Contrasting carbon cycle responses of semiarid abandoned farmland to simulated warmer-drier and warmer-wetter climates.

Rewilding abandoned farmlands provides a nature-based climate solution via carbon (C) offsetting; however, the C-cycle-climate feedback in such restored ecosystems is poorly understood. Therefore, we conducted a 2-year field experiment in Loess Plateau, China, to determine the impacts of warming (~1.4 °C) and altered precipitation (±25 %, ±50 %, and ambient), alone or in concert on soil C pools and associated C fluxes. Experimental warming significantly enhanced soil respiration without affecting the ecosystem net C uptake and soil C storage; these variables tended to increase along the manipulated precipitation gradient. Their interactions increased ecosystem net C uptake (synergism) but decreased soil respiration and soil C accumulation (antagonism) compared with a single warming or altered precipitation. Additionally, most variables related to the C cycle tended to be more responsive to increased precipitation, but the ecosystem net C uptake responded intensely to warming and decreased precipitation. Overall, ecosystem net C uptake and soil C storage increased by 94.4 % and 8.2 %, respectively, under the warmer-wetter scenario; however, phosphorus deficiency restricted soil C accumulation under these climatic conditions. By contrast, ecosystem net C uptake and soil C storage decreased by 56.6 % and 13.6 %, respectively, when exposed to the warmer-drier climate, intensifying its tendency toward a C source. Therefore, the C sink function of semiarid abandoned farmland was unsustainable. Our findings emphasize the need for management of post-abandonment regeneration to sustain ecosystem C sequestration in the context of climate change, aiding policymakers in the development of C-neutral routes in abandoned regions.

Spatial heterogeneity, sediment-water exchange, and diffusion mechanisms of organophosphate esters from river to coastal aquatic system in a typical economic circle of northern China.

Organophosphate esters (OPEs) have proven to be pervasive in aquatic environments globally. However, understanding their partitioning behavior and mechanisms at the sediment-water interface remains limited. This study elucidated the spatial heterogeneity, interfacial exchange, and diffusion mechanisms of 14 OPEs (∑14OPEs) from river to coastal aquatic system. The transport tendencies of OPEs at the sediment-water interface were quantitatively assessed using fugacity methods. The total ∑14OPEs concentrations in water and sediments ranged from 154 ng/L to 528 ng/L and 2.41 ng/g dry weight (dw) to 230 ng/g dw, respectively. This result indicated a descending spatial tendency with moderate variability. OPE distribution was primarily influenced by temperature, pH, and dissolved oxygen levels. As the carbon atom number increased, alkyl and chlorinated OPEs transitioned from diffusion towards the aqueous phase to equilibrium. In contrast, aryl OPEs and triphenylphosphine oxide, which had equivalent carbon atom counts, maintained equilibrium throughout. Diffusion trends of individual OPE congener at the sediment-water interface varied at the same total organic carbon contents (foc). As the foc increased, the fugacity fraction values for all OPE homologs showed a declining trend. The distinct molecular structure of each OPE monomer might lead to unique diffusive behaviors at the sediment-water interface. Higher soot carbon content had a more pronounced effect on the distribution patterns of OPEs. The sediment-water distribution of OPEs was primarily influenced by total organic carbon, sediment particle size, dry density, and moisture content. OPEs displayed the highest sensitivity to fluctuations in ammonium and dissolved organic carbon. This study holds significant scientific and theoretical implications for elucidating the interfacial transport and driving forces of OPEs and comprehending their fate and endogenous release in aquatic ecosystems.

Improving groundwater vulnerability assessment in structurally controlled hard rock aquifer: insight from lineament density and land use/land cover pattern.

A comprehensive seasonal assessment of groundwater vulnerability was conducted in the weathered hard rock aquifer of the upper Swarnrekha watershed in Ranchi district, India. Lineament density (Ld) and land use/land cover (LULC) were integrated into the conventional DRASTIC and Pesticide DRASTIC (P-DRASTIC) models and were extensively compared with six modified models, viz. DRASTIC-Ld, DRASTIC-Lu, DRASTIC-LdLu, P-DRASTIC-Ld, P-DRASTIC-Lu, and P-DRASTIC-LdLu, to identify the most optimal model for vulnerability mapping in hard rock terrain of the region. Findings were geochemically validated using NO3- concentrations of 68 wells during pre-monsoon (Pre-M) and post-monsoon (Post-M) 2022. Irrespective of the applied model, groundwater vulnerability shows significant seasonal variation, with > 45% of the region classified as high to very high vulnerability in the pre-M, increasing to Ì´67% in post-M season, highlighting the importance of seasonal vulnerability assessments. Agriculture and industries' dominant southern region showed higher vulnerability, followed by regions with high Ld and thin weathered zone. Incorporating Ld and LULC parameters into DRASTIC-LdLu and P-DRASTIC-LdLu models increases the 'Very High' vulnerability zones to 17.4% and 17.6% for pre-M and 29.4% and 27.9% for post-M, respectively. Similarly, 'High' vulnerable zones increase from 32.5% and 25% in pre-M to 33.8% and 35.3% in post-M for respective models. Model output comparisons suggest that modified DRASTIC-LdLu and P-DRASTIC-LdLu perform better, with accurate estimations of 83.8% and 89.7% for pre-M and post-M, respectively. However, results of geochemical validation suggest that among all the applied modified models, DRASTIC-LdLu performs best, with accurate estimations of 34.4% and 20.6% for pre-M and post-M, respectively.

Physics-informed machine learning algorithms for forecasting sediment yield: an analysis of physical consistency, sensitivity, and interpretability.

The sediment transport, involving the movement of the bedload and suspended sediment in the basins, is a critical environmental concern that worsens water scarcity and leads to degradation of land and its ecosystems. Machine learning (ML) algorithms have emerged as powerful tools for predicting sediment yield. However, their use by decision-makers can be attributed to concerns regarding their consistency with the involved physical processes. In light of this issue, this study aims to develop a physics-informed ML approach for predicting sediment yield. To achieve this objective, Gaussian, Center, Regular, and Direct Copulas were employed to generate virtual combinations of physical of the sub-basins and hydrological datasets. These datasets were then utilized to train deep neural network (DNN), conventional neural network (CNN), Extra Tree, and XGBoost (XGB) models. The performance of these models was compared with the modified universal soil loss equation (MUSLE), which serves as a process-based model. The results demonstrated that the ML models outperformed the MUSLE model, exhibiting improvements in Nash-Sutcliffe efficiency (NSE) of approximately 10%, 18%, 32%, and 41% for the DNN, CNN, Extra Tree, and XGB models, respectively. Furthermore, through Sobol sensitivity and Shapley additive explanation-based interpretability analyses, it was revealed that the Extra Tree model displayed greater consistency with the physical processes underlying sediment transport as modeled by MUSLE. The proposed framework provides new insights into enhancing the accuracy and applicability of ML models in forecasting sediment yield while maintaining consistency with natural processes. Consequently, it can prove valuable in simulating process-related strategies aimed at mitigating sediment transport at watershed scales, such as the implementation of best management practices.

Economic evaluation of submerged anaerobic hybrid membrane bioreactor operating at mesophilic temperature.

A laboratory-scale mesophilic submerged anaerobic hybrid membrane bioreactor (An-HMBR) was operated for 270 days for the treatment of high-strength synthetic wastewater at different hydraulic retention times (HRTs) (3 days, 2 days, 1 day, and 0.5 days). Chemical oxygen demand (COD) removal efficiency of 92% was obtained with methane yield rate of 0.18 LCH4/g CODremoval at 1-day HRT. The results of lab scale reactor at 1-day HRT were utilized for upscaling and cost analysis. Cost analysis revealed that the total capital cost comprised tank system (48%), membrane cost (32%), screen and PUF sponge (5% each), PLCs (4%), liquid pumps (3%), and others (2%). The operational cost comprised chemical cost (46%), pumping energy (42%), and sludge disposal (12%). The results revealed that the tank and heating costs accounted for the largest fraction of the total life cycle cost for full-scale An-HMBR. The heating cost can be compensated by gas recovery. Sensitivity analysis revealed that the interest rates, influent flow, and membrane flux were the most crucial parameters which affected the total cost of An-HMBR.

Modeling and analysis of a human papilloma virus transmission model with impact of media.

The human papillomavirus (HPV) is threatening human health as it spreads globally in varying degrees. On the other hand, the speed and scope of information transmission continues to increase, as well as the significant increase in the number of HPV-related news reports, it has never been more important to explore the role of media news coverage in the spread and control of the virus. Using a decreasing factor that captures the impact of media on the actions of people, this paper develops a model that characterizes the dynamics of HPV transmission with media impact, vaccination and recovery. We obtain global stability of equilibrium points employing geometric method, and further yield effective methods to contain the HPV pandemic by sensitivity analysis. With the center manifold theory, we show that there is a forward bifurcation when R0=1. Our study suggested that, besides controlling contact between infected and susceptible populations and improving effective vaccine coverage, a better intervention would be to strengthen media coverage. In addition, we demonstrated that contact rate and the effect of media coverage result in multiple epidemics of infection when certain conditions are met, implying that interventions need to be tailored to specific situations.

A mathematical model for wound healing in the reef-building coral Pocillopora damicornis.

Coral reefs, among the most diverse ecosystems on Earth, currently face major threats from pollution, unsustainable fishing practices , and perturbations in environmental parameters brought on by climate change. Corals also sustain regular wounding from other sea life and human activity. Recent reef restoration practices have even involved intentional wounding by systematically breaking coral fragments and relocating them to revitalize damaged reefs, a practice known as microfragmentation. Despite its importance, very little research has explored the inner mechanisms of wound healing in corals. Some reef-building corals have been observed to initiate an immunological response to wounding similar to that observed in mammalian species. Utilizing prior models of wound healing in mammalian species as the mathematical basis, we formulated a mechanistic model of wound healing, including observations of the immune response and tissue repair in scleractinian corals for the species Pocillopora damicornis. The model consists of four differential equations which track changes in remaining wound debris, number of cells involved in inflammation, number of cells involved in proliferation, and amount of wound closure through re-epithelialization. The model is fit to experimental wound size data from linear and circular shaped wounds on a live coral fragment. Mathematical methods, including numerical simulations and local sensitivity analysis, were used to analyze the resulting model. The parameter space was also explored to investigate drivers of other possible wound outcomes. This model serves as a first step in generating mathematical models for wound healing in corals that will not only aid in the understanding of wound healing as a whole, but also help optimize reef restoration practices and predict recovery behavior after major wounding events.

Fuzzy random sensitivity analysis for the overall structure reliability of reinforced concrete freezing wellbores in deep alluvium based on hidden Markov model.

To address the shortcomings of traditional reliability theory in characterizing the stability of deep underground structures, the advanced first order second moment of reliability was improved to obtain fuzzy random reliability, which is more consistent with the working conditions. The traditional sensitivity analysis model was optimized using fuzzy random optimization, and an analytical calculation model of the mean and standard deviation of the fuzzy random reliability sensitivity was established. A big data hidden Markov model and expectation-maximization algorithm were used to improve the digital characteristics of fuzzy random variables. The fuzzy random sensitivity optimization model was used to confirm the effect of concrete compressive strength, thick-diameter ratio, reinforcement ratio, uncertainty coefficient of calculation model, and soil depth on the overall structural reliability of a reinforced concrete double-layer wellbore in deep alluvial soil. Through numerical calculations, these characteristics were observed to be the main influencing factors. Furthermore, while the soil depth was negatively correlated, the other influencing factors were all positively correlated with the overall reliability. This study provides an effective reference for the safe construction of deep underground structures in the future.

Machine learning prediction of methane, nitrogen, and natural gas mixture viscosities under normal and harsh conditions.

The accurate estimation of gas viscosity remains a pivotal concern for petroleum engineers, exerting substantial influence on the modeling efficacy of natural gas operations. Due to their time-consuming and costly nature, experimental measurements of gas viscosity are challenging. Data-based machine learning (ML) techniques afford a resourceful and less exhausting substitution, aiding research and industry at gas modeling that is incredible to reach in the laboratory. Statistical approaches were used to analyze the experimental data before applying machine learning. Seven machine learning techniques specifically Linear Regression, random forest (RF), decision trees, gradient boosting, K-nearest neighbors, Nu support vector regression (NuSVR), and artificial neural network (ANN) were applied for the prediction of methane (CH4), nitrogen (N2), and natural gas mixture viscosities. More than 4304 datasets from real experimental data utilizing pressure, temperature, and gas density were employed for developing ML models. Furthermore, three novel correlations have developed for the viscosity of CH4, N2, and composite gas using ANN. Results revealed that models and anticipated correlations predicted methane, nitrogen, and natural gas mixture viscosities with high precision. Results designated that the ANN, RF, and gradient Boosting models have performed better with a coefficient of determination (R2) of 0.99 for testing data sets of methane, nitrogen, and natural gas mixture viscosities. However, linear regression and NuSVR have performed poorly with a coefficient of determination (R2) of 0.07 and - 0.01 respectively for testing data sets of nitrogen viscosity. Such machine learning models offer the industry and research a cost-effective and fast tool for accurately approximating the viscosities of methane, nitrogen, and gas mixture under normal and harsh conditions.

Evolutionary game analysis between regional governments and shipping companies: Considering the impact of government subsidy on shipping companies.

Maritime agencies are imposing stricter limits on fuel sulfur content, and regional governments are encouraging the reduction of various emissions through subsidies. In this study, an evolutionary game model is constructed to analyze the interaction between regional governments and shipping companies under the fixed and dynamic subsidies. The sensitivity analysis reveals the effect of parameters on stabilization strategies. The results show that the bilateral stakeholders can adopt stabilization strategies under dynamic subsidies. The fines, maximum subsidies and extra cost paid by regional governments have a significant impact on these strategies. To reduce the dependence of shipping companies on subsidy policies, it is recommended to improve the LSFO refining technology in the future. Expanding the implementation scope of LSFO subsidy policies will increase the utilization of LSFO by shipping companies. This study offers insights for governments to optimize the LSFO subsidy policy and shipping companies to choose sulfur oxides reduction approaches.

How many Monte Carlo samples are needed for probabilistic cost-effectiveness analyses?

OBJECTIVE: Probabilistic sensitivity analysis (PSA) is conducted to account for the uncertainty in cost and effect of decision options under consideration. PSA involves obtaining a large sample of input parameter values (N) to estimate the expected cost and effect of each alternative in the presence of parameter uncertainty. When the analysis involves using stochastic models (e.g., individual-level models), the model is further replicated P times for each sampled parameter set. We study how N and P should be determined. METHODS: We show that PSA could be structured such that P can be an arbitrary number (say, P=1). To determine N, we derive a formula based on Chebyshev's inequality such that the error in estimating the incremental cost-effectiveness ratio (ICER) of alternatives (or equivalently, the willingness-to-pay value at which the optimal decision option changes) is within a desired level of accuracy. We described two methods to confirmed, visually and quantitatively, that the N informed by this method results in ICER estimates within the specified level of accuracy. RESULTS: When N is arbitrarily selected, the estimated ICERs could be substantially different from the true ICER (even as P increases), which could lead misleading conclusions. Using a simple resource allocation model, we demonstrate that the proposed approach can minimize the potential for this error. CONCLUSIONS: The number of parameter samples in probabilistic CEAs should not be arbitrarily selected. We describe three methods to ensure that enough parameter samples are used in probabilistic CEAs.

NITIRSOIL: A model that balances complexity with prediction uncertainty for improving nitrogen fertilization in agriculture.

Mismanagement of the nitrogen (N) fertilization in agriculture leads to low N use efficiency (NUE) and therefore pollution of waters and atmosphere due to NO3- leaching, and N2O and NH3 emissions. The use of N simulation models of the soil-plant system can help improve the N fertilizer management increasing NUE and decreasing N pollution issues. However, many N simulation models lack balance between complexity and uncertainty with the result that they are not applied in actual practice. The NITIRSOIL is a one-dimensional transient-state model with a monthly time step that aims at addressing this lack in the estimation of, mainly, dry matter yield (DMY), crop N uptake (Nupt), soil mineral N (Nmin), and NO3- leaching in agricultural fields. According to its global sensitivity analysis for horticulture, the NITIRSOIL simulations of the aforementioned outputs mostly depend on the critical N dilution curve, harvest index, dry matter fraction, potential fresh yield and nitrification coefficients. According to its validation for 35 nitrogen fertilization trials with 11 vegetables under semi-arid Mediterranean climate in Eastern Spain, the NITIRSOIL presents indices of agreement between 0.87 and 0.97 for the prediction of total dry matter, DMY, Nupt, NO3- leaching and soil Nmin at crop season end. Therefore, the NITIRSOIL model can be used in actual practice to improve the sustainability of the N management in, particularly horticulture, due to the balance it features between complexity and prediction uncertainty. For this aim, the NITRISOIL can be used either on its own, or in combination with "Nmin" on-site N fertilization recommendation methods, or even could be implemented as the calculation core of decision support systems.

Mathematical and sensitivity analysis for chemical species in multistep dynamical system: A computational study.

This study presents a significant contribution to the field of chemical kinetics by providing a detailed analysis of a multi-step chemical kinetic process using ordinary differential equations (ODEs). The aim is to describe complex chemical processes' kinetics and the steady-state behavior of chemical species. The research employs reduction techniques to simplify the model by separating fast and slow processes based on their time scales, with a focus on a two-step reversible reaction mechanism. Special consideration is given to the phase flow of solution trajectories near equilibrium points, providing a clear depiction of system behavior. MATLAB simulations demonstrate the physical properties of observed data, while sensitivity analysis reveals parameters' impact on species behavior. Overall, this study enhances our understanding of chemical kinetics and offers insights into modeling complex reaction processes, with implications for various applications in chemistry and related fields.

Impact of variable economic conditions on the cost of energy and the economic viability of floating photovoltaics.

This work evaluates the effects of economic conditions' variations on the costs and viability of floating photovoltaics, a novel solution where modules are installed on or above water. A sensitivity analysis of key economic criteria is conducted across multiple European countries, first generating country-specific baseline scenarios and then introducing systematic variations into the input parameters. The results show that capital expenditure and electricity prices, which have both experienced significant variations in recent years, have the largest influence on the net present value and the internal rate of return. Similarly, capital expenditure and discount rate are found to be the most influencing factors for the levelized cost of electricity. Overall, this study contributes to the literature by identifying the correlations between the economic variables and the viability of floating photovoltaics. The findings can be used to assess the effectiveness of potential government policies and support mechanisms and to evaluate the viability of this technology under varying national and international economic conditions.

Model simplification and sensitivity analysis of chemical species for oxidation behavior in multi route complex chemical mechanism.

This study employs a Model Reduction Technique (MRT) to simplify the four-step catalytic carbon monoxide (CO) oxidation reaction. The C-matrix method identifies key elements, key/non key components, and key reactions, while the Intrinsic Low-Dimensional Manifold (ILDM) pinpoints a Slow-Invariant Manifold (SIM) important for understanding key species behavior. Sensitivity analysis can be considered for measuring the efficiency of the chemical species in detailed mechanism. This systematic approach contributes to optimizing and controlling complex reactions offering broad application potential. In addition to the mathematical proof, the validation of the given chemical model is rectified. The comparison between the slow invariant manifold of both reaction routes is reported and the computational based results performed in this study are obtained through MATLAB.

Investigating the effects of spatial scales on social vulnerability index: A hybrid uncertainty and sensitivity analysis approach combined with remote sensing land cover data.

Investigating the effects of spatial scales on the uncertainty and sensitivity analysis of the social vulnerability index (SoVI) model output is critical, especially for spatial scales finer than the census block group or census block. This study applied the intelligent dasymetric mapping approach to spatially disaggregate the census tract scale SoVI model into a 300-m grids resolution SoVI map in Davidson County, Nashville. Then, uncertainty analysis and variance-based global sensitivity analysis were conducted on two scales of SoVI models: (a) census tract scale; (b) 300-m grids scale. Uncertainty analysis results indicate that the SoVI model has better confidence in identifying places with a higher socially vulnerable status, no matter the spatial scales in which the SoVI is constructed. However, the spatial scale of SoVI does affect the sensitivity analysis results. The sensitivity analysis suggests that for census tract scale SoVI, the indicator transformation and weighting scheme are the two major uncertainty contributors in the SoVI index modeling stages. While for finer spatial scales like the 300-m grid's resolution, the weighting scheme becomes the uttermost dominant uncertainty contributor, absorbing uncertainty contributions from indicator transformation.

Visualization for better understanding global sensitivity analysis results: The case of safety assessment of radioactive waste disposal.

Sensitivity analysis answers questions about the influence of parameters on the simulation results and plays a significant role in the development of environmental models by helping to understand the relations within the model and test its adequacy. Comparison of various sensitivity analysis approaches is often also quite useful because different methods employ different measures for ranking model parameters and their unconformities and disagreements provide additional information on model behavior. The visual representation of numerical results is crucial for their correct interpretation, and at first sight, the visualizations for the sensitivity analysis should be quite universal because in most cases an outcome of sensitivity analysis is the same: a set of indices measuring the significance of model inputs for the selected output. Surprisingly, it is not so straightforward. This paper compares visualization types suitable for the graphical representation of the sensitivity indices and demonstrates their benefits and caveats in different cases.

Assessment of groundwater quality in arid regions utilizing principal component analysis, GIS, and machine learning techniques.

Assessing water quality in arid regions is vital due to scarce resources, impacting health and sustainable management.This study examines groundwater quality in Assuit Governorate, Egypt, using Principal Component Analysis, GIS, and Machine Learning Techniques. Data from 217 wells across 12 parameters were analyzed, including TDS, EC, Cl-, Fe++, Ca++, Mg++, Na+, SO4--, Mn++, HCO3-, K+, and pH. The Water Quality Index (WQI) was calculated, and ArcGIS mapped its spatial distribution. Machine learning algorithms, including Ridge Regression, XGBoost, Decision Tree, Random Forest, and K-Nearest Neighbors, were used for predictive analysis. Higher concentrations of Na, K, Ca, Mg, Mn, and Fe were correlated with industrial and densely populated areas. Most samples exhibited excellent or good quality, with a small percentage unsuitable for consumption. Ridge Regression showed the lowest MAPE rates (0.22 % training, 0.26 % in testing). This research highlights the importance of advanced machine learning for sustainable groundwater management in arid regions. Thus, our results could provide valuable assistance to both national and local authorities involved in water management decisions, particularly for water resource managers and decision-makers. This information can aid in the development of regulations aimed at safeguarding and sustainably managing groundwater resources, which are essential for the overall prosperity of the country.

Scenario design for infectious disease projections: Integrating concepts from decision analysis and experimental design.

Across many fields, scenario modeling has become an important tool for exploring long-term projections and how they might depend on potential interventions and critical uncertainties, with relevance to both decision makers and scientists. In the past decade, and especially during the COVID-19 pandemic, the field of epidemiology has seen substantial growth in the use of scenario projections. Multiple scenarios are often projected at the same time, allowing important comparisons that can guide the choice of intervention, the prioritization of research topics, or public communication. The design of the scenarios is central to their ability to inform important questions. In this paper, we draw on the fields of decision analysis and statistical design of experiments to propose a framework for scenario design in epidemiology, with relevance also to other fields. We identify six different fundamental purposes for scenario designs (decision making, sensitivity analysis, situational awareness, horizon scanning, forecasting, and value of information) and discuss how those purposes guide the structure of scenarios. We discuss other aspects of the content and process of scenario design, broadly for all settings and specifically for multi-model ensemble projections. As an illustrative case study, we examine the first 17 rounds of scenarios from the U.S. COVID-19 Scenario Modeling Hub, then reflect on future advancements that could improve the design of scenarios in epidemiological settings.

Development of similar materials for fluid-solid coupling model testing and application in damage constitutive models.

In order to provide suitable material selection for such fluid-solid coupling model tests, orthogonal experimental studies were conducted using iron concentrate powder and barite powder as aggregates, cement as cementitious materials, and gypsum and clay as modifiers. This research showed: (1) The ATC plays a dominant role in controlling the strength indexes and water absorption of the material, and these indexes show a significant decrease with the increase of the bone adhesive ratio. For each level of ATC increase, the compressive strength decreases by 0.2 MPa, the elastic modulus decreases by 10-20 MPa, and the cohesion decreases by 25-45 kPa. (2) Mixing gypsum and cement cannot jointly promote strength growth. (3) With the increase of GTC, the water absorption rate of the material increases, while the softening coefficient and permeability coefficient decrease obviously. Gypsum, which accounts for 4-16% of cement content, can be suitable for studying the hydraulic properties of similar materials for most sedimentary rock. Based on Weibull statistical damage theory, a damage constitutive model for the entire process of rock triaxial compression under the combined action of rainwater infiltration and load was established. Due to the influence of internal pores, the experimental and theoretical results have a certain deviation, the higher the confining pressure, the more obvious the deviation. In addition, the higher the rock strength, the less obvious the deviation caused by pores. This damage model can better describe the progressive failure process of rocks after rainwater infiltration, and can provide theoretical reference for the study of slope stability caused by rainwater infiltration.