Shengnan Ma,Yi Song,Jiawei Liu,Xingyu Kang,Zhongqi Quentin Yue

Department of Civil Engineering,The University of Hong Kong,Hong Kong,China

Keywords: Particle size distribution (PSD)General soil Silt Clay Wet sieving Physical and chemical properties

ABSTRACT The traditional standard wet sieving method uses steel sieves with aperture ≥0.063 mm and can only determine the particle size distribution (PSD) of gravel and sand in general soil.This paper extends the traditional method and presents an extended wet sieving method.The extended method uses both the steel sieves and the nylon filter cloth sieves.The apertures of the cloth sieves are smaller than 0.063 mm and equal 0.048 mm,0.038 mm,0.014 mm,0.012 mm,0.0063 mm,0.004 mm,0.003 mm,0.002 mm,and 0.001 mm,respectively.The extended method uses five steps to separate the general soil into many material sub-groups of gravel,sand,silt and clay with known particle size ranges.The complete PSD of the general soil is then calculated from the dry masses of the individual material sub-groups.The extended method is demonstrated with a general soil of completely decomposed granite(CDG) in Hong Kong,China.The silt and clay materials with different particle size ranges are further examined,checked and verified using stereomicroscopic observation,physical and chemical property tests.The results further confirm the correctness of the extended wet sieving method.

1.Introduction

Soils can have various combinations of different particles with sizes from gravel,sand,silt,to clay.The particle size distribution(PSD)of soil is used to quantify the combinations and to define the soil name.PSD is a basic property of soils for geotechnical engineering and soil mechanics,and it can be used to define the names of soils and to estimate the physico-mechanical behaviours of soils,such as permeability,pore sizes,and water retention (Valsangkar,1992;Craig,1997;Gupta,2016;Chapuis,2021;Ng et al.,2022;Wang et al.,2023).In geotechnical testing,the wet sieving method and sedimentation methods are commonly used as the standard methods to determine the soil PSD (BS 1377-2:1990,1990;ASTM D422-63,2007;Geospec 3,2017a;GB/T 50123-2019,2019).

The standard wet sieving method uses steel sieve to separate and quantify the distribution of gravels and sands with particle size larger than 0.063 mm.It washes and removes the silt and clay particles in soil as waste.It then uses dry sieving method to separate the gravel and sand mixture into sub-groups with different particle sizes by shaking the mixture on the steel sieves with different apertures.The results are of high accuracy and can be checked independently.However,the steel sieves have a low aperture limit of 0.063 mm so that it cannot be used to test the particle sizes of silt and clay.

Instead,the standard sedimentation methods are used to determine the particle sizes of silt and clay mixture with particle sizes smaller than 0.063 mm.They include the hydrometer method and the pipette method(Bouyoucos,1926;Day,1965).The standard sedimentation methods are based on Stokes’ Law with the assumption of spherical particle shape,which usually cannot be met by general soils(Ghasemy et al.,2019).Furthermore,different pretreatments and suspension concentrations can lead to significant different results for the same soil(Lu et al.,2000,2021;Papuga et al.,2021).Third,they are time-consumption and need many test operation steps under controlled environment such as water temperature in bath tank.Due to the limitations in the two sedimentation methods,some new methods were developed in recent years,such as laser diffraction method,single particle optical sizing method,electrical sensing zone method,and imaging method(Abbireddy and Clayton,2009;Bittelli et al.,2022).The methods are based on different physical principles and their results may not be accurate (Valsangkar,1992;Chapuis,2021).

This paper aims to present an extended wet sieving method for accurate measurement of the particle sizes of silt and clay mixture.It is a logical extension of the existing standard wet sieving method with steel sieve for soil particle sizes larger than 0.063 mm.It uses a new industrial product of nylon filter cloth with aperture size of 0.048 mm,0.038 mm,0.014 mm,0.012 mm,0.0063 mm,0.004 mm,0.003 mm,0.002 mm,0.001 mm,or 0.0008 mm,respectively,as the sieve.This paper finds that the nylon cloth sieves can separate the silt and clay mixture into different size groups of silt or clay.It is independent to the standard sedimentation methods and can accurately determine the mass-based PSD of silt and clay up to smaller than 0.001 mm or 0.0008 mm.Hence,the extended wet sieving method can separate and divide the soil into many subgroups of gravel,sand,silt,and clay particles.

2.Extended wet sieving method for silt and clay in soil

2.1.General

A completely decomposed granitic(CDG)soil is used as the test material,which is obtained from a construction site at Happy Valley,Hong Kong.Its basic properties are tested using the standard methods in BS 1377-2:1990 (1990).Its specific gravity is 2.68.The plastic limit,the liquid limit,and the plasticity index for soil particles smaller than 0.425 mm are 31.1%,75.9%,and 44.8%,respectively.The plastic limit,the liquid limit,and the plasticity index for silt and clay mixture of particle size smaller than 0.063 mm are 34.8%,98.3%,and 63.5%,respectively.The extended method is divided into five steps.Each step is described below.

2.2.Step I: extended wet sieving method for general soil with steel sieve

The Step I uses the standard wet sieving method with a steel sieve of aperture 0.063 mm to separate and divide the CDG soil into the first portion of gravel and sand mixture and the second portion of mud slurry (Fig.1).The mud slurry is a mixture of silt and clay particles with water.The CDG soil is washed and sieved on a steel sieve with aperture of 0.063 mm(Fig.1).The steel sieve is set on a bucket.The bucket collects the mud slurry.Then the soil is stirred and rinsed with water on the steel sieve while the mud slurry is leaked through the steel aperture into the bucket.This operation is completed when both the sand and gravel particles on the steel sieve and the mud slurry seeping out become clean.

Fig.1.Procedure and results of Step I of the extended wet sieving method with steel sieve of aperture 0.063 mm:(a)Wet sieving using the steel sieve with aperture of 0.063 mm;(b) Wet clean gravel and sand particles after wet sieving;and (c) Mud slurry.

The natural and dry masses of the CDG soil sample used in this Step I are 3530 g and 3484.1 g,respectively.The dry mass of clean gravel and sand mixture portion is 1895.3 g and 54.4% of the total mass of the dry CDG soil sample.The dry gravel and sand mixture are sieved with traditional mechanical shaking and separated into 14 sub-groups of different particle size ranges with standard steel sieves.The standard steel sieve has the aperture of 63 mm,10 mm,6.3 mm,5 mm,3.35 mm,2.36 mm,2 mm,1.18 mm,0.6 mm,0.425 mm,0.3 mm,0.212 mm,0.15 mm,0.075 mm,or 0.063 mm,respectively.The gravel or sand materials of the 14 sub-groups are shown in the 14 photographs of Fig.2.They are mainly the mineral of quartz.

Fig.2.Photographs for dry sieving results of the 14 sub-group materials of the gravel and sand in CDG soil with the particle size ranges of (a) 10-6.3 mm;(b) 6.3-5 mm;(c) 5-3.35 mm;(d)3.35-2.36 mm;(e)2.36-2 mm;(f)2-1.18 mm;(g)1.18-0.6 mm;(h)0.6-0.425 mm;(i)0.425-0.3 mm;(j)0.3-0.212 mm;(k)0.212-0.15 mm;(l)0.15-0.075 mm;(m)0.075-0.063 mm;and (n) 0.063-0.048 mm.

The mass and density of the mud slurry are 40 kg and 1.025 g/cm3,respectively.The mass of dry silt and clay mixture in the mud slurry is 1588.8 g(=3484.1-1895.3 g)and 45.6% of the total mass of the dry CDG soil sample.This calculated total dry mass of silt and clay mixture shall be equal to the actual total mass of the dry silt and clay materials obtained in Section 2.7.For checking and calibrating the accuracy of the extended wet sieving method,the mud slurry is further separated into three sets of 20 kg,13 kg,and 7 kg,respectively.Each set is used in the following steps.

2.3.Step II:extended wet sieving method for mud slurry with cloth sieve

Step II uses the nylon filter cloth as the sieve.The nylon filter cloth has the best abrasion resistance for sieving in comparison with other filter materials such as polypropylene,polyester,and cotton cloth (Zerin and Datta,2018).It is robust and is not easily deformed and damaged after many times usages.Its smooth surface makes it easy for completely removing silt or clay out of the cloth.Originally,the nylon filter cloth is used for tailings dewatering in mining,foulant filtration in wastewater treatment,and biological residue filtration in beverage industry (Zhao et al.,2016;Werner et al.,2020;Fr?nkle et al.,2021).

The literature review shows that the nylon filter cloth was not used for sieving soils in open publications.The extended wet sieving method proposed in this paper uses the nylon filter cloth as the sieve for separating silt and clay particles,which is original and novel.The aperture of each type of nylon filter cloth can be different and equal to 0.048 mm,0.038 mm,0.014 mm,0.012 mm,0.0063 mm,0.004 mm,0.003 mm,0.002 mm,or 0.001 mm,respectively.Details of the nine types of nylon filter cloths can be observed with the stereomicroscope and shown in the photographs(see Fig.3).This Step II uses the nylon cloth sieve of aperture 0.002 mm to wash and sieve each of the three sets of mud slurry,as illustrated in Figs.4 and 5.

Fig.3.Stereomicroscopic images of nylon cloth sieve.

Fig.4.Illustration of the extended wet sieving method with nylon cloth sieve of aperture 0.002 mm (or other size from 0.048 mm to 0.001 mm).

The nylon filter cloth forms a cloth sieve bag.The upper portion of the bag is tightened by a circular plastic stretcher to form a circular hole of 25 cm in diameter.The lower portion of the cloth sieve bag is put into a plastic bucket.The bucket collects the clay slurry seeping out of the cloth sieve bag.The clay slurry shall contain only the particles with sizes smaller than 0.002 mm.

The mud slurry and new water are added with cups into the cloth sieve bag via the circular hole (Fig.5a).The two hands hold the circular plastic stretcher,and shake and rotate the cloth sieve bag with mud slurry in a clockwise direction(Fig.5b).The shaking or rotating frequency is about 120-150 rpm (revolutions per minute).The shaking and rotating can apply a centrifugal force to the mud slurry in the bag and force the clay slurry to seep out of the bag.The particles with sizes larger than the aperture size stay within the bag.The clay slurry is a mixture of water and clay particles with the size smaller than the 0.002 mm aperture of the cloth sieve bag.The seepage of clay slurry through the cloth sieve bag is very slow.The shaking and rotating operation takes many minutes.With elapsed time,the mud slurry within the bag becomes dense and dense,and the seeping of clay slurry becomes less and less.More new water has to be added to dilute the mud slurry in the bag.The shaking and rotating operation is completed when the clay slurry passing through the cloth bag is clean or water only.The results of this Step II are listed in Table 1.The colours of the silt slurry(Fig.5c)and the clay slurry in the bucket(Fig.5d)are brown and yellowish brown,respectively.

Table 1Results of mud slurry with cloth sieve in Step II.

Fig.5.Photographs showing the extended wet sieving method for separating silt and clay: (a) Pour the mud slurry into cloth sieve bag;(b) Shaking and rotating;(c)Separated first silt slurry;and (d) Separated first clay slurry.

Fig.7.Photographs showing medium to fine silts in CDG soil after drying: (a) 0.012-0.0063 mm;(b) 0.0063-0.004 mm;(c) 0.004-0.003 mm;and (d) 0.003-0.002 mm.

Fig.8.Photographs showing coarse and fine clay in CDG soil after drying: (a) 0.002-0.001 mm;and (b) ＜0.001 mm.

2.4.Step III: extended wet sieving method for silt slurry with cloth sieves

Three sets of silt slurry with masses of 120 g,90 g,and 50 g respectively are obtained from Step II.Step III is similar to Step II and applies to each set of silt slurry.The nylon cloth sieve bag of aperture 0.002 mm is replaced by another nylon cloth sieve bag of aperture 0.048 mm,0.038 mm,0.014 mm,0.012 mm,0.0063 mm,0.004 mm,or 0.003 mm,respectively.The results of this Step III for the three sets of the silt slurry are listed in Table 2.The operation is as follows.

Table 2Results of first silt slurry with cloth sieve in Step III.

In the beginning,the set of 120 g silt slurry is sieved with the cloth sieve bag of aperture 0.048 mm.The first silt slurry is then separated into the wet silt of 15 g in the bag and the second silt slurry of 5.105 kg in the bucket.The added new water is about 5 kg.The wet sieving operation is completed when the liquid passing through the cloth sieve bag is clean or contains water only.This operation lasts for about 12 min.The wet silt contains only the silt particles of size between 0.063 mm and 0.048 mm.The second silt slurry contains only the silt particles of size smaller than 0.048 mm.Subsequently,the second silt slurry is treated as the new first silt slurry.The above operation is applied to this new first silt slurry with the cloth sieve bag with aperture of 0.038 mm.So,the new wet silt and the second silt slurry are obtained.Repetitively,the operation continues with the cloth sieve bag with aperture of 0.014 mm,0.012 mm,0.0063 mm,0.004 mm,and 0.003 mm,respectively.The similar operation is also applied to the other two sets of the first silt slurries of 90 g and 50 g,respectively.

2.5.Step IV:extended wet sieving method for clay slurry with cloth sieve

Three sets of clay slurry with masses of 30 kg,21 kg,and 13 kg respectively are obtained from Step II.Step IV is also similar to Step II and is applied to each set of the clay slurry.The nylon cloth sieve bag of aperture 0.002 mm is replaced by another nylon cloth sieve bag of aperture 0.001 mm.The results of this Step IV are listed in Table 3.When the passing liquid is clean or contains water only,the wet sieving operation is completed.The operations on the three sets of clay slurry take about 120 min,90 min,and 60 min and use new water of 13 kg,12 kg,and 10 kg,respectively.The time and water used for the clay slurry are much more than those for the silt slurry,due to the fact that the clay has much higher cohesion and low permeability than the silt.

Table 3Results of first clay slurry with cloth sieve in Step IV.

2.6.Step V: extended wet sieving method for recycling used water from slurry

Because the silt has high permeability,the used water in the wet silt can seep out rapidly.Hence,each wet silt contains only a small amount of water.The silt particles can settle to the bottom of their containers within 10 min.For example,the above three sets of the last silt slurry passing the cloth bag with aperture of 0.003 mm can recycle 11.004 kg,11.002 kg,and 11.001 kg clean water,respectively.After the water recycling,the three sets of the wet silt with the size of 0.003-0.002 mm have the mass of 12 g,8 g,and 4 g,respectively.Their water contents are 38%,39%,and 42%,respectively.

The clay slurry has the density from 1.047 g/cm3to 1.0054 g/cm3.It can contain water of mass 20-200 times more than the mass of clay particles.After it is placed in a container or bucket statically,the clay slurry would experience gravity-induced sedimentation of clay particles in the lower portion and have the presence of clean water in the upper portion.After 16 h of static sedimentation,more than 85% of the water in the original clay slurry would present in the upper portion of the container.The new clay slurry would become highly saturated soft clay and have less water.The water can be recycled for re-use in the extended wet sieving method.

The used water in the upper portion of the container with clay slurry is tested for its purity using Cary 100 UV-Visible Spectrophotometer.The ten water samples in three groups are tested.Each test sample has a volume of 30 mL.The used water from the clay slurry is the experimental group and has three test samples that are obtained after the static sedimentation for 1 h,2 h,and 3 h,respectively.The fresh tap water is the blank control group and has one test sample.The control group has six test samples.They are obtained by adding clay particles (＜0.002 mm) of masses of 0.0104 g,0.0052 g,0.0021 g,0.0012 g,0.0005 g,and 0.0001 g,respectively into 30 mL fresh tap water.

The six samples in the control group have the absorbance values of 0.1828,0.0754,0.0408,0.0237,0.0107,and 0.0085,respectively.The absorbance values of the three used water samples are 0.007,0.0068,and 0.0062,respectively,which are between the absorbance value 0.0085 for the sixth control sample with 0.0001 g clay and the absorbance value 0.0008 for the blank fresh tap water sample.Hence,the used water from the static sedimentation of the clay slurry is relatively clean and has the clay content less than 3.33 ppm.

2.7.PSD result for the silt and clay portion of general soil

The silt and clay materials in the ten sub-groups are oven-dried and the dry masses are measured(see Table 4).Figs.6-8 show the ten photographs of the ten sub-groups of oven dried silt and clay materials.The silt contains coarse silt,medium silt,and fine silt according to their particle size ranging from 0.063 mm to 0.02 mm,0.02 to 0.0063 mm,and 0.0063 to 0.002 mm,respectively (ISO 14688-1:2017,2018).The clay contains coarse clay and fine clay according to the particle size ranging from 0.002 mm to 0.001 mm and smaller than 0.001 mm,respectively.

Table 4Final results of ten sub-groups of silt and clay.

The PSD curve of the silt and clay mixture for each of the three sets can be calculated from the dry masses of its 10 sub-groups of silt and clay:

wherePSDsilt&clayis the cumulative passing percentage of theKth cloth sieve aperture (K=1,2,3,…,10);Waiis the dry mass of the sub-group material with particle sizes between the(i-1)th and theith sieve apertures (i=1,2,3,…,or 10);Wtotalsilt&claymixture=Waiand is the total mass of dry silt and clay mixture.The 0th aperture is zero.The 10th sieve aperture is 0.063 mm and is the steel sieve in Step I.Theith aperture(i=1,2,3,…,9)is 0.001 mm,0.002 mm,0.003 mm,0.004 mm,0.0063 mm,0.012 mm,0.014 mm,0.038 mm,and 0.048 mm,respectively.

The three PSD curves for the three sets of dry silt and clay mixtures are shown in Fig.9 and are almost identical.Such result shows the high accuracy of the extended wet sieving method.

Fig.9.PSD of the three sets of silt and clay mixtures obtained from the Steps I to V of the extended wet sieving method.

The PSD curve of the total silt to clay mixture in the general CDG soil can be calculated by adding three dry masses of the three sets according to their same sub-group size ranges,respectively.The results are given in Table 5 and Fig.10.The total mass of the dry silt and dry clay is 1587.13 g and is the 99.89% of the total dry mass of 1588.8 g that is calculated for the mud slurry in Step I.The clay and silt contents are respectively 92.74% and 7.26% of the silt and clay mixture in CDG soil.The coarse,medium and fine silt contents are about 4.38%,1.66%,and 1.22%,respectively.The coarse and fine clay contents are about 27.77% and 64.97%,respectively.This silt and clay mixture can be classified as slightly silty clay of extremely high plasticity (Geoguide 3,2017b).

Table 5Final results of extended wet sieving method for general soil.

Fig.10.PSD curves of the general CDG soil,its gravel and sand portion (b),and its silt and clay portion (a).

2.8.PSD result for gravel and sand portion of general soil

Similarly,the PSD of the gravel and sand mixture can be calculated:

wherePSDgravel &sand is the cumulative passing percentage of theKth steel sieve aperture(K=10,11,12,…,24);Wbiis the dry mass of the sub-group material with particle sizes between the(i-1)th and theith sieve apertures (i=10,11,12,…,or 24);Wtotalgavel&sandmixture=Wbiand is the total mass of dry gravel and sand mixture.Theith aperture(i=9,10,11,12,…,24)is 0.048 mm,0.063 mm,0.075 mm,0.15 mm,0.212 mm,0.3 mm,0.425 mm,0.6 mm,1.18 mm,2 mm,2.36 mm,3.35 mm,5 mm,6.3 mm,10 mm,and 63 mm,respectively.

The gravel contains medium and fine sizes (ISO 14688-1:2017,2018).The sand contains coarse,medium and fine sizes (ISO 14688-1:2017,2018).The masses of the gravel and sand are 31.24% and 68.76% of their total mass,respectively.This gravel and sand mixture can be classified as well graded very gravelly sand(Geoguide 3,2017b).

2.9.Complete PSD result for general soil

The complete PSD of the general soil can be calculated as follows:

wherePSDgeneralsoilis the cumulative passing percentage of theKth cloth or steel sieve aperture,andWgeneralsoil=Wtotal gravel &sand mixture+Wtotalsilt&claymixture.

This general CDG soil covers a wide range of grain sizes from gravel to clay.Its gravel,sand,silt and clay are 16.97%,37.34%,3.42%,and 42.27% of the total mass,respectively.It can be classified as widely graded gravelly sandy clay of very high plasticity(Geoguide 3,2017b).

3.Verification of individual silt and clay particles

3.1.Stereomicroscopic observation

The Leica M205C stereomicroscope is used to observe the sieved particles of the eight sub-groups of silt and two sub-groups of clay.For observation,each sub-group of the silt particles and clay powder are uniformly stuck onto a glass slide to form a thin seam of particles.The glass slide with the silt particles or clay powder is placed on the platform of the stereomicroscope for observation.

Figs.11 and 12 show the stereomicroscopic photographs of the eight sub-groups of coarse silt to fine silt.Individual solid mineral particles are evidently and mainly quartz particles and are not stuck together.These silt particles are the natural extensions of fine sand particles.Fig.13 shows the stereomicroscopic photographs of the coarse clay of particle size between 0.002 mm and 0.001 mm,and the fine clay of particle size smaller than 0.001 mm.Fig.13a clearly shows the presence of some individual solid mineral particles and some clumps while Fig.13b evidently shows the presence of mainly particle clumps.The individual solid particles are the natural extension of the fine silt particles.The particle clumps consist of the clay particles.

3.2.Verification of sizes of silt particles and clay clumps

Each of the digital images in Fig.11a to 13a is then used to calculate the major and minor lengths of an individual silt particle using the ImageJ software.The directions of the major and minor lengths of a silt particle are perpendicular to each other.Six individual silt particles are randomly selected for the image calculation.Each selected particle is outlined with a yellow curve in each of the nine photographs.The major length is marked in a red line and the minor length is marked in a blue line.The calculated results are shown in Fig.14.

Fig.11.Stereomicroscopic photographs of sieved coarse to medium silt particles in CDG soil: (a) 0.063-0.048 mm;(b) 0.048-0.038 mm;(c) 0.038-0.014 mm;and (d) 0.014-0.012 mm.

Fig.12.Stereomicroscopic photographs of sieved medium to fine silt particles in CDG soil: (a) 0.012-0.0063 mm;(b) 0.0063-0.004 mm;(c) 0.004-0.003 mm;and (d) 0.003-0.002 mm.

As shown in Fig.14,a majority of the major lengths of the selected silt particles are larger than the individual upper limits of their sub-groups.All the minor lengths of the selected silt particles or clay clumps are smaller and larger than the individual upper and lower limits of their sub-groups,respectively.The above results can demonstrate that the minor length of a particle is the determinant length that determines whether or not the particle can pass through the aperture of a nylon cloth sieve.Hence,a particle that is washed and sieved into a specific sub-group is determined by its minor length.The upper and lower limits of a sub-group represent the upper and lower limits of particle minor lengths,respectively.

Furthermore,six smallest clay clumps are also selected from the digital image in Fig.13b to do the image calculation.The results are also given in Fig.14.The major and minor lengths of the six clay clumps are equal to or smaller than the upper limit 0.001 mm of the sieve aperture,which shows that all the clay sizes can be smaller than 0.001 mm.

Fig.13.Stereomicroscopic photographs of sieved clay particles in CDG soil: (a) 0.002-0.001 mm;and (b) ＜0.001 mm.

Fig.14.Quantitative verification of sizes of silt particles and clay clumps.

On the other hand,the particle form of an individual silt particle or clay clump can be represented by the ratio of its minor length over its major length.As shown in Fig.14,the minor/major ratios have the minimum 0.333,the medium 0.667,the mean 0.693,the maximum 1,the standard deviation 0.154,and the coefficient of variation 0.223.Hence,the forms of silt particles tend to be nearly equidimensional.

3.3.Discussion on particle size dividing silt and clay

The size definition of silt and clay particles in different standards can be different.In ISO 14688-1:2017 (2018) and Geoguide 3(2017b),the particles with sizes ranging from 0.063 mm to 0.002 mm are defined as silt and the particles with sizes smaller than 0.002 mm are defined as clay.In ASTM D422-63(2007)and GB 50021-2001 (2009),the particle sizes for silt are defined from 0.075 mm to 0.005 mm and the particle sizes for clay are defined to be smaller than 0.005 mm.

The silt has the particle sizes smaller than that of the fine sand and is an extension of fine sand.Similar to fine sand particles,silt particles should have only solid particles of siliceous minerals such as quartz and have relatively high permeability and low plasticity.The two size definitions of 0.075 mm and 0.063 mm for dividing silt and fine sand may not give any noticeable effect on the functions of silt and sand in the soil.

However,the silt and clay have definite differences in mineral composition,grain structure,permeability,cohesion,and shear strength (Lambe and Whitman,1979;Craig,1997).Clay should be composed of only clay minerals and have extremely low permeability and high plasticity.The above two size definitions of 0.005 mm and 0.002 mm for dividing silt and clay can give sound effect on the functions of silt and clay in the soil.Such two definitions for dividing silt and clay may be due to the fact that the standard sedimentation methods cannot provide the actual material samples of silt and clay for checking and verification.

The results given in Figs.11-14 can provide a solution to the issue of the different dividing sizes for silt and clay particles in different standards.The size of 0.005 mm as the cut-off size limit dividing silt and clay would result in more siliceous (quartz) mineral particles into the clay mineral content.The size of 0.002 mm as the cut-off size limit dividing silt and clay would result in less siliceous (quartz) mineral particles into the clay mineral content.Our test results further demonstrate that the particle size range from 0.002 mm to 0.001 mm is the transitional zone from silt to clay or from siliceous mineral particles to clay mineral particles,and that the particle size of 0.001 mm can be a smallest size limit for silt(siliceous mineral particles)and an upper size limit for pure clay mineral particles.

3.4.Discussion on silt and clay in CDG soil in Hong Kong

The properties of CDG soils in Hong Kong were examined extensively by many researchers over the past six decades due to the fact that landslides frequently occur in hillside slopes composed of CDG soils (e.g.Lumb,1962;Yue et al.,2004;Yin,2009;Madhusudhan and Baudet,2014).The PSD of CDG soils is one of the basic physical parameters examined in these studies.The mass percentages of gravel,sand,silt,and clay of 17 CDG soils at different locations in Hong Kong,China in the literature are summarized in Table 6.

Table 6Summary of the mass percentages of gravel,sand,silt,and clay of CDG soils in Hong Kong from literature and this paper.

In the past studies,the PSDs of the CDG soils are determined with the steel sieving method for the sand and gravel portion and the sedimentation methods for the silt and clay portion(BS 1377-2:1990,1990;Geospec 3,2017a).These PSD data show that the portions of silt and clay in CDG soil are 4.4%-37.5%,and 2.2%-26.5%,respectively.Such large variations in silt and clay contents are considered acceptable due to the large variations in both the lithologies and structures of granitic rocks and the degree of chemical and physical weathering(Fyfe et al.,2000).It is noted that these results of the silt and clay contents in CDG soils are not independently checked and verified for their accuracy.

In this study,the total dry masses of silt and clay are 119.29 g and 1471.87 g,respectively.They are the 3.42% and 42.27% of the total mass of the dry CDG soil,respectively.As shown in Table 6,the silt content in this study is the lowest,but the clay content in this study is the highest in comparison with the other 17 data sets of the silt and clay contents of the CDG soils in Hong Kong,China.This result of the lowest silt content and highest clay content demonstrates that the extended wet sieving method can separate the clay material from sticking on the silt and break the clay clumps into individual clay particles.

3.5.Calibration of the apertures of the steel and cloth sieves

To ensure repeatability and operability of this extended wet sieving method,the apertures of the used steel and cloth sieves should be calibrated regularly.The aperture sizes and shapes can be checked and tested with the techniques standardized in ASTM E11-16 (2016),BS 410-1: 2000 (2000),and ISO 3310-1: 2016 (2016).These techniques can calibrate the metal wire cloth aperture by measuring the sizes and shapes of apertures of steel sieves.They can be extended to measure and examine the aperture of the nylon cloth used in this paper.The nylon wire woven apertures can be viewed when they magnified with microscope,as shown in Fig.3.The minor length of the nylon cloth aperture can control the particle sizes of the extended wet sieving results (Fig.14).

Second,the particle sizes of separated sand,silt and clay can be tested and examined as shown in Figs.11-14.After having obtained the different groups of individual silt and clay materials,the particle sizes can be checked with microscope observation.The minor lengths of silt particles are the determinant lengths for them to pass or not the aperture of the nylon filter cloth with water.

Third,the standard wet sieve method with steel sieves uses the calibration technique of micro-spherical glass (Fig.15) to calibrate the aperture of the steel sieve(McManus,1963;Rideal et al.,2000;Rideal,2001).Similarly,the micro-spherical glass or other artificial micro-solid particles can be used to calibrate the aperture of the nylon filter cloth.The micro-solid particles have a known PSD.They can be used to calibrate the different apertures of nylon filter cloths.In particular,a group of sand and silt(quartz)particles with known PSD (down to 0.001 mm) can be pre-determined and established.They can be used as the standard particles for the aperture calibration of both the steel and the cloth sieves.Since the extended wet sieve method uses water as the sieving medium,the sieving process would not make damage to these solid particles when they are mixed with water during sieving vibration.

Fig.15.Standard micro-spherical glasses with diameters equal or smaller than 2 mm.

4.Physical and chemical properties of individual silt and clay materials

4.1.General

Previous studies show that the physico-chemical properties of fine soils(or silt and clay mixtures)have been examined intensively(Lambe and Whitman,1979;Craig,1997).However,there are few publications regarding the physico-chemical properties of silt or clay whose particle size is within each of the ten individual narrow size groups.Hence,this section aims to examine the basic properties of the ten individual size groups of the silt and/or clay materials.

4.2.Atterberg limits and plasticity index

The Atterberg limits(i.e.plastic limit and liquid limit)are tested for each of the ten sub-groups of silt and clay materials using the standard methods in BS 1377-2:1990(1990)and Geospec 3(2017a).Fig.16 plots the plasticity index versus the liquid limit for each of ten sub-groups of silt and clay materials and the CDG soil.

Fig.16.Results of plasticity index versus liquid limit for coarse silt to fine clay.

As shown in Fig.16,the two points of the pairs of the plasticity index versus the liquid limit values for the coarse and fine clay are well above the A-line.Both coarse and fine clay can be classified as extremely high plasticity clay (CE).Both liquid limit (110%) and plasticity index(72.4%)of the fine clay are much higher than these 96.0% and 62.2% of the coarse clay,which demonstrates that the fine the clay,the high the liquid limit and the plasticity index.

The plots of the pairs of the plasticity index versus the liquid limit values for the eight sub-groups of silt material are clustered together and below the A-line.They all can be classified as intermediate plasticity silt (MI).As the silt particle size decreases from the upper coarse silt(the first sub-group)to the lower fine silt(the eight sub-group),the liquid limit increases from 41.5% to 43.5%,and the plasticity index increases from 10.9% to 16.1%.These results further show the correctness of the extended wet sieving method.

Furthermore,the point of the plasticity index versus the liquid limit for the CDG soil with particle size smaller than 0.425 mm is located between the two points for the two clay materials and the eight points for the eight silt materials.This is due to the presence of 21% medium and fine sand and silt in the particles smaller than 0.425 mm.On the other hand,the point of the plasticity index versus the liquid limit for the silt and clay mixture is located between the point for the coarse clay material and the point for the fine clay material and above the A-line,due to the presence of only 7.26% silt in the silt and clay mixture.

The results further show that the extended wet sieving method with the nylon filter cloth sieve can accurately separate and divide the silt and clay mixture into the ten sub-groups of individual silt and clay materials with different particle sizes.

4.3.Permeability of individual silt and clay materials

The permeability coefficient is tested for each of the ten subgroups of silt and clay materials using the standard method for permeability coefficient in GB/T 50123-2019 (2019).For sufficient verification,three repeatability tests are conducted for each of the ten sub-groups of silt and clay materials.The sample properties and test results are listed in Table 7.In particular,the average void ratios for the coarse silt to fine clay test samples are 0.925,0.926,0.932,0.921,0.922,0.921,0.935,0.93,1.05,and 1.037,respectively.Fig.17 plots the curves of the permeability coefficients versus its particle size for the three tests.The three curves for the three tests are almost identical,which shows the high accuracy of the tests.Furthermore,the permeability coefficient value increases as the particle size increases.In particular,the values of the average permeability coefficient of coarse silt to fine clay are displayed in Table 7.

Table 7Test results for permeability coefficients of coarse silt to fine clay.

Fig.17.Permeability coefficient for coarse silt to fine clay.

The permeability coefficient value of the coarse clay is 1.63 times larger than that of the fine clay.The permeability coefficient values of the eight silt materials from the smallest to the largest sizes are 19.72,19.75,19.92,20.1,21,27.83,59.92,and 84.44 times larger than that of the fine clay.Li et al.(2005a,2005b) determined that the permeability of a CDG soil in borehole is from 1 × 10-7m/s to 1×10-5m/s,which indicates that the presence of 75.1% gravel and sand in this CDG soil (Table 6) can increase its permeability significantly.

4.4.Chemical elements of individual silt and clay materials

The silt and clay materials in the ten sub-groups are analysed using a scanning electron microscope (SEM).Their chemical elements are tested using an energy-dispersive spectroscopy (EDS)detector associated with ZEISS SEM system linked to an Oxford Instruments X-Max 50 EDS detector with Aztec software at the Electron Microscope Unit of The University of Hong Kong,China.

Eleven chemical elements including silicon,aluminium,oxygen,potassium,calcium,sodium,magnesium,iron,titanium,sulfur,and chlorine are found in the coarse and fine clays.Nine elements including silicon,aluminium,oxygen,potassium,calcium,sodium,magnesium,iron,and titanium are found in the silt materials.Fig.18 presents the weight percentage with respect to the particle size for each of the eleven chemical elements.

Fig.18.Distribution of weight percentages of each of eleven chemical elements with particle size from coarse silt to fine clay:(a)Calcium;(b)Sodium;(c)Magnesium;(d)Oxygen;(e) Potassium;(f) Silicon;(g) Aluminium;(h) Iron;(i) Titanium;(j) Sulfur;and (k) Chlorine.

Except to the titanium,the other eight chemical elements in both the silt and clay materials are consistent with the chemical elements in the four main minerals of the parent granitic rock.They are the quartz (SiO2),the orthoclase feldspar (KAlSi3O8),the plagioclase feldspar (NaAlSi3O8-CaAl2Si2O8),and the biotite(K(Mg,Fe)3(AlSi3O10)(OH)2).The titanium can come from the minor minerals of the parent granitic rock.The two additional chemical elements(sulfur and chlorine)in the clay materials may come from the weathering process.

The clay materials have high contents of calcium,sodium,and magnesium while the silt materials have near zero contents of these three elements (see Fig.18a-c).This indicates that the two main minerals of plagioclase feldspar and the biotite are almost completely decomposed into clay minerals.On the other hand,the contents of silicon and aluminium in silt materials are much higher than those in the clay materials (see Fig.18f and g),but their contents of oxygen and potassium are less than those in the clay materials (see Fig.18d and e),in which the quartz is not decomposed and the orthoclase feldspar is partially decomposed.The iron in the silt materials is much higher than that in the clay materials and is variable with size of the silt particles,which indicates that the silt can have some iron oxide particles as an additional product from chemical weathering of granitic rock.

The results of the chemical elements and their weight percentages in the silt and clay materials show that the silt materials have significantly different minerals than those in the clay materials,which further demonstrates the high accuracy of the extended wet sieving method.

5.Conclusions

This paper presents the extended wet sieving method for accurately determining the complete PSD of general soil.The results are obtained by completely separating and dividing the general soil into 24 sub-groups of individual gravel,sand,silt and clay materials with different particle size ranges.In particular,the ten sub-groups of individual silt and clay materials are checked and verified using stereomicroscopic observations,digital image analysis,and physical and chemical property tests.The main findings can be drawn as follows:

(1) The extended wet sieving method with nylon filter cloth can sieve and separate the silt and clay mixture in a CDG soil.The mass balance of the soil before and after testing can be checked and verified accurately.The availability of the individual silt and clay materials offers the conditions for determinations of the particle size and the material properties using stereomicroscopic images,physico-chemical property tests as well as further utilizations in engineering science.This method is simple and easy to operate,and the results are accurate and can be verified accurately and duplicated and re-used.The used water can be recycled.

(2) The test results can further check and confirm the accuracy and correctness of the extended wet sieving method.The results of the digital image analysis show that the minor lengths of silt particles are the determinant length for them to pass or not the aperture of the nylon filter cloth with water.In addition,the micro-spherical glass with known diameters and/or the separated sand and silt particles with known sizes can be used as the standard particles for calibration of the apertures of the steel and cloth sieves.

(3) The liquid limit and the plasticity index of the tested CDG soil are much higher than those of the silt materials in the eight sub-groups and much less than those of the coarse and fine clay materials.The fine the silt or clay particles,the low the permeability coefficient value.The permeability coefficient of the coarse silt can be 84.44 times higher than that of the fine clay.The major chemical elements of silicon,aluminium,and oxygen dominate the minerals of silt and clay materials.The other chemical elements of calcium,sodium,magnesium,sulfur,and chlorine mainly exist in the clay materials.Iron oxides can present in the silt materials.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The work described in this paper was partially supported by grants from the Research Grant Council of the Hong Kong Special Administrative Region,China (Project Nos.HKU 17207518 and R5037-18).The first to fourth authors thank the University of Hong Kong for the scholarship for their Ph.D.studies.The authors thank Mr.Junqi Feng and Soils &Materials Engineering Co.,Ltd.in Hong Kong for using their standardized test facilities to carry out soil material tests.