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# Design of geotechnical structures in urban areas

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Geotechnical Design
Homework 2:
Design of geotechnical structures in urban areas
Prof. Dr. Cristina Jommi, Dr. Nicola Pontani
A.Y. 2021-2022
1 Introduction
Due to the high demand for new residential and commercial spaces, the municipality of
Parma plans an extension of the existing urban area. The new buildings will typically be
built on either side of the routes leading out of the city centre (Fig. 1). Most of them will
be reinforced concrete multi-storey frames built on shallow strip foundations (Fig. 3). In
view of the growing number of people who will interest the area, the municipality is also
thinking to an extension of the city’s railway line. The new infrastructure will be built
underneath the existing road adopting the top-down technique while the excavation will
be supported by reinforced concrete diaphragms walls (Fig.s 1 and 2).
The geognostic and geotechnical investigation campaign led to the reconstruction of a
geotechnical profile of the subsoil formed by a shallow sandy silt and an intermediate layer
of slightly over-consolidated silty clay on a deep sand deposit (Fig.1). The characteristic
values of the mechanical and physical quantities of each of the layers are summarized in
Tab. 1.
Layer H γsat ϕ
′ su Eep Eur ν e0 cv Cc Cs Ip
– m kN/m3 ° kPa MPa MPa – – cm/s2 – – %
A 4 19 32.0 – 30.0 50.0 0.3 – – – – –
B 11 18.5 27.0 40 20.0 30.0 0.3 0.75 3.e-3 0.25 0.03 20
C 7 19 31.5 – 40.0 70.0 0.3 – – – – –
Table 1: Geotechnical profile and characteristic values of the involved quantities. The
stiffness parameters are given at the reference atmospheric pressure patm.
1
Figure 1: Section.
2
Figure 2: Cross section of the railway tunnel. The top of the upper slab is 15 cm above
the ground level (i.e., the length of the wall is 18.50 m).
2 Design of the foundation for bearing capacity
Design a strip foundation for the concrete building of Figure 3. The building is made of
four floors, whose main floor framing and vertical cross section are reported in Figures 4
and 5. The embedment depth of foundation is 1.5 m and the groundwater level is located
at 2.0 m from the ground surface (Fig. 6) with a seasonal variation of ±0.5 m.
From the structural analysis, the characteristic values of permanent and variable vertical
loads, Gk and Qk, for each of the six columns have been obtained as summarized in Tab.
2 and Figure 6. For no-seismic design situation, shear forces and bending moments can
be assumed to be negligible.
Questions
• Using the approaches suggested by the Eurocode 7, DA1-2 and DA2, design the size
B of the strip foundation by imposing Rd = Vd and summarise the adopted factors
and the results obtained into a table like Tab.3.
3
Column Normal forces kN
C1 Gk -368.2
Qk -86.5
C2 Gk -549.7
Qk -177.9
C3 Gk -502.2
Qk -123.2
C4 Gk -499.1
Qk -121.8
C5 Gk -548.0
Qk -177.8
C6 Gk -333.6
Qk -86.5
Table 2: Characteristic values of the permanent and variable loads from the superstruc-
ture, Gk and Qk.
DA1-2 DA2
Partial factors A2+M2+R1 A1+M1+R2
Vd (kN)
Nq
Nγ
sq
sγ
Rd (kN)
Rd/Vd
B (m)
Table 3: Adopted factors and results obtained by using the different design approaches.
4
Figure 3: Superstructure and foundation.
Figure 4: Main floor framing.
Figure 5: Vertical cross section of the building.
5
Figure 6: Cross section of the beam foundation with the characteristic values of the
permanent and variable loads from the superstructure, Gk and Qk.
6
3 Serviceability check of the foundation
In order to verify the functionality of the structure, both the immediate and the long-term
settlement must be assessed:
w(t) = w0 + Umwoed (1)
The former can be computed from the linear elastic solution, taking care of the presence
of different layers (Fig. 7, Fig. 8 and Fig. 9)1:
w0 = qB
n∑
i=1
I(Hi)− I(Hi−1)
Ei
(1− ν2) (2)
The latter, can be evaluated by means of the Terzaghi’s one dimensional consolidation
theory (Fig. 10):
Um = 1−
8
π2
∞∑
n=1
1
(2n− 1)2
exp
{
−(2n− 1)2π
2
4
Tv
}
Tv =
cvt
H2
(3)
The calculation of the consolidation settlement can be limited at a depth where the stress
increment is lower than 10% of the in situ effective stress.
Questions
• Plot the patterns of time settlement curves (accounting also the immediate settle-
ment) and assess the fulfilment of the condition wmax < 0.05m.
• Considering the same load configuration for all the foundation beams, estimate the
expected average settlement of the building.
Figure 7: Calculation of the immediate settlement (elastic solution).
1the elasto-plastic Young modulus (Eep) of each layer can be used for this computation.
7
Figure 8: Determination of µ0 and µ1 for the calculation of the influence factor I = µ0µ1.
Figure 9: Empirical correlation between Eu, Su and OCR.
8
Figure 10: Terzaghi’s solution for the one dimensional consolidation problem.
4 Soil Structure Interaction: design of the foundation beam
Investigate the soil-foundation interaction by the use of the Winkler’s method.
Questions
• Provide a reliable estimation of the Winkler’s constant k.
• Plot the diagrams of the settlements w, bending moment M and shear force T along
the foundation beam.
• Design the steel reinforcement of the beam (optional).
9
5 Geotechnical Design of the excavation
The excavation is planned to be made in five phases:
– PHASE 1 (Fig. 11): installation of the two reinforced concrete diaphragms. The
presence of the buildings at the sides of the excavation is modeled as a uniform
vertical pressure q. The water table is located at a depth of 2.0 m from the ground.
– PHASE 2 (Fig. 12): the first 3 m of soil are removed. Inside the excavation, the
water table is kept at the bottom, while its position remains unchanged outside.
– PHASE 3 (Fig. 13): construction of the top connecting slab.
– PHASE 4 (Fig. 14): the excavation is carried out to a depth of 8.2 m from the
ground. Inside the excavation, the water table is kept at the bottom, while its
position remains unchanged outside.
– PHASE 5 (Fig. 15): The bottom slab is inserted. Application of operating loads:
permanent gk,t=5 kPa, gk,b=13.55 kPa and variable qk,t=37.2 kPa, qk,b=20 kPa.
Inside the excavation, the water table is kept at the bottom, while its position
remains unchanged outside.
Questions
• Check the Geotechnical ULS for overturning at the excavation phases 2, 3 and 4,
assuming each diaphragm as a rigid body. For the sake of safety, consider a null
interface friction angle at the active side.
• Establish which of the excavation phases may incur into the risk of uplifting or heave,
and carry out the hydraulic ULS checks.
10
Figure 11: Phase 1.
Figure 12: Phase 2.
11
Figure 13: Phase 3.
Figure 14: Phase 4.
12
Figure 15: Phase 5.
13
6 Soil Structure Interaction: diaphragm walls
Questions
• Define an appropriate constitutive law for the horizontal springs representing the
soil, assuming an elastic-plastic response.
• For each excavation phase, evaluate the profiles of the bending moment and the
shear stress generated on the diaphragms over depth. Report an envelope of the
maximum and minimum values obtained.
• Determine the maximum compressive stress on the two slabs during the different
excavation phases.
• Plot the horizontal displacements of the diaphragms for all the excavation phases
and check the serviceability limit state assuming a maximum allowable displacement
of 5cm.
• Provide an estimation of the vertical settlements induced by the excavation on the
close buildings.
• Design the reinforcement of the cross section of the diaphragms (optional).
• In your opinion, is it appropriate to do the excavation so close to the existing build-
ings? Suppose you had known that the excavation was going to be carried out, would
you still have chosen shallow foundations or not?
14

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