VREDNOTENJE ZMANJŠANJA VELIKOSTI ZOŽITVE ZRNATIH FILTROV ZARADI INTERNE EROZIJE OSNOVNIH KOHEZIVNIH ZEMLJIN Izvleček Ta študija obravnava analizo filtrirnih zožitev in njeno uporabo glede zmanjšanja por in zožitev med filtriranjem tal. Eksperimentalna preiskava vključuje kombinirane preizkuse erozije-filtriranja v luknji z več zemljinami in filtri. Osnovno zemljino predstavlja peščena glina, medtem, ko so zrnati filtri izbrani glede na običajna filtracijska merila. Kombinacija eksperimentalnih podatkov o spreminjanju poroznosti in analitičnih rezultatov analize porazdelitve zožitve (CSD) je bila uporabljena za vrednotenje zmanjšanja velikosti zožitev zaradi filtracij-skih procesov. Globina filtracije je bila ocenjena tudi glede na zadržano maso zemljine in zmanjšanje poroznosti, ki izhaja iz izmerjene hidravlične prepustnosti. Za ocenitev zmanjšanja zožitev je bil uporabljen analitični model CSD, ki je upošteval eksperimentalne rezultate. Glede na dobljene rezultate je predlagana neenakomerna zožitev glede na efektivno globino filtracije, ki potrjuje dinamično delovanje filtra. Samira Azirou Université de Bejaia, Faculté de Technologie, Laboratoire de Génie de la Construction et Architecture 06000 Bejaia, Alžirija E-pošta: azirousamira@gmail.com Normandie Univ UNIHAVRE, CNRS, LOMC, 76600 Le Havre, Francija Ahmed Benamar Normandie Univ UNIHAVRE, CNRS, LOMC, 76600 Le Havre, Francija Abdelkader Tahakourt Université de Bejaia, Faculté de Technologie, Laboratoire de Génie de la Construction et Architecture 06000 Bejaia, Alžirija Ključne besede resonančna kolona; resonančna frekvenca; strižni modul; relativna gostota; efektivni konsolidacijski tlak; dinamični strižni modul 28. Acta Geotechnica Slovenica, 2018/1 EVALUATION OF THE CONSTRICTION SIZE REDUCTION OF GRANULAR FILTERS DUE TO UPSTREAM COHESIVE BASE-SOIL EROSION Samira Azirou Université de Bejaia, Faculté de Technologie, Laboratoire de Génie de la Construction et Architecture 06000 Bejaia, Algeria E-mail: azirousamira@gmail.com Normandie Univ UNIHAVRE, CNRS, LOMC, 76600 Le Havre, France Ahmed Benamar Normandie Univ UNIHAVRE, CNRS, LOMC, 76600 Le Havre, France Abdelkader Tahakourt Université de Bejaia, Faculté de Technologie, Laboratoire de Génie de la Construction et Architecture 06000 Bejaia, Algeria Keywords granular filter, internal erosion, constriction, porosity, filtration index https://doi.org/10.18690/actageotechslov.15.1.29-41.2018 Abstract This study is devoted to filter-constrictions analysis and its application with respect to void and constrictions reduction during soil filtration. The experimental investigation involves combined Hole Erosion-Filtration tests using several soils and filters. The base soils are lean clays and the granular filters are selected according to the usual filtration criteria. The combination of the experimental data for porosity variation and the analytical results from the Constriction Size Distribution (CSD) analysis was used to evaluate the constrictions size reduction subsequent to the filtration process. The filtration depth was also estimated according to the retained soil mass and the porosity reduction deduced from the measured hydraulic conductivity. An analytical model of the CSD was applied to the experimental results in order to assess the constrictions reduction. As regards the obtained results, a nonuniform constriction reduction was suggested according to the effective filtration depth, advocating a dynamic filter action. 1 INTRODUCTION Filters in hydraulic works are designed and constructed to achieve specific goals such as preventing the internal soil erosion and controlling the drainage. The filters managed in zoned dams are designed according to criteria based on the grain size distribution of both filter and erodible soil. Many laboratory researches devoted to filter criteria have been developed for cohesionless soils, and resulted in relationships related to grain size [1, 2, 3, 4, 5, 6, 7, 8]. Since filter pores and their connectivity define their ability to retain transported particles by seepage, very important basic concepts defined the voids (constrictions) in the filter and the material density as the key parameters governing filtration and preventing the erosion of base soil. The filter criteria are often designed using the particle size distribution (PSD) [1, 3, 9, 10], whereas the filtration process mainly involves the constriction size distribution (CSD). A spherical particle model can provide an estimation of the apparent pore size of a granular filter, and it is controlled by the grain size distribution and material density. A new approach based on the constrictions distribution was introduced by Silveira (1964) [11] in a geometrical model of the pore space existing between a filter's grains. Silveira et al. (1975) [12] suggested a cubic pack (four particles) for assessing the constriction size. Ziems (1968) [13] brought criteria from the Silveira (1964) [11] method and transformed the volumetric or mass distribution to a number distribution of particles. In this way, he reached a distribution involving smaller DOI Acta Geotechnica Slovenica, 2018/1 29. S. Azirou et al.: Evaluation of the constriction size reduction of granular filters due to upstream cohesive base-soil erosion pores dp min with a limit of 0.155Dmin, and larger pores dp,max limited by 0.155Dmax, where Dmin and Dmax are the smallest and largest particle sizes of the filter, respectively. Wittmann (1979) [14] proposed the concept of soil filtration, taking more care of the real geometrical and structural properties of the porous media, and an average pore area was determined theoretically and verified in initial experiments by measuring the whole distribution of the pore areas. A granular soil is modeled as a three-dimensional collection of particles that forms pores of different size and shape. These models assume pores involving a regular three-dimensional structure, such as a cubic or tetrahedral arrangement [11, 12, 15]. Previous approaches [11, 12, 14, 15] could not provide a constrictions distribution at intermediate densities between the densest and the loosest states. A critical review of the two models based on three or four particles, reported by Silveira (1964, 1975) [11, 12], was proposed by Wang and Yousif (2014)[16], who indicated that a number of likely particle groups is missed, leading to the fact that the number of unique groups calculated in these models is less than the actual number. They then proposed correction factors that are not intrinsic, but depend on both the density and the particle size distribution. Indraratna et al. (1997, 2007), Locke et al. (2001), Reboul et al. (2008), Vincens et al. (2014) [17, 18, 19, 20, 21] grouped all the parameters and suggested a complete model of the voids distribution for any relative density, usually based on a filter's particle size distribu- tion (PSD) by area. Taylor et al. (2015) [22] proposed a new method to measure and visualize void constrictions in sands using micro-CT data, with a view to assessing the granular filter's performance. In this study the CSD model of Locke et al. (2001) [18] was used to address the constrictions size reduction of filters tested downstream of cohesive base soils. An analysis of the constriction size reduction was presented, based on a filter porosity variation under successive hydraulic loads. 2 EXPERIMENTAL METHODOLOGY 2.1 Materials In order to investigate the filter's efficiency with respect to base soil erosion from a simulated crack (hole), two cohesive base soils and two granular filters were selected. Table 1 summarizes the main characteristics and classification of different tested materials according to ASTM D2487 (2011) [23]. The two selected base soils are classified as Lean Clay (CL), whereas filters F1 and F2 are classified as Poorly Graded sand according to the Standard Soil Classification System [23]. Table 2 summarizes the additional geotechnical parameters of the used base soils, measured according to ASTM standards. The shear resistance was measured using a vane shear test and the plasticity index (Atterberg Limits) provides a slightly plastic clay for both CL1 and CL2. 10 10* 10 10' 10' Diameter (mm) Figure 1. Particle size distribution of used materials (filters and base soils) [24]. 30. Acta Geotechnica Slovenica, 2018/1 S. Azirou et al.: Evaluation of the constriction size reduction of granular filters due to upstream cohesive base-soil erosion Table 1. Classification of different tested materials (ASTM D2487 [23]). Coefficient Soil classification Soil Type Fca (%) Gcb (%) Dry density Specific gravity Uniformity (Cuc) Curvature (Ccd) (ASTM D2487, [23]) F1 0 10 1.65 2.65 5 1.25 SP: Poorly graded sand F2 0 10 1.65 2.65 3.15 0.78 SP: Poorly graded sand CL1 85 0 1.60 2.60 7.97 1.83 CL: lean clay CL2 85 0 1.60 2.60 8.77 0.96 CL: lean clay Fca: fines content (mass fraction in percentage of particles finer than 75|im). Gcb: gravel content (mass fraction in percentage of particles coarser than 4.75mm). Cuc: uniformity coefficient (Cu Ccd: curvature coefficient (Cc = = D60 / D10) (D30)2 / (D!0XD6C)) Table 2. Geotechnical parameters of used soils (ASTM D2487, 2011)[23]. Atterberg limits D15/d85 Lean Clay type WL (%) Wp (%) Plasticity Index (%) F0 F1 F2 CL1 (Namur) 33 21 12 (slightly Plastic) 7 4.4 11 13.8 CL2 (Normandy) 34 21 13 (slightly Plastic) 8 2.7 6.7 10.8 Fig. 1 shows the PSD curves of different materials used in the laboratory Erosion-Filtration tests, and the grading range limit of the USBR design criteria [24] for dam filters. The grain size of the base soil CL1 ranges from 0.40 ^m to 120 ^m, while the CL2 grains provide a larger size (from 0.40 ^m to 361 ^m). The base soils CL1 and CL2 were collected from Namur (Belgium) and Normandy region (France), respectively. Two granular filters made of silica sand, collected from Seine River (France) were selected by sieving according to USBR (1994) filter criteria [24]. The finer filter F1 presents a grading range between 0.40 mm and 6.30 mm, whereas the coarser filter F2 provides a grain size ranging from 0.63 to 6.30 mm. As illustrated in Fig. 1, filter F2 was designed to not meet the usual filter criteria. It is important to emphasize that a first designed filter F0 was tested, and owing to its internal instability it was rapidly suffering suffusion and so not included in this study. In order to investigate the filtration process involving constrictions size, the CSD model described in Appendix A was implemented using a material relative density close to Dr=0.65, involving the loosest and the densest states of the filters. Fig. 2 displays PSD and CSD Equivalent Diameter (mm) Figure 2. CSD of filters Fj and F2 (densest, loosest and for Dr = 0.65 cases). Acta Geotechnica Slovenica, 2018/1 31. S. Azirou et al.: Evaluation of the constriction size reduction of granular filters due to upstream cohesive base-soil erosion plots for the filters F1 and F2 in the loosest and densest cases calculated from the analytical model using Eq.11 (Appendix A) with different available series of grain diameters. The CSD obtained for a relative density of 0.65 for both filters, as expected from the Locke et al. (2001) [18] model, highlights that the CSD of filter F2 provides larger constrictions than that of filter F1. 2.2 Test setup For studying filtration, the processes of particles erosion from the base soil and their subsequent filtration by a downstream filter are investigated. Filtration studies usually involve direct experimentation through laboratory tests. Sherard and Dunnigan (1989) [10] designed the NEF (No Erosion Filter) test to simulate the filtration of cohesive soils (arising from base soil crack erosion) in a granular filter. The used experimental apparatus, shown in Figure 3, involves a permeameter (cylindrical cell made of Plexiglas) that is 140 mm in diameter and 280 mm high, connected to a tap-water (temperature of 18°C and pH of 6.8) supply, which provides a selected pressure. The inlet cell is equipped with a pressure gauge and the outlet is directed to a turbidity meter and a flow meter providing continuous records of the measured values. The cell is mainly composed of four compartments: The filter layer (150 mm) compacted on a glass-beads (8-mm diameter) layer, the base soil (25-mm thin) compacted (water content close to 12 %) to a target density (Table 1) above a steel plate, and at the top of the cell a gravel layer is placed for flow spreading. A 10-mm diameter pinhole was drilled through the base soil and the steel plate in order to introduce a concentrated flow through the hole and simulate how to match the erosion results. Glass beads forming the bottom layer involve a sufficiently high filtration to avoid the retention of particles released from the tested filter above. A vertical upstream flow was induced with a very low pressure through the soil-filter system and once satura- tion is reached, the downstream flow generates the water pressure, gradually increased by steps corresponding to selected pressure test values (25, 50 and 75 kPa). The particle concentration of the outlet suspension is derived using a previous correlation between the concentration and the turbidity (NTU: Nephelometric Turbidity Unit). The processes of particle erosion from the base soil and the filtration are first decoupled by performing the hole erosion test alone. 2.2.1 Hole Erosion Test In order to investigate the internal erosion of the base soil a series of hole erosion experiments without a filter are conducted. They are devoted to evaluate the solid flux eroded from the base soil under fixed hydraulic conditions and thereby the susceptibility of the base soil to erosion. The results will also be used later as the limit conditions at the filter inlet to quantify the soil mass entering at each pressure step. For each applied pressure, the turbidity of the outflow and the flow rate are recorded continuously, and so the erosion rate and the eroded mass are derived. 2.2.2 Combined Erosion-Filtration Test Experiments combining the base soil erosion with a downstream filter are carried out in order to investigate the extent to which the internal erosion is minimized from the soil protected by a filter. The filtration tests involve the different base soils combined with each filter. Fig. 3 shows the cell used in the filtration test with a water supply and data-acquisition systems. The measurements performed during the test include the flow rate and the particle concentration of the effluent. The performance of the filter is observed during a processing time of up to one hour. The results presented in this study involve two base soils and two filters. Figure 3. Experimental set-up of the Hole-Erosion and Erosion-Filtration tests and device pictures. 32. Acta Geotechnica Slovenica, 2018/1 S. Azirou et al.: Evaluation of the constriction size reduction of granular filters due to upstream cohesive base-soil erosion 3 CONSTRICTION SIZE REDUCTION APPROACH A continuous approach of the filtration process can be integrated as an internal variable in the cumulated distribution of constriction sizes. Appendix A details the approach developed for constriction size reduction during filtration. Starting from this point, the deposited particles of base soil within the filter pores modify the constrictions distribution by reducing the space of accessible constrictions (constrictions that are many times larger than filtered particle size). 3.1 Effective filtration volume: Iteration model Filtration processes can be classified in accordance with the location of the retained particles that can either be deposited on the outer surface of the filter medium (surface filtration) or inside the whole filter medium (depth filtration). Filtration is affected by CSD, which continuously evolves with the porosity reduction, leading to more and more retention of the base soil during the filtration process. Understanding the factors that control the transport of soil particles detached by the water flow is essential for predicting the contingency of the internal and surface erosion of embankments. The effective volume (Vef) was defined as the actual volume in which the filtration occurs. To evaluate the effective volume (Vef) of filtration it is assumed that the filter medium is homogeneous. For each pressure step Pj (where i represents the pressure value: 25, 50 or 75kPa), the retained dry mass mi in the filter was derived as the difference between the eroded mass from the base soil (the hole-erosion test) and the eroded mass from the soil-filter system. Then the void occupied by the deposited particles (m/yd) within the filter was subtracted from the total void volume of the filter (Vvi) to obtain the released void volume. The actual porosity (n) is calculated as the ratio of this released void volume to the total volume (Vj). The actual porosity ni was compared to the porosity (n^) deduced from the measured hydraulic conductivity through the Kozeny-Carman formula [25, 26]. Because the decrease of the hydraulic conductivity is due to the deposited particles within the constrictions, this parameter can be linked to the CSD evolution. Whereas the retained mass is a global amount, non-uniformly distributed (Benamar, 2013) [27], the hydraulic conductivity decrease is strongly impacted by the particle accumulation and so advocates the concept of a local depth where the porosity decreases. The ratio of the two porosity values (n^/n,) is defined as the filtration index for each pressure step. The iterative process for such an assessment is described in the flowchart of Fig.4. The effective filtration volume is distributed through the filter according to the CSD and can fill, in the first approximation, a partial height of the sample containing the effective constrictions and defined by the filtration index X (Eq. 1). The effective height (volume) can be described by the filtration depth as: Hf = X x H (1) where Hf is the filtration depth, H is the filter height. Pi.n ii,"ii I No | Pi : pressure step (i= pressure value (25, 50 or 75kPa); mi : retained mass within a filter Yd : dry unit weight of the deposited particles Vvi : total void volume of the filter (Vvi= n0*Vj) ni : actual porosity Vj : total volume nk : porosity from the Kozeny-Carman relation X : filtration index Figure 4. Flowchart of the evaluation of the filtration index. 3.2 Evaluation of the constrictions size reduction In granular soil, many authors provide a correlation between the grain sizes of the filter material and the hydraulic conductivity [8, 24], whereas other models relate the hydraulic conductivity to the porosity like the Kozeny-Carman relation (Eq. 2). The work presented here attempts an alternative to previous approaches by linking the constrictions size variation to the filter porosity reduction. Since the porosity reduction is deduced from the hydraulic conductivity decrease, which is mainly due to the constrictions size reduction, it is permissible to allocate the void decrease to the constrictions size reduction. In order to study the dimensions variation of the constrictions, some assumptions are allowed, such as: Acta Geotechnica Slovenica, 2018/1 33. S. Azirou et al.: Evaluation of the constriction size reduction of granular filters due to upstream cohesive base-soil erosion - the particle deposition in the constriction void was uniformly distributed along the constriction wall (Fig. 5); - the particles are assimilated to spheres; - if a large particle is blocked in any constriction, its diameter will be reduced and then smaller particles arriving at this same constriction will be blocked again; - the constriction size decrease is related to the porosity reduction in the filter, estimated by the relative value nk/n0; - in order to calculate the constriction reduction, the retained particles are deposited within the constrictions. To take into consideration the error from such an assumption, the size reduction of the constriction is addressed in terms of the constriction volume as defined by Eq. 3; - the filtration is uniform, according to the filter depth. The average diameter of the constrictions change can be estimated using Eq.4, moving from the initial constriction size Dc0 to the final constriction size Dcf, using the values of the initial porosity n0 of the clear filter and the final porosity nk (deduced from the Kozeny-Carman relation [25, 26], Eq. 2). The formula's applicability is generally limited to particles that meet the following relation: 0.01 cm < D10 (particle size for which 10% of the filter is finer) < 0.3 cm [25]. The filters used in this study provide a D10 value in the range of 0.1 to 3 mm (Fig. 1), thus allowing the use of the Kozeny-Carman equation [25, 26], defined as follows: k = k,nl (1 - n) 1(1 - nk r (2) where k0 is the initial hydraulic conductivity (global value) of the filter measured in an additional test with the filter alone; k is the hydraulic conductivity (global value) mesured during the erosion-filtration test from the flow measurement; n0 is the initial porosity of the clean filter; and nk is the porosity from Eq. 2. The final volume of the constriction Vcf is related to the initial constriction volume Vq) by the porosity ratio, as follows (Eq. 3): VCf =- nD, Cf V (3) So the diameter of the reduced constriction (Dq) can be deduced from the initial constriction (Dc0), as follows: D = 3p X Dc0 vnn (4) The equivalent hydraulic conductivity measured over the specimen length can be a significant global parameter of the filtration magnitude, but if a great local reduction occurs, the use of the filtration depth will make the model more realistic. During filtration the constriction size reduction also depends on the depth filtration. Eq. 3 provides a uniform distribution of the void constrictions over the whole filter volume, but if using the filtration index X (Eq. 1) of accessible constrictions, which was assumed by describing the effective volume of filtration, the results must be improved. In order to start from the same principle as that of constriction (combining the densest and loosest cases through the relative density, Dr [18]) and to investigate the quantitative void reduction following the filter depth, the constriction size reduction caused by the retained base soil is carried out using Eq. 5, where the reduced diameter (dr) is computed as a value located between the initial constriction (Dc0) and the extreme case (Dcf). The two cases being related to the filtration index X, as defined by Eq. 5. Schematic of constriction deposit Section A-A Figure 5. Schematic drawing of the constriction (diameter) size reduction. v no J 34. Acta Geotechnica Slovenica, 2018/1 S. Azirou et al.: Evaluation of the constriction size reduction of granular filters due to upstream cohesive base-soil erosion d = D + X(Dc0 -Df) (5) As a result, for a greater value of X the constriction size dr is reduced by a smaller amount because the depth of the filtration is greater, allowing the particles to deposit on a larger depth (deep filtration). A smaller value of X produces a larger size reduction (lower value of dr), meaning that all the particles remain in a reduced filter layer (surface filtration). 4 RESULTS AND DISCUSSION_ 4.1 Hydraulic conductivity and porosity reduction The filtration process induces soil-particle retention within the medium, leading to porosity and hydraulic conductivity reduction. During the test, the hydraulic conductivity (using flow-rate measurements) of the filter was recorded periodically at the outlet and this parameter variation indicates the consistency of the particle retention within the filter. In order to assess the porosity reduction during the test, including several loading steps, the Kozeny-Carman equation [25] was used to derive the filter porosity (nj). The results of the porosity and the hydraulic conductivity evolution versus the applied pressure for different combinations of soil-filter are illustrated in Figs 6 and 7 below. They described the hydraulic conductivity and porosity decrease over the testing time as a nonlinear trend, showing a severe decrease during the first pressure step before reaching an asymptotic value after successive pressure steps. The hydraulic conductivity in the filter initially decreased drastically as the erosion of the soil operates and detached particles flow into the filter under pressure load, where most of them deposit. It is obvious that the soil CL2 causes the highest hydraulic conductivity reduction in filter Fi, while filter F2 presents the lowest hydraulic conductivity reduction, whatever the tested soil. The drastic hydraulic conductivity decrease, similar to clogging, can be caused by the surface-deposition process of large particles of the soil CL2 on the upper side of the filter Fj. As regards to the hydraulic conductivity requirement in the filter design, filter F1 combined with base soil CL2 evolves towards a clogged filter, which rapidly drives to uplift pressures. Filter F2 shows a similar trend with both base soils (CL1 and CL2). As regards to the porosity reduction (Fig. 6), Filter Fi shows the highest reduction, reaching a porosity value close to 0.22, when operating with soil CL2, while filter F2 reaches a porosity close to 0.36 with the same base soil (CL2) (Fig. 7). If comparing the filtration ability of filter Fi towards the tested soils, after successive hydraulic loads, the porosity is lowered to 0.33 and 0.22 when filtering CLl and CL2 soils, respectively. So, the porosity reduction of filter Fi caused by the soil erosion is much more important with CL2 than with CLi owing to the large particles encountered in the soil CL2. This drastic reduction of the filter porosity can be attributed to the kind of filtration process that can be a surface filtration when the soil particles are enough large, while a deep filtration (filtration occurs more deeply in the filter and the eroded particles are moved in the filter at a distance farther than the top of the filter) is expected when the particles are smaller than they are in soil CL2. The lowest porosity value (0.36) was obtained for filter F2, whatever the tested soil (Fig. 7), owing to the larger voids available in that porous medium. The highest porosity reduction is operated in filter Fi with soil CL2 and approaches a relative value of 0.22, providing the lowest hydraulic conductivity close to (Fig. 6). !t,35 (J.i flfSiiiif (tPal Figure 6. Hydraulic conductivity and porosity evolution in filter Fi. 7 r i i O.OE+O U k-t.U - * -k-CLZ ---— H-OJ -^i— i.-CU U.tJi U.OO Figure 7. Hydraulic conductivity and porosity evolution in filter F2. Acta Geotechnica Slovenica, 2018/1 35. S. Azirou et al.: Evaluation of the constriction size reduction of granular filters due to upstream cohesive base-soil erosion 4.2 Filtration depth and constrictions size reduction The concept of filtration depth was reported in several studies [11, 17, 28] showing an asymptotic distribution of the retained mass along a porous medium. The effective void volume contributing to the particle retention can be expressed as a filtration depth (Eq. 1). Fig.8 illustrates the evolution of the filtration depth in filter F1 at various steps of the applied pressure and the resulting filter porosity (displayed within the chart histogram bars). The chart's bars describe the filtration depth for each base soil (CL1 and CL2) in the filter F1 and the value inside represents the porosity along this depth. The comparison between the filtration of soils CL1 and CL2 indicates that the filtration depth is more important with CL1 (13.1 cm at a pressure of 25kPa, representing 87.5% of the filter height) than with CL2 (9 cm, representing 60% of the filter height) over all the tested pressures. Because of the fine particles contained in soil CL1, they deposit deeply, while large particles involved in the soil CL2 provide self-filtration (surface filtration), leading to a reduced filtration depth. We can note that large values of the final porosity are recorded in the cases of deep filtration. Because soil CL2 creates a strong porosity reduction and likely clogging occurrence within filter F1, the comparison of the behavior of both tested filters against the flowing particles of soil CL2 was assessed. Fig.9 illustrates a comparison of the filtration depth and reduced porosity in both filters after successive load 25iPa Pressure 50kFa 75kPa 0 T £ I ■T5 e 1 h*. 0.38 0.25 1134 0.23 0.33 0.21 □ F1CL1 □ F1CL2 Figure 8. Evolution of the porosity and filtration depth with hydraulic pressure in filter F with soils CL\ and CL2. pressure steps. As regards to the filtration process, filter F2 is more efficient, reaching a filtration depth of 99 % and holding the filter in a range of sustainable porosity and easy water flow, whereas filter F1 concentrates the particle retention within a thin layer, drastically reducing the local pore volume, leading to severe hydraulic conductivity reduction and likely clogging. The opera- ting difference between the two filters is related to the large constriction size of the filter F2, which provides an easy transport of the largest particles of soil CL2 and so a deeper penetration within the filter. Unlike the smaller constriction size of filter F1 this leads to the easy retention of the soil particles, involving self-filtration, which in turn leads to a thin (9 cm) depth filtration. For the first load step (P=25 kPa) the relative depth filtration obtained in filter F1 operating with soil CL2 is close to 9/15 (the eroded particles can be transported to a depth of 9 cm among 15 cm, see Fig. 9), representing 60 % of the accessible constrictions that undergo a size reduction. At the second pressure step (P=50 kPa) only 53 % of the filter depth is so submitted to a second successive size reduction. When applying a pressure of 75 kPa, only 50 % of the depth is of concern and the constriction size is reduced again by particle retention. fcessuie 25kPa 50k?a »