WeightVolumeWAirWWaterWVV.WSolidSFigure2Idealizedthree-phasesoil system.The meaning of the symbols used in figure 2 is as follows:vw==total volumetotal weightVa=Wa=volume of airweight of air = 0VwWw==volume of waterweightofwater=Vw*YwVs=Wsvolumeof solids=weight of solids = V, *ysVv==volumeofvoidsdensity of waterYw=Ysdensity of solidsUsing these values some important quantities, which are often used in road engineering,arecalculated:Dry densitypdWsweight of solids2N/mPd =Jtotal volumeWatercontentwWwweight of waterL*100%*100%[%]W=Wsweight of solidsVoid ratio eVyvolume of voids[H]e=Vsvolumeof solidsPorosity nVvvolumeofvoids[H]n=Vtotal volume2
2 Figure 2 Idealized three-phase soil system. The meaning of the symbols used in figure 2 is as follows: V = total volume W = total weight Va = volume of air Wa = weight of air = 0 Vw = volume of water Ww = weight of water = Vw * w Vs = volume of solids Ws = weight of solids = Vs * s Vv = volume of voids w = density of water s = density of solids Using these values some important quantities, which are often used in road engineering, are calculated: Dry densityd d = 3 N/m total volume weight of solids V Ws Water content w W = * 100% % weight of solids weight of water * 100% Ws Ww Void ratio e e = volume of solids volume of voids s V v V Porosity n n = total volume volume of voids V v V
DegreeofsaturationS,Vw*100%weight of water * 100%[%SrVvvolumeof voidsEspeciallythedrydensityandthewatercontentare of importancebecausetheystronglyinfluence the structural behaviour of a given soil or granular material. That is whytheseparametersmustbespecified whena roadhastobebuilt.Compactiontests inthelaboratoryaretherefore performed to establishtheoptimumvalues.These compactiontests will bedescribed in a separate paragraph.The degree of saturation is strongly related with soil suction and pore pressure.Soil suctiondevelops withlowerdegreesof saturation,especially infinegrained soils,andleadstohigherstiffnessesduetoextrainducedcompressivestresses,whereasporepressuresmaydevelopifthe degree of saturation reaches 100%,resulting in reduced effective stresses and possiblyshear.The void ratio e and porosity n are related to each other following:11and e:n1+e1-nAnother importantparameter is the specified gravity Gs,of thegrains, in some countriesalsocalled relative density.It is defined as the ratio between themass of dry solids and the massof distilled water displaced by the dry soil particles. As it is a ratio between two quantitieswith thesamedimension,the specificgravity itself isdimensionless:Ws *1weight of solids[-1G, =VsvolumeofsolidsPH20PH20The specific gravity is used in the calculation of the degree of saturation and in thecalculationofthesedimentationspeedofsoilparticleswithadiameterlessthan75um.Thiswill be discussed in the paragraph on particle size analysis. In the case of porous materials itshould be noted that enclosed pores in the material are supposed to be a part of thematerial.Inthenextexamplethecalculationof thedegreeof saturationisdemonstratedforaspecificDutch sand under conditions of maximum density Pd.max and optimum water content WoptExampleGiven1668 [kg/m"]Pd.max-=15.7 [%]Wopt=Gs2.65 [-]Consider 1 m3 of compacted material. The volume of the solids is then calculated from thedry density and the specific gravity of the grains, according to:VsVolume of solids=1668 / 2650 = 0.629 [m′]The volume of voids and the volume of the solids together make 1 m3, so that the volume ofthe voids is equal to:Vv1 - 0.629 = 0.371 [m′]Volumeof voids=3
3 Degree of saturation Sr Sr = * 100% % volume of voids weight of water * 100% v V Vw Especially the dry density and the water content are of importance because they strongly influence the structural behaviour of a given soil or granular material. That is why these parameters must be specified when a road has to be built. Compaction tests in the laboratory are therefore performed to establish the optimum values. These compaction tests will be described in a separate paragraph. The degree of saturation is strongly related with soil suction and pore pressure. Soil suction develops with lower degrees of saturation, especially in fine grained soils, and leads to higher stiffnesses due to extra induced compressive stresses, whereas pore pressures may develop if the degree of saturation reaches 100%, resulting in reduced effective stresses and possibly shear. The void ratio e and porosity n are related to each other following: 1 e 1 n and 1 n 1 e Another important parameter is the specified gravity Gs , of the grains, in some countries also called relative density. It is defined as the ratio between the mass of dry solids and the mass of distilled water displaced by the dry soil particles. As it is a ratio between two quantities with the same dimension, the specific gravity itself is dimensionless: Gs = o 2 H ρ 1 * volume of solids weight of solids o 2 H ρ 1 * s V Ws The specific gravity is used in the calculation of the degree of saturation and in the calculation of the sedimentation speed of soil particles with a diameter less than 75 m. This will be discussed in the paragraph on particle size analysis. In the case of porous materials it should be noted that enclosed pores in the material are supposed to be a part of the material. In the next example the calculation of the degree of saturation is demonstrated for a specific Dutch sand under conditions of maximum density d.max and optimum water content wopt. Example Given d.max = 1668 [kg/m 3 ] wopt = 15.7 [%] Gs = 2.65 [-] Consider 1 m3 of compacted material. The volume of the solids is then calculated from the dry density and the specific gravity of the grains, according to: Volume of solids Vs = 1668 / 2650 = 0.629 [m3 ] The volume of voids and the volume of the solids together make 1 m3 , so that the volume of the voids is equal to: Volume of voids Vv = 1 – 0.629 = 0.371 [m3 ]
Thewatercontentasrelatedtothedrymassofthematerial containedin1m3,is15.7%,which impliesthattheamountofwater equals:Weight of waterWw0.157 * 1668 = 262 [kg]=For normal engineering purposes the density of water is 1000 [kg/m'j. For the volume ofwaterthensimplyfollows:Vw262 / 1000 = 0.262 [m2]VolumeofwaterThe degree of saturation is calculated from the volume of water related to the volume ofvoids, expressed asa percentage:Degree of saturationSrVw/V,=0.262/0.371=71%Itisnoteworthythatatoptimumwatercontentsome70%ofthevoidsisfilledwithwater.However, for sands this is a quitecommon value.3.Particlesize distributionandinteractionwithmoisture of soils and granular materialsSoilsandgranularmaterialsconsistofanarrangementofparticles.Inbetweentheparticlesthere are voids and these voids may be (partly) filled with moisture. Typical examples of sucharrangements are given in figure 3.(a) Aggregate with(b) Aggregate with(c) Aggregate withno finessufficient fines forgreat amount of finesmaximum densityGrain-to-grain contactGrain-to-grain contactGrain-to-grain contactWith increased resistancedestroyed, aggregatefloating'in soilAgainst deformationVariable densityIncreased densityDecreased densityPerviousPractically imperviousPractically imperviousNon-frost-susceptibleFrost-susceptibleFrost-susceptibleHigh stability ifHigh stability inLow stabilityConfined, low ifconfinedorunconfinedUnconfinedconditionsNot affected byNot affected byGreatly affected byAdversewaterconditionadversewaterconditionadversewaterconditionVery difficult toModerately difficult toNot difficult tocompactcompactcompactFigure 3 Three physical states of soil-aggregate mixtures [1].4
4 The water content as related to the dry mass of the material contained in 1 m3 , is 15.7%, which implies that the amount of water equals: Weight of water Ww = 0.157 * 1668 = 262 [kg] For normal engineering purposes the density of water is 1000 [kg/m3 ]. For the volume of water then simply follows: Volume of water Vw = 262 / 1000 = 0.262 [m3 ] The degree of saturation is calculated from the volume of water related to the volume of voids, expressed as a percentage: Degree of saturation Sr = Vw / Vv = 0.262 / 0.371 = 71% It is noteworthy that at optimum water content some 70% of the voids is filled with water. However, for sands this is a quite common value. 3. Particle size distribution and interaction with moisture of soils and granular materials Soils and granular materials consist of an arrangement of particles. In between the particles there are voids and these voids may be (partly) filled with moisture. Typical examples of such arrangements are given in figure 3. (a) Aggregate with (b) Aggregate with (c) Aggregate with no fines sufficient fines for great amount of fines maximum density Grain-to-grain contact Grain-to-grain contact Grain-to-grain contact With increased resistance destroyed, aggregate Against deformation ‘floating’ in soil Variable density Increased density Decreased density Pervious Practically impervious Practically impervious Non-frost-susceptible Frost-susceptible Frost-susceptible High stability if High stability in Low stability Confined, low if confined or unconfined Unconfined conditions Not affected by Not affected by Greatly affected by Adverse water condition adverse water condition adverse water condition Very difficult to Moderately difficult to Not difficult to compact compact compact Figure 3 Three physical states of soil-aggregate mixtures [1]
Figure 3 shows three soil particle arrangements but a fourth one should be identified as well.That is the particle arrangement where no coarse particles are present and the soil onlyconsists of fineparticlesIn figure 3, the coarse particles are stones with a specific hardness which can be anythingranging fromgranite to siliceous river gravel.The fine particles are usually products of furtherdeterioration or weathering of the parent material.As will be discussed later on, especiallythefineparticles interactwithwaterwhichmeansthatthebehaviourof thefines inrelationto water is important information.If those fine particles are e.g.clay,then structure b and cwill beratherstrongwhendrybecauseclayisahardandstrongmaterial whendry.Ontheother hand structurec will loose its strength when wet because clay has only limited strengthwhen wet. Particle arrangement b is much less affected by wet conditions because in thatcasethecoarseparticles willprovidethetransferthe loads.What becomesclearfromthispicture isthat oneneedstoknowtheparticle sizedistributionandthebehaviourofthefinesinrelationwithmoistureParticulartypesofsoilshowever,suchascollapsingsoils,haveastructureliketheoneshownin figure 4.Figure 4 Honeycomb structure in a granular soil [1].Thistype of"houseof cards"structure might havea highbearing capacityfor static loads,but might collapse easily under dynamic loads. In addition, if the moisture content increasesaftera static load is applied,this can sometimes result indramatic collapse settlement.In thisparticular case one needs not only to know the grain size distribution but also the bulkdensityofthesoilmassandthespecificdensityofthegrains.Ifthebulkdensityofthesoilmass is muchlower than the specific densityof thegrains, thenoneknowsthat the soil massmust contain a large amount of voids.Examplesofparticlesizedistributioncurvesareshown infigure5.CurveA istypicalfor an uniformly graded sand.CurveB is typical fora well graded silty-sandgravel, while curve C is typical for a gap graded material. Gap graded means in this case thattherearenoparticles available witha diameterbetween0.6and3mm.Figure 5b shows that all four grain size distribution curves indicate the presence of clay,silt,sand and to some extent gravel.This makes the definition of names a rather complex taskand in orderto get someorderinthisatriangular classification chart, shown in figure6,hasbeen developed. In this figure all seven respective grain size distribution curves arerepresented (A to G) with the exclusion of all particles > 2 mm i.e., so all the percentages hadto be adjusted.5
5 Figure 3 shows three soil particle arrangements but a fourth one should be identified as well. That is the particle arrangement where no coarse particles are present and the soil only consists of fine particles. In figure 3, the coarse particles are stones with a specific hardness which can be anything ranging from granite to siliceous river gravel. The fine particles are usually products of further deterioration or weathering of the parent material. As will be discussed later on, especially the fine particles interact with water which means that the behaviour of the fines in relation to water is important information. If those fine particles are e.g. clay, then structure b and c will be rather strong when dry because clay is a hard and strong material when dry. On the other hand structure c will loose its strength when wet because clay has only limited strength when wet. Particle arrangement b is much less affected by wet conditions because in that case the coarse particles will provide the transfer the loads. What becomes clear from this picture is that one needs to know the particle size distribution and the behaviour of the fines in relation with moisture. Particular types of soils however, such as collapsing soils, have a structure like the one shown in figure 4. Figure 4 Honeycomb structure in a granular soil [1]. This type of “house of cards” structure might have a high bearing capacity for static loads, but might collapse easily under dynamic loads. In addition, if the moisture content increases after a static load is applied, this can sometimes result in dramatic collapse settlement. In this particular case one needs not only to know the grain size distribution but also the bulk density of the soil mass and the specific density of the grains. If the bulk density of the soil mass is much lower than the specific density of the grains, then one knows that the soil mass must contain a large amount of voids. Examples of particle size distribution curves are shown in figure 5. Curve A is typical for an uniformly graded sand. Curve B is typical for a well graded silty-sand gravel, while curve C is typical for a gap graded material. Gap graded means in this case that there are no particles available with a diameter between 0.6 and 3 mm. Figure 5b shows that all four grain size distribution curves indicate the presence of clay, silt, sand and to some extent gravel. This makes the definition of names a rather complex task and in order to get some order in this a triangular classification chart, shown in figure 6, has been developed. In this figure all seven respective grain size distribution curves are represented (A to G) with the exclusion of all particles 2 mm i.e., so all the percentages had to be adjusted
BRITISHSTANDARD SIEVESIZE6-32037-5200cOrFigure5aExamplesofparticlesizedistributioncurvesforsandsandgravels[2]BRITISHSTANDARO SIEVE SIZESA.GAAVEFigure5b Examplesofparticlesizedistributioncurvesforsandsandgravels[2]
6 Figure 5a Examples of particle size distribution curves for sands and gravels [2]. Figure 5b Examples of particle size distribution curves for sands and gravels [2]