The compaction of a cohesionless soil with a vibratory compactor can be simulated with the penetration of a square steel pile driven with a vibratory pile driver as indicated in Fig. 8.13. Base on the penetration of pile theory (section 2.5), the ultimate point resistance qp in a homogeneous soil can be calculated. For example, after the 123 seconds of vibratory compaction, the measured surface settlement was 40.3 mm. So the overburden pressure at the base of the compactor q’ = 0.62 kN/m2. Before compaction, the soil unit weight of density was 15.6 kN/m2. And the soil friction angle was 31°. In Fig. 2.13, the bearing capacity factor Nq* = 60 was determined. The ultimate point resistance qp at 123 seconds of compaction is estimated with Eq. 2.12 was 37.44 kN/m2. By repeating the above-mentioned procedures, the ultimate load qp after 7, 20 and 46 seconds of compaction could be estimated as 19.66, 27.14 and 32.92 kN/m2, respectively. As the compaction time increasing, the ultimate point resistance qp increased to the cyclic compacting stress σcyc = 34.9 kN/m2 applied on the surface of soil. It is suggested that in the vibratory compaction process, the soil mass will settle until the ultimate load qp and the cyclic compacting stress σcyc reached an equilibrium.
Chapter 9
CONCLUSIONS
Based on the vertical and horizontal earth pressure for loose sand and the surface settlement, change of soil density and earth pressures after the vibratory compaction at a point, the following conclusions were drawn.
1. For a loose backfill, the vertical and horizontal earth pressures in the soil mass can be properly estimated with the equation σv = γz and Jaky’s equation, respectively.
2. The compaction of a cohesionless soil with a vibratory compactor can be simulated with the penetration of a square steel pile driven with a vibratory pile hammer. In the compaction process, the soils under the compacting plate settled until the ultimate tip resistance qp and the cyclic compacting stress σcyc reached an equilibrium.
3. The depth of the relative density contour (Dr = 36 %) increased with increasing time of compaction. The peak relative density in the soil also increased with increasing time of compaction.
4. It was obvious that the peak Δσv (3.60, 3.99, 4.44, 4.96, kN/m2) and Δσh (1.93, 2.41, 3.16, 3.32 kN/m2) increased with increasing compaction time. This is because, with increasing compaction time, more compaction energy was transmitted to the soil.
5. After the removal of the compactor, residual stresses in the soil mass were measured due to the vibratory compaction. The point of peak Δσv, as the compaction time increased, moved downward slightly from the depth of 250 mm to the depth of 350 mm.
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Table 3.1. Technical Information of the Acentric Motor
Manufacture Mikasa Type KJ75-2P
Power (Watt) 75
Voltage (Volt) 220
Frequency (Hz) 50/60
Vibration Per Minute 3000/3600
Mass (kg) 6.2
Table 4.1. Properties of Ottawa Sand
Shape Rounded
emax 0.76
emin 0.50
G s 2.65
60,
D mm 0.32
10,
D mm 0.21
C u 1.78
Table 6.1. Determination of Compaction Time for Testing with
Time, t (s) Compaction Time for Testing (s)
Table 6.2. Compaction Time with Corresponding Average Settlement
Compaction Time
Table 6.3. Compaction between the NCTU’s Compaction Tests and D’Appolonia’s Field Tests
Item NCTU D’ Appolonia
Soil Ottawa Sand Sand Dune
Compaction Hand tamper Vibratory roller
Size Small (12.1 kg) Heavy
Method Point Area Energy Small Large
Depth influence 0.4m 1.83m
Lift height 1.5m 2.44m
Vibratory Compactor
Ottawa Sand Model
Wall d
Fig. 1.1. Compaction on the surface of a 1500 mm-thick loose sand
Fig. 1.2. Compaction of backfill using hand tamper (after Day, 1998)
Fig. 2.1. Development of in-situ stresses (after Chen, 2003)
Fig. 2.2. Principal stresses in soil element (after Chen, 2003)
x
y
z v
σ
hσ σ
σ
=
σ =σ
=
hFig. 2.3. Jaky’s formulation of the relationship between Ko on OC and φ mobilized in OAB (after Mesri and Hayat, 1993)
φ φ τ
φ
Principal Stress Trajectories
90-45+ 2
A B C D
O z
z
r
r
z
Parabolic Interpolation of between OB and OC
O
O
Fig. 2.4. (a) Mode of foundation failure in sand (after Vesic, 1973)
Fig. 2.4. (b) Definition of failure mode (after Vesic, 1973)
Fig 2.5. Settlement of circular and rectangular plates used to achieve an ultimate load (Df / B = 0) in sand (after Vesic, 1963)
Fig. 2.6. Growth curves for a silty clay - relationship between dry unit weight and number of passes of 84.5 kN three-wheel roller when the soil
is compacted in 229 mm loose layers at different moisture contents (after Johnson and Sallberg, 1960)
Fig. 2.7. Vibratory compaction of a sand - variation of dry unit weight with number of roller passes; thickness of lift = 2.45 m
(after D’Appolonia, et al., 1969)
Fig. 2.8. Principles of vibratory rollers (after D’Appolonia, et al., 1969)
τ
yxτ σ
yzzτ τ
zyzxτ τ
xzxyσ
yσ
xy x
r
R
y
x
z Q
Fig. 2.9. Stresses due to a vertical point load in rectangular coordinates (after Boussinesq, 1883)
x y
z
L
q
oB
A
Fig. 2.10. Stresses below the corner of a rectangular loaded area
Qu
q’
Qs
Qp
Fig. 2.11. Ultimate load-carrying capacity of pile (after Das, 2004)
Fig. 2.12. Nature of variation of unit point resistance in a homogeneous sand (after Das, 2004)
Fig. 2.13. Variation of the maximum values of Nq＊ with soil friction with soil friction angle φ’(after Meyerhof, 1976)