Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues:...
-
Upload
maya-zimmerman -
Category
Documents
-
view
214 -
download
0
Transcript of Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues:...
![Page 1: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/1.jpg)
Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading
IntroductionProf. ing. Claudio di Prisco
![Page 2: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/2.jpg)
2
Prof. ing. Claudio di Prisco
Experimental device
10 20 30–800
–400
0
400
800
Time (sec)
Acc
. (g
al) Max= 712 gal
20 40 60 80 100 120–600–400–200
0200400600
Time (sec)
Acc
. (g
al) Max= 608 gal
Shear stacksShear stacks
![Page 3: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/3.jpg)
3
Prof. ing. Claudio di Prisco
Experimental evidence
![Page 4: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/4.jpg)
4
Prof. ing. Claudio di Prisco
The elasto-perfectly plastic approach
![Page 5: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/5.jpg)
5
Prof. ing. Claudio di Prisco
Coupled elastoplastic CONSTITUTIVE RELATIONSHIP
qqQQDQ pttt ))(,,(
dq C dQ
Defined in quasi static conditions:
THE MACRO-ELEMENT THE MACRO-ELEMENT CONCEPTCONCEPT
333231
232221
131211
CCC
CCC
CCC
C
Incremental constitutive relationship
FOUNDATION
NEAR FIELD
FAR FIELD
![Page 6: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/6.jpg)
6
Prof. ing. Claudio di Prisco
The interaction domain for rigid footings
Interaction domain for rigid strip Interaction domain for rigid strip footings and elasto-perfectly plastic footings and elasto-perfectly plastic approachapproach
m = M/ψBVMAX,
h = H/μVMAX
ξ = V/VMAX
1. To each point belonging to the failure locus a distinct failure mechanism corresponds
2. Difficulty in defining the failure locus when loose sand strata are concerned
3. Non-associated flow rule
4. Within the failure locus the mechanical behaviour is assumed to be elastic and uncoupled
5. Extension to rectangular footings
MONOTONOUSLY INCREASING LOADING
![Page 7: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/7.jpg)
7
Prof. ing. Claudio di Prisco
Settlements
-0.002 -0.001 0 0.001 0.002horizontal displacement (m )
-120
-80
-40
0
40
80
120
ho
rizo
nta
l lo
ad
(k
N/m
)
Cyclic Load
Centered vertical load Centered inclined load
Cyclic inclined loading
anisotropic hardening
Cremer et al, 2001
![Page 8: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/8.jpg)
8
Prof. ing. Claudio di Prisco
Hardening
22 2
2 1 0c
M H Vf V
B V
Isotropic hardening (Nova and Montrasio, 1991)
Swipe testsButterfield and Gottardi, 2003
H
V
V
M/B
c=Vc / VMAX
Hardening parameter
![Page 9: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/9.jpg)
9
Prof. ing. Claudio di Prisco
Inclined-eccentric loads
Nova and Montrasio, 1991
Inclined and eccentric loadingInclined and eccentric loading
![Page 10: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/10.jpg)
10
Prof. ing. Claudio di Prisco
How can R0 be determined?
Some hints about settlement evaluation
Homogeneous stratigraphic profiles
![Page 11: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/11.jpg)
11
Prof. ing. Claudio di Prisco
Settlement evaluation
• Irreversibility of the material mechanical response
• Non-linearity
• Dependency of stiffness on confining pressure
![Page 12: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/12.jpg)
12
Prof. ing. Claudio di Prisco
The elastic solution
Poulos e Davis (1974)
Gibson (1973)
Winkler (1867)
Dependency of stiffness on confining pressure:
0( )E z E z
Eo/λD
1
0
0.5
r/D0 1
= 0.5
![Page 13: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/13.jpg)
13
Prof. ing. Claudio di Prisco
Settlement evaluation
The elastic solutionThe elastic solution
21q BI
E
Linear loading distribution Strip loading distribution
Rectangular loading distribution
![Page 14: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/14.jpg)
14
Prof. ing. Claudio di Prisco
Generalised plasticity
dq I)pl
( ( , ) ciclig
Q
![Page 15: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/15.jpg)
15
Prof. ing. Claudio di Prisco
Numerical validation
![Page 16: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/16.jpg)
16
Prof. ing. Claudio di Prisco
![Page 17: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/17.jpg)
17
Prof. ing. Claudio di Prisco
Cyclic loads
c)
b)
a)
Loose sandLoose sand Dense sandDense sand
![Page 18: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/18.jpg)
18
Prof. ing. Claudio di Prisco
Numerical validation
![Page 19: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/19.jpg)
19
Prof. ing. Claudio di Prisco
Numerical results
1E-005 0.0001 0.001 0.01 0.1
rocking angle (rad)
0
0.2
0.4
0.6
0.8
1
K
/ K 0
(-)
dense sandVM A X /V = 2VM A X /V = 4VM A X /V = 6VM A X /V = 8VM A X /V = 10
1E-005 0.0001 0.001 0.01 0.1
rocking angle (rad)
0
0.2
0.4
0.6
0.8
1
K
/ K 0
(-)
medium density sandVM A X /V = 2VM A X /V = 4VM A X /V = 6VM A X /V = 8VM A X /V = 10
1E-005 0.0001 0.001 0.01
rocking angle (rad)
0
0.1
0.2
0.3
0.4
dam
pin
g (
-)
dense sandV M A X /V = 2V M A X /V = 4V M A X /V = 6V M A X /V = 8V M A X /V = 10
1E-005 0.0001 0.001 0.01
rocking angle (rad)
0
0.1
0.2
0.3
0.4
dam
pin
g (
-)
m edium density sandV M A X /V = 2V M A X /V = 4V M A X /V = 6V M A X /V = 8V M A X /V = 10
![Page 20: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/20.jpg)
20
Prof. ing. Claudio di Prisco
Cyclic consequences of the mechanical coupling
![Page 21: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/21.jpg)
21
Prof. ing. Claudio di Prisco
![Page 22: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/22.jpg)
22
Prof. ing. Claudio di Prisco
![Page 23: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/23.jpg)
23
Prof. ing. Claudio di Prisco
A dynamic/non seismic problem
![Page 24: Mechanical response of shallow foundations - Some experimental/theoretical and numerical issues: monotonic loading Introduction Prof. ing. Claudio di Prisco.](https://reader035.fdocuments.in/reader035/viewer/2022062618/5513e38655034674748b557b/html5/thumbnails/24.jpg)
24
Prof. ing. Claudio di Prisco