Baøi giaûng A. Prof. Dr Chaâu Ngoïc AÅn

1. Baøi giaûng A. Prof. Dr Chaâu Ngoïc AÅn ÖÙNG SUAÁT TRONG NEÀN ÑAÁT

2. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn ÖÙNG SUAÁT HÖÕU HIEÄU VAØ AÙP LÖÏC NÖÔÙC LOÃ ROÃNG Haït theùp nöôùc Ñaát baõo hoøa nöôùc

3. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn ÖÙNG SUAÁT HÖÕU HIEÄU VAØ AÙP LÖÏC NÖÔÙC LOÃ ROÃNG Haït theùp nöôùc Ñaát baõo hoøa nöôùc * bình beân traùi theâm vaøo treân maët lôùp ñaát caùc haït theùp taïo moät aùp löïc p, maãu ñaát bò luùn xuoáng. AÙp löïc p coù aûnh höôûng leân öùng suaát khung neân laø öùng suaát höõu hieäu, kyù hieäu laø ’ * bình beân phaûi theâm nöôùc treân maët ñeå taïo aùp löïc p, maãu ñaát khoâng luùn xuoáng vì nöôùc theâm vaøo thoâng vôùi nöôùc trong loã roãng taùc ñoäng leân ñaùy bình chöùa, p do coät nöôùc khoâng aûnh höôûng leân khung haït (trung hoøa).

4. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn ÖÙng suaát  taïi moät ñieåm trong neàn ñaát goàm “öùng suaát giöõa caùc haït” hay öùng suaát höõu hieäu ’ vaø aùp löïc nöôùc trong loã roãng u, theo ñònh ñeà Terzaghi  = ’ + u

5. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn TÍNH ÖÙNG SUAÁT TRONG ÑAÁT NEÀN DO TROÏNG LÖÔÏNG BAÛN THAÂN ÖÙng suaát toång do troïng löôïng baûn thaân ñaát theo phöông thaúng ñöùng kyù hieäu laø bt hay v taïi moät ñieåm baát kyø trong ñaát caùch maët ñaát moät chieàu saâu baèng H, coù theå tính nhö laø troïng löôïng khoái ñaát beân treân truyeàn xuoáng.

6. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn vôùi K0 laø heä soá aùp löïc ngang ôû traïng thaùi tónh cuûa ñaát coá keát thöôøng (ñaëc ñieåm coá keát thöôøng vaø coá keát tröôùc seõ ñöôïc phaân tích trong caùc chöông sau). Khoaûng nöûa theá kyû tröôùc, heä soá aùp löïc ngang ñöôïc vay möôïn töø lyù thuyeát ñaøn hoài vôùi kyù hieäu laø  vaø coù daïng : trong ñoù  laø heä soá Poisson. Vôùi toång keát töø raát nhieàu keát quaû thí nghieäm vaø ño ñaïc giaùn tieáp, Jaky ñaõ ñöa ra moät coâng thöùc ñeå tính heä soá aùp löïc ngang ôû traïng thaùi tónh (cuûa ñaát coá keát thöôøng) nhö sau : K0 = 1 - sin’ Vôùi ’ laø goùc ma saùt trong ñieàu kieän caét thoaùt nöôùc (seõ phaân tích roõ trong chöông choáng caét). Coâng thöùc cuûa Jaky phuø hôïp cho ñaát rôøi hoaëc ñaát loaïi caùt. Neáu goùc ma saùt ’= 350 thì K0 = 1 – sin350 = 0,426 Ñoái vôùi ñaát dính hoaëc ñaát loaïi seùt coá keát thöôøng, Alpan ñeà nghò moät coâng thöùc thöïc nghieäm. K0 = 0,19 + 0,233logIP Neáu moät maãu seùt coù chæ soá deûo IP = 20, thì heä soá aùp löïc ngang ôû traïng thaùi tónh K0 theo coâng thöùc Alpan laø : K0 = 0,19 + 0,233log20 = 0,493

7. hW hS1 Caùùt, s1 Seùt, c1 hC1 hS2 Caùùt, s2 u ’V Seùt, c2 hC2 V Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn

8. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn ’ z u hW1 hS1 BS Caùùt, S1 BC hC1 Seùt, C1 hS2 hW2 Caùùt, S2 Seùt, C2 hC2

9. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn Nguyeân lyù ño aùp löïc nöôùc loã roãngtrong ñaát

10. Soil loaded by water weighing W Soil loaded by an applied weight W W W

11. Soil loaded by water weighing W Soil loaded by an applied weight W W W Compression No deformation

12. Definition of Total and Effective Stress (1)

13. Definition of Total and Effective Stress (1) Effective vertical stress (2)

14. Definition of Total and Effective Stress (1) Effective vertical stress (2)

15. Definition of Total and Effective Stress (1) Effective vertical stress (2)

16. N T Effective Stress Water pressure uw Fig 2 Two Pieces of Rock in Contact

17. N T Effective Stress Water pressure uw Effective Force (3a) U = uw ( A - Ac )

18. N T Effective Stress Water pressure uw Effective Force (3a) U = uw ( A - Ac ) Frictional Failure

19. N T Effective Stress Water pressure uw Effective Force (3a) U = uw ( A - Ac ) Frictional Failure Failure in terms of stress (3b)

20. Calculation of Effective Stress Surcharge q d1 Layer 1 Layer 2 d2 z Layer 3 d3 Fig 3 Soil Profile

21. Calculation of Total Vertical Stress z Elevation q Force on base = Force on top + Weight of soil d1 d2 z Plan A

22. Calculation of Total Vertical Stress z Elevation q Force on base = Force on top + Weight of soil A sv = A q + A g1 d1 + A g2 d2 + A g3 ( z - d1 - d2 ) d1 d2 z Plan A

23. Calculation of Total Vertical Stress z Elevation q Force on base = Force on top + Weight of soil A sv = A q + A g1 d1 + A g2 d2 + A g3 ( z - d1 - d2 ) sv = q + g1 d1 + g2 d2 +g3 ( z - d1 - d2 ) d1 d2 z (4) Plan A

24. Calculation of pore water pressure Water table H (5) P Fig 4 Soil with a static water table

25. Calculation of pore water pressure Water table H (5) P Fig 4 Soil with a static water table • The water table is the level of the water surface in a borehole.

26. Calculation of pore water pressure Water table H (5) P Fig 4 Soil with a static water table • The water table is the level of the water surface in a borehole. • It is the level at which the pore water pressure uw = 0

27. Example: determining the effective stress Step 1: Draw ground profile showing soil stratigraphy and water table Dry 2 m 3m Saturated Fig 5 Soil Stratigraphy

28. Example Step 2: Calculation of relevant bulk unit weights Vv=e Vs = 0.7m3 Voids Vs= 1m3 Solid Distribution by Volume

29. Example Step 2: Calculation of relevant bulk unit weights Vv=e Vs = 0.7m3 W= 0 Voids Vs= 1m3 Solid Distribution by weight for the dry soil Distribution by Volume

30. Example Step 2: Calculation of relevant bulk unit weights Vv=e Vs = 0.7m3 W= 0 Voids Vs= 1m3 Solid Distribution by weight for the dry soil Distribution by Volume Distribution by weight for the saturated soil

31. Example Step 2: Calculation of relevant bulk unit weights Vv=e Vs = 0.7m3 Ww=0 Voids Vs= 1m3 Solid Distribution by weight for the dry soil Distribution by Volume Distribution by weight for the saturated soil 26 . 46 kN G g 3 s w g = = 15 . 56 kN / m = dry 3 1 + e 1 . 70 m

32. Example Step 2: Calculation of relevant bulk unit weights Vv=e Vs = 0.7m3 Ww=0 Voids Vs= 1m3 Solid Distribution by weight for the dry soil Distribution by Volume Distribution by weight for the saturated soil

33. Example Step 3 Calculate total stress 2 m 3m

34. Example Step 3 Calculate total stress 2 m Step 4 Calculate pore water pressure 3m

35. Example Step 3 Calculate total stress 2 m Step 4 Calculate pore water pressure 3m Step 5 Calculate effective stress

36. Vertical stress and pore pressure variation 0 50 100 150 kPa 0m 2m 4m Total Stress (5m) pore water pressure 6m Effective stress Depth 8m

37. Stresses acting on a soil element z z y x x Fig 7 Definition of Stress Components

38. Principle of Effective Stress Effective stress relations for general stress states (10)

39. Example 1 m Initial GWL 3 m Lowered GWL z Clay Rock aquifer

40. Example 1 m Initial GWL 3 m Lowered GWL z Clay Rock aquifer

41. Example • Effective stress increases - soil compresses - ground surface settles • Effective stress decreases- soil swells - ground surface heaves. The following problems may then occur • surface flooding • flooding of basements built when GWL lowered • uplift of buildings • failure of retaining structures • failures due to reductions in bearing capacity

42. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn ÖÙNG SUAÁT TRONG NEÀN ÑAÁT DO TAÛI NGOAØI

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44. P d R  c c1 a1 a R Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn Döôùi taùc duïng cuûa P ñieåm M chuyeån vò moät ñoaïn S theo phöông baùn kính R. M caøng xa O thì S caøng nhoû. Maët khaùc, vôùi R = const, goùc  caøng lôùn thì S cuõng caøng nhoû. Xuaát phaùt töø nhaän xeùt ñoù, ta coù theå vieát bieåu thöùc S coù daïng : Tröông töï, taïi M1 caùch M moät ñoaïn dR, coù chuyeån vò S1

45. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn Bieán daïng töông ñoái R cuûa ñoaïn dR laø: Boû qua R.dR vì raát nhoû so vôùi R2 Theo giaû thuyeát quan heä giöõa öùng suaát vaø bieán daïng laø tuyeán tính do ñoù öùng suaát xuyeân taâm R gaây neân bieán daïng R ñöôïc xaùc ñònh nhö sau Trò soá A.B coù theå xaùc ñònh döïa theo ñieàu caân baèng tónh hoïc. Xeùt ñieàu kieän caân baèng tónh hoïc cuûa baùn caàu (O; R)

46. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn Trong ñoù: dF – dieän tích maët ñai troøn caa1c1 dF = 2(Rsin)(Rd)

47. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn

48. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn Chuyeån vò theo chieàu caùc truïc :

49. Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn

50. h R2 O x h P z R1 y A M(x,y,z) r z Baøi giaûng Prof. Dr. Chaâu Ngoïc AÅn Baøi toaùn Mindlin