Empirical Formulation Research Articles

Evaluation of Flow Liquefaction Susceptibility in Non-Plastic Silty Soils Using the Seismic Cone

The state parameter allows the evaluation of the in situ state of soils, which can be particularly useful in tailings impoundments where flow liquefaction is the most common failure model. Positive state parameter values characterize a contractive response during shearing and, for non-plastic soils, can indicate flow liquefaction susceptibility. This paper presents a methodology to classify and estimate the state parameter (Ψ) for non-plastic silty soils based on seismic cone penetration measurements. The method expands on a previous methodology developed for sands that use the ratio of the small strain shear modulus and the cone tip resistance G0/qt for classification and Ψ assessment. For non-plastic silty soils, drainage conditions during cone penetration must be accounted for and are used to allow soil classification and correct the cone tip resistance. An empirical formulation is proposed to correct qt for partial drainage measurements and predict Ψ for non-plastic silty soils. Mining tailings results of in situ and laboratory tests were used to validate the proposed methodology producing promising responses. The Ψ value estimated through the proposed methodology are in the range of those obtained from laboratory tests, indicating an adequate prediction of behavior for non-plastic silty soils.

Simulation and Data-Driven Modeling of the Transport Properties of the Mie Fluid.

This work reports the computation and modeling of the self-diffusivity (D*), shear viscosity (η*), and thermal conductivity (κ*) of the Mie fluid. The transport properties were computed using equilibrium molecular dynamics simulations for the Mie fluid with repulsive exponents (λr) ranging from 7 to 34 and at a fixed attractive exponent (λa) of 6 over the whole fluid density (ρ*) range and over a wide temperature (T*) range. The computed database consists of 17,212, 14,288, and 13,099 data points for self-diffusivity, shear viscosity, and thermal conductivity, respectively. The database is successfully validated against published simulation data. The above-mentioned transport properties are correlated using artificial neural networks (ANNs). Two modeling approaches were tested: a semiempirical formulation based on entropy scaling and an empirical formulation based on density and temperature as input variables. For the former, it was found that a unique formulation based on entropy scaling does not yield satisfactory results over the entire density range due to a divergent and incorrect scaling of the transport properties at low densities. For the latter empirical modeling approach, it was found that regularizing the data, e.g., modeling ρ*D* instead of D*, ln η* instead of η*, and ln κ* instead of κ*, as well as using the inverse of the temperature as an input feature, helps to ease the interpolation efforts of the artificial neural networks. The trained ANNs can model seen and unseen data over a wide range of density and temperature. Ultimately, the ANNs can be used alongside equations of state to regress effective force field parameters from volumetric and transport data.

On assessing the carbon capture performance of graphynes with particle swarm optimization.

Tackling climate change is one of the greatest challenges of current times and therefore the development of efficient technologies to limit anthropogenic emissions is of utmost urgency. Recent research towards this goal has alluded to the use of carbon-based solid sorbents for carbon capture. Graphynes (GYs), an interesting class of porous carbon membranes, have recently proven their potential as excellent membranes for gas adsorption and separation. Herein, we explored the CO2 and N2 adsorption characteristics and CO2/N2 selectivities of a class of GYs, namely γ-GY-1, γ-GY-2 and γ-GY-4. We investigated the putative global minimum geometries of adsorbed unary (n = 2-10) and binary (n : m; n, m ∈ [1, 8]) clusters of CO2 and N2 by employing a stochastic global optimization method called particle swarm optimization in conjunction with empirical intermolecular force field formulations. The intervening interactions are modeled using various pairwise potentials, including Lennard-Jones potential, improved Lennard-Jones potential, Buckingham potential and Coulombic potential. The binding energies for both unary and binary clusters are highest for adsorption on γ-GY-1, followed by γ-GY-2. The putative global minimum geometries suggested that N2 molecules preferred binding over the pore centres while CO2 molecules showed higher clustering propensity than any binding site preference. The predicted interaction energies suggested higher selectivity for CO2 over N2 for all the three γ-GYs.

Fatigue behavior of short-headed studs embedded in Ultra-high Toughness Cementitious Composites (UHTCC)

The multi-cracking and strain-hardening capacities of Ultra-high Toughness Cementitious Composites (UHTCC) make it feasible for orthotropic steel bridge decks (OSBDs) applications to control crack width. In this composite bridge deck, shear connectors play an important role in providing good shear strength and ensuring structural service performance. To evaluate the shear resistance of short-headed studs embedded in ultra-thin UHTCC layer, three series of push-out tests were conducted in this study. The test results including shear strength, fatigue strength, failure modes, dynamic slip, stiffness degradation, plastic slip and residual mechanical properties were all considered and carefully discussed. In this study, the shear force of shear connectors was calculated and compared with current codes. The stress amplitude-fatigue life (S-N) relationship of studs was fitted by different codes. Then the empirical formulation was developed to predict the load-slip behavior and stiffness degradation of studs during fatigue loading. The relationship between plastic slip and fatigue life was established and normalized. Furthermore, based on post-fatigue static test results and test results in previous research, a new machine learning model was proposed to predict the residual shear strength of studs and contrasted with previous model. Then Analysis of Variance (ANOVA) with two parameters (i.e. load amplitude, maximum repeated force) was conducted and revealed that the peak load significantly impacted the residual shear strength of push-out specimens compared with load amplitude. Moreover, a parametric study was conducted to further investigate the degradation of studs under various working conditions. By experimental and theoretical analysis, UHTCC could fully develop the shear strength of studs embedded in ultra-thin cover thickness. And related models were established to predict the static and fatigue behavior of steel-UHTCC push-out specimen.

Rainfall-Runoff Response of A Suburban Area

Batu Pahat experiences flash floods whenever intense rainfall coincides with high tide. Among the factors which cause flash floods are due to Batu Pahat river catchment's flat and low-lying geographical features as well as high-intensity rainfall. The goals of the study are to analyse the frequency of rainfall events for SMK Munshi Sulaiman station and to investigate runoff due to severe rainfall events within the study area. The observed daily rainfall depth record between 2010 and 2021 was obtained from the Department of Irrigation and Drainage (DID) Malaysia. The frequency of rainfall events within the 11-year period is examined using empirical rainfall intensity formulation. Rainfall-runoff of the five most heavy rainfall events in 2021 within the study area are simulated using HEC-HMS. It has been found that most daily rainfall events have a frequency of a 1-year return period. Only three events were found to have a return period of up to 2-year ARI, with a maximum rainfall depth of 110.67 mm. Five heaviest rainfall events in 2021 were obtained from DID's real-time online platform for rainfall-runoff simulations. One of the events, which occurred in June 2021 has a frequency larger than a 100-year return period while other events have return periods ranging from 1-year to 5-year. Simulations produced by HEC-HMS for these events in January, April, May, June, and September 2021 have resulted in peak flow of 6.7 m3/s, 26.8 m3/s, 24.7 m3/s, 39.9 m3/s, and 39.9 m3/s, respectively. Based on frequency analysis, rainfall-runoff simulations, and field observations, it can be concluded that flash floods are highly possible due to high-intensity rainfall as well as lowland topographical features of the study area. Therefore, flood mitigation measures need to be carried out to improve the drainage system for the suburban area.

Dynamics of single bubble ascension in stagnant liquid: An investigation into multiphase flow effects on hydrodynamic characteristics using computational simulation

Industrial operations often involve multiphase flows, where the motion of bubbles plays a crucial role in determining hydrodynamic properties. In the context of modern practices, advanced computational solvers are increasingly employed to simulate the interactions and trajectories of bubbles within complex flows. This study stands out in its unique examination of the computational software COMSOL's capability to accurately simulate the upward motion of a single bubble within quiescent water, akin to a liquid-like environment. The novelty lies in the comprehensive coverage of various container diameters (ranging from 10 to 80 mm) and heights (from 25 to 300 mm) relative to the air bubble diameter (ranging from 0.5 to 8 mm). Through meticulous comparisons between nine empirical formulas and numerically projected bubble ascent through a water column, a remarkable level of agreement emerges, underscoring the precision and consistency of the simulations. These simulations unveil intriguing findings, shedding light on the intricate interplay of forces governing bubble behavior. Notably, variations in drag forces induce changes in bubble shapes as a function of diameter, while the ascent of bubbles is accompanied by distinctive vortices, resulting in fascinating asymmetry. Furthermore, vorticity concentrates within the bubble, particularly in lighter fluid regions characterized by reduced pressure. The study also unveils how larger aspect ratios minimize flow drag, consequently boosting ascent velocities, and demonstrates the influence of container diameter on the rising velocity. Gravitational forces are found to reduce ascent velocities at greater column heights, while the rate of air bubble rise escalates with its size. This meticulous exploration of bubble dynamics in multiphase flows yields invaluable insights for diverse industrial applications, ultimately enhancing our understanding of this complex phenomenon. The strong alignment observed between empirical formulations and numerical simulations within the COMSOL framework underscores the utility of such computational tools for the study and design of multiphase flows' intricate dynamics.

The fate of vegetation carbon stocks of India: Insights from a remote-sensed evaluation of carbon use efficiency

Vegetation carbon use efficiency (CUE), defined as the ratio of the net primary productivity (NPP) to gross primary productivity (GPP), is a critical metric for assessing the extent of sequestration of atmospheric carbon by vegetation into biomass. Evaluating CUE is essential for policymakers to devise carbon sequestration policies and also identify hotspots of carbon storage loss. Indian ecosystems face variable weather conditions across the year. However, the roles of weather variability, spatial patterns, and temporal dynamics are poorly understood, as much as the resilience to hydroclimatic perturbations that may influence CUE in Indian terrestrial ecosystems, particularly at sub-annual scales. The lack of sub-annual NPP datasets hinders remote sensing-based sub-annual CUE assessments. However, this study derived an 8-day scale NPP dataset through an empirical formulation on moderate-resolution imaging spectroradiometer (MODIS) products. This study assessed CUE dynamics for India across its six homogeneous meteorological regions (HMRs) including the major biomes of each HMR, encompassing croplands, forests, and grasslands, through a fine-scale remote sensing approach for 2000–2021. The results show pronounced variability of CUE across spatiotemporal scales governed by the water availability and temperature interplay, with hilly 0.59±0.01 and northwestern 0.33±0.02 regions exhibiting the highest and lowest CUE on an annual scale. Distinct patterns have been observed among the biomes, depending on the HMRs dictated by the land management practices of the regions. Similar pronounced CUE variability has been observed on seasonal scales. The study also derived sustainability maps of carbon stocks for India from the trend-persistence interplay of CUE, revealing alarming concerns across most HMRs, with peninsular India exhibiting a persistent decrease in CUE for 82% of its cropland area. A widespread loss of resilience of carbon stocks was observed, primarily caused by increased precipitation and warming under meteorological drivers, along with aridity induced by soil and atmospheric conditions. Overall, this study highlights the critical role of CUE in assessing the carbon sequestration potential of Indian ecosystems and the need for a better understanding of the factors that influence it to develop effective carbon sequestration policies.

Improved groundwater modeling by incorporating geological information from hydrogeological sections

Geological cross-sections are usually employed in the hydrogeological model conceptualization, but their usage may not be easily exploited in subsequent modeling phases. The spatial distribution of geological facies along a geological section’s track may significantly vary when using random facies fields, and these may not be faithful to the original conceptualization described by the geological section. The present work offers a novel framework for improving available hydrogeological models using geological sections as a more quantitative source of information, hence by taking into account of information coming from a geological section. Then, this information given by the change in the distribution of porosities is transferred from the section’s track to surrounding locations through a proper kriging procedure upon a chosen Correlation Scale (R), which is exponentially correlated in space. This procedure is tested by using porosity distributions upon several R, associating a conductivity value with each porosity one through empirical formulations, and informing several numerical models related to a real case study (an aquifer in the province of Lecco, Northern Italy). The proposed procedure enables to significantly outperform the former calibrated numerical model. Best-calibrated models show that the convenient R could be from 2 to 5 kilometers long, consistent with the width of the alluvial and fluvioglacial floodplain that characterizes the aquifer under examination.

Ship grounding model tests in a water tank: An experimental study

Ship grounding experiments are important benchmarks used to validate numerical analysis, analytical and empirical formulation. They are key to the understanding of damage mechanism. A set of small-scale ship model grounding tests over a sharp rock are conducted in a water tank considering the influence of surrounding water. Two damage modes are observed in the grounding tests, Mode I for discontinuous fracture/tear and Mode II for continuous fracture/tear. The horizontal grounding resistance forces, damage extents of ship bottom plates, and ship motions are recorded and discussed in detail. Moreover, the energy dissipation process of ship model during grounding process is analyzed based on the test results. The influence of the initial velocity, the initial relative height between the upper surface of the horizontal ship bottom plate and the rock tip, and the rock eccentricity on the ship motion response and structural damage are studied.

Mixture modeling to simulate helium boiling: Helium gas bubble trapped in high magnetic field

Multi-phase flow hydrodynamics is an essential theoretical foundation for modernizing engineering and is important in guiding and developing modernizing engineering. In the realm of superconducting power technology, it is imperative to submerge and cool high-field superconducting magnets and superconducting cables, constructed from superconducting materials, in cryogenic fluids in order to maintain a superconducting state. Even minor thermal disturbances can induce boiling of the cryogenic fluid, leading to a two-phase flow regime. In the case of high-field superconducting magnets, the presence of liquid helium as the cooling medium gives rise to a diamagnetic effect. Consequently, the formation of a bubble resulting from boiling is confined in close proximity to the central aperture of the magnet owing to the influence of the magnetic field force. This confinement adversely affects the heat transmission properties of the magnet. This work presents a comprehensive analysis of the flow state during the boiling process of liquid helium, using the finite element approach and the mixture model. The heat transfer in a two-phase flow is analyzed by treating the system as a single pseudo-fluid. The model is consistent with empirical formulations of liquid helium boiling in large vessels and is also suitable for modeling the effect of heating surface orientation on the critical heat flux. Consequently, the analysis of the retention of helium bubbles generated by boiling in a high-field magnet has been further examined, using this particular model. The results of numerical hydrodynamic studies show that the width of the helium bubble stagnation zone is larger compared to the results of hydrostatic calculations. This poses a major challenge for superconducting magnets operating at high magnetic fields and high temperatures. The paper further analyses the effect of supercooled liquid helium on helium bubble stagnation, thus providing valuable insight into the construction of superconducting magnets with high magnetic fields.

Empirical formula to assess ultimate strength of side shell on passenger ship under combined axial and shear load based on experimental and numerical analysis

This study proposes an empirical formulation to assess the ultimate strength of side shells on passenger ships subjected to combined effects of axial compression and shear loads. The deteriorating effects of large openings and strengthening effects of stiffener reinforcements were considered in the proposed formulation for a wider range of applications. To verify accuracy of the empirical formula, an experimental test was first conducted to inspect the collapse behaviour and influential parameters of the side shell. More than 5000 side-shell scenarios were subsequently adopted as the input dataset based on the experimentally validated nonlinear finite element method. A simplified polynomial shape was proposed for the empirical formula by comparing various generation sets of the four-parameter-based formulations. A reliable solution to the proposed empirical formula was obtained with respect to a high determination coefficient compared to the numerical results. The developed empirical formula can be considered as applicable and beneficial for practical structural design work of side shells with large openings in modern passenger ships.

VPP Driven Parametric Design of AC75 Hydrofoils

Hydrofoils are a vital part of modern racing yachts such as the AC75, which was sailed in the 36th America’s Cup and should hence be optimised thoroughly. The literature shows that hydrofoil design and optimisation usually focuses on the lift and drag characteristics in isolation of the yacht ‘system’. Although these characteristics relate to hydrofoil performance, they do not directly translate to the performance of the yacht on the race course. In this paper we perform a parametric study of the main design variables of the hydrofoil that is based on a model of the entire yacht in the Velocity Prediction Program (VPP) FS-Equilibrium. The hydrofoil forces are modelled using an advanced lifting line method and empirical formulations for a bulb. This accurately captures the foil design influence on the boat´s performance. The VPP is coupled to a parametric model of the foil based on NURBS surfaces (Non-uniform rational B-Splines) which was used to systematically generate 72 different designs. The candidates were tested in three wind speeds for up and downwind performance. The best performing design has maximum span and anhedral angle, and minimum chord with some of the weight stored in a bulb. The study shows that the assessment of hydrofoils where the performance is measured in boat speed is an extremely valuable tool.

Faktor Kerentanan Banjir Rob Kecamatan Medan Belawan Kota Medan

The rise in sea level has impacted the emergence of a flood disaster in the district of Belawan City Field. The flooding of these robs caused the sinking of settlements, industries and ports. The height of flooding that increases every year has an impact on the increased shortages caused and increased economic losses of communities working in vulnerable sectors. Therefore, vulnerability factors are necessary to determine effective adaptation directions. The research was carried out in the district of the Field of Belawan City of Medan where there are 6 (six) floods affected by the flood of rob: the Kelurahan Belawa I, Belawana II, Blawan Bahari, Balawan Pulau Sicanang and Bagan Deli. The study begins with the theoretical and empirical formulation related to vulnerability to flood areas followed by interviews with stakeholders aimed at finding issues more openly in which the interviewed parties are asked for opinions. The stakeholder used is the stakeholder who knows the phenomenon of the flooding of rob that occurs in the research area consists of 3 (three) groups representing the government and society. Factors affecting the level of vulnerability to flooding in the area are grouped into physical, social, economic and environmental vulnerability factors.

Novel Fractional Order and Stochastic Formulations for the Precise Prediction of Commercial Photovoltaic Curves

To effectively represent photovoltaic (PV) modules while considering their dependency on changing environmental conditions, three novel mathematical and empirical formulations are proposed in this study to model PV curves with minimum effort and short timing. The three approaches rely on distinct mathematical techniques and definitions to formulate PV curves using function representations. We develop our models through fractional derivatives and stochastic white noise. The first empirical model is proposed using a fractional regression tool driven by the Liouville-Caputo fractional derivative and then implemented by the Mittag-Leffler function representation. Further, the fractional-order stochastic ordinary differential equation (ODE) tool is employed to generate two effective generic models. In this work, multiple commercial PV modules are modeled using the proposed fractional and stochastic formulations. Using the experimental data of the studied PV panels at different climatic conditions, we evaluate the proposed models’ accuracy using two effective statistical indices: the root mean squares error (RMSE) and the determination coefficient (R2). Finally, the proposed approaches are compared to several integer-order models in the literature where the proposed models’ precisely follow the real PV curves with a higher R2 and lower RMSE values at different irradiance levels lower than 800 w/m2, and module temperature levels higher than 50 °C.

Running safety analysis of a train-bridge coupled system under near-fault ground motions considering rupture directivity effects

The implementation of China’s high-speed railroad network and the “Bridges Instead of Roads” construction concept has raised concerns over earthquake safety. The complex mechanism of near-field ground motions poses greater risks than far-field ground motions due to the rupture directivity effect, and Hanging-wall/Footwall effects. The PEER earthquake database lacks earthquake records with fault distances less than 20 km, making it difficult to study train running safety (TRS) under near-fault ground motions. To address this issue, an empirical formulation method is adopted for near-fault three-dimensional seismic synthesis that considers source and site characteristics as well as rupture directivity effects using regression analysis. The method is verified with respect to directivity pulse and a train-bridge coupled system (TBCS) model is developed to verify its accuracy under earthquakes. Responses of the TBCS model under near-fault ground motions synthesized with different fault types, closest distances to the fault surface, and directivity parameters are analyzed by taking the average of the largest part of the response for comparison. Results show that dip-slip faults pose a greater danger than strike-slip faults, and the main reason for the hazard caused by rupture directivity effects is the generation of a forward directivity pulse, which makes the TBCS highly susceptible to derailment under near-fault pulse-like ground motions.

Morphology and Transport Characterization of Catalyst Layers for CO2 Reduction

Gas diffusion electrodes (GDEs) help to reduce transport limitations in devices for electrochemical CO2 reduction. Homogenized modeling of such devices requires input of morphological characteristics and effective transport properties of the porous structure, which can be obtained by pore-scale methods. Due to the small pore sizes and layer thicknesses, such characterization of the catalyst layer (CL) is difficult. In this work, CL structures digitalized by FIB-SEM nano-tomography were analyzed to obtain a set of morphological descriptors and were considered as geometrical domains in direct pore-scale simulations to calculate tensors of effective diffusion coefficient, permeability, tortuosity, and effective ionic and electronic conductivity. The CL properties vary significantly depending on the diffusion and flow direction, and samples of similar composition and synthesis technique exhibit different transport behaviors. The reported results provide a quantitative morphological analysis and a reliable set of effective properties to be used in homogenized device modeling, a net improvement over the most commonly used empirical or analytical formulations. The data set was obtained directly from the pore-scale structure of real CLs and contributes to making device-scale homogenized modeling of GDEs more accurate and reliable.

Advancing Understanding of Just-in-Time States for Supporting Physical Activity (Project JustWalk JITAI): Protocol for a System ID Study of Just-in-Time Adaptive Interventions.

Just-in-time adaptive interventions (JITAIs) are designed to provide support when individuals are receptive and can respond beneficially to the prompt. The notion of a just-in-time (JIT) state is critical for JITAIs. To date, JIT states have been formulated either in a largely data-driven way or based on theory alone. There is a need for an approach that enables rigorous theory testing and optimization of the JIT state concept. The purpose of this system ID experiment was to investigate JIT states empirically and enable the empirical optimization of a JITAI intended to increase physical activity (steps/d). We recruited physically inactive English-speaking adults aged ≥25 years who owned smartphones. Participants wore a Fitbit Versa 3 and used the study app for 270 days. The JustWalk JITAI project uses system ID methods to study JIT states. Specifically, provision of support systematically varied across different theoretically plausible operationalizations of JIT states to enable a more rigorous and systematic study of the concept. We experimentally varied 2 intervention components: notifications delivered up to 4 times per day designed to increase a person's steps within the next 3 hours and suggested daily step goals. Notifications to walk were experimentally provided across varied operationalizations of JIT states accounting for need (ie, whether daily step goals were previously met or not), opportunity (ie, whether the next 3 h were a time window during which a person had previously walked), and receptivity (ie, a person previously walked after receiving notifications). Suggested daily step goals varied systematically within a range related to a person's baseline level of steps per day (eg, 4000) until they met clinically meaningful targets (eg, averaging 8000 steps/d as the lower threshold across a cycle). A series of system ID estimation approaches will be used to analyze the data and obtain control-oriented dynamical models to study JIT states. The estimated models from all approaches will be contrasted, with the ultimate goal of guiding rigorous, replicable, empirical formulation and study of JIT states to inform a future JITAI. As is common in system ID, we conducted a series of simulation studies to formulate the experiment. The results of our simulation studies illustrated the plausibility of this approach for generating informative and unique data for studying JIT states. The study began enrolling participants in June 2022, with a final enrollment of 48 participants. Data collection concluded in April 2023. Upon completion of the analyses, the results of this study are expected to be submitted for publication in the fourth quarter of 2023. This study will be the first empirical investigation of JIT states that uses system ID methods to inform the optimization of a scalable JITAI for physical activity. ClinicalTrials.gov NCT05273437; https://clinicaltrials.gov/ct2/show/NCT05273437. DERR1-10.2196/52161.

A probabilistic framework for post-disaster recovery modeling of buildings and electric power networks in developing countries

Post-disaster recovery is a significant challenge, especially in developing countries. Various technical, environmental, socioeconomic, political, and cultural factors substantially influence post-disaster recovery. As a result, methodologies relevant in developed nations may not be directly applicable in Global South contexts. This study introduces a probabilistic framework for modeling the post-disaster recovery of buildings and electric power networks (EPNs) in developing countries. The proposed framework combines an asset-level assessment of individual buildings with a community-level assessment of EPNs to evaluate a building portfolio's post-event functionality state. As part of the framework, a stochastic network analysis is proposed to estimate the recovery time of damaged buildings while accounting for technical, environmental, socioeconomic, political, and cultural factors, quantified using empirical data gathered from past events. A probabilistic modeling approach is proposed to quantify the EPN's initial post-event outage levels. Empirical formulations for estimating the recovery time of an EPN as a function of its initial post-event outage levels are calibrated using post-event data from developing countries. A case study is presented to illustrate the application of the proposed framework to model the post-earthquake recovery of a synthetic low-income residential community. The analysis shows that negative technical, environmental, socioeconomic, political, and cultural factors could amplify the reconstruction time of damaged buildings by a factor of almost three. The proposed framework can support decision-makers in disaster planning and management strategies for vulnerable low-income communities.

Chloride Transport Characteristics of Concrete Exposed to Coastal Dredger Fill Silty Soil Environment

In contrast to the marine environment, coastal regions encompass substantial saline soils characterized by complex corrosive chemical compositions. This poses notable challenges to the durability of concrete structures erected in coastal dredger fill silty soil environments. This research undertook concrete chloride corrosion assessments in both a dredger fill silty soil environment and a simulated solution environment. The findings demonstrated a progressive escalation in the free chloride concentration within concrete specimens, as the exposure duration was extended from 60 to 120 d, and discernible convection zones were observed with depths ranging from 6 to 8 mm. The investigation revealed a diminishing trend in the apparent chloride diffusion coefficient, corresponding to the elongation of exposure time and the augmentation of burial depth. Paradoxically, the burial depth and exposure duration exhibited converse effects on the apparent surface chloride concentration. Empirical formulations were derived to express the apparent surface chloride concentrations and apparent chloride diffusion coefficients as dependent on the exposure time and burial depth variables. These models exhibited an excellent goodness of fit, reaching up to 0.96. Notably, concrete specimens interred at a depth of 0.0 m displayed a favorable likeness to the simulated solution environment throughout the 60 d exposure period.

A simplified machine learning empirical model for biomimetic crack healing of bio-inspired concrete

Bio-inspired self-healing is an effective technique to extend the durability and longevity of concrete infrastructures. However, factors influencing biomimetic crack healing need to be understood for effective strategies. This study aims to develop an interpretable empirical prediction model for self-healing concrete using Multivariate linear regression (MVLR). Other machine learning (ML) techniques like deep neural networks (DNN), extreme gradient boosting (XGBoost), and convolutional neural network (CNN) were also employed for comparison. Although the XGBoost model performed best with R2 of 0.95 and the least statistical errors, however, MVLR offered a more interpretable approach. The developed empirical formulation revealed that immobilizer and bacterial strain had the strongest impact on biomimetic crack healing, followed by initial crack width and healing duration. The formulated mathematical expression was moreover experimentally validated, yielding minimal Mean Squared Error and Root Mean Squared Error values of 0.0057 and 0.0588, respectively. Thus, these findings can be utilized for the effective implementation of bio-inspired concrete in the field of construction.