Study on Soil Erosion Model Under Different Slopes in Southwest Karst Mountain Area

The aim was to further research soil erosion characteristics and accurately predict soil erosion amount in karst areas. Based on field surveys and research achievements available, yellow soils, which are widely distributed, were chosen as test soil samples and slope, rain intensity, vegetation coverage and bare-rock ratio were taken as soil erosion factors. Artificial rain simulation instruments （needle-type） were made use of to simulate correlation of rain intensity, vegetation coverage, and bare-rock ratio with soil erosion quantity. Furthermore, multiple-factor linear regression analysis, stepwise regression analysis and multiple-factor non-linear regression analy- sis were made to establish a multiple-factor formula of soil erosion modulus with dif- ferent slopes and select regression models with high correlation coefficients. The re- sults show that a non-linear regression model reached extremely significant level or significant level （0.692〈FF〈0.988） and linear regression model achieved significant lev- el （0.523〈FF〈0.634）. The effects of erosion modulus changed from decreasing to in- creasing and the erosion factors from high to low were rain intensity, vegetation cov- erage and bare-rock ratio when slope gradient was at 6~, 16~, 26~ and 36~. The mod- el is of high accuracy for predicting gentle slope and abtupt slope, which reveals correlation of erosion modulus with erosion factors in karst areas.

Modeling Soil Organic Carbon Storage and Its Dynamics in Croplands of China

Soil organic carbon （SOC） is one of the centre issues related to not only soil fertility but also environmental safety. Assessing SOC dynamics in croplands has been a challenge in China for long due to the lack of appropriate methodologies and data sources. As an alternative approach for studying SOC dynamics, process-based models are adopted to meet the needs. In this paper, a process-based model, DeNitrification-DeComposition （DNDC）, was applied to quantify the SOC storage and the spatial distribution in croplands of China in 2003, with the support of a newly compiled county-level soil/ climate/land use database. The simulated results showed that the total SOC storage in the top layer （0-30 cm） of the 1.18 × 10^8 ha croplands of China is 4.7-5.2 Pg C in 2003 with an average value of 4.95 Pg C. The SOC storage in the northeastern provinces （1.3 Pg C） accounts for about 1/4 of the whole national totals due to their dominantly fertile soils with high organic matter content. SOC density ranges from 3.9 to 4.4 kg C m 2, with an average of 4.2 kg C m^-2, a level is much lower than the world average level. The model results also indicated that high rates of SOC losses occurred in the croplands with the most common cropping patterns in China as like single soybean 〉 maize 〉 paddy 〉 cotton 〉 winter wheat and corn rotation. The results reported in this paper showed that there was still a great potential for improving SOC status in most croplands of China by adopting proper farming practices and land-use pattern. Therefore, long-term policy to protect SOC is urgently needed.

The Numerical Scheme Development of a Simplified Frozen Soil Model

In almost all frozen soil models used currently, three variables of temperature, ice content and moisture content are used as prognostic variables and the rate term, accounting for the contribution of the phase change between water and ice, is shown explicitly in both the energy and mass balance equations. The models must be solved by a numerical method with an iterative process, and the rate term of the phase change needs to be pre-estimated at the beginning in each iteration step. Since the rate term of the phase change in the energy equation is closely related to the release or absorption of the great amount of fusion heat, a small error in the rate term estimation will introduce greater error in the energy balance, which will amplify the error in the temperature calculation and in turn, cause problems for the numerical solution convergence. In this work, in order to first reduce the trouble, the methodology of the variable transformation is applied to a simplified frozen soil model used currently, which leads to new frozen soil scheme used in this work. In the new scheme, the enthalpy and the total water equivalent are used as predictive variables in the governing equations to replace temperature, volumetric soil moisture and ice content used in many current models. By doing so, the rate terms of the phase change are not shown explicitly in both the mass and energy equations and its pre-estimation is avoided. Secondly, in order to solve this new scheme more functionally, the development of the numerical scheme to the new scheme is described and a numerical algorithm appropriate to the numerical scheme is developed. In order to evaluate the new scheme of the frozen soil model and its relevant algorithm, a series of model evaluations are conducted by comparing numerical results from the new model scheme with three observational data sets. The comparisons show that the results from the model are in good agreement with these data sets in both the change trend of variables and their magnitude values, and the new scheme, together with the algorithm, is more efficient and saves more computer time.

Modeling the contribution of abiotic exchange to CO_2 flux in alkaline soils of arid areas

Recent studies on alkaline soils of arid areas suggest a possible contribution of abiotic exchange to soil CO2 flux(Fc).However,both the overall contribution of abiotic CO2 exchange and its drivers remain unknown.Here we analyzed the environmental variables suggested as possible drivers by previous studies and constructed a function of these variables to model the contribution of abiotic exchange to Fc in alkaline soils of arid areas.An automated flux system was employed to measure Fc in the Manas River Basin of Xinjiang Uygur autonomous region,China.Soil pH,soil temperature at 0–5 cm(Ts),soil volumetric water content at 0–5 cm(θs)and air temperature at10 cm above the soil surface(Tas)were simultaneously analyzed.Results highlight reduced sensitivity of Fc to Ts and good prediction of Fc by the model Fc=R10Q10(Tas–10)/10+r7q7(pH–7)+λTas+μθs+e which represents Fc as a sum of biotic and abiotic components.This presents an approximate method to quantify the contribution of soil abiotic CO2 exchange to Fc in alkaline soils of arid areas.

Vortex-Induced Vibrations of A Free-Spanning Pipe Based on A Nonlinear Hysteretic Soil Model at the Shoulders

The pipe-soil interactions at shoulders can significantly affect the vortex-induced vibrations (VIV) of free-spanning pipes in the subsea. In this paper, the seabed soil reacting force on the pipe is directly calculated with a nonlinear hysteretic soil model. For the VIV in the middle span, a classic van der Pol wake oscillator is adopted. Based on the Euler-Bernoulli beam theory, the vibration equations of the pipe are obtained which are different in the middle span and at the two end shoulders. The static configuration of the pipe is firstly calculated and then the VIV is simulated.The present model is validated with the comparisons of VIV experiment, pipe-soil interaction experiment and the simulation results of VIV of free-spanning pipes in which the seabed soil is modelled with spring-dashpots. With the present model, the influence of seabed soil on the VIV of a free-spanning pipe is analyzed. The parametric studies show that when the seabed soil has a larger suction area, the pipe vibrates with smaller bending stresses and is safer.While with the increase of the shear strength of the seabed soil, the bending stresses increase and the pipe faces more danger.

Modeling the triaxial behavior of riverbed and blasted quarried rockfill materials using hardening soil model

Riverbed modeled rockfill material from Noa Dehing dam project, Arunachal Pradesh, India and blasted quarried modeled rockfill material from Kol dam project, Himachal Pradesh, India were considered for this research. Riverbed rockfill material is rounded to sub-rounded and quarried rockfill material is angular to sub-angular in shape. Prototype rockfill materials were modeled into maximum particle size （dmax） of 4.75 mm, 10 mm, 19 mm, 25 mm, 5O mm and 80 mm for testing in the laboratory. Consolidated drained triaxial tests were conducted on modeled rockfill materials with a specimen size of 381 mm in diameter and 813 mm in height to study the stress-strain-volume change behavior for both rockfill materials. Index properties, i.e. uncompacted void content （UVC） and uniaxial compressive strength （UCS）, were determined for both rockfill materials in association with material parameters. An elasto- plastic hardening soil （HS） constitutive model was used to predict the behavior of modeled rockfill materials. Comparing the predicted and observed stress-strain-volume change behavior, it is found that both observed and predicted behaviors match closely. The procedures were developed to predict the shear strength and elastic parameters of rockfill materials using the index properties, i.e. UCS, UVC and relative density （RD）, and predictions were made satisfactorily. Comparing the predicted and experi- mentally determined shear strengths and elastic parameters, it is observed that both values match closely. Then these procedures were used to predict the elastic and shear strength parameters of large- size prototype rockfill materials. Correlations were also developed between index properties and ma- terial strength parameters （dilatancy angle, ~, and initial void ratio, einit, required for HS model） of modeled rockfill materials and the same correlations were used to predict the strength parameters for the prototype rockfill materials. Using the predicted material parameters, the stress-strain-volume change behavior of prototype rockfill material was predicted using elastoplastic HS constitutive model. The advantage of the proposed methods is that only index properties, i.e. UCS, UVC, RD, modulus of elasticity of intact rock, Eir, and Poisson＇s ratio of intact rock, Vir, are required to determine the angle of shearing resistance, Ф, modulus of elasticity, E50^ref and Poisson＇s ratio, , of rockfill materials, and there is E50＆ref no need of triaxial testing. It is believed that the proposed methods are more realistic, economical, and can be used where large-size triaxial testing facilities are not available.

Application of transparent soil model tests to study the soil-rock interfacial sliding mechanism

When transparent soil technology is used to study the displacement of a slope, the internal deformation of the slope can be visualized. We studied the sliding mechanism of the soil-rock slope by using transparent soil technology and considering the influence of the rock mass Barton joint roughness coefficient, angle of the soil mass, angle of the rock mass and soil thickness factors on slope stability. We obtained the deformation characteristics of the soil and rock slope with particle image velocimetry and the laser speckle technique. The test analysis shows that the slope sliding can be divided into three parts: displacements at the top, the middle, and the bottom of the slope; the decrease in the rock mass Barton joint roughness coefficient, and the increase in soil thickness, angles of the rock mass and soil mass lead to larger sliding displacements. Furthermore, we analyzed the different angles between the rock mass and soil thickness. The test result shows that the displacement of slope increases with larger angle of the rock mass. Conclusively, all these results can help to explain the soil-rock interfacial sliding mechanism.

An improved Mesri creep model for unsaturated weak intercalated soils

The weak intercalated soils in redbed soft rocks of Badong formation have obvious creep characters. In order to predict the unsaturated creep behaviors of weak intercalated soils, an unsaturated creep model was established based on the unsaturated creep tests of weak intercalated soils by using GDS triaxial apparatus. The results show that the creep behaviors of intercalated soils are apparent and significantly affected by matric suction. Based on this, an empirical Mesri creep model for intercalated soils under varying matric suctions was built. The fitting results show that the parameters Ed and m of this model are in good power relations with matric suction s and stress level Dr, respectively. An improved Mesri creep model was established involving stress-matric suction-strain-time, which is more precise than the Mesri creep model in predicting the unsaturated creep behaviors of weak intercalated soils.

Effectiveness of Fiber Bragg Grating monitoring in the centrifugal model test of soil slope under rainfall conditions

Centrifugal model testsare playing an increasingly importantrolein investigating slope characteristics under rainfall conditions. However, conventional electronic transducers usually fail during centrifugal model tests because of the impacts of limitedtest space, high centrifugal force, and presence of water, with the result that limited valid data is obtained. In this study, Fiber Bragg Grating(FBG) sensing technology is employed in the design and development of displacement gauge, an anchor force gauge and an anti-slide pile moment gauge for use on centrifugal model slopes with and without a retaining structure. The two model slopes were installed and monitored at a centrifugal acceleration of 100 g. The test results show that the sensors developed succeed in capturing the deformation and retaining structure mechanical response of the model slopes during and after rainfall. The deformation curvefor the slope without retaining structure shows a steepresponse that turns gradualfor the slope with retaining structure. Importantly, for the slope with the retaining structure, results suggest that more attention be paid to increase of anchor force and antislide pile moment during rainfall. This study verifies the effectiveness of FBG sensing technology in centrifuge research and presents a new and innovative method for slope model testing under rainfall conditions.

Observation and modeling on irregular purple soil water infiltration process

The infiltration process is a critical link between surface water and groundwater. In this research, a specific device to observe infiltration processes in homogeneous and heterogeneous soils with triangular and inverted triangular profiles was designed, and the Green-Ampt model was employed for the process simulation. The results indicate that(1) the wetting front in coarse texture soils transports faster than in fine texture soils;(2) for the homogeneous case, the wetting front in triangularshaped soils transports faster than the inverted triangular type, but the triangular-shaped soils show a lower infiltration rate;(3) in the initial step, the wetting front in triangular-shaped soils shows higher transport speed, but depicts lower speed with increase in the time;(4) both the wetting front and infiltration rate show a significant exponential relation with the time. From these findings, an empirical model was developed which agrees well with the observed data and provides a useful method for this field of soil research.

An analytical p-y curve method based on compressive soil pressure model in sand soil

With the high-quality development of urban buildings,higher requirements are come up with for lateral bearing capacity of laterally loaded piles.Consequently,a more accurate analysis to predict the lateral response of the pile within an allowable displacement is an important issue.However,the current p-y curve methods cannot fully take into account the pile-soil interaction,which will lead to a large calculation difference.In this paper,a new analytical p-y curve is established and a finite difference method for determining the lateral response of pile is proposed,which can consider the separation effect of pile-soil interface and the coefficient of circumferential friction resistance.In particular,an analytical expression is developed to determine the compressive soil pressure by dividing the compressive soil pressure into two parts:initial compressive soil pressure and increment of compressive soil pressure.In addition,the relationship between compressive soil pressure and horizontal displacement of the pile is established based on the reasonable assumption.The correctness of the proposed method is verified through four examples.Based on the verified method,a parametric analysis is also conducted to investigate the influences of factors on lateral response of the pile,including internal friction angle,pile length and elastic modulus of pile.

Modeling Reforestation’s Role in Climate-Proofing Watersheds from Flooding and Soil Erosion

The mitigation potential of reforestation for offsetting the deleterious effects of increased flooding and soil erosion projected to occur in Atlantic Canada through future climate change was investigated. Modelling determined a strong but non-linear relationship between extent of vegetative cover and runoff volume and discharge rate for a Nova Scotian watershed, suggesting that reforestation will reduce, but not completely prevent, flooding. Predicted erosion rates were found to be progressively reduced in relation to the extent of upland reforestation. Of three scenarios examined in which 60%, 65%, and 85% of the entire watershed are randomly reforested, only the latter would reduce the elevated erosion expected to occur through climate change back to present-day existing levels. Additional modelling revealed that comparable mitigation of soil erosion can ensue through implementation of 70 m streamside buffer strips, which would only take up 19% of the total surface area. Prioritizing riparian zones for reforestation will therefore subsume less of the overall productive land area and therefore enact a less severe socio-economic impact on agriculture and forestry.

Dynamic Monitoring of Plant Cover and Soil Erosion Using Remote Sensing, Mathematical Modeling, Computer Simulation and GIS Techniques

Dynamic monitoring of plant cover and soil erosion often uses remote sensing data, especially for estimating the plant cover rate (vegetation coverage) by vegetation index. However, the latter is influenced by atmospheric effects and methods for correcting them are still imperfect and disputed. This research supposed and practiced an indirect, fast, and operational method to conduct atmospheric correction of images for getting comparable vegetation index values in different times. It tries to find a variable free from atmospheric effects, e.g., the mean vegetation coverage value of the whole study area, as a basis to reduce atmospheric correction parameters by establishing mathematical models and conducting simulation calculations. Using these parameters, the images can be atmospherically corrected. And then, the vegetation index and corresponding vegetation coverage values for all pixels, the vegetation coverage maps and coverage grade maps for different years were calculated, i.e., the plant cover monitoring was realized. Using the vegetation coverage grade maps and the ground slope grade map from a DEM to generate soil erosion grade maps for different years, the soil erosion monitoring was also realized. The results show that in the study area the vegetation coverage was the lowest in 1976, much better in 1989, but a bit worse again in 2001. Towards the soil erosion, it had been mitigated continuously from 1976 to 1989 and then to 2001. It is interesting that a little decrease of vegetation coverage from 1989 to 2001 did not lead to increase of soil erosion. The reason is that the decrease of vegetation coverage was chiefly caused by urbanization and thus mainly occurred in very gentle terrains, where soil erosion was naturally slight. The results clearly indicate the details of plant cover and soil erosion change in 25 years and also offer a scientific foundation for plant and soil conservation.

Use of Kostiakov’s Infiltration Model on Michael Okpara University of Agriculture, Umudike Soils, Southeastern, Nigeria

The main purpose of this study is to obtain the water infiltration parameters of the soils of Michael Okpara University of Agriculture, Umudike. This could be used in simulating infiltration for these soils when designing irrigation projects, thereby saving time and cost of field measurement. Field measurements of infiltration were first made using a double ring infiltrometer. The test lasted for 180 mins in each location. Infiltration values ranged from 0.03 cm/min to 0.1 cm/min. The highest value was obtained in the Forest Block. Kostiakov’s infiltration model was then applied on the field data in order to determine the soils’ infiltration parameters and equations. The model empirical constants or parameters obtained were “m” and “n”. For “m” the values were: 0.53 for the soil of Forest Block, 0.42 for Poultry block, 0.50 for P.G. block, 0.41 for the soils of Staff School and Guest House. The corresponding “n” values were: 1.37, 1.12, 0.37, 1.79, and 1.38. Infiltration equations: 0.4It1.38, 0.4lt1.79, 0.42t1.12, and 0.53t1.37 were determined for the locations. These were used to simulate data which were evaluated by comparing them with the field data. The two data sets showed closed relationships. This implied that the model could be used to simulate water infiltration during irrigation projects in the farms of Michael Okpara University of Agriculture, Umudike.

Basic Soil Productivity of Spring Maize in Black Soil Under Long-Term Fertilization Based on DSSAT Model

Increasing basic farmland soil productivity has significance in reducing fertilizer application and maintaining high yield of crops. In this study, we defined that the basic soil productivity （BSP） is the production capacity of a farmland soil with its own physical and chemical properties for a specific crop season under local environment and field management. Based on 22-yr （1990-2011） long-term experimental data on black soil （Typic hapludoll） in Gongzhuling, Jilin Province, Northeast China, the decision support system for an agro-technology transfer （DSSAT）-CERES-Maize model was applied to simulate the yield by BSP of spring maize （Zea mays L.） to examine the effects of long-term fertilization on changes of BSP and explore the mechanisms of BSP increasing. Five treatments were examined： （1） no-fertilization control （control）; （2） chemical nitrogen, phosphorus, and potassium （NPK）; （3） NPK plus farmyard manure （NPKM）; （4） 1.5 time of NPKM （1.5NPKM） and （5） NPK plus straw （NPKS）. Results showed that after 22-yr fertilization, the yield by BSP of spring maize significantly increased 78.0, 101.2, and 69.4% under the NPKM, 1.5NPKM and NPKS, respectively, compared to the initial value （in 1992）, but not significant under NPK （26.9% increase） and the control （8.9% decrease）. The contribution percentage of BSP showed a significant rising trend （P〈0.05） under 1.5NPKM. The average contribution percentage of BSP among fertilizations ranged from 74.4 to 84.7%, and ranked as 1.5NPKM〉NPKM〉NPK〉NPKS, indicating that organic manure combined with chemical fertilizers （I.5NPKM and NPKM） could more effectively increase BSP compared with the inorganic fertilizer application alone （NPK） in the black soil. This study showed that soil organic matter （SOM） was the key factor among various fertility factors that could affect BSP in the black soil, and total N, total P and/or available P also played important role in BSP increasing. Compared with the chemical fertilization, a balanced chemical plus manure or straw fertilization （NPKM or NPKS） not only increased the concentrations of soil nutrient, but also improved the soil physical properties, and structure and diversity of soil microbial population, resulting in an iincrease of BSP. We recommend that a balanced chemical plus manure or straw fertilization （NPKM or NPKS） should be the fertilization practices to enhance spring maize yield and improve BSP in the black soil of Northeast China.

Modeling spatial and temporal change of soil erosion based on multi-temporal remotely sensed data

In order to monitor the pattern, distribution, and trend of land use/cover change （LUCC） and its impacts on soil erosion, it is highly appropriate to adopt Remote Sensing （RS） data and Geographic Information System （GIS） to analyze, assess, simulate, and predict the spatial and temporal evolution dynamics. In this paper, multi-temporal Landsat TM/ETM＋ re- motely sensed data are used to generate land cover maps by image classification, and the Cellular Automata Markov （CA_Markov） model is employed to simulate the evolution and trend of landscape pattern change. Furthermore, the Re- vised Universal Soil Loss Equation （RUSLE） is used to evaluate the situation of soil erosion in the case study mining area. The trend of soil erosion is analyzed according to total/average amount of soil erosion, and the rainfall （R）, cover man- agement （C）, and support practice （P） factors in RUSLE relevant to soil erosion are determined. The change trends of soil erosion and the relationship between land cover types and soil erosion amount are analyzed. The results demonstrate that the CA_Markov model is suitable to simulate and predict LUCC trends with good efficiency and accuracy, and RUSLE can calculate the total soil erosion effectively. In the study area, there was minimal erosion grade and this is expected to con- tinue to decline in the next few years, according to our prediction results.

Modelling and mapping soil erosion potential in China

Soil erosion is an important environmental threat in China.However,quantitative estimates of soil erosion in China have rarely been reported in the literature.In this study,soil loss potential in China was estimated by integrating satellite images,field samples,and ground observations based on the Revised Universal Soil Loss Equation(RUSLE).The rainfall erosivity factor was estimated from merged rainfall data using Collocated CoKriging(ColCOK)and downscaled by geographically weighted regression(GWR).The Random Forest(RF)regression approach was used as a tool for understanding and predicting the relationship between the soil erodibility factor and a set of environment factors.Our results show that the average erosion rate in China is 1.44 t ha^(–1) yr^(–1).More than 60%of the territory in China is influenced by soil erosion limitedly,with an average potential erosion rate less than 0.1 t ha^(–1) yr^(–1).Other unused land and other forested woodlands showed the highest erosion risk.Our estimates are comparable to those of runoff plot studies.Our results provide a useful tool for soil loss assessments and ecological environment protections.

Simulation and Prediction of Soil Organic Carbon Dynamics in Jiangsu Province Based on Model and GIS Techniques

Based on the databases of soils, meteorology, crop production, and agricultural management, changes in the soil organic carbon (SOC) of agro ecosystems in Jiangsu Province were simulated by using a soil organic carbon model with a linkage of GIS. Four data sets of soil organic carbon measured from various field experiments in Jiangsu Province were used to validate the model. It was demonstrated that the model simulation in general agreed with the field measurements. Model simulation indicated that the SOC content in approximately 77% of the agricultural soils in Jiangsu Province has increased since the Second National Soil Survey completed in the early 1980s. Compared with the values in 1985, the SOC content in 2000 was estimated to increase by 1.03.0 g kg 1 for the north and the coastal areas of the province, and by 3.55.0 g kg 1 for the region of Tai Lake in the south. A slight decrease (about 0.51.5 g kg 1 ) was estimated for the central region of Jiangsu Province and the Nanjing Zhenjiang hilly area. Model prediction for 2010 A.D. under two scena rios, i.e., with 30 and 50% of the harvested crop straw incorporation, suggested that the SOC in Jiangsu Province would increase, and thus that the agricultural soils would have potential as organic carbon storage. The incorporation of crop straw into soils is of great benefit to increase soil carbon storage, consequently to benefit the control of the rise of atmospheric CO 2 concentration and to maintain the sustainable development of agriculture.

Prediction model for mercury transfer from soil to corn grain and its cross-species extrapolation

In this study the transfer characteristics of mercury（Hg） from a wide range of Chinese soils to corn grain（cultivar Zhengdan 958） were investigated. Prediction models were developed for determining the Hg bioconcentration factor（BCF） of Zhengdan 958 from soil, including the soil properties, such as p H, organic matter（OM） concentration, cation exchange capacity（CEC）, total nitrogen concentration（TN）, total phosphorus concentration（TP）, total potassium concentration（TK）, and total Hg concentration（THg）, using multiple stepwise regression analysis. These prediction models were applied to other non-model corn cultivars using a cross-species extrapolation approach. The results indicated that the soil p H was the most important factor associated with the transfer of Hg from soil to corn grain. Hg bioaccumulation in corn grain increased with the decreasing p H. No significant differences were found between two prediction models derived from different rates of Hg applied to the soil as HgCl2. The prediction models established in this study can be applied to other non-model corn cultivars and are useful for predicting Hg bioconcentration in corn grain and assessing the ecological risk of Hg in different soils.

A ^(210)Pb_(ex) mass balance model in cultivated soils in consideration of the radionuclide diffusion

The existing^(210)Pb_(ex)mass balance models for the assessment of cultivated soil erosion are based on an assumption that^(210)Pb_(ex)is quite evenly mixed within the plough layer.However,the amount of^(210)Pb_(ex)distributed in the soils below the plough depth,like a downward tail in the lower part of the^(210)Pb_(ex)profile,has been largely ignored.In fact,after the initial cultivation of undisturbed soils,^(210)Pb_(ex)will diffuse downward from plough layer to the plough pan layer due to the concentration gradient.Assuming^(210)Pb_(ex)inventory is constant,the depth distribution in the two layers of the cultivated soils will achieve a steady state after continuous cultivation for 10.37 years,when^(210)Pb_(ex)is evenly distributed in the soils of the plough layer with an exponential concentration decline with depth in the soils of the plough pan layer,and the^(210)Pb_(ex)concentration at any depth will be invariable with time.The work reported in this paper attempts to explain the formation of the^(210)Pb_(ex)tail in the soil profile below the plough depth by theoretical derivation of the^(210)Pb_(ex)depth distribution process in the two layers of the cultivated soils,propose a^(210)Pb_(ex)mass balance model considering^(210)Pb_(ex)diffusion based on the existing model,and discuss the influence of the^(210)Pb_(ex)tail to the existing model.