Download Compressibility of Soil-Soil Mechanics and Foundations 25 and more Slides Soil Mechanics and Foundations in PDF only on Docsity! CE 240 Soil Mechanics & Foundations Lecture 9.1 Compressibility of Soil I (Das, Ch. 10) Class Outline • Introduction of compressibility • Elastic settlement • Elastic settlement calculation • Improved relationship for elastic settlement • Introduction to consolidation Compression - Introduction • Structure foundation cause excessive stress (load) • Surface stress (load) cause soil settlement • Soil settlement can be divided into 3 categories: – Elastic settlement (immediate settlement) can be described by the Hooke’s law – Primary consolidation settlement due to expulsion of pore water – Secondary consolidation settlement due to plastic adjustment of soil skeletons. • In a mathematic expression we have (next page ) Settlement T c s e S = total settlement S = primary consolidation settlement S = secondary consolidation settlement S = elastic settlement T c s eS S S S where Significance • The amount of soil volume change that will occur is often one of the governing design criteria of a project; • If the settlement is not kept to tolerable limit, the desire use of the structure may be impaired and the design life of the structure may be reduced; • It is therefore important to have a means of prediction of the amount of soil compression or consolidation; • It is also important to know the rate of consolidation as well as the total consolidation to be expected. Figure 10.1 stress strain stress strain perfectly rigid foundation on clay perfectly flexible foundation on clay Figure 10.2 perfectly rigid foundation on sand perfectly flexible foundation on sand Young’s modulus E Young’s modulus is the stress needed to compress the solid to shorten in a unit strain. Poisson’s ratio Poisson’s measures the relativity of the expansion in the lateral directions and compression in the direction in which the uni-axial compression applies. zz E / 1 zz rr / / Table 10.2 Representative Values of the Modulus of Elasticity of Soil
E,
Soil type kN/m? Ib /in.?
Soft clay 1,800-—3,500 250-500
Hard clay 6,000 —14,000 850 -—2,000
Loose sand 10,000 —28,000 1,500—4,000
Dense sand 35,000 —70,000 5,000 —10,000
Table 10.3 Representative Values of Poisson’s Ratio
Type of soil Poisson's ratio, u,
Loose sand 0.2-0.4
Medium sand 0.25-0.4
Dense sand 0.3-0.45
Silty sand 0.2-0.4
Soft clay 0.15-0.25
Medium clay 0.2—0.5
Improved relationship for elastic settlement 4 (rectangular ) (circular) e e BLB B B Modulus increase with depth 1.0
0.8
0.6
0.4
0.0
Se
Eo
_ AoBilotrle y 2
>30
10.0
5.0
1.0
(O25)
h/B, = 0.2
0.01
7; im Fle al T Steal T Tipe cit
2 4 6 80.1 I 10
100
Figure 10.4
Reading Assignment: Das, Ch. 10 Homework: 10.2 Refer to Figure 10.3. For a square foundation measuring 3 m X 3 m in plan
supported by a layer of sand and given that D; = 1.5 m, t= 0.25 m, Ey =
16,000 KN/m?, k = 400 kN/m’, pw, = 0.3, h = 20 m, E; = 15 X 10° KN/m’,
and Av = 100 kKN/m”, calculate the elastic settlement. Use Eq. (10.5).
ii Compressible soil layer
EB
Ss
Ms
Rigid layer
Depth, z
Figure 10.3 Improved relationship for elastic settlement
(1-7)
oO
Equation (10.5): S, = AoB,IgIp1,
Ao= 100 kN/m
iz 2
Se ae j2er = 3385 m
U u
H, = 0.3; E, = 16,000 KN / m?
p= ee a
kB, (400)(3.385) :
B, 3.385
En
oo
From Figure 10.4, J, ~ 0.89. From Equation (10.6):
