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6. Settlement of Shallow Footings

6. Settlement of Shallow Footings. CIV4249: Foundation Engineering Monash University. (change of) Height Applied Load . Void Ratio Applied Stress. Oedometer Test. Particular Sample Measurements:. General Derived Relationship:. h. height vs time plots. height. h o.

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6. Settlement of Shallow Footings

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  1. 6. Settlementof Shallow Footings CIV4249: Foundation Engineering Monash University

  2. (change of) Height Applied Load Void Ratio Applied Stress Oedometer Test Particular Sample Measurements: General Derived Relationship: h

  3. height vs time plots height ho typically take measurements at 15s, 30s, 1m, 2m, 3m, 5m, 10m, 15m, 30m, 1h, 2h, 3h, 6h, 12h, 24h, 36h, 48h, 60h ….etc. elastic primary consolidation secondary compression typically repeat for 12.5, 25, 50, 100, 200, 400, 800 and 1600 KPa log time

  4. Void ratio = f(h) 1.00 e e = 0.8 1 2.65 Relative Volume Specific Gravity h = 1.9 cm dia = 6.0 cm W = 103.0 g 1 + e 1.917

  5. Instantaneous component Occurs prior to expulsion of water Undrained parameters Instantaneous component Expulsion of water cannot be separated Drained parameters Not truly elastic Elastic Settlement By definition - fully reversible, no energy loss, instantaneous Water flow is not fully reversible, results in energy loss, and time depends on permeability Sand Clay

  6. Eu Soft clay Firm clay Stiff Clay V stiff / hard clay Eu/cu most clays nu All clays 2000 - 5000 kPa 5000 - 10000 kPa 10000 - 25000 kPa 25000 - 60000 kPa 200 - 300 0.5 (no vol. change) Elastic parameters - clay

  7. Ed Loose sand Medium sand Dense sand V dense sand nd Loose sand Dense sand 10000 - 17000 kPa 17500 - 25000 kPa 25000 - 50000 kPa 50000 - 85000 kPa 0.1 to 0.3 0.3 to 0.4 note volume change! Elastic parameters - sand

  8. H ez ¥ r = ez.dz 0 Elastic Settlement Q r = Hs/E = H.ez s E E Generalized stress and strain field

  9. Distribution of Stress Q • Boussinesq solution e.g. sz = Q Is z2 y z R sz Is is stress influence factor r Is = 3 1 2p [1+(r/z)2]5/2 sr sq

  10. Uniformly loaded circular area load, q dr By integration of Boussinesq solution over complete area: dq a r z sz = q [1- 1 ] = q.Is [1+(a/z)2]3/2 sz

  11. 2mn(m2+n2+1)1/2 Is= 1 2mn(m2+n2+1)1/2 . m2+n2+2 + tan-1 4p m2+n2-m2n2+1 m2+n2+1 m2+n2-m2n2+1 Stresses under rectangular area L B • Solution after Newmark for stresses under the cornerof a uniformly loaded flexible rectangular area: • Define m = B/z and n = L/z • Solution by charts or numerically • sz = q.Is sz z

  12. Total stress change Is z/B

  13. ߥ ¥ r = ez.dz 0 ⥠Computation of settlement Q 1. Determine vertical strains: 2. Integrate strains: y ez = 1[sz - n (sr + sq)] E ez = Q .(1+n).cos3y.(3cos2y-2n) 2pz2E z R sz r sr r = Q (1-n2 ) prE sq

  14. r = 2q(1-n2).a E r = 4q(1-n2).a pE Settlement of a circular area load, q dr Centre : dq a r Edge : z sz

  15. 1 - n2 Ir r = q.B E 1+ m2 + 1 1 p m+ m2 + 1 Ir = m ln + ln m Settlement at the corner of a flexible rectangular area L B Schleicher’s solution sz z m = L/B

  16. L/2 B/2 1 - n2 rcentre = 4q.B 2 Ir E Settlement at the centre of a flexible rectangular area L B Superposition for any other point under the footing

  17. 1 - n2 1-2n Ir rcorner = q.B Ir = F1 + F2 E 1-n X Y Settlement under a finite layer - Steinbrenner method q B H E “Rigid”

  18. Superposition using Steinbrenner method L B

  19. Multi-layer systems q r = r(H1,E1) +r(H1+H2,E2) - r(H1,E2) B E1 H1 E2 H2 “Rigid”

  20. Primary Consolidation • A phenomenon which occurs in both sands and clays • Can only be isolated as a separate phenomenon in clays • Expulsion of water from soils accompanied by increase in effective stress and strength • Amount can be reasonably estimated in lab, but rate is often poorly estimated in lab • Only partially recoverable

  21. Total stress change Is z/B

  22. Pore pressure and effective stress changes Ds= Du + Ds¢ At t = 0 : Ds = Du At t = ¥: Ds = Ds¢ s¢f s¢i

  23. Stress non-linearity qnet z

  24. p¢c s¢i s¢f p¢c Cr H 1+eo Cc H 1+ec r = S log + log Cr Cc s¢i p¢c s¢f Soil non-linearity e sv

  25. (1+eo).mv Coeff volume compressibility r = Smv.Ds¢.DH e sv

  26. h = H / 2 h = H Flow Flow Rate of Consolidation T = cv ti/ H2 U = 90% : T = 0.848

  27. Coefficient of Consolidation • Coefficient of consolidation, cv(m2/yr) • Notoriously underestimated from laboratory tests • Determine time required for (90% of) primary consolidation • Why?

  28. De caH ca = r = log (t2/t1) log (t2 / t1) (1+ep) Secondary Compression • Creep phenomenon • No pore pressure change • Commences at completion of primary consolidation • ca/Cc»0.05

  29. Flexible vs Rigid F F stress stress deflection deflection rcentre RF = 0.8 0.8 rcentre

  30. Depth Correction B z

  31. Total Settlement rtot = RF x DF ( relas+ rpr.con + rsec )

  32. Field Settlement for Clays(Bjerrum, 1962)

  33. Differential Settlements Guiding values • Isolated foundations on clay < 65 mm • Isolated foundations on sand <40 mm Structural damage to buildings 1/150 (Considerable cracking in brick and panel walls) For the above max settlement values flexible structure <1/300 rigid structure <1/500

  34. Settlement in Sand via CPT Results (Schmertmann, 1970)

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