Question

Light Post A weighed 25,000 lb is proposed to be constructed 5 ft away from your Los Angeles house. As a civil engineer student who is taking the Geotechnical Engineering class, your education raised your concern in settlement induced by the construction of the Light Post A. The settlement could crack the slab of your house's foundation. To protect your property, you are driven to conduct a settlement analysis. You have gathered openly accessed information regarding SO CAL geology and soil properties and is depicted in the following figure. Answer the following questions: A. Which geological formation(s) (Artificial Fill, Young Alluvial, Old Alluvial, or Lakewood) you would expect significant primary consolidation settlement? B. Calculate the settlement in the Young Alluvial formation induced by the construction of Light POs A, which can be modeled as a point load. A one-sublayer analysis is sufficient. C. Calculate the settlement in the Old Alluvial formation induced by the construction of Light Post A which can be modeled as a point load. A one-sublayer analysis is sufficient. D.Alternatively, Light Post B weighted 18,000 lb is proposed to be constructed 3 ft away from your house. Which proposed Light Post, A or B, would provide less primary consolidation settlement? Write a few sentences to explain your reasons. While a detailed settlement analysis is not required here, show simple calculation if needed.

Answer 1

Solution:

a) The young alluvial formation - fat clay has more primary consolidation than the other three soil layers.

Because the artificial fill has sand and gravel which does not undergo consolidation, so this layer does not posses primary settlement.

The other two layers namely, old alluvial soil and lake wood formation undergoes consolidation but the primary settlement of these layers are less than the young alluvial formation as these layers undergoes consolidation prior to the young alluvial layer.    

b) Primary consolidation of young alluvial formation due to light post A:

$\Delta H=H_{o}*C_{c}*log_{10}[\sigma _{f}^{'}/\sigma _{o}^{'}]/(1+e_{o})$

where,

H_o = Initial thickness of the soil layer = 14'

C_c - COmpression index = 0.32

e_o - Initial void ratio = 1.20

$\sigma _{o}^{'}$ - Initial stress = 120*1+(93-62.4)*7 = 334.20 lb/sq.ft

$\sigma _{f}^{'}$ - Final stress - Stress due to overlying soil and excess stress induced by the light post A

$\sigma _{f}^{'} = \sigma _{o}^{'} +\Delta \sigma ^{'}$

By Bousinessq's equation,

$\Delta \sigma ^{'}={Q*3/(Z^{2}*2\Pi )}*(1/(1+(r/z)^{2})^{5/2}$

Layer Load, kN Depth, m 1/2 Τ Δσ 18 Young Alluvial Soil | 25000 Old Alluvial Soil 25000 Young Alluvial Soil 18000 Old Alluvial Soil 18000 0.63 0.28 0.38 0.17 81.82699 30.60945 96.69342 24.78227 18

$\Delta H=H_{o}*C_{c}*log_{10}[\sigma _{f}^{'}/\sigma _{o}^{'}]/(1+e_{o})$

= 14*0.32*log((334.2+81.83)/334.2)/(1+1.2)

= 0.193 ft = 58.10mm

c) Primary consolidation of old alluvial formation due to light post A:

$\Delta H=H_{o}*C_{c}*log_{10}[\sigma _{f}^{'}/\sigma _{o}^{'}]/(1+e_{o})$

where,

H_o = Initial thickness of the soil layer = 6'

C_c - COmpression index = 0.18

e_o - Initial void ratio = 0.80

$\sigma _{o}^{'}$ - Initial stress = 120*1+(93-62.4)*14+3*(110-62.4) = 691.20 lb/sq.ft

$\sigma _{f}^{'}$ - Final stress - Stress due to overlying soil and excess stress induced by the light post A

$\sigma _{f}^{'} = \sigma _{o}^{'} +\Delta \sigma ^{'}$ =691.20+30.60 = 721.80 lb/sq.ft

By Bousinessq's equation,

$\Delta \sigma ^{'}={Q*3/(Z^{2}*2\Pi )}*(1/(1+(r/z)^{2})^{5/2}$ = 30.60 lb/sq.ft

$\Delta H=H_{o}*C_{c}*log_{10}[\sigma _{f}^{'}/\sigma _{o}^{'}]/(1+e_{o})$

= 6*0.18*log((721.80/691.20)/(1+0.80)

= 3.38mm

d) Compare the Primary COnsolidation induced by Post A and Post B:

Primary consolidation of the young alluvial layer due to the Post B,

$\sigma _{f}^{'} = \sigma _{p}^{'} +\Delta \sigma ^{'}$ =300+96.69 = 396.69 lb/sq.ft

$\Delta H=H_{o}*C_{r}*log_{10}[\sigma _{f}^{'}/\sigma _{p}^{'}]/(1+e_{o})$

= 14*0.07*log(396.96/300)/(1+1.2)

= 16.25 mm

Primary consolidation of the old alluvial layer due to the Post B,

$\sigma _{f}^{'} = \sigma _{p}^{'} +\Delta \sigma ^{'}$ =600+24.78 = 624.78 lb/sq.ft

$\Delta H=H_{o}*C_{r}*log_{10}[\sigma _{f}^{'}/\sigma _{p}^{'}]/(1+e_{o})$

= 6*0.02*log(624.78/600)/(1+0.8)

= 0.35 mm

From the above results it was found that the young alluvial layer settles or consolidates due to Post A is more compared to the other layers by the load from Post A or Post B.