy bone has the ability to resist deformation and fracture, while adapting to applied mechanical loads. These properties of bone depend on characteristics of its extracellular matrix. This review focuses on the contribution of bone quality and quantity to bone health and highlights current and promising future clinical approaches to measure bone health in the pediatric population. Bone’s unique material properties are derived from its highly organized, hierarchical composite structure, together with its modeling and remodeling dynamics and microdamage mechanisms. Pediatric bone diseases and disorders affect the biological processes that regulate its quality, negatively impacting the extracellular matrix and causing bone fragility. Laboratory bone analysis from human biopsies or animal models of human bone diseases allows high detail examination of the mechanisms contributing to bone fragility. Conversely, clinical measurements of bone fragility are difficult and limited due to the inaccessibility of the material. Because bone quality directly affects fracture resistance, both structure and composition should be used in fracture risk calculation rather than bone mineral density or bone quantity alone. Thus, to advance clinical evaluation of bone fragility, future studies are needed to determine which characteristics of bone quality can be applied to clinical practice to predict bone fragility. New and effective clinical tools are needed to predict fracture risk taking bone quality into consideration. Key Concepts(1)Bone quality and bone quantity are both fundamental for resistance to deformity and fracture.(2)Pediatric bone diseases and disorders alter bone’s composition and structure, compromising bone quality and increasing vulnerability to fracture.(3)Current clinical approaches to assess bone fragility and fracture risk rely mainly on bone quantity measurements from DEXA scans.(4)DEXA bone mineral density poorly correlates with bone’s resistance to fracture, both in adults and children.(5)Future clinical approaches to measure bone health should account for bone quality in order to predict fracture risk.

Evaluating financial fragility: a case study of Chinese banking and finance systems

Global financial systems are inherently fragile due to their complexities. Thus, it is of great interest to devise various methods to assess the dynamics of financial fragility. As such, this study builds a financial fragility evaluation index system. The study finds three major fluctuations in the trend of financial fragility due to the great recession in 2008, the huge financial volatility in 2015, and the COVID-19 pandemic in 2019. It also tests the index system on the Chinese finance market from 2007 to 2022. Observations of capital adequacy, non-performing loans, and liquidity ratios, in addition to the average return on total assets, are used to assess banking fragility. The results attained show that amongst the tested banks, the Bank of Ningbo has the lowest vulnerability score, mainly due to its higher average return on total assets, capital adequacy ratios, and lower non-performing loan ratio. On the other end of the spectrum, China Minsheng Bank has the highest vulnerability score due to its lower capital adequacy and higher non-performing loan ratios. These findings provide valuable insights into the banking sector in China for policy formulation.

Seismic fragility evaluation of the Nepalese pagoda temple: A case study of Laxmi Narsingha temple

The preservation of cultural heritage has been a global concern. In the context of vulnerability assessments and risk reduction strategies studied, historical monument rehabilitation in Nepal has often occurred without a comprehensive damage grade analysis. This paper addresses this gap by presenting a seismic fragility assessment of a two-tier Nepalese pagoda temple, with the Laxmi Narsingha temple as a case study. This pagoda temple features load-bearing brick masonry with timber posts and crossbeams. Comparative finite element (FE) models—one with a masonry-timber interface and one without—were analyzed and subjected to pushover analysis. The failure mechanisms (cracks) in these models revealed distinct behavioral differences. The study further examined the influence and sensitivity of masonry properties on the temple's response quantities through parametric assessments. Furthermore, fragility analysis of the temple's analytical models was done for three performance levels- Immediate Occupancy (IO), Life Safety (LS), and Collapse Prevention (CP). The fragility analysis results indicate that the model with a masonry-timber interface recorded a higher likelihood of exceeding the limit states over the one without interface characteristics counterpart. The study helps to analyze and decide over the selection of a suitable analytical procedure to represent the failure mechanisms exhibited by the pagoda structure.

Seismic fragility analysis of high‐strength concrete frame structures reinforced with high‐strength steel bars

SummaryTo investigate the influence of using high‐strength steel bars in columns on the seismic resistance capacity and seismic resilience of frame structures, seismic fragility evaluation of three 8‐story reinforced concrete (RC) frame structures was conducted based on the incremental dynamic analysis (IDA) using 11 ground motion records. The main parameter is the longitudinal reinforcement configuration in the frame columns, where the first structure is reinforced with HRB 600 grade steel bars in the columns, the second structure is replaced with equal area ultra‐high‐strength (UHS) steel bars (i.e., with a yield strength of approximately 1425 MPa), and the third structure is replaced with equal strength UHS steel bars. A numerical model of the RC frame structure was developed and then validated using previous experimental results. The exceeding probabilities at various performance limit states were calculated based on two typical engineering demand parameters (EDPs) of maximum interstory drift and residual interstory drift. The results showed that using UHS longitudinal steel bars instead of HRB 600 grade steel bars in frame columns could reduce the energy dissipation capacity of the structure, inevitably leading to an increase in the maximum interstory response of the frame. However, much lower exceedance probability was observed in the UHS‐enhanced frame under the repair available limit state based on the residual interstory drift, indicating that the UHS‐enhanced RC frame had higher seismic resilience. In addition, compared to equal area substitution, equal strength substitution is a more ideal design method that can use fewer UHS steel bars to achieve comparable reparability and a smaller increase in maximum interstory drift.

Deep learning enabled seismic fragility evaluation of structures subjected to mainshock-aftershock earthquakes

Mainshock-aftershock earthquakes have gained significant attention since accumulated damages induced by multiple shocks are likely to cause failure of structures. This paper presents a deep learning approach based on a Gated Recurrent Unit (GRU) network for assessing the seismic fragility of structures under mainshock-aftershock scenarios. The GRU network is utilized to create a surrogate model that captures the nonlinear relationship between seismic responses and mainshock-aftershock earthquakes. Subsequently, seismic fragility analysis is conducted based on double incremental dynamic analysis, employing the trained GRU network. A single-degree-of-freedom system with Bouc-Wen hysteretic behavior was investigated to demonstrate the proposed approach. The results indicate that the approach shows a substantial reduction in computational costs and holds promising potential for evaluating the seismic fragility of structures exposed to mainshock-aftershock earthquakes.

Fragility Assessment of a Long-Unit Prestressed Concrete Composite Continuous Girder Bridge with Corrugated Steel Webs Subjected to Near-Fault Pulse-like Ground Motions Considering Spatial Variability Effects

Prestressed concrete composite girder bridges with corrugated steel webs (PCCGBCSWs) are extensively employed in bridge construction because of their low dead weight, fast construction, and high prestressing efficiency. Moreover, PCCGBCSWs will experience deformation and failure of the corrugated steel webs, including steel fatigue and fracture, during earthquakes. These changes will introduce safety hazards, which can be addressed via bridge disaster prevention and mitigation. Because near-fault pulse-like ground motions (NFPLGMs) have high peak accelerations, these motions can easily cause damage to a bridge. Therefore, in this study, a seismic fragility assessment is performed for long-unit PCCGBCSWs subjected to NFPLGMs considering spatial variability effects, and a sensitivity evaluation of the seismic fragility is conducted considering girder type, bearing type, ground motion type, and apparent wave velocity to offer a point of reference for seismic design. The results show that PCCGBCSWs are less vulnerable than concrete bridges. The shock absorption effect of the friction pendulum bearing is better than that of the viscous damper. The impact of NFPLGMs on bridges is greater than that of near-fault non-pulse-like ground motions (NFNPLMs) and far-fault ground motions (FFGMs). The seismic fragility under nonuniform excitation conditions is greater than that under uniform excitation conditions, showing an increasing trend with decreasing apparent wave velocity.