Prliinary Dfiniions and Rlaions 1 CHAPTER 2 PRELIMINARY DEFINITIONS AND RELATIONS يتكون حجم معيه مه التربة مه حبيبات صلببة هولواو هملاو اميلاي جوفيللة أه ميللاي (.للصدر همقلل ) ال للو فللي التربللة وللو ال بيبللات القببةر أما الهواو هالميلاي الموجلوييه فلي الفراغلات المتقلبة بليه ال بيبلات فبليم لهملا أى م اهملةر للفل فلإن ت يل وةلبة ال بيبلات القببة في التربة هكافة العالقلات ال جميلة هالويويلة بليه مكوولات التربة الثالثة اال بيبات الماو الهواود يعتبر أساسا لبتعامل مل التربة حةابيا هوى سيار 2.1 Soil as hr phas sys A soil ass is a hr phas sys consising of: (a) solid paricls (grains) (b) war (c) air Th void spac bwn soil paricls is filld parly wih war and parly wih air, Fig 2.1 (a). In cas of fully saurad soil, h voids ar coplly filld wih war. Th hr soil consiuns ar ixd oghr foring crain soil srucur. For calculaion purpos, i is always or convnin o show hs consiuns in spara spacs, as shown in Fig. 2.1 (b). Th oal volu of soil () consiss of :
2 Fundanals of Soil Mchanics ar Air Solids v a S Air ar Solids S (a) (b) Fig. 2.1 Subsiuions for phas calculaions (a) olu of air ( a ) (b) olu of war ( w ) (c) olu of solids ( s ) Th oal volu of voids ( v ) is givn by: v = a + w Th oal wigh of soil () consiss of: (a) igh of war ( w ) (b) igh of solids ( s ). 2.2 Dfiniions م توى الرطوبة (w) 2.21 war conn: Th war conn (also calld h oisur conn) is dfind as h raio bwn h wigh of war ( w ) and h wigh of solids ( s ) in a givn soil ass, i.: w w.......... (2.1) s Th war conn is usually xprssd in prcnag:
Prliinary Dfiniions and Rlaions 1 w (%) w 100.......... (2.2) s 2.2.2 Uni wigh of solid ass: (Dnsiy of soil) الكثافة الكبية ) b (a) Bulk Dnsiy: (γ Th bulk dnsiy of soil is dfind as h oal wigh of soil ass () pr uni of is oal volu (), i.: b.......... (2.) الكثافة الجافة ) d (b) Dry Dnsiy: (γ Th dry dnsiy is dfind as h wigh of solids ( s ) pr uni of is oal volu (), i.: s d.......... (2.4) الكثافة المشبعة ) sa (c) Saurad Dnsiy: (γ hn h soil is fully saurad wih war, is bulk dnsiy is calld saurad dnsiy. Thus, i is dfind as h oal wigh of a saurad soil ass pr uni of is oal volu, i.:. sa. sa = w s +v v x γ w v (2.5).......... الكثافة المغمو( ) sub. (d) Subrgd Dnsiy: (γ hn a soil ass is subrgd undr war is wigh is rducd du o bouyancy. Th upward forc is qual o h volu uliplid by h dnsiy of war (γ w ): sub w w sa. w.......... (2.6) For γ w = 1 g / c (or 1 / ):
2 Fundanals of Soil Mchanics sub. sa. 1.......... (2.7) Th dnsiy of soil is gnrally xprssd in g/c or / unis. I is considrd as bulk dnsiy (also calld unsaurad dnsiy) unlss ohrwis sad. Naural dnsiy is h bulk dnsiy of naural soil. I is gnrally akn as bulk dnsiy unlss h soil in h fild is saurad or dry. الوين الىوعي ) s 2.2. Spcific graviy: (G Th spcific graviy of soil is dfind as h raio bwn uni wigh of soil solids o ha of war, i.: Th spcific graviy is hrfor a dinsionlss valu. وةبة الفراغات () 2.2.4 oid raio:.......... (2.8) Th void raio is dfind as h raio bwn volu of voids o volu of soil solids, i.. : v.......... (2.9) s المةامية (n) 2.2.5 Porosiy: Th porosiy is dfind as h raio bwn volu of voids o oal volu of soil, i.. : n v.......... (2.10) Th rlaionship bwn h porosiy and void raio is : Also: G s s s 1 w n.......... (2.11)
Prliinary Dfiniions and Rlaions 1 n.......... (2.12) n ي(جة التشب (S) 2.2.6 Dgr of sauraion: Th volu of voids in a soil ass is gnrally occupid by war and air. Th raio bwn volu of war and volu of voids is calld h dgr of sauraion, i.. : S w.......... (2.1) v Th dgr of sauraion is also xprssd as prcnag, i.. : S (%) w 100.......... (2.14) v In a saurad soil whr h voids ar oally filld wih war h dgr of sauraion S = 1 (or 100%). For dry soil S = 0. 2. Funcional rlaions Rlaions bwn soil parars dfind in Scion 2.2 ar givn as follows : S Gs w.......... (2.15) Gs.S b. w.......... (2.16) G s d. w.......... (2.17) Gs sa.. w.......... (2.18) Gs 1 sub.. w.......... (2.19) w.......... (2.20) b d
2 Fundanals of Soil Mchanics 2.4 Exapls (1) Th wigh of a parially saurad soil sapl is 600 g and is volu is 65 c. Afr ovn drying h wigh of h sapl rducs o 54 g. Taking h spcific graviy 2.67, find h war conn, void raio and dgr of sauraion. If h sapl is saurad wih war wihou chang of is volu, find h saurad dnsiy. Soluion: 600 54 w 0.105 10.5 % 54 b d (1 w) 600 b 1.644 g/c 65 1.644 d (1 0.105) 1.488 g/c d G s d w 2.67 1.488 x 1 0.794 S Gs w (0.794) S 2.67(0.105) S 0.5 5. % sa. sa. G s w 2.67 0.794 x 1 1.9 g/c 0.794 حجوم 65 G s = 2.67 المعطيات : أهيان 600 54
Prliinary Dfiniions and Rlaions 1 (2) Th bulk dnsiy of a soil sapl is 1.97 g/c and is war conn is 20.6 %. Taking h spcific graviy 2.65, find h void raio and dgr of sauraion. Draw h -phas diagra aking s = 1. Chck, h valu of void raio. Soluion: 0.076 1.622 0.622 0.546 0.546.196 1 2.65 (a) b d( w) 1.97 d( 0.206) 1.6 g/c d Gs d w 2.65 1.6 1 0.622 S Gs.w 0.622S 2.65 0.206 S 0.877 87.7 % (b) To s 1 s 2.65 w 2.65 0.206 0.546 2.65 0.546.196.196 1.97 1.622 v 1.622 1 0.622 w 0.546 a 0.076 copl 0.622 1 0.622 h - phas diagra : (O.K.)
2 Fundanals of Soil Mchanics () Th bulk and dry dnsiis of a soil sapl ar 1.77 and 1.5 /, rspcivly. If h dgr of sauraion is 60 %, wha will b h spcific graviy and porosiy. Draw h -phas diagra aking = 1. Chck h obaind valus of spcific graviy and porosiy, hn calcula h quaniy of war addd pr uni volu for full sauraion (wihou chang of volu). 1 0.45 0.27 0.55 0.27 1.5 1.77 b d (1 w) 1.77 1.5(1 w) w 0.6 G s d w 0.6 1.5 0.18 1 0.818 0.6 G s 0.818 ( ) 0.18 2.7 n n 0.18 S G s.w Gs 0.18 1 0.818 1 0.818 0.45 45 % 1 1.77 s 1.50 w 1.77 1.50 0.27 w 0.27 0.27 v 0.45 0.6 s 1-0.45 0.55 1.50 Gs 2.7 0.55 0.45 n 0.45 45 % 1 w 0.45 0.27 0.18
Prliinary Dfiniions and Rlaions 1 (4) An arh bankn is o b copacd o a dry dnsiy of 1.84 /. Th bulk dnsiy and war conn of h borrow pi ar 1.77 / and 8 %, rspcivly. Calcula h volu of xcavaion in h borrow pi which corrsponds o 1 of h bankn. Soluion: Ebankn م جر - pi Borrow d = 1.84 / b = 1.77 / w = 8 % In ransporing soil fro h borrow pis o h bankn, h wigh of h solids rains unchangd. Solving h shown -phas diagras for 1 of h bankn, w hav: 2 1 0.147 1.987 1.84 1.84 For 1 s 1.84 For borrow pis : s w bankn 1.84 1.84 0.08 0.147 2 1.987 1.77 : 1.12
2 Fundanals of Soil Mchanics 2.5 Probls (1) Th porosiy of a soil sapl is % and is spcific graviy is 2.68. Calcula h void raio, dry dnsiy, bulk dnsiy for 46 % dgr of sauraion, and saurad dnsiy. (Tak war dnsiy = 1 g/c ) (2) Th bulk dnsiy of a soil sapl is 1.85 /, and is spcific graviy is 2.7. Calcula h void raio assuing ha: (a) Th sapl is dry, (b) Th sapl has a war conn of 8. %. (Tak war dnsiy = 1 / ) () A soil has a bulk dnsiy of 1.9 / and war conn of 44 %. Calcula h war conn, if h dnsiy rducs o 1.76 / wihou chang of volu. (4) A soil sapl has a void raio of 0.81, dgr of sauraion of 84 % and spcific graviy of 2.71. Calcula h bulk dnsiy and war conn. ha will b h war conn a full sauraion wihou chang of volu. (Tak war dnsiy = 1 g/c ) (5) A soil sapl has a dry dnsiy of 1.55 /. Th porosiy and war conn ar 42 % and 25 %, rspcivly. Calcula h spcific graviy and dgr of sauraion. (Tak war dnsiy = 1 / ) (6) Th wigh of a soil sapl is 690 g and is volu is 90 c. hn 8 g of war wr addd o h sapl, wihou chang of volu, is war conn incrasd by 8 %. Calcula h saurad dnsiy and porosiy. Tak spcific graviy 2.7. (Tak war dnsiy = 1 g/c ) (7) Th wigh of a soil sapl is 20 g and is volu is 210 c. Th war conn is 17 % and h spcific graviy is 2.68. Draw h -phas diagra fro which find volu of air voids, void raio and dgr of sauraion.
Prliinary Dfiniions and Rlaions 1 Phoo 2: Thin layrs of swlling clay wihin wakly cnd sand (Madin Nasr, Cairo)