A Note on Void Ratio of Fibre-Reinforced Soils

Transcription

1 TECHNICAL NOTE A Note on oid Ratio of Fibe-Reinfoced Soils Sanjay Kuma Shukla 1 Mohamed A. Shahin *2 Hazim Abu-Taleb 3 Abstact This technical note extends the concept of void atio, pesented taditionally in soil mechanics, fo fibe-einfoced soils. Phase elationships elated to the void atio of fibe-einfoced soils ae pesented along with thei definitions. A simple analytical model veified with expeimental data fo estimating the void atio of fibe-einfoced soils is developed which can be used to expe the compeibility of fibe-einfoced soils in geotechnical engineeing applications. The esults indicate that the void atio of fibe-einfoced soils is dependent on the volume atio of fibe-soil solid. Keywods Fibe Soil oid atio Reinfocement * Coesponding autho, Mohamed A. Shahin m.shahin@cutin.edu.au 1 Discipline of Civil and Envionmental Engineeing, School of Engineeing, Edith Cowan Univesity, 270 Joondalup Dive, Joondalup, Peth, WA 6027, Austalia, s.shukla@ecu.edu.au, sanjaykshukla1@gmail.com 2 Depatment of Civil Engineeing, Cutin Univesity, Peth, WA 6845, Austalia, m.shahin@cutin.edu.au 3 Gaduate Enginee, Peth, Austalia

2 Intoduction The concept of phase elationships of soil mechanics is extensively used in geotechnical engineeing to quantify the engineeing behavio of soils due to the fact that the elative popotions of each phase in an element of soil have a significant impact on its engineeing behavio. An element of soil ma can be epesented as shown in Fig. 1 by a thee-phase system containing soil solid (mineal paticles), liquid (usually wate), and gas (usually ai). The space occupied by the ai and/o wate in a soil ma epesents the volume of soil void. The atio of the volume of soil void to the volume of soil solid in a given soil ma is called the void atio of soil. The impotance of the void atio lies in the fact that it significantly affects the soil behavio, such as compeibility, which is geneally studied in tems of the change in the soil void atio while ignoing the change in the volume of the individual solid paticles due to the fact that cushing and factuing of the solid paticles unde applied stees ae insignificant [1-3]. In ecent yeas, synthetic fibes have been developed fom seveal wastes such as plastic and old ties, and have been used fo impoving the engineeing behavio of soils by the addition of andom distibution of fibes within the soil ma o by placing one o moe layes of fibes in the fom of geosynthetic poducts within the soil ma [4]. An element of fibe ma can be epesented as shown in Fig. 2 by a thee-phase system containing fibe solid, liquid and gas. When fibe is added to the soil matix, a simila phase system to that used fo soils can be poposed fo fibe-einfoced soils. Howeve, it is well expected that the addition of fibe to uneinfoced soils, foming the fibeeinfoced soils, affects the phase elationships of fibe-einfoced soils. The popeties of added fibe unde applied stees ae expected to behave diffeently fom those of the 2/21

3 soil matix alone; thus, the soil solid and fibe solid should be dealt with as two diffeent components of the phase system of fibe-einfoced soils. Consequently, an additional phase can be embedded into the phase system of fibe-einfoced soils to epesent the solid volume of fibe, leading to the fou-phase system shown in Fig. 3. Diamba et al. [5] and Ibahim et al. [6] biefly discued the fibe content in tems of the total dy unit weight and total volume of fibe-einfoced soil to study the behavio of fibe-einfoced sands, without focusing on the void atio. When dealing with the behavio of fibeeinfoced soils in most studies found in the liteatue on the fibe-einfoced soils, both the fibe solid and soil solid ae combined togethe as one component and no special attention has been paid to the volume of fibe (i.e., fibe void volume + fibe solid volume) to develop the phase elationships fo fibe-einfoced soils. Keeping the need fo developing phase elationships in mind, the concept of void atio needs to be extended in ode to make it poible to explain the behavio of fibeeinfoced soils, following the appoach used widely in soil mechanics fo analyzing the uneinfoced soils. In the pesent wok, an attempt is made to extend the taditional concept of the phase elationships fo the void atio of fibe-einfoced soils, which has not eceived due attention in the past but is consideed to be an impotant facto in geotechnical engineeing applications of fibe-einfoced soils. oid Ratio of Fibe-Reinfoced Soils In the context of the phase diagam of an element of fibe-einfoced soil, as shown in Fig. 3, the following phase elationships ae poposed along with thei definitions: oid atio of einfoced soil ma, 3/21

4 v e = (1) s oid atio of soil ma, vs e s = (2) oid atio of fibe ma, vf e f = (3) olume atio of fibe-soil solid, m = (4) whee v is the volume of void of fibe-einfoced soil, s is the volume of solid of fibeeinfoced soil, vs is the volume of soil void, is the volume of soil solid, volume of fibe void, and is the volume of fibe solid. vf is the A deivation of an expeion fo the void atio of fibe-einfoced soil, e, can be obtained in tems of the void atio of soil, e s, void atio of fibe, e f, and volume atio of fibe-soil solid, m, as follows: 4/21

5 e = v s = vs + + vf = vs vf + 1+ es + me f = 1+ m (5) Fom Eq. (5), the following two exteme special cases may be obseved: (a) As the volume atio of fibe-soil solid, m, tends to 0, the void atio of fibeeinfoced soil, e, becomes equal to the void atio of soil, e s ; and (b) As the volume atio of fibe-soil solid, m, tends to, the void atio of fibeeinfoced soil, e, becomes equal to the void atio of fibe, e f. aiation of the void atio of fibe-einfoced soil, e, with the volume atio of fibe-soil solid, m, can be obseved gaphically, as shown in Fig. 4, fo typical andomly selected values of void atio of soil, e s, and void atio of fibe, e f, equal to 0.8 and 1.5, espectively. It can be noticed that the void atio of fibe-einfoced soil, e, is geatly dependent on the volume atio of fibe-soil solid, m. In the following section, a vaiation of e with m will also be obseved expeimentally so that an expeion that coelates e with m can be established, which can be used fo pediction of e. Expeimental Pogamme Testing mateials The soil used in this study is Bickies sand, claified in accodance with the Unified Soil Claification System (USCS) as pooly gaded sand (SP). Fig. 5 shows the paticle-size distibution cuve of the sand used and Table 1 summaizes its basic popeties. The fibe 5/21

6 used as einfocement is vigin homo-polyme polypopylene, with the popeties given in Table 2 and stuctue shown in Fig. 6. Pepaation of specimens In this section, a seies of laboatoy tests wee conducted on fibe-einfoced soils in an attempt to establish an empiical expeion to pedict e fom m. Befoe conducting the tests, it was impotant to elate both e and m to some othe popeties that can be measued in the laboatoy. To do so, m was expeed in tems of the weights of fibe solid and soil solid as well as the specific gavity of fibe and soil instead of the volumes of fibe solid and soil solid, as follows: ( W / γ wg ) W G m = = = = ( W / γ G ) W G w G p G (6) whee to W is the weight of fibe solid; W is the weight of soil solid; p is the atio of W, that is, the fibe content by dy weight of soil; γ w is the unit weight of wate; is the specific gavity of soil; and G is the specific gavity of fibe. W G On the othe hand, using the soil mechanics phase elationships, e can be calculated as follows: e Gsγ w = γ d 1 (7) 6/21

7 whee: G s is the specific gavity of fibe-einfoced soil mixtue; γ w is the unit weight of wate; and γ d is the dy unit weight of fibe-einfoced soil mixtue. In geotechnical engineeing applications of fibe-einfoced soils, the mixtue of soil and fibe should be compacted to each its optimum compaction, hence, γ d in Eq. (7) is that coesponds to the maximum dy unit weight, γ d(max). In ode to develop the elationship between the void atio of fibe-einfoced soil, e, and volume atio of fibe-soil solid, m, a numbe of specimens of sand-fibe mixtues wee pepaed at seven diffeent values of p = 0.25%, 0.5%, 1.0%, 2.0%, 3.0%, 4.0%, and 5.0%. Fo each sand-fibe mixtue, a specific gavity test was pefomed to obtain Gs and the standad Pocto compaction test was also caied out to obtain γ d(max). The fibe-einfoced soil samples wee pepaed by mixing dy sand with fibe using Hobat mixe, and wate was added to the mixtue to achieve equied moistue content. The pepaed samples wee mixed fo 90 seconds to allow homogeneity and wee then placed in polyethylene bags, tied up and left ovenight fo wate to be unifomly distibuted pio to testing. Using the expeimental data obtained togethe with Eqs. (6) and (7), seven diffeent values of m and coesponding e wee calculated and used to develop the elationship between m and e, as explained below. Test Results ad Discuion The esults of specific gavity tests caied out on the sand-fibe mixtues fo diffeent values of fibe content p ae pesented in Fig. 7. It can be seen that the specific gavity of mixtues deceases with an incease of p, as expected. In the cuent wok, it was also 7/21

8 poible to develop an analytical deivation fo detemination of the specific gavity of the sand-fibe mixtue based on the specific gavity of both the soil and fibe, as follows: W W + W s W + p W Gs = = = s γ w ( + ) γ w W + W γ w G γ w G γ w 1 W p W p = = = (1 + ) p p + W 1 + p W + p G G G G G G (8) The validity of Eq. (8) was veified by the expeimental data in Fig. 7 and the esults show an excellent ageement. The esults of the compaction tests ae pesented in Fig. 8, which indicates that the maximum dy density of the sand-fibe mixtues deceases with an incease of fibe content, as expected. Using the esults of the above tests, the values of m and coesponding e wee calculated and plotted in Fig. 9, which shows that the void atio of the sand-fibe mixtue inceases with an incease of the volume atio m of the mixtue. The tend in Fig. 9 obtained fom the expeimental esults is in a good ageement with that obseved in Fig. 4 obtained analytically using Eq. (5). The data shown in Fig. 9 can be e-plotted on log scale in the hoizontal axis, as shown in Fig. 10. It can be seen fom Fig. 10 that m was adjusted to be ( 100m + 1) to make the value of m fits moe adequately on the log scale and to avoid the poblem of having log of zeo. Based on the data shown in Fig. 10, a linea model is poposed fo the elationship between m and e, as follows: 8/21

9 e = a ln( 100m + 1) + b (9) whee: a = is the slope of the linea elationship and epesent the type of fibe used (i.e., vigin homo-polyme polypopylene) and b = is the value of e at m = 0 and epesents the type of sand used (i.e., pooly gaded silica sand). Fo othe types of fibe and/o sand, a and b can be obtained fom the data obtained fom a minimum of fou compaction tests on the fibe-einfoced soil at hand fom which the measued values of m and the coesponding e can be calculated and used to detemine a and b, then Eq. (9) can be used fo futue pediction the void atio of that fibeeinfoced soil. Concluding Remaks The concept of phase elationships, being adopted widely in soil mechanics fo uneinfoced soils, was utilized fo developing the phase elationships elated to the void atio of fibe-einfoced soils. The phase elationships ae faily of geneal natue and can be utilized in seveal applications of fibe-einfoced soils especially in design of foundations. An analytical linea egeion model fo the elationship between the void atio of fibe-einfoced soil and logaithmic of volume atio of fibe-soil solid was deived, which can be useful fo expeing the fibe-einfoced soil compeibility, elative density and pemeability in a way simila to that taditionally used in soil mechanics fo analysis of uneinfoced soils. The developed elationship includes two dependent empiical paametes, one fo the soil type and the othe fo the fibe type. These two paametes can be detemined fo any soil-fibe mixtue fom the data obtained 9/21

10 fom a minimum of fou compaction tests on the fibe-einfoced soil of inteest. The developed void atio of sand-fibe mixtue educes the gap knowledge in soil mechanics of fibe-einfoced soils. It should be noted that othe eseaches may cay out expeimental studies with seveal fibe types and also fo cemented fibe-einfoced soils to compae thei esults with the developed phase elationships. Refeences 1. Lambe TW, Whitman R (1979) Soil mechanics, SI vesion. John Wiley & Sons, New Yok 2. Tezaghi K, Peck RB, Mesi G (1996) Soil mechanics in engineeing pactice, 3d edn. John Wiley & Sons, New Yok 3. Shukla SK (2014) Coe pinciples of soil mechanics. ICE Publishing, London 4. Shukla SK, Sivakugan N, Das BM (2009) Fundamental concepts of soil einfocement an oveview. Intenational Jounal of Geotechnical Engineeing 3(3): Diamba, A., Ibahim, E., Mui Wood, D., Ruell, A.R Fibe einfoced sands: expeiments and modeling. Geotextiles and Geomembanes, 28(3), Ibahim E, Diamba A, Mui Wood D, Ruell AR (2010) Static liquefaction of fibe einfoced sand unde monotonic loading. Geotextiles and Geomembanes 28(4): /21

11 Table 1 Popeties of the sand used Popety alue Specific gavity 2.65 Maximum dy unit weight * (kn/m 3 ) 17.4 Paticle size D 10 (mm) 0.18 D 30 (mm) 0.32 D 60 (mm) 0.50 Coefficient of unifomity, C u 2.78 Coefficient of cuvatue, C c 1.14 * Standad Pocto. Table 2 Popeties of the fibe used Popety alue Specific gavity 0.91 Length (mm) 19 Tensile stength (MPa) /21

12 Ai Wate vs Soil solid Fig. 1 An element of soil ma epesented by a thee-phase system 12/21

13 Ai Wate vf Fibe solid Fig. 2 An element of fibe ma epesented by a thee-phase system 13/21

14 Ai Wate v = vf + vs Fibe solid Soil solid s = + Fig. 3 An element of fibe-einfoced soil ma epesented by a thee-phase system 14/21

15 e e s = 0.8 e f = m Fig. 4 Effect of volume atio of fibe-soil solid, m, on void atio of fibe-einfoced soil, e based on Eq. (5) 15/21

16 % Paing by weight Paticle size (mm) Fig. 5 Paticle-size distibution of the sand used 16/21

17 Fig. 6 igin homo-polyme polypopylene fibe 17/21

18 G s Measued Pedicted p (%) Fig. 7 aiation of the specific gavity Gs of sand-fibe mixtues with the fibe content p 18/21

19 Dy unit weight, γ d (kn/m 3 ) Moistue content, w (%) Sand alone p = 0.25% p = 0.5% p = 1% p = 2% p = 3% p = 4% p = 5% Fig. 8 Compaction cuves fo vaious sand-fibe mixtues 19/21

20 e m Fig. 9 Effect of volume atio of fibe-soil solid, m, on void atio of fibe-einfoced soil, e, based on the expeimental data 20/21

21 y = ln(x) R² = e m + 1 Fig. 10 aiation of void atio, e, of the sand-fibe mixtue used with logaithm of ( 100m + 1) 21/21