Inverse reliability analysis and design for tunnel face stability considering soil spatial variability

The traditional deterministic analysis for tunnel face stability neglects the uncertainties of geotechnical parameters,while the simplified reliability analysis which models the potential uncertainties by means of random variables usually fails to account for soil spatial variability.To overcome these limitations,this study proposes an efficient framework for conducting reliability analysis and reliability-based design(RBD)of tunnel face stability in spatially variable soil strata.The three-dimensional(3D)rotational failure mechanism of the tunnel face is extended to account for the soil spatial variability,and a probabilistic framework is established by coupling the extended mechanism with the improved Hasofer-Lind-Rackwits-Fiessler recursive algorithm(iHLRF)as well as its inverse analysis formulation.The proposed framework allows for rapid and precise reliability analysis and RBD of tunnel face stability.To demonstrate the feasibility and efficacy of the proposed framework,an illustrative case of tunnelling in frictional soils is presented,where the soil's cohesion and friction angle are modelled as two anisotropic cross-correlated lognormal random fields.The results show that the proposed method can accurately estimate the failure probability(or reliability index)regarding the tunnel face stability and can efficiently determine the required supporting pressure for a target reliability index with soil spatial variability being taken into account.Furthermore,this study reveals the impact of various factors on the support pressure,including coefficient of variation,cross-correlation between cohesion and friction angle,as well as autocorrelation distance of spatially variable soil strata.The results also demonstrate the feasibility of using the forward and/or inverse first-order reliability method(FORM)in high-dimensional stochastic problems.It is hoped that this study may provide a practical and reliable framework for determining the stability of tunnels in complex soil strata.

Stochastic analysis of excavation-induced wall deflection and box culvert settlement considering spatial variability of soil stiffness

In this study, a three-dimensional (3D) finite element modelling (FEM) analysis is carried out to investigate the effects of soil spatial variability on the response of retaining walls and an adjacent box culvert due to a braced excavation. The spatial variability of soil stiffness is modelled using a variogram and calibrated by high-quality experimental data. Multiple random field samples (RFSs) of soil stiffness are generated using geostatistical analysis and mapped onto a finite element mesh for stochastic analysis of excavation-induced structural responses by Monte Carlo simulation. It is found that the spatial variability of soil stiffness can be described by an exponential variogram, and the associated vertical correlation length is varied from 1.3 m to 1.6 m. It also reveals that the spatial variability of soil stiffness has a significant effect on the variations of retaining wall deflections and box culvert settlements. The ignorance of spatial variability in 3D FEM can result in an underestimation of lateral wall deflections and culvert settlements. Thus, the stochastic structural responses obtained from the 3D analysis could serve as an effective aid for probabilistic design and analysis of excavations.

On Spatial Variability and Distribution of Soil Nutrients in Different Nitraria tangutorum Bobr.Populations in Tsaidam Basin

In this paper,six important distribution areas of Nitraria tangutorum Bobr.in Tsaidam Basin were selected as research objects,to study spatial variability and distribution of soil nutrients in different N.tangutorum populations and analyze the relationship between soil nutrient contents and geographical location,by measuring soil pH and the contents of organic matter（OM）,total nitrogen（N）,total phosphorus（P）,total potassium（K）,hydrolysis N,available P and available K in soils.Results showed that：（1） soil nutrient contents among different populations showed significant spatial variability,and soil depth had a significant effect on soil nutrients contents,but the variation rules were not obvious.（2）Average pH and average contents of OM,total N,total P,total K,hydrolysis N,available P and available K in soils with different depths（0-15,15-30,30-45 cm） varied in the range of 8.37-9.21,3.34-20.68,0.18-1.21,0.35-0.75,16.12-22.04,5.13-553.28,1.10-52.54 and 103.83-562.28 mg/kg,respectively.（3） The analysis results of correlation between average values of pH and contents of nutrient indexes in soils with different depths（0-15,15-30,30-45 cm） showed that the correlation of these indexes were different.（4）OM and total N contents in soils with different depths（0-15,15-30,30-45 cm） all had a significant positive correlation with latitude and negative correlation with longitude and altitude,and the correlation of available P and available K contents in surface soils（0-15 cm） with latitude,longitude and altitude were significant positive,significant negative and significant negative,respectively;moreover,longitude and latitude also showed a significant impact on soil available K contents with the depth of 30-45 cm.In addition,comprehensive analysis result of nutrient contents showed that N.tangutorum populations in Huaitou Tala Town had the highest fertility,and the fertility levels of N.tangutorum populations in Chaka Town and Wulan Keke Town were relatively lower.

Spatial Variability of Nutrient Properties in Black Soil of Northeast China

A total of 1400 soil samples from the plow layer （0-20 cm） at an approximate interval of 5 km were collected in the autumn of 2002 over the entire black soil arable crops region to determine the spatial variability of seven variables, such as total organic matter content （OMC）, total N, total P, total K, alkali-dissolvable N （AN）, available P （AP） and available K （AK）, with classical statistics and geostatistical analysis across the entire black soil area in Northeast China. In nonsampled areas ordinary kriging was utilized for interpolation of estimated nutrient determinations. Classical statistics revealed highly significant （P ≤ 0.01） correlations with all seven of the soil properties, except for OMC with AP and total K with AK. In addition, using coefficients of variation, all soil properties, except for total K, were moderately variable. A geostatistical analysis indicated that structural factors, such as parent material, terrain, and water table, were the main causes of the spatial correlations. Strong spatial correlations were noted with OMC, total N, total P, AN, and AP, while they were moderate for total K and AK. The effective spatial autocorrelation of OMC, total N, total P, and AN ranged from 1 037 to 1353 km, whereas the ranges of total K, AP, and AK were only from 6 to 138 km. The fit of the experimental scmi-variograms to the theoretical models indicated that except for AN, kriging could successfully interpolate other six variables. Thns, the geostatistical method used on a large scale could accurately evaluate the spatial variability of most black soil nutrient properties in Northeast China.

Spatial variability and pattern analysis of soil properties in Dehui city, Jilin province

Based on regionalized variable theory, semivariograms of geo-statistics wereused to research the spatial variation of soil properties quantitatively. The results showed thatthe semivariogram of soil organic matter is best described by spherical model, the best model forsemivariograms of soil total N and available K is exponential models and that of available P belongsto linear with sill model. Those soil properties have different spatial correlations respectively,the lag of organic matter is the highest and that of available P is the lowest, the spatialcorrelation of N and available K belongs to moderate degree. Spatial heterogeneities are differenttoo, the degree of organic matter and total N are higher, the degree of available K is in the nextplace and that of available P is the lowest. Influenced by the shape, topography and soil of thestudy area, all isotropies of available P are obvious in all directions while anisotropies of othersare manifested. According to the analytical results, supported by GIS, Kriging and IDW methods areapplied to describe and analyze the spatial distribution of soil properties. The results indicatethat soil organic matter, total N and available K are distributed regularly from northeast tosouthwest, while available P is distributed randomly.

Spatial variability of soil organic carbon in the forestlands of northeast China

Soil organic carbon （SOC） is an effective indicator of soil fertility and productivity, and it varies spatially and temporally in relation to other soil properties. Spatial variability of SOC in the forestlands of northeast China was characterized using geostatistics. Soil samples at the depths of 0-20 era, 20-40 cm and 40-60 cm were collected from six- ty-three temporary plots to evaluate SOC concentration and density （SOCD） and other soil properties. We analyzed correlations between SOC and soil properties. Soil organic carbon concentrations were high. The total amount of C stored in soil （0-60 cm） was 16.23 kg·m-2 with the highest SOCD of 7.98 kg·m-2 in topsoil. Soil properties in most cases differed by horizon, suggesting different processes and effects in each horizon. Soil organic carbon had positive relationships with total N, P and K as well as readily available K, but did not show a significant posi- tive correlation with available P. Spatial factors including elevation, slope and aspect affected SOC distribution. Soil organic carbon at 0-60 cm had strong spatial autocorrelation with nugget/sill ratio of 5.7%, and moderate structured dependence was found at 0-20 cm, which indicated the existence of a highly developed spatial structure. Spatial distributionsof SOC concentration and SOCD were estimated using regres- sion-kriging, with higher prediction accuracy than ordinary kriging. The fractal dimension of SOC indicated the preferential pattern of SOC dis- tribution, with the greatest spatial heterogeneity and strongest spatial dependence in the northeast-southwest direction.

Reliability analysis of slopes considering spatial variability of soil properties based on efficiently identified representative slip surfaces

Slope reliability analysis considering inherent spatial variability(ISV)of soil properties is timeconsuming when response surface method(RSM)is used,because of the"curse of dimensionality".This paper proposes an effective method for identification of representative slip surfaces(RSSs)of slopes with spatially varied soils within the framework of limit equilibrium method(LEM),which utilizes an adaptive K-means clustering approach.Then,an improved slope reliability analysis based on the RSSs and RSM considering soil spatial variability,in perspective of computation efficiency,is established.The detailed implementation procedure of the proposed method is well documented,and the ability of the method in identifying RSSs and estimating reliability is investigated via three slope examples.Results show that the proposed method can automatically identify the RSSs of slope with only one evaluation of the conventional deterministic slope stability model.The RSSs are invariant with the statistics of soil properties,which allows parametric studies that are often required in slope reliability analysis to be efficiently achieved with ease.It is also found that the proposed method provides comparable values of factor of safety(FS)and probability of failure(Pf)of slopes with those obtained from direct analysis and lite rature.

Spatial Variability of Soil Chemical Properties in the Reclaiming Marine Foreland to Yellow Sea of China

Precise information about the spatial variability of soil properties is essential in developing site-specific soil management, such as variable rate application of fertilizers. In this study the sampling grid of 100 m × 100 m was established to collect 1 703 soil samples at the depth of 0-20 cm, and examine spatial patterns including 13 soil chemical properties （pH, OM, NH4^＋, P, K, Ca, Mg, S, B, Cu, Fe, Mn, and Zn） in a 1 760 ha rice field in Haifeng farm, China, from 6th to 22nd of April, 2006, before fertilizer application and planting. Soil analysis was performed by ASI （Agro Services International） and data were analyzed both statistically and geostatistically. Results showed that the contents of soil OM, NH4^＋, and Zn in Haifeng farm were very low for rice production and those of others were enough to meet the need for rice cultivation. The spatial distribution model and spatial dependence level for 13 soil chemical properties varied in the field. Soil Mg and B showed strong spatial variability on both descriptive statistics and geostatistics, and other properties showed moderate spatial variability. The maximum ranges for K, Ca, Mg, S, Cu and Mn were all - 3 990.6 m and the minimum ranges for soil pH, OM, NH4^＋, P, Fe, and Zn ranged from 516.7 to 1 166.2 m. Clear patchy distribution of N, P, K, Mg, S, B, Mn, and Zn were found from their spatial distribution maps. This proved that sampling strategy for estimating variability should be adapted to the different soil chemical properties and field management. Therefore, the spatial variability of soil chemical properties with strong spatial dependence could be readily managed and a site-specific fertilization scheme for precision farming could be easily developed.

Delineation of Site-Specific Management Zones Based on Temporal and Spatial Variability of Soil Electrical Conductivity

A coastal saline field of 10.5 ha was selected as the study site and 122 bulk electrical conductivity (ECb) measurements were performed thrice in situ in the topsoil (0-20 cm) across the field using a hand held device to assess the spatial variability and temporal stability of the distribution of soil electrical conductivity (EC), to identify the management zones using cluster analysis based on the spatiotemporal variability of soil EC, and to evaluate the probable potential for site-specific management in coastal regions with conventional statistics and geostatistical techniques. The results indicated high coefficients of variation for topsoil salinity over all the three samplings. The spatial structure of the salinity variability remained relatively stable with time. Kriged contour maps, drawn on the basis of spatial variance structure of the data, showed the spatial trend of the salinity distribution and revealed areas of consistently high or consistently low salinity, while a temporal stability map indicated stable and unstable regions. On the basis of the spatiotemporal characteristics, cluster analysis divided the site into three potential management zones, each with different characteristics that could have an impact on the way the field was managed. On the basis of the clearly defined management zones it was concluded that coastal saline land could be managed in a site-specific way.

Small-Scale Spatial Variability of Soil Nutrients and Vegetation Properties in Semi-Arid Northern China

A field experiment was conducted at Kezuohouqi County, Inner Mongolia Autonomous Region of China, which was located on the southeastern edge of the Horqin Sandy Land, to study the spatial variability of soil nutrients for a smallscale, nutrient-poor, sandy site in a semi-arid region of northern China; to investigate whether or not there were 'islands of fertility' at the experimental site; and to determine the key nutrient elements that sustained ecosystem stability. Results obtained from geostatistical analysis indicated that the spatial distribution pattern of soil total nitrogen (STN) was far different from those of soil organic matter (SOM), total phosphorus (STP), and total potassium (STK). Compared to SOM, STP, and STK, STN had a lower structural heterogeneity ratio and a longer range, while other elements were all similar. In addition, STN had an isotropic spatial structure, whereas the others had an anisotropic spatial structure. The spatial structure patterns of herbage species, cover,and height also differed, indicating that spatial variability was subjected to different ecological factors. Differences in the spatial variability patterns among soil nutrients and vegetation properties showed that soil nutrients for a small-scale were not the primary limiting factors that influenced herbage spatial distribution patterns. Incorporating spatial distribution patterns of tree species, namely, Pinus sylvestris var. mongolica Litv. and shrub Lespedeza bicolor Turcz. in a research plot and using fractal dimension,SOM, STP, and STK were shown to contribute to the 'islands of fertility' phenomenon, however STN was not, possibly meaning that nitrogen was a key limiting element. Therefore, during restoration of similar ecosystems more attention should be given to soil nitrogen.

Spatial variability of organochlorine pesticides (DDTs and HCHs) in surface soils from the alluvial region of Beijing,China

The spatial variability in the concentrations of 1,2,3,4,5,6-hexachlorocyclohexane （HCH） and 1,1,1-trichloro-2,2-bis-（p-chloro- phenyl） ethane （DDT） in surface soils was studied on the basis of the analysis of 131 soil samples collected from the surface layer （0-20 cm depth） of the alluvial region of Beijing, China. The concentrations of total HCHs （including α-,β-, γ-, and δ-isomers） and total DDTs （including p,p＇-DDT, p,p＇-DDD, p,p＇-DDE, and o,p＇-DDT） in the surface soils tested were in the range from nondetectable to 31.72 μg/kg dry soil, with a mean value of 0.91, and from nondetectable to 5910.83 μg/kg dry soil, with a mean value of 32.13, respectively. It was observed that concentrations of HCHs in all soil samples and concentrations of DDTs in 112 soil samples were much lower than the first grade （50 μg/kg） permitted in ＂Environment quality standard for soils in China （GB 15618-1995）＂. This suggests that the pollution due to organochlorine pesticides was generally not significant in the farmland soils in the Beijing alluvial region. In this study, the spatial distribution and trend of HCHs and DDTs were analyzed using Geostatistical Analyst and GS＋（513）. Spatial distribution indicated how these pesticides had been applied in the past. Trend analysis showed that the concentrations of HCHs, DDTs, and their related metabolites followed an obvious distribution trend in the surface soils from the alluvial region of Beijing.

Spatial Variability of Soil Cation Exchange Capacity in Hilly Tea Plantation Soils Under Different Sampling Scales

Studies on the spatial variability of the soil cation exchange capacity （CEC） were made to provide a theoretical basis for an ecological tea plantation and management of soil fertilizer in the tea plantation. Geostatistics were used to analyze the spatial variability of soil CEC in the tea plantation site on Mengding Mountain in Sichuan Province of China on two sampling scales. It was found that, （1） on the small scale, the soil CEC was intensively spatially correlative, the rate of nugget to sill was 18.84% and the spatially dependent range was 1 818 m, and structural factors were the main factors that affected the spatial variability of the soil CEC; （2） on the microscale, the soil CEC was also consumingly spatially dependent, and the rate of nugget to sill was 16.52%, the spatially dependent range was 311 m, and the main factors affecting the spatial variability were just the same as mentioned earlier. On the small scale, soil CEC had a stronger anisotropic structure on the slope aspect, and a weaker one on the lateral side. According to the ordinary Kriging method, the equivalence of soil CEC distributed along the lateral aspect of the slope from northeast to southwest, and the soil CEC reduced as the elevation went down. On the microscale, the anisotropic structure was different from that measured on the small scale. It had a stronger anisotropic structure on the aspect that was near the aspect of the slope, and a weaker one near the lateral aspect of the slope. The soil CEC distributed along the lateral aspect of the slope and some distributed in the form of plots. From the top to the bottom of the slope, the soil CEC increased initially, and then reduced, and finally increased.

Spatial variability of soil organic carbon and total nitrogen in the hilly red soil region of Southern China

To obtain accurate spatial distribution maps of soil organic carbon(SOC)and total nitrogen(TN)in the Hetian Town in Fujian Province,China,soil samples from three depths(0–20,20–40,and 40–60 cm)at 59 sampling sites were sampled by using traditional analysis and geostatistical approach.The SOC and TN ranged from 2.26 to 47.54 g kg-1,and from 0.28 to 2.71 g kg-1,respectively.The coefficient of variation for SOC and TN was moderate at 49.02–55.87%for all depths.According to the nuggetto-sill ratio values,a moderate spatial dependence of SOC content and a strong spatial dependence of TN content were found in different soil depths,demonstrating that SOC content was affected by both extrinsic and intrinsic factors while TN content was mainly influenced by intrinsic factors.Indices of cross-validation,such as mean error,mean standardized error,were close to zero,indicating that ordinary kriging interpolation is a reliable method to predict the spatial distribution of SOC and TN in different soil depths.Interpolation using ordinary kriging indicated the spatial pattern of SOC and TN were characterized by higher in the periphery and lower in the middle.To improve the accuracy of spatial interpolation for soil properties,it is necessary and important to incorporate a probabilistic and machine learning methods in the future study.

Spatial variability of soil properties in red soil and its implications for site-specific fertilizer management

Assessing spatial variability and mapping of soil properties constitute important prerequisites for soil and crop management in agricultural areas. To explore the relationship between soil spatial variability and land management, 256 samples were randomly collected at two depths (surface layer 0–20 cm and subsurface layer 20–40 cm) under different land use types and soil parent materials in Yujiang County, Jiangxi Province, a red soil region of China. The pH, soil organic matter (SOM), total nitrogen (TN), cation exchange capacity (CEC), and base saturation (BS) of the soil samples were examined and mapped. The results indicated that soils in Yujiang were acidified, with an average pH of 4.87 (4.03–6.46) in the surface layer and 4.99 (4.03–6.24) in the subsurface layer. SOM and TN were significantly higher in the surface layer (27.6 and 1.50 g kg–1, respectively) than in the subsurface layer (12.1 and 0.70 g kg–1, respectively), while both CEC and BS were low (9.0 and 8.0 cmol kg–1, 29 and 38% for surface and subsurface layers, respectively). Paddy soil had higher pH (mean 4.99) than upland and forest soils, while soil derived from river alluvial deposits (RAD) had higher pH (mean 5.05) than the other three parent materials in both layers. Geostatistical analysis revealed that the best fit models were exponential for pH and TN, and spherical for BS in both layers, while spherical and Gaussian were the best fitted for SOM and CEC in the surface and subsurface layers. Spatial dependency varied from weak to strong for the different soil properties in both soil layers. The maps produced by selecting the best predictive variables showed that SOM, TN, and CEC had moderate levels in most parts of the study area. This study highlights the importance of site-specific agricultural management and suggests guidelines for appropriate land management decisions.

Spatial variability effect of internal friction angle on the post-failure behavior of landslides using a random and non-Newtonian fluid based SPH method

This study proposed a random Smoothed Particle Hydrodynamics method for analyzing the post-failure behavior of landslides,which is based on the Karhunen-Loeve(K-L) expansion,the non-Newtonian fluid model,and the OpenMP parallel framework.Then,the applicability of this method was validated by comparing the generated random field with theoretical result and by simulating the post-failure process of an actual landslide.Thereafter,an illustrative landslide example was created and simulated to obtain the spatial variability effect of internal friction angle on the post-failure behavior of landslides under different coefficients of variation(COVs) and correlation lengths(CLs).As a conclusion,the reinforcement with materials of a larger friction angle can reduce the runout distance and impact the force of a landslide.As the increase of COV,the distribution range of influence zones also increases,which indicates that the deviation of influence zones becomes large.In addition,the correlation length in Monte Carlo simulations should not be too small,otherwise the variation range of influence zones will be underestimated.

Probabilistic stability analysis of embankment slopes considering the spatial variability of soil properties and seismic randomness

The safety of embankments under seismic conditions is a primary concern for geotechnical engineering societies.The reliability analysis approach offers an effective tool to quantify the safety margin of geotechnical structures from a probabilistic perspective and has gained increasing popularity in geotechnical engineering.This study presents an approach for probabilistic stability analysis of embankment slopes under transient seepage considering both the spatial variability of soil parameters and seismic randomness.The spatial varying soil parameters are firstly characterized by the random field theory,where a large number of random field samples of the soil parameters can be readily generated.Then,the factor of safety(FS)of the embankment slope under seismic conditions corresponding to each random field sample is evaluated through performing seismic stability analysis based on the pseudo-static method.A hypothetical embankment example is adopted in this study for illustration,and the influences of shear strength parameters,seismic coefficient,and the external water level on the embankment slope failure probability are systematically investigated.Results show that the coefficient of variation of the friction angle and the horizontal scale of fluctuation have more significant effects on the embankment slope failure probability.Besides,the seismic coefficient also affects the embankment slope failure probability considerably.For a given external water level,the failure probability corresponding to the downstream slope of the embankment is larger than that in the upstream slope.

Spatial variability and its main controlling factors of the permafrost soil-moisture on the northern-slope of Bayan Har Mountains in Qinghai-Tibet Plateau

The soil moisture movement is an important carrier of material cycle and energy flow among the various geo-spheres in the cold regions.Thus, this research takes the north slope of Bayan Har Mountains in Qinghai-Tibet Plateau as a case study.The present study firstly investigates the change of permafrost moisture in different slope positions and depths. Based on this investigation, this article attempts to investigate the spatial variability of permafrost moisture and identifies the key influence factors in different terrain conditions. The method of classification and regression tree(CART) is adopted to identify the main controlling factors influencing the soil moisture movement. The relationships between soil moisture and environmental factors are revealed by the use of the method of canonical correspondence analysis(CCA). The results show that: 1) Due to the terrain slope and the freezing-thawing process, the horizontal flow weakens in the freezing period. The vertical migration of the soil moisture movement strengthens. It will lead to that the soil-moisture content in the up-slope is higher than that in the down-slope. The conclusion is contrary during the melting period. 2) Elevation, soil texture, soil temperature and vegetation coverage are the main environmental factors which affect the slopepermafrost soil-moisture. 3) Slope, elevation and vegetation coverage are the main factors that affect the slope-permafrost soil-moisture at the shallow depth of 0-20 cm. It is complex at the middle and lower depth.

Influencing factors of sediment deposition and their spatial variability in riparian zone of the Three Gorges Reservoir,China

Many factors can affect the sediment deposition and soil erosion process in riparian zone, including terrain, sediment transport and water level fluctuations. Clarifying the factors influencing sediment deposition process in the riparian zone of the Three Gorges Reservoirs is an important problem to determine the key area of sediment deposition and its trend of development in the study area. In order to reveal the influence of these environmental factors on the sediment deposition in riparian zone of the Three Gorges Reservoir, this study investigated 1） the amount of deposited sediment in different environmental conditions, 2） the potential factors affecting sediment deposition in riparian zone of the Three Gorges Reservoir, 3） the relationship between the deposited sediment amount and these factors previously mentioned using correlation analysis, and 4） the influence of human activities considered as an additional factor. This study found that 1） slope gradient, elevation, inundating duration and human activities were the main factors influencing sedimentation in riparian zone of the Three Gorges Reservoir, and 2） the impact of each factor varied with spaces. Specifically, in the upper reach from Jiangjin to Fuling, human activities such as gravel dredging, bank revetment and ports and wharfs constructing disturbed considerable amounts of deposited sediment, as a result, there was no natural law to dictate the distribution. In the middle reach from Fuling to Fengjie, slope gradient and inundating duration were the controlling factors, and the sediment deposition amount was greater in the areas with a gentler slope or lower elevation. Water flow on gentler slopes generally had lower velocity, resulting in more sediment to deposit. Sites with lower elevations would be drowned by sediment-laden flow with a longer duration resulting from hydrologic regime controlled by the operating strategy of the Three Gorges Reservoir, leading to a larger amount of sediment deposition. In the lower reach from Fengjie to Zigni, slope gradient was similar to the middle reach, performing a primary factor, while other factors showed little relationship with sediment amount.

Multifractal characteristics and spatial variability of soil particle-size distribution in different land use patterns in a small catchment of the Three Gorges Reservoir Region,China

Characterizing soil particle-size distribution is a key measure towards soil property.The purpose of this study was to evaluate the multifractal characteristics of soil particle-size distribution among different land-use from a purple soil catchment and to generalize the spatial variation trend of multifractal parameters across the catchment.A total of 84 soil samples were collected from four kinds of land use patterns(dry land,orchard,paddy,and forest)in an agricultural catchment in the Three Gorges Reservoir Region,China.The multifractal analysis method was applied to quantitatively characterize the soil particle size distribution.Six soil particle size distribution(PSD)multifractal parameters(D(0),D(1),D(2),(35)a(q),(35)f[a(q)],α(0))were computed.Additionally,a geostatistical analysis was employed to reveal the spatial differentiation and map the spatial distribution of these parameters.Evident multifractal characteristics were found.The trend of generalized dimension spectrum of four land use patterns was basically consistent with the range of 0.8 to 2.0.However,orchard showed the largest monotonic decline,while the forest demonstrated the smallest decrease.D(0)of the four land use patterns were ranked as:dry land<orchard<forest<paddy,the order of D(1)was:dry land<paddy<orchard<forest,D(2)presented a rand-size relationship as dry land<forest<paddy<orchard.Furthermore,all land-use patterns presented asΔf[α(q)]<0.The rand-size relationship ofα(0)was same as D(0).The best-fitting model for D(0),D(1),D(2)andΔf[α(q)]was spherical model,forΔα(q)was gaussian model,and forα(0)was exponential model with structure variance ratio was 1.03%,49.83%,0.84%,1.48%,22.20%and 10.60%,respectively.The results showed that soil particles of each land use pattern were distributed unevenly.The multifractal parameters under different land use have significant differences,except forΔα(q).Differences in the composition of soil particles lead to differences in the multifractal properties even though they belong to the same soil texture.Farming behavior may refine particles and enhance the heterogeneity of soil particle distribution.Our results provide an effective reference for quantifying the impact of human activities on soil system in the Three Gorges Reservoir region.

A Study of Spatial Variability on Aquifer Hydraulic Conductivity K

A structural analysis of K of an aquifer system in the study area is presented, and the main direction and degree of the variability of K are found by using the unstationary regionalized variable theory of geostatistics. Optimal estimation of K has been made by universal kriging method (U K M ). Both spatial variability distribution map and division map of K are given.