1. 6. Settlement of Shallow Footings
CIV4249: Foundation Engineering
Monash University

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

13. height vs time plots height ho elastic primary consolidation secondary
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

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

15. 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
Clay
Sand
Instantaneous component
Occurs prior to expulsion of water
Undrained parameters
Instantaneous component
Expulsion of water cannot be separated
Drained parameters
Not truly elastic

16. Elastic parameters - clayEu
Soft clay
Firm clay
Stiff Clay
V stiff / hard clay
Eu/cu
most clays nu
All clays
kPa
kPa
kPa
kPa
0.5 (no vol. change)

17. Elastic parameters - sandEd
Loose sand
Medium sand
Dense sand
V dense sand nd
kPa
kPa
kPa
kPa
0.1 to 0.3
0.3 to 0.4
note volume change!

18. Elastic Settlement E E ez r = H s/E = H.ez Q s H Generalized stress
and strain field
r = ez .dz
r = H s/E = H.ez

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

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

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

22. Total stress change Is
z/B

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

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

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

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

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

30. Superposition using Steinbrenner methodL B

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

32. 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

33. Total stress change Is
z/B

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

35. Stress non-linearity
qnet z

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

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

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

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

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

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

42. Depth Correction B z

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

44. Field Settlement for Clays (Bjerrum, 1962)

45. 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

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