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The pile responses induced by adjacent tunnel excavation have been a hot research topic in geotechnical engineering. Tunnel excavation may exert disturbance to the surrounding soil mass and then influence the adjacent pile foundations. In this paper, the random finite difference analysis considering the spatial variations of soil properties is conducted to explore the effect of tunnel excavation on the adjacent pile response by varying the distance of pile away from the tunnel centerline (D), the pile length (L), the pile diameter (dp), the tunnel depth (h), and the anisotropic ratio between the horizontal and the vertical scales of fluctuation (δx/δy). A set of pile response curves are developed to assess the influence of tunnel excavation on the adjacent passive pile foundations in spatially variable clays and provide guidelines for the tunnel excavation in the complex constructed environment.

Urban tunnels crossing faults are always at the risk of severe damages. In this paper, the effects of a reverse and a normal fault movement on a transversely crossing shallow shotcreted tunnel are investigated by 3D finite difference analysis. After verifying the accuracy of the numerical simulation predictions with the centrifuge physical model results, a parametric study is then conducted. That is, the effects of various parameters such as the sprayed concrete thickness, the geo-mechanical properties of soil, the tunnel depth, and the fault plane dip angle are studied on the displacements of the ground surface and the tunnel structure, and on the plastic strains of the soil mass around tunnel. The results of each case of reverse and normal faulting are independently discussed and then compared with each other. It is obtained that deeper tunnels show greater displacements for both types of faulting.

Geocells are three-dimensional cellular expandable mats used to improve the load-carrying capacity of weak subgrades. The expanded geocell pockets take the shape of a honeycomb connected to their neighbouring pockets. This manuscript deals with the importance of considering the exact shape of the geocell pockets in three-dimensional numerical modelling. The data for the calibration of the numerical models was obtained through laboratory plate load tests. The numerical simulations were carried out using finite difference software, Fast Lagrangian Analysis of Continua in Three Dimensions (FLAC3D). The walls of the geocell were modelled using geogrid elements having only tensile load capacity. The interfaces between the geocell walls and the infill soils were modelled using Mohr-Coulomb yield criterion. Three shapes of geocell pockets, viz. an exact honeycomb shape and simplified shapes (square and diamond), were considered in the numerical simulations. The numerical models with an exact shape of pockets have shown better agreement with experimental data, while the models with approximated shape overestimated the actual load capacity. The paper describes the modelling approach and the reasons for more accurate numerical predictions with the exact shape of geocell pockets compared to simplified pocket shapes.

Low height embankments are widely used for construction of highways and rural roads in India. Sometimes, it becomes necessary to construct such types of embankment on soft foundation soil under unavoidable circumstances. In addition to the stability under static loading, seismic excitation very often plays a major role in the stability of such an embankment. So, to study the behaviour of such embankment under seismic loading becomes very important as the failures may lead to huge loss of property and life. The present study analyses the response of a low height embankment overlying soft foundation soil under seismic loading with the help of finite difference analysis using FLAC. The Mohr-Coulomb failure criterion is used to define the soil constitutive model for both embankment and foundation soil. A stiffer half-space has been considered below the soft foundation soil and the analysis has been performed varying the shear wave velocity of the stiffer half-space. Low to moderate level of shaking has been applied at the base of the stiffer half-space by scaling the original input motion of 1987 Loma Prieta earthquake.

This paper proposed a method for analysis of a drilled pile under vertical load at the crest of rock slope. Based on wedge theory, a modified model of normal stiffness of socket wall affected by the slope is obtained. Analyze the shear behaviors of the pile-rock interface, an analytical solution of load transfer of pile at the crest of rock slope is obtained. To evaluate the accuracy of the new method, this method is compared with the results of finite difference analysis. Finally, the method is used to analyze the effect of slope, pile, and rock properties on the unit side resistance and axial force.

This study investigates the lateral behavior of pile foundations socketed into bedrocks using 3D finite difference analysis. The lateral load-displacement curve, pile deflection, and bending moment distribution were obtained for different bedrock depths between 3 and 20 m. It was discovered that bedrocks that have a depth of 7 m (7D) or less influence the lateral behavior of the pile. The p-y curves were collected at depths of 2.0–4.5 m, and the effect of the bedrock on the curves was evaluated. It was observed that the p-y curves were significantly affected by the material properties of the bedrock if the rock is located in close proximity (within 3D), but the effect is diminished if the p-y curves were 3.5 m (3.5D) or farther from the bedrock.

An enhanced cohesion weakening and friction strengthening model is proposed to simulate the progressive failure of hard rock pillars using two- and three-dimensional finite difference analysis. The documented behavior of 85 pillars in two mines was used for model validation. The numerical models successfully separated unstable/failed pillars from stable pillars and also captured the observed mechanism of progressive failure in hard rock pillars. Pillar stress-strain curves indicated that while pillars with W/H

In this paper, the ultimate bearing capacity of two closely spaced rigid strip footings with rough base on granular soil is examined based on enhanced limit equilibrium, plastic limit analy...

Pile foundation has been widely used in supporting various structures, for example, bridges and tall buildings in Taiwan. With the development of mountainous area, pile foundation has been used as mitigation slope movement. Batter piles used in a group pile subjected to lateral forces are common. In this study, we used 3D finite difference program to analyze the mechanical response of a batter pile subjected to lateral soil movement. In order to verify the correction of the numerical simulation, its validation was compared with a published case study. The analysis of a single pile in different incline angles subjected to lateral soil movement was modeled. Results of the analysis show that batter pile under the conditions of lateral soil movement will cause pile larger lateral displacement and increasing bending moment on the pile shaft. The pile displacement reduced with the increasing pile incline angle. Vertical pile shaft subjected to negative and positive moment during soil movement, while, only positive moment distributed in the batter pile shaft. The moment is higher in batter pile shaft in weak layer than in non-weak layer. The pile shaft maximum moment occurred nearby the interface of weak layer and stable layer. The moment increased with the incline angle of batter pile. While, the moment increasing ratio reduced with the increased incline angle.

In order to verify the reliability of numerical site response analysis program, both soil free-field and base rock input motions should be provided. Beside the field earthquake motion records, the most effective testing method for obtaining the above motions is the dynamic geotechnical centrifuge test. However, need is to verify if the motion recorded at the base of the soil model container in the centrifuge facility is the true base rock input motion or not. In this paper, the appropriate input motion measurement method for the verification of seismic response analysis is examined by dynamic geotechnical centrifuge test and using three-dimensional finite difference analysis results. From the results, it appears that the ESB (equivalent shear beam) model container distorts downward the propagating wave with larger magnitude of centrifugal acceleration and base rock input motion. Thus, the distortion makes the measurement of the base rock outcrop motion difficult which is essential for extracting the base rock incident motion. However, the base rock outcrop motion generated by using deconvolution method is free from the distortion effect of centrifugal acceleration.

LEM (Limit Equilibrium Method) based programs are commonly used for the designs of soil nailing as a slope reinforcement. However, there is a drawback that the interaction between ground and soil nailing is not properly reflected in those programs, which needs to be solved. For economical constructions and designs, research is also required on the support pattern of soil nailing. In this study, therefore, reinforcement effects of soil nailing were compared and analyzed by performing finite difference analyses which could properly consider the interaction between ground and soil nailing. As a result, when the angle from slope to nail is , failure slip surface becomes the largest and thus the factor of safety becomes maximum.

Underground structures are currently widely used and are built as urbanism develops. The interactions between perpendicularly crossing and parallel tunnels in the Tehran region are investigated by using a full three-dimensional (3D) finite difference analysis with elastic-plastic material models. Special attention is paid to the effect of subsequent tunneling on the support system, i.e., the shotcrete lining and rock bolts of the existing tunnel. Eventually, as the tunnels are excavated at certain levels, the interaction between the tunnels will certainly have a significant influence on both stress distribution and consequently deformations. Since multilayer tunneling is a three-dimensional phenomenon in nature, 3D numerical solutions must be utilized for analyzing effect of perpendicularly crossing tunnels at various levels. As Tohid twin tunnels and Line 7 pass beneath the Line 4 metro tunnel, changes in stress distribution, deformations, and surface settlements are studied for various conditions and the results are presented in this paper. Consequently, it is shown that there is a significant interaction between tunnels that necessitate certain preventive measures to maintain a stable tunneling operation.

A numerical analysis of pile driving for tapered piles is presented in this paper. A three-dimensional finite difference analysis for tapered angle and geometry effects has been used on pile driving response of tapered piles. The simulation considers an idealization for pile–soil system in drivability. The vertical pile is assumed to have linear and elastic behavior. It is also assumed that the soil is elasto-plastic material and its failure stage is controlled using the Mohr–Coulomb failure criterion. At the soil–pile contact surfaces along the pile shaft and pile toe, slip is allowed to occur during the driving procedure using interface elements. Quiet boundaries are used to prevent waves traveling in the lateral and vertical directions for the soil. Cylindrical, fully tapered, and semi-tapered piles were analyzed. The results obtained from numerical analyses were compared with those obtained from available laboratory tests and also other available numerical data, resulting in a satisfactory agreement. The results have shown that among piles of the same length and material volume, with increasing the taper angle from zero (representing a cylindrical pile), the driving stresses decrease and the permanent pile toe settlement (set) increases. These are interesting in pile driving and are on the safe side for driven piles and increasing the driving efficiency. It has also been found that the geometry of the pile can generally influence the pile drivability. Generally speaking, tapered and partially tapered piles offer better drivability performance than cylindrical piles of the same volume and length.

Hunchun Mining Co., Ltd. for a 11910 face return air drift mine for the study of the background, using the finite difference software (FLAC) simulated roadway excavation and shoring, anchors through simulation analysis supporting roadway network cable and rock deformation stress distribution, simulation results show that the design of the anchor mesh-supporting design a good change of rock mechanical properties, enhanced adhesion of rock, effectively inhibited the expansion phenomenon, so that the stress distribution roadway more reasonable engineering practice shows that after verification and simulation to determine the support scheme is feasible.

To facilitate the design of seismic remediation for Tuttle Creek Dam in east central Kansas, a seismic finite difference analysis of the dam was performed using the software FLAC and the UBCSAND and UBCTOT soil constitutive models. The FLAC software has a key advantage because it can use calibrated site-specific constitutive models. Earlier deformation analyses using a hyperbolic constitutive model for the foundation fine-grained materials did not properly represent the modulus and strength reduction and predicted extremely large permanent deformations. Cyclic triaxial laboratory tests using high-quality samples and in situ vane shear tests were used to calibrate the FLAC constitutive model herein. The resulting FLAC analysis of the unremediated dam predicted an upstream slope toe deformation of about 0.6 m, a crest settlement of about 0.6 m, and a downstream slope toe deformation of about 1.5 m using the design ground motion. Based on the estimated permanent deformations and other factors, it was decided that the anticipated upstream slope and crest deformations were tolerable and only the downstream slope had to be remediated to protect the downstream seepage control system.

It was presented for the results of 3D finite difference analysis on the behavior of single pile in clay. Firstly, it was discussed to the effect of model’s mesh fineness and soil parameters on pile response. And it was founded that the mesh size less than 0.2d (diameter of pile) was reasonable. In additions, when the soil was soft or the E(soil elastic modulus) was small, the effect E of on lateral capacity of pile was larger than the soil was stiff clay with soil elastic modulus increasing. Lastly, the results of the numerical simulation carried out in this study were compared with a published field lateral loading tests, a good correlation between the field test and the numerical simulation was obtained based on reasonable mesh size and material parameters.

Deformation and focused fluid flow within a mineralized system are critical in the genesis of hydrothermal ore deposits. Dilation and integrated fluid flux due to coupled deformation and fluid flow in simple strike–slip fault geometries were examined using finite difference analysis in three dimensions. A series of generic fault bend and fault jog geometries consistent with those seen in the western Mount Isa Inlier were modelled in order to understand how fault geometry parameters influence the dilation and integrated fluid flux. Fault dip, fault width, bend/jog angle, and length were varied, and a cross-cutting fault and contrasting rock types were included. The results demonstrate that low fault dips, the presence of contrasts in rock type, and wide faults produce highest dilation and integrated fluid flux values. Increasing fault bend lengths and angles increases dilation and integrated fluid flux, but increasing fault jog length or angle has the opposite effect. There is minimal difference between the outputs from the releasing and restraining fault bend and jog geometries. Model characteristics producing greater fluid flows and/or gradients can be used in a predictive capacity in order to focus exploration on regions with more favorable fault geometries, provided that the mineralized rocks had Mohr–Coulomb rheologies similar to the ones used in the models.

Controlled-source electromagnetic (CSEM) field surveys offer a geophysical method to discriminate between high and low hydrocarbon saturations in a potential reservoir. However, the same geological processes that create the possible hydrocarbon reservoir may also create topography and near-surface variations of resistivity (e.g., shallow gas or hydrates) that can complicate the interpretation of CSEM data. In this paper, we discuss the interpretation of such data over a thrust belt prospect in deepwater Sabah, Malaysia. We show that detailed modeling of the key scenarios can help us understand the contributions of topography, near-surface hydrates, and possible hydrocarbons at reservoir depth. Complexity at the surface and at depth requires a 3D electromagnetic modeling code that can handle realistic ten-million-cell models. This has been achieved by using an iterative solver based on a multigrid preconditioner, finite-difference approach with frequency-dependent grid adaptation.

Seismic stability, liquefaction, and deformation of earth structures are critical issues in geotechnical earthquake engineering practice. At present, the equivalent linear approach is considered the ‘state of practice’ in common use. More recently, dynamic analyses incorporating nonlinear, effective-stress-based soil models have been used more frequently in engineering applications. This paper describes a bounding surface hypoplasticity model for sand [Wang ZL. Bounding surface hypoplasticity model for granular soils and its applications. PhD Dissertation for the University of California at Davis, U.M.I. Dissertation Information Service, Order No. 9110679; 1990; Wang ZL, Dafalias YF, Shen CK. Bounding surface hypoplasticity model for sand. ASCE, J Eng Mech 1990;116(5):983–1001; Wang ZL, Makdisi FI. Implementing a bounding surface hypoplasticity model for sand into the FLAC program. In: Proceedings of the international symposium on numerical modeling in geomechanics. Minnesota, USA; 1999. p. 483–90] incorporated into a two-dimensional finite difference analysis program [Itasca Consulting Group, Inc. FLAC (Fast Lagrangian Analysis of Continua), Version 4. Minneapolis, MN; 2000] to perform nonlinear, effective-stress analyses of soil structures. The soil properties needed to support such analyses are generally similar to those currently used for equivalent linear and approximate effective-stress analyses. The advantages of using a nonlinear approach are illustrated by comparison with results from the equivalent linear approach for a rockfill dam. The earthquake performance of a waterfront slope and an earth dam were evaluated to demonstrate the model's ability to simulate pore-pressure generation and liquefaction in cohesionless soils.

The study covered by this paper was focused on the historical case of the Calitri landslide, which was repeatedly reactivated by earthquakes, as reported since 1694. The town of Calitri (Southern Italy) is located on a ridge whose southern slope, from its top to the Ofanto river valley floor, has been historically affected by major landsliding. The last record of recurrence of the Calitri landslide leads back to the 1980 Irpinia earthquake, which caused significant damage to the town and had pervasive and visible ground effects. Based on a detailed historical reconstruction of landsliding and seismicity at Calitri, the study analysed the current static and dynamic stability of the landsliding slope by means of a finite-difference numerical analysis, taking into account the various factors of landslide initiation and kinematics. The results of the numerical analysis: (i) were consistent with the roto-translational mechanism observed upon the latest reactivation of the landslide; (ii) demonstrated that excess pore pressure redistribution caused a lag between the seismic trigger and the initiation of landsliding; and (iii) showed the impact of seismic input frequency on propagation and depth of slope instability.

The authors have derived the bearing capacity factor Nqon sloping ground based on the slip line method and have verified it using finite difference analysis. The bearing capacity factor Nγon sloping ground is obtained by an iterative finite difference solution of the slip line equations, and the results are close to those from laboratory testing. Design figures for Nγon sloping ground are prepared for rapid engineering use. For earthquake loading, the authors have applied the concept of equivalent horizontal acceleration and have derived Nqand Nγbased on slip line analysis.Key words: bearing capacity, slip line, finite difference, sloping ground, earthquake.

Pile length is one of the parameters affecting the behaviour of piles under lateral loads caused by soil displacements. Even though piles are traditionally designed with an embedded length equal at least to the thickness of the sliding soil layer, sometimes shorter piles can be a cost effective choice. Piles can be shortened in the sliding layer and in stable layer until they are able to give a shear strength increment along the sliding surface. In the paper the effectiveness of short “sewing piles” has been analyzed by means of a finite difference analysis. Preliminary results show that also short piles could be effective, even though pile length must be carefully selected because it rules not only the value of the slope safety factor but also the position of the critical sliding surface.

A three-dimensional (3-D) finite-difference model for elastic waves in the ground has been developed and implemented. The model has been created to supplement the development of a sensor that uses elastic waves to detect buried land mines. The model is used to investigate the propagation characteristics of elastic waves in the ground and to explore the interaction of elastic waves with buried land mines. When elastic waves interact with a buried mine, a strong resonance occurs at the mine location. The resonance can be used to enhance the mine's signature and to distinguish the mine from clutter. Results presented in this paper explain the features of elastic wave propagation in the ground and show the interaction of elastic waves with both an anti-personnel mine and an anti-tank mine.

This paper presents the effect of bedrock depth on the lateral behavior of monopiles in terms of load-displacement curve at pile head, displacement and moment along the pile. Finite difference analysis program, FLAC3D, was adopted to create a 1-m diameter monopile embedded into sands. The bedrock depth was varied from 5 m to 30 m from ground surface. In this study, it was observed that the lateral behavior of monopile was significantly affected when the bed is as shallow as 5 m deep; the differences were negligible for other cases with depth greater than 10 m.

Many high-rise buildings, bridges, and transmission towers are constructed on steep slopes in Hong Kong and are supported by large-diameter piles. These structures may be subjected to large lateral loads, such as those caused by typhoons, earthquakes, and high-speed vehicles. The margin of safety of the slope may decrease as a result of stresses transferred from the piles to the slope. To minimize the transfer of lateral load from the buildings to the shallow depths of the slope, an annulus of compressible material (sleeving) is sometimes formed between the piles and the adjacent soils. In this paper, a three-dimensional analysis is carried out to investigate the effects of unsleeved and sleeved single piles and pile groups on the stability of a cut slope. Mechanisms of load transfer from the piles to the slope are studied. The stability of the slope is evaluated using the strength reduction technique. The evolution of slope failure is examined and the factors of safety for both initiation of instability and global failure of the slope are identified from the numerical analyses. The sleeving technique is found to be capable of significantly reducing the stresses in the shallow depths of the slope in front of the piles, thus improving the local stability of the slope, but offers limited benefit with respect to global stability.Key words: laterally loaded pile and pile group, sleeving, slope stability, three-dimensional analysis, load transfer mechanism, factor of safety.

Modelling of 2D resistivity imaging was done in order to understand the principle resolution of the technique in different geological situations, and for assessing the behaviour of the interpretation methods under controlled circumstances. The Wenner array was used throughout. The results show that the 1D approximation only provides reasonable results in environments with very gradual lateral resistivity changes, otherwise the result may be strongly misleading. Inversion using the 2D quasi-Newton technique results in adequate resolution of the structures in moderately complex environments, but the Gauss–Newton method holds a significant advantage in some complicated cases. The data density can also be of crucial importance for the resolution capability, notably of narrow structures.

A multi barrier concept of disposal is adopted for both low and intermediate level radioactive waste disposal to prevent the spread of radionuclides into the human environment. Concrete engineered barrier is a part of multi barrier system for radioactive waste disposal. As long as the concrete barrier is intact, the containment of radioactive waste within the disposal facility is assured. However, every concrete structure has a finite lifetime. Concrete barriers degrade with time with lifetime dependent on type of concrete, external and internal environmental factors. This degradation allows the free moment of the radionuclides out of the concrete barrier. Hence an attempt was made to model the Calcium (Ca) leaching from side wall of a concrete engineered barrier in a Near Surface Disposal Facility (NSDF) and its influence on radionuclide migration across the concrete barrier, limited to conditions specified in the paper. The conceptual model assumes that rain water seeps into the engineered barrier through the top cover and dissolves radionuclides from the nuclear waste matrix. The modelling was attempted with Finite Difference analysis and validated with the results available in literature. The influence of Ca leaching on radionuclide migration in concrete barrier has been discussed for eight different radionuclides (Cs-137, Sr-90, I-129, H-3, Pu-239, Am-241, Co-60 and Tc-99).

Stability under horizontal (H) and vertical (V) loading is an important design consideration for seabed lain subsea pipelines. From initial installation, extending through their design life, these pipelines are subjected to a combination of H and V loading due to various external and internal driving mechanisms. These mechanisms include self weight loading, forces applied during installation, temperature and pressure driven expansion and in some cases significant hydrodynamic loading. All these aspects need to be considered in design, requiring an understanding of the interaction between the pipeline and the seabed it rests upon, i.e. pipe-soil interaction. In the past, emphasis has been placed on empirical methods of considering pipe-soil interaction. Typically model testing has been used to consider vertical and subsequent horizontal load response. Recently, progress has been made away from purely empirical methods to include the derivation of theoretical upper bound solutions for combined H-V loading and the use of numerical analysis to calculate H-V stability envelopes. This and previous work relating to the H-V stability of pipelines has largely been confined to the case of a flat seabed with no consideration of the influence of seabed slopes. This paper presents a suite of finite difference analysis undertaken to investigate the influence of a seabed slope on pipeline H-V stability envelopes. Initially modeling considers a slope on weightless soil with subsequent modeling considering the additional influence of soil weight. Analysis comprised a series of displacement controlled excursion through H-V load space, defining stability envelopes for a range of conditions. For a weightless soil the pipeline stability envelope was seen to rotate through H-V load space reducing vertical resistance to penetration and producing significant asymmetry in the horizontal load response. In addition to this rotation consideration of soil weight introduced a change in the geometry of the stability envelope. The results presented in this paper suggest that the influence of seabed slope on pipe soil interaction and the stability envelope in H-V load space is significant and worthy of consideration in design.Copyright © 2009 by ASME

Flow through a saturated idealized hillslope with a single soil pipe was simulated using a finite difference solution to the equation for three-dimensional Darcian flow in saturated heterogeneous media. The proportions of hillslope discharge originating from flow through the soil matrix and from flow through a soil pipe were determined, considering such factors as the radius, depth and length of the pipe, pipe spacing, and the length and slope of the hillslope. Results demonstrate that soil pipes can contribute a significant amount, and in many instances, the majority of total subsurface stormflow.

The nonlinear Dupuit-Forchheimer theory and two linearized versions are considered as to their applicability for giving accurate results on recharge mound shapes beneath strip and square basins. Results on mound rises from the approximate theories are compared with those from the nonlinear theory to determine criteria for the use of the approximate theories.

In this paper, a new empirical method is developed by which the surface settlement profile can be accurately estimated. The new empirical method is an extension of the Hsieh and Ou method, which showed that the surface settlement profile could be reasonably constructed if the maximum surface settlement (δ vm ) was known. However, there is no reliable method to predict δ vm with good accuracy. To this end, a simple procedure is established by which δ vm can be accurately estimated from the maximum wall deflection (δ hm ). This procedure includes two elements: 1) an empirical equation for estimating the ratio of δ vm over δ hm ( R = δ vm /δ hm ), and 2) a means to determine δ hm . Since the latter can be accurately estimated with a routine finite element or finite difference analysis, the focus of the paper is on the former. To this end, a set of empirical equations for the ratio R is developed. The accuracy of the proposed method is verified with well-documented case histories of braced excavation.

A hybrid boundary element—finite-difference program, FFFLOW, has been developed for the modelling of fluid flow in deformable, jointed rock. The model has been used to simulate reservoirs with variable joint orientations, injection rates, joint dilation angles and variable far-field stresses. The formulation and example results are presented.

Centrifugal filtration through porous matermls, under both saturated as well as unsaturated flow condmons, plays an important role in diversified fields of science and technology, such as soft physics, groundwater hydrology, sludge dewaterlng, pharmacology, and petroleum engmeenng It is of specml interest in certain industrial processes that involve fluid extraction and drying, e g , in the sugar and paper pulp industries To meet the needs to evaluate centrifugal filtraUon in all these cases, studies have been conducted leading to formulas that express relations among the many variables that describe the process Most of these studies have been expenmental ones, leading to empirical relations that describe the filtration capacity In some cases, results have been obtained by using very simple models of the filtration phenomenon Because of the nature of these investigations, each result could be apphed only to a specific case, or to a hmlted range of cases The absence of a umform methodology for the design of centrifuges has forced engineers to use pdot-scale evaluation procedures In what follows, we shall show how the theory of flmd flow through a deformable porous medmm, in the presence ofa centnfugal force, may serve as a basis for the construction of a rather general model of centrifugal filtration