( ) e + e ( ) ( ) e + e () ( ) e e Τ ( ) e e ( ) ( ) () () ( ) ( ) ( ) ( )

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1 n n (n) (n) (n) (n) n n ( n) n n n n n en1, en ( n) nen1 + nen nen1, nen

2 ( ) e + e ( ) ( ) e + e () ( ) e e Τ ( ) e e ( ) ( ) () () ( ) ( ) ( ) ( )

3 ( n) Τ n n n ( n) n + n ( n) (n) n + n n n n n n n n n n n n n * n (n) (n) n (n) * 1 0 e, e 0 1 Τ ( ) e 1 0 ( ) Τ e 0 1 1

4 (1) θ θ X (, ) (, ) X (, ) (, ) cosθ + sinθ sinθ + cosθ cosθ sinθ θ () sinθ cosθ cosθ Q sinθ sinθ Q Q I cosθ (n) (n ) ( n ) ( n) Q ()

5 ( n) (n ) n + n (n) n n (4) (n) () ( n) n + n n Q n (5) n n () n Qn n n Qn Q n (6) n n (7) Q Q (8) Q Q,, (9) Q Q (8) (9) cosθ sinθ sinθ cosθ cosθ sinθ sinθ cosθ (10) sinθ cosθ cos θ + sin θ + 1+ cosθ 1 cosθ + + sin θ + + cos θ + sin θ (11) + cosθ sin θ sin θ + cos θ (1) (1) θ θ ( n ) n + n (n) ( n ) n + n n n n θ

6 + cosθ + sin θ + cos θ + sin θ + ( ) sin θ cos θ (14) sin θ + cos θ ( ) sin θ cos θ (15) (, ) (, ) θ 0 (, ) (, ) +, 0 n n λn Τ ( n) n λn n λn 0 0 λi ( λi) n 0 n 0 λ ( λ λ)( λ) 0 λ 1 + ± λ + λ

7 θ n θ θ n θ n cosθ sinθ + n cos θ n sinθ 0 (16) cosθ cosθ + n sin θ + n cosθ 0 (17) cosθ cosθ / tanθ (16)(17) n + n tanθ + tanθ tan θ tanθ + n n

8 n n n + cos θ + sin θ sinθ cosθ + + cosθ + sin θ n sin θ cosθ θ n n θ θ n

9 θ θ θ θ (, ) (, ) > 180 (Pole)

10 (, ) (, ) (, ) (, ) θ θ (, ) (, ) θ

11 cos θ + sin θ sin θ + cos θ o o + cos( 45 ) + ( 0)sin( 45 ) o o sin( 45 ) + ( 0) cos( 45 ) 40 kpa 45 θ +45 o 50 (kpa) 40 (kpa)

12 λ 40 λ 0 (40 λ)(10 λ) ( 0) λ 0 10 λ λ 160λ ( λ 0)( λ 10) 0 λ 0, 10 10(kPa) 45 ( 40) ( 40, 0) 40(kPa) 0(kPa) 0 40(kPa) o θ 90 ( 10, 0) ( 50, - 40) 10(kPa) (kpa) (kpa) (50, -40) ( ) 80, 0

13 50 ( ) 0, 80 10(kPa) 0(kPa) 5 ) 40 0 tan 1 ( α o 18.4 ) 40 0 ( tan 1 1 α θ α B o 18.4 ) 40 0 ( tan 1 1 α θ 0) 10, ( 0) 40, ( 0) 0, ( ( ) ( ) 0, ) 10, ( α α 10 (kpa) o 18.4 o

14 45 ( 40, 0) 0 ( 10, 0) o (, ) (50, 40) ( 40, 0) 90 0 ( 0,0) θ ( 10,0) 0 ( 10, 0) 0 o θ tan 1 ( )

15 00 kpa o + cos (kpa) o sin (kpa) o + cos o 175 (kpa) sin (kpa) ( 100,0) ( 00,0) 60 o 10 o ( 15, - 5 ) ( 175, - 5 )

16 0 (, ) (15, - 5 ) 60 (, ) (175, - 5 ) ( 100,0) ( 00,0) ( 15, - 5 ) 0 o ( 175, o ) (, ) (15, - 5 ) 60 (, ) (175, - 5 )

17 F N µ F µn N φ F N µn F µn N r r φ tanφ

18 c + tanφ < c + tanφ φ c c + tanφ c c φ c + tanφ φ c

19 P 550mm 80100mm UU CU 1 CD CU,CD 1 UU cm

20 CD CU c φ l l ε ε l 0 l 0 l ε l ε l 0 l CU CD

21 c cu c' 0 c cu c' 0 0 φ φ cu φ φ cu CU (1) 1 1 CU ()

22 φ φ d c d c' 1 1 CU CD CU CU CD 1 ( 1, ) ( λ1, λ) ( 1, ) ( λ1, λ) ( 1, ) ( 1, ) ( λ 1, λ ) λ1 1λ 1 (1) λ λ () (1) λ λ λ1 1λ λ1 λ1 λ 1λ1 λ () () λ1 λ1 λ λ1 λ (4) ()(4) 1λ1 λ λ1 λ ( 1 ) λ 1 λ 0 (5) 1 (5) λ1 λ 0 λ 1 λ

23 φ c c φ c + tanφ CU CD f ( )

24 c + tanφ φ c + tan (, ) 1 (, ) sinφ 1 cosφ 1 1 c + tanφ ccosφ + sinφ ccosφ + ( ) sinφ ( ccotφ + )sinφ c φ 1 + φ c + tanφ

25 c + tanφ φ φ ( φcu ) c ( ccu ) c 1 c + tanφ (, ) sinφ, 1 cosφ (,0) (, ) π φ π φ + 4 4

26 φ π φ (, ) + c + tanφ c φ CU π φ + 4

27 CD dilatanc (Renolds 1885)

28 1 1 ε ε ε ε CU 1 1 ε ε ε ε + +

29 c,φ c,φ φ c, cd, φd c,φ c, φ c, φ' * cd, φd cd, (c, φ' * CD UU φu0 cu c, φcu, 0 CU cu cu/p c, φccu, φcu cu cu/ptan φcu * uw c, φ' * CU

30 c, φ c, φ c, φ' c 0 c, φ cd, φd c, φ' (a)- c, φ' cu, 0 c << cu φ'>> φu0 c 0 c c cu c, φ c, φ' c> c φ> φ' c c c c

31 u q u c s u u s s u ) ( u u c q z s s u u u 0 0 < s s u u u s s u u u

32 c φ u 0 u φ 1 c u ( 1 ) f f cu cu φu 0 0 c u qu 1 f cu q u e

33 ( c u ) ( c ( c u ) u ) 1 ( cu ) c c ( u ) u ( ) 1 ( ) ( ) p ( c u ) 1 ( ) 1 ( ) ( ) CU c,φ φu 0 c u CU c,φ CD CU c,φ φ CU CU ( u f ) 1 ( u f ) ( u f )

34 e

35 c,φ cu q 1 ( 1 ) 1 1 p ( ) ( 1 + ) p q ( 1,, q ) 1 p q p p q 1 ) ( 1,, 1 ( 1,, ) ( 1,, ) 1 p q p q

36 1 p + q 1 ( 1 ) q ( 1 ) q 0 p 1 + p q q B B 1 A ε a A p q q A A B ε a u e B B u e A 1 p

37 u B{ + A( 1 )} B u + A( 1 ) 0 1 u A A q q A q B1 q B1 B B u e 1 A ε a A p A CU CD p CU B CD A B B 1 CD CU CD B1 B 1 B

38 q ( q u ) ( qu ) 1 ( qu ) ( q u ) ε a cu cu D L (H) 150mm or 100mm (D) 75mm or 50mm (L)750mm or 500mm H

2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h)

2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h) 1 16 10 5 1 2 2.1 a a a 1 1 1 2.2 h h l L h L = l cot h (1) (1) L l L l l = L tan h (2) (2) L l 2 l 3 h 2.3 a h a h (a, h) 4 2 3 4 2 5 2.4 x y (x,y) l a x = l cot h cos a, (3) y = l cot h sin a (4) h a

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