In order to study the safety factor and instability process of cohesive soil slope, the discrete element method(DEM) was applied. DEM software PFC2 D was used to simulate the triaxial test to study the influence of th...In order to study the safety factor and instability process of cohesive soil slope, the discrete element method(DEM) was applied. DEM software PFC2 D was used to simulate the triaxial test to study the influence of the particle micro parameters on the macroscopic characteristics of cohesive soil and calibrate the micro parameters of DEM model on this basis. Embankment slope stability analysis was carried out by strength reduction and gravity increase method, it is shown that the safety factor obtained by strength reduction method is more conservative, and the arc-shaped feature of the sliding surface under the gravity increase method is more obvious. Throughout the progressive failure process, the failure trends, maximum displacements, and velocity changes obtained by the two methods were consistent. When slope was destroyed, the upper part was cracked, the middle part was sheared, and the lower part was destroyed by extrusion. The conclusions of this paper can be applied to the safety factor calculation of cohesive soil slopes and the analysis of the instability process.展开更多
To investigate the stability of rock mass in high geostress underground powerhouse caverns subjected to excavation,a microseismic(MS)monitoring system was established and the discrete element method(DEM)-based numeric...To investigate the stability of rock mass in high geostress underground powerhouse caverns subjected to excavation,a microseismic(MS)monitoring system was established and the discrete element method(DEM)-based numerical simulation was carried out.The tempo-spatial damage characteristics of rock mass were analyzed.The evolution laws of MS source parameters during the formation of a rock collapse controlled by high geostress and geological structure were investigated.Additionally,a three-dimensional DEM model of the underground powerhouse caverns was built to reveal the deformation characteristics of rock mass.The results indicated that the MS events induced by excavation of high geostress underground powerhouse caverns occurred frequently.The large-stake crown of the main powerhouse was the main damage area.Prior to the rock collapse,the MS event count and accumulated energy release increased rapidly,while the apparent stress sharply increased and then decreased.The amount and proportion of shear and mixed MS events remarkably increased.The maximum displacement was generally located near the spandrel areas.The MS monitoring data and numerical simulation were in good agreement,which can provide significant references for damage evaluation and disaster forecasting in high geostress underground powerhouse caverns.展开更多
In this paper, we present a new ear-following model, i.e. comprehensive optimal velocity model (COVM), whose optimal velocity function not only depends on the following distance of the preceding vehicle, but also de...In this paper, we present a new ear-following model, i.e. comprehensive optimal velocity model (COVM), whose optimal velocity function not only depends on the following distance of the preceding vehicle, but also depends on the velocity difference with preceding vehicle. Simulation results show that COVM is an improvement over the previous ones theoretically. Then, the stability condition of the model is obtained by the linear stability analysis, which has shown that the model could obtain a bigger stable region than previous models in the phase diagram. Through the nonlinear analysis, the Burgers, Korteweg-de Vries (KdV) and modified KdV (mKdV) equations are derived for the triangular shock wave, the soliton wave, and the kink-antikink soliton wave. At the same time, numerical simulations are also carried out to show that the model could simulate these density waves.展开更多
Wellbore stability analysis is a growing concern in oil industries. There are many parameters affecting the stability of a wellbore including geomechanical properties (e.g., elastic modulus, uni-axial compressive stre...Wellbore stability analysis is a growing concern in oil industries. There are many parameters affecting the stability of a wellbore including geomechanical properties (e.g., elastic modulus, uni-axial compressive strength (UCS) and cohesion) and acting forces (e.g., field stresses and mud pressure). Accurate determination of these parameters is time-consuming, expensive and sometimes even impossible. This work offers a systematic sensitivity analysis to quantify the amount of each parameter’s effect on the stability of a wellbore. Maximum wellbore wall displacement is used as a stability factor to study the stability of a wellbore. A 3D finite difference method with Mohr model is used for the numerical modeling. The numerical model is verified against an analytical solution. A dimensionless sensitivity factor is developed in order to compare the results of various parameters in the sensitivity analysis. The results show a different order of importance of parameters based on rock strength. The most sensitive properties for a weak rock are the maximum horizontal stress, internal friction angle and formation pressure, respectively, while for a strong rock, the most sensitive parameters are the maximum horizontal stress, mud pressure and pore pressure, respectively. The amount of error in wellbore stability analysis inflicted by the error in estimation of each parameter was also derived.展开更多
We adopt the concept of generalized plane strain to model a roadway in a stress field.This can avoid limitations caused by simplifying the stress analysis as plane strain.FLAC3D was used to investigate the maximum ten...We adopt the concept of generalized plane strain to model a roadway in a stress field.This can avoid limitations caused by simplifying the stress analysis as plane strain.FLAC3D was used to investigate the maximum tensile stress and displacement of a roadway in a known stress field for angles,α,between the roadway axial direction and the maximum principal stress of 0°,30°,45°,60° and 90°.This theory was applied to the analysis of an engineering case.The results indicate that stress and displacement of the surrounding rock increase as the angle,α,increases.This provides some significant guidance for a reasonable layout of roadways in a known stress field.展开更多
Based on the principle of 3D particle flow code,a numerical landslide run-out model is presented to simulate the failure process of the Zhenggang landslide(in southwestern China) under the effect of water after a rain...Based on the principle of 3D particle flow code,a numerical landslide run-out model is presented to simulate the failure process of the Zhenggang landslide(in southwestern China) under the effect of water after a rainfall.The relationship between the micro-mechanical parameters and the macro-shear strength of the grain material is determined through numerical calibrations.Then the rainfall effect is considered in numerical simulations and rain-induced sliding processes are performed,which help us to discuss the mechanism of deformation and failure of this landslide together with field observations.It shows the Zhenggang landslide would most likely be activated in Zone I and would gain momentum in Zone II.In order to prevent the potential disaster,a tailing dam is advised to be designed about 175 m downstream from the current landslide boundary of Zone II.Verified by field observations,the presented landslide model can reflect the failure mechanism after rainfall.It can also provide a method to predict the potential disaster and draft disaster prevention measures.展开更多
According to fluid dynamics analysis during the fire, the criteria k-ε two-equation model for solving three-dimensional turbulence was determined, the pollutants generated in the fire disaster were set by adopting Mi...According to fluid dynamics analysis during the fire, the criteria k-ε two-equation model for solving three-dimensional turbulence was determined, the pollutants generated in the fire disaster were set by adopting Mixture multiphase flow, and the SIMPLE algorithm was used for solving on the basis of comprehensive consideration on the heat radia- tion and components transmission during fire. By simulating the airflow flowing state inside the tunnel during fire disaster of downward ventilation, drift ventilation, and ascensional ventilation, respectively, with regard to the actual situation of No.l, No.3, and No.5 belt roadway in Kongzhuang Coal Mine, the velocity vector distributions of pollutants under different inlet air volumes were obtained, and the damage degree and influential factors of disaster were also clear, which is helpful to control and avoid disaster during belt roadway fire.展开更多
In order to study the influence of depth-thickness ratio on bedding slope stability, whose sliding surface is flexural concave in shape under mining conditions, this paper aims to study the characteristics ofdeformari...In order to study the influence of depth-thickness ratio on bedding slope stability, whose sliding surface is flexural concave in shape under mining conditions, this paper aims to study the characteristics ofdeformarion and damage of bedding sliding with depth-thickness ratios of 200:1,150:1,120:1,100:1 and 50:1 by adopting numerical simulation analysis software combined with laboratory-made "under the influence of mining variable sliding surface slope similar simulation test bed", and to propose identification methods for slope stability under the infuence of mining. The results show that mining activities under the slope reduce slope stability. With a decrease in the mining depth ratio, the influence of mining on the slope increases gradually, and the damage to the slope gradually expands, the stability of the slope grad- ually reduces, fracture occurs on the slope toe and the central fissure gradually develops to the surface, and reaches slide threshold when the depth-thickness ratio is 50:1.展开更多
The volume of influence of excavation at the right bank slope of Dagangshan Hydropower Station, southwest China, is essentially determined from microseismic monitoring, numerical modeling and conventional measurements...The volume of influence of excavation at the right bank slope of Dagangshan Hydropower Station, southwest China, is essentially determined from microseismic monitoring, numerical modeling and conventional measurements as well as in situ observations. Microseismic monitoring is a new application technique for investigating microcrackings in rock slopes. A micro- seismic monitoring network has been systematically used to monitor rock masses unloading relaxation due to continuous exca- vation of rock slope and stress redistribution caused by dam impoundment later on, and to identify and delineate the potential slippage regions since May, 2010. An important database of seismic source locations is available. The analysis of microseismic events showed a particular tempo-spatial distribution. Seismic events predominantly occurred around the upstream slope of 1180 m elevation, especially focusing on the hanging wall of fault XL316-1. Such phenomenon was interpreted by numerical modeling using RFPA-SRM code (realistic failure process analysis-strength reduction method). By comparing microseismic activity and results of numerical simulation with in site observation and conventional measurements results, a strong correlation can he obtained between seismic source locations and excavation-induced stress distribution in the working areas. The volume of influence of the rock slope is thus determined. Engineering practices show microseismic monitoring can accurately diagnose magnitude, intensity and associated tempo-spatial characteristics of tectonic activities such as faults and unloading zones. The integrated technique combining seismic monitoring with numerical modeling, as well as in site observation and conventional surveying, leads to a better understanding of the internal effect and relationship between microseismic activity and stress field in the right bank slope from different perspectives.展开更多
The configurations of near space hypersonic flying vehicles are considerably different from those of conventional aircrafts.Their configurations are relatively slender;hence their moment of inertia around the longitud...The configurations of near space hypersonic flying vehicles are considerably different from those of conventional aircrafts.Their configurations are relatively slender;hence their moment of inertia around the longitudinal axis is much smaller than those around the other two axes,resulting in strong coupling of rotations around the three axes.Thus,the stability analysis of rolling motion for such flying vehicles is more complicated than those for conventional aircrafts,and there is no available result of stability analysis which can readily be applied to such cases.This paper is mainly concerned with the stated problem.Considering the practical situation,our investigation is targeted a slightly simpler problem,namely the rolling stability of flying vehicle under known pitching motion.The stability criterion of rolling motion is obtained with and without lateral motions.We also conducted numerical simulation for the pitching-rolling coupled motions of flying vehicles by solving Navier-Stokes equations coupled with dynamic equations of flight.The results of simulation agree well with those of theoretical analysis and experiments.展开更多
Ratio-dependent predator prey models are favored by many animal ecologists recently as more suitable ones for predator-prey interactions where predation involves searching process. In this paper, a ratio-dependent pre...Ratio-dependent predator prey models are favored by many animal ecologists recently as more suitable ones for predator-prey interactions where predation involves searching process. In this paper, a ratio-dependent predator prey model with stage structure and time delay for prey is proposed and analyzed. In this model, we only consider the stage structure of immature and mature prey species and not consider the stage structure of predator species. We assume that the predator only feed on the mature prey and the time for prey from birth to maturity represented by a constant time delay. At first, we investigate the permanence and existence of the proposed model and sufficient conditions are derived. Then the global stability of the nonnegative equilibria are derived. We also get the sufficient criteria for stability switch of the positive equilibrium. Finally, some numerical simulations are carried out for supporting the analytic results.展开更多
This paper deals with the stability analysis to a three-species food chain model with crossdiffusion, the results of which show that there is no Turing instability but crossdiffusion makes the model instability possib...This paper deals with the stability analysis to a three-species food chain model with crossdiffusion, the results of which show that there is no Turing instability but crossdiffusion makes the model instability possible. We then show that the spatial patterns are spotted patterns by using numerical simulations. In order to understand why the spatial patterns happen, the existence of the nonhomogeneous steady states is investigated. Finally, using the Leray-Schauder theory, we demonstrate that cross-diffusion creates nonhomogeneous stationary patterns.展开更多
We propose and analyze mathematical models to study the dynamics of smoking behavior under the influence of educational programs and also individual's determination to quit smoking. We establish the positivity and bo...We propose and analyze mathematical models to study the dynamics of smoking behavior under the influence of educational programs and also individual's determination to quit smoking. We establish the positivity and boundedness of the solutions in a biologically feasible region. A threshold value responsible for persistence of smoking is obtained and stability analysis on models is performed. We find that determination alone is not enough to eradicate smoking but it can reduce the prevalence of smoker population. Whereas the increase in education can possibly eradicate it. We performed numerical simulation for representative set of parameters to verify and discuss results obtained analytically.展开更多
In this work, we investigate the dynamical behavior of a fractional-order toxin producing on a phytoplankton-zooplankton (TPPZ) system with nutrient cycling. We propose a mathematical system to model this situation....In this work, we investigate the dynamical behavior of a fractional-order toxin producing on a phytoplankton-zooplankton (TPPZ) system with nutrient cycling. We propose a mathematical system to model this situation. All the feasible equilibria of the system are obtained and the conditions for the existence of the equilibriums are determined. Local stability analysis of the TPPZ is studied by using the fractional Routh-Hurwitz stability conditions. Numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings.展开更多
基金Project(51808116) supported by the National Natural Science Foundation of ChinaProject(BK20180404) supported by the Natural Science Foundation of Jiangsu Province, China+1 种基金Project(KFJ170106) supported by the Changsha University of Science & Technology via Open Fund of National Engineering Laboratory of Highway Maintenance Technology,ChinaProject(242020R40133) supported by Fundamental Research Funds for the Central Universities, China。
文摘In order to study the safety factor and instability process of cohesive soil slope, the discrete element method(DEM) was applied. DEM software PFC2 D was used to simulate the triaxial test to study the influence of the particle micro parameters on the macroscopic characteristics of cohesive soil and calibrate the micro parameters of DEM model on this basis. Embankment slope stability analysis was carried out by strength reduction and gravity increase method, it is shown that the safety factor obtained by strength reduction method is more conservative, and the arc-shaped feature of the sliding surface under the gravity increase method is more obvious. Throughout the progressive failure process, the failure trends, maximum displacements, and velocity changes obtained by the two methods were consistent. When slope was destroyed, the upper part was cracked, the middle part was sheared, and the lower part was destroyed by extrusion. The conclusions of this paper can be applied to the safety factor calculation of cohesive soil slopes and the analysis of the instability process.
基金Project(2017YFC1501100)supported by the National Key R&D Program of ChinaProjects(51809221,51679158)supported by the National Natural Science Foundation of China。
文摘To investigate the stability of rock mass in high geostress underground powerhouse caverns subjected to excavation,a microseismic(MS)monitoring system was established and the discrete element method(DEM)-based numerical simulation was carried out.The tempo-spatial damage characteristics of rock mass were analyzed.The evolution laws of MS source parameters during the formation of a rock collapse controlled by high geostress and geological structure were investigated.Additionally,a three-dimensional DEM model of the underground powerhouse caverns was built to reveal the deformation characteristics of rock mass.The results indicated that the MS events induced by excavation of high geostress underground powerhouse caverns occurred frequently.The large-stake crown of the main powerhouse was the main damage area.Prior to the rock collapse,the MS event count and accumulated energy release increased rapidly,while the apparent stress sharply increased and then decreased.The amount and proportion of shear and mixed MS events remarkably increased.The maximum displacement was generally located near the spandrel areas.The MS monitoring data and numerical simulation were in good agreement,which can provide significant references for damage evaluation and disaster forecasting in high geostress underground powerhouse caverns.
基金Supported by the National Natural Science Foundation of China under Grant Nos.71071013,71001004,and 71071012Foundation of Beijing Jiaotong University under Grant No.2009JBZ012-2
文摘In this paper, we present a new ear-following model, i.e. comprehensive optimal velocity model (COVM), whose optimal velocity function not only depends on the following distance of the preceding vehicle, but also depends on the velocity difference with preceding vehicle. Simulation results show that COVM is an improvement over the previous ones theoretically. Then, the stability condition of the model is obtained by the linear stability analysis, which has shown that the model could obtain a bigger stable region than previous models in the phase diagram. Through the nonlinear analysis, the Burgers, Korteweg-de Vries (KdV) and modified KdV (mKdV) equations are derived for the triangular shock wave, the soliton wave, and the kink-antikink soliton wave. At the same time, numerical simulations are also carried out to show that the model could simulate these density waves.
文摘Wellbore stability analysis is a growing concern in oil industries. There are many parameters affecting the stability of a wellbore including geomechanical properties (e.g., elastic modulus, uni-axial compressive strength (UCS) and cohesion) and acting forces (e.g., field stresses and mud pressure). Accurate determination of these parameters is time-consuming, expensive and sometimes even impossible. This work offers a systematic sensitivity analysis to quantify the amount of each parameter’s effect on the stability of a wellbore. Maximum wellbore wall displacement is used as a stability factor to study the stability of a wellbore. A 3D finite difference method with Mohr model is used for the numerical modeling. The numerical model is verified against an analytical solution. A dimensionless sensitivity factor is developed in order to compare the results of various parameters in the sensitivity analysis. The results show a different order of importance of parameters based on rock strength. The most sensitive properties for a weak rock are the maximum horizontal stress, internal friction angle and formation pressure, respectively, while for a strong rock, the most sensitive parameters are the maximum horizontal stress, mud pressure and pore pressure, respectively. The amount of error in wellbore stability analysis inflicted by the error in estimation of each parameter was also derived.
基金supported by the National Basic Research Program of China (No.2010CB226805)the National Natural Science Foundation of China (Nos.50874103 and 50974115)+1 种基金the Natural Science Foundation of Jiangsu Province (No.KB2008135)the State Key Laboratory Fund (No.SKLGDUEK 0905)
文摘We adopt the concept of generalized plane strain to model a roadway in a stress field.This can avoid limitations caused by simplifying the stress analysis as plane strain.FLAC3D was used to investigate the maximum tensile stress and displacement of a roadway in a known stress field for angles,α,between the roadway axial direction and the maximum principal stress of 0°,30°,45°,60° and 90°.This theory was applied to the analysis of an engineering case.The results indicate that stress and displacement of the surrounding rock increase as the angle,α,increases.This provides some significant guidance for a reasonable layout of roadways in a known stress field.
基金The National Natural Science Foundation of China(Grants Nos.51309089,41472272 and 11202063)the National Key Technology R&D Program(Grant No.2013BAB06B00)+1 种基金the Natural Science Foundation of Jiangsu Province(Grant No.BK20130846)the Fundamental Research Funds for the Central Universities(Grant No.2015B06014)supported this work
文摘Based on the principle of 3D particle flow code,a numerical landslide run-out model is presented to simulate the failure process of the Zhenggang landslide(in southwestern China) under the effect of water after a rainfall.The relationship between the micro-mechanical parameters and the macro-shear strength of the grain material is determined through numerical calibrations.Then the rainfall effect is considered in numerical simulations and rain-induced sliding processes are performed,which help us to discuss the mechanism of deformation and failure of this landslide together with field observations.It shows the Zhenggang landslide would most likely be activated in Zone I and would gain momentum in Zone II.In order to prevent the potential disaster,a tailing dam is advised to be designed about 175 m downstream from the current landslide boundary of Zone II.Verified by field observations,the presented landslide model can reflect the failure mechanism after rainfall.It can also provide a method to predict the potential disaster and draft disaster prevention measures.
基金Supported by the International Science and Technology Cooperation Projects(2009DFA71840)Basic Research Business Projects of China Academy of Safety Science and Technology(2009JBKY07)
文摘According to fluid dynamics analysis during the fire, the criteria k-ε two-equation model for solving three-dimensional turbulence was determined, the pollutants generated in the fire disaster were set by adopting Mixture multiphase flow, and the SIMPLE algorithm was used for solving on the basis of comprehensive consideration on the heat radia- tion and components transmission during fire. By simulating the airflow flowing state inside the tunnel during fire disaster of downward ventilation, drift ventilation, and ascensional ventilation, respectively, with regard to the actual situation of No.l, No.3, and No.5 belt roadway in Kongzhuang Coal Mine, the velocity vector distributions of pollutants under different inlet air volumes were obtained, and the damage degree and influential factors of disaster were also clear, which is helpful to control and avoid disaster during belt roadway fire.
文摘In order to study the influence of depth-thickness ratio on bedding slope stability, whose sliding surface is flexural concave in shape under mining conditions, this paper aims to study the characteristics ofdeformarion and damage of bedding sliding with depth-thickness ratios of 200:1,150:1,120:1,100:1 and 50:1 by adopting numerical simulation analysis software combined with laboratory-made "under the influence of mining variable sliding surface slope similar simulation test bed", and to propose identification methods for slope stability under the infuence of mining. The results show that mining activities under the slope reduce slope stability. With a decrease in the mining depth ratio, the influence of mining on the slope increases gradually, and the damage to the slope gradually expands, the stability of the slope grad- ually reduces, fracture occurs on the slope toe and the central fissure gradually develops to the surface, and reaches slide threshold when the depth-thickness ratio is 50:1.
基金supported by the National Natural Science Foundation of China (Nos. 50820125405, 50909013 and 50804006)the National Basic Research Program (973) of China (No. 2007CB209404)
文摘The volume of influence of excavation at the right bank slope of Dagangshan Hydropower Station, southwest China, is essentially determined from microseismic monitoring, numerical modeling and conventional measurements as well as in situ observations. Microseismic monitoring is a new application technique for investigating microcrackings in rock slopes. A micro- seismic monitoring network has been systematically used to monitor rock masses unloading relaxation due to continuous exca- vation of rock slope and stress redistribution caused by dam impoundment later on, and to identify and delineate the potential slippage regions since May, 2010. An important database of seismic source locations is available. The analysis of microseismic events showed a particular tempo-spatial distribution. Seismic events predominantly occurred around the upstream slope of 1180 m elevation, especially focusing on the hanging wall of fault XL316-1. Such phenomenon was interpreted by numerical modeling using RFPA-SRM code (realistic failure process analysis-strength reduction method). By comparing microseismic activity and results of numerical simulation with in site observation and conventional measurements results, a strong correlation can he obtained between seismic source locations and excavation-induced stress distribution in the working areas. The volume of influence of the rock slope is thus determined. Engineering practices show microseismic monitoring can accurately diagnose magnitude, intensity and associated tempo-spatial characteristics of tectonic activities such as faults and unloading zones. The integrated technique combining seismic monitoring with numerical modeling, as well as in site observation and conventional surveying, leads to a better understanding of the internal effect and relationship between microseismic activity and stress field in the right bank slope from different perspectives.
基金supported by the National Natural Science Foundation of China(Grant Nos.91216203 and 91216304)
文摘The configurations of near space hypersonic flying vehicles are considerably different from those of conventional aircrafts.Their configurations are relatively slender;hence their moment of inertia around the longitudinal axis is much smaller than those around the other two axes,resulting in strong coupling of rotations around the three axes.Thus,the stability analysis of rolling motion for such flying vehicles is more complicated than those for conventional aircrafts,and there is no available result of stability analysis which can readily be applied to such cases.This paper is mainly concerned with the stated problem.Considering the practical situation,our investigation is targeted a slightly simpler problem,namely the rolling stability of flying vehicle under known pitching motion.The stability criterion of rolling motion is obtained with and without lateral motions.We also conducted numerical simulation for the pitching-rolling coupled motions of flying vehicles by solving Navier-Stokes equations coupled with dynamic equations of flight.The results of simulation agree well with those of theoretical analysis and experiments.
文摘Ratio-dependent predator prey models are favored by many animal ecologists recently as more suitable ones for predator-prey interactions where predation involves searching process. In this paper, a ratio-dependent predator prey model with stage structure and time delay for prey is proposed and analyzed. In this model, we only consider the stage structure of immature and mature prey species and not consider the stage structure of predator species. We assume that the predator only feed on the mature prey and the time for prey from birth to maturity represented by a constant time delay. At first, we investigate the permanence and existence of the proposed model and sufficient conditions are derived. Then the global stability of the nonnegative equilibria are derived. We also get the sufficient criteria for stability switch of the positive equilibrium. Finally, some numerical simulations are carried out for supporting the analytic results.
文摘This paper deals with the stability analysis to a three-species food chain model with crossdiffusion, the results of which show that there is no Turing instability but crossdiffusion makes the model instability possible. We then show that the spatial patterns are spotted patterns by using numerical simulations. In order to understand why the spatial patterns happen, the existence of the nonhomogeneous steady states is investigated. Finally, using the Leray-Schauder theory, we demonstrate that cross-diffusion creates nonhomogeneous stationary patterns.
文摘We propose and analyze mathematical models to study the dynamics of smoking behavior under the influence of educational programs and also individual's determination to quit smoking. We establish the positivity and boundedness of the solutions in a biologically feasible region. A threshold value responsible for persistence of smoking is obtained and stability analysis on models is performed. We find that determination alone is not enough to eradicate smoking but it can reduce the prevalence of smoker population. Whereas the increase in education can possibly eradicate it. We performed numerical simulation for representative set of parameters to verify and discuss results obtained analytically.
文摘In this work, we investigate the dynamical behavior of a fractional-order toxin producing on a phytoplankton-zooplankton (TPPZ) system with nutrient cycling. We propose a mathematical system to model this situation. All the feasible equilibria of the system are obtained and the conditions for the existence of the equilibriums are determined. Local stability analysis of the TPPZ is studied by using the fractional Routh-Hurwitz stability conditions. Numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings.