Chapter 3:
Application of Reliability Based Design to
everyday geotechnical problems
© Jones & Wagener (Pty) Ltd. All rights reserved
GeoRisk 2017 Denver, 4-6 June 2017
Practical RBD
1. What did we do ?
2. Why did we do it ?
3. What did we find ?
GeoRisk 2017 Denver, 4-6 June 2017
What did we do ?
What did we do ?
•
•
•
•
•
•
Chose 7 simple structures
(Orr, 2005)
One soil type
(sand, f’k = 32o, gk = 20kN/m3)
Found Eurocode-compliant solution
Determined b
(FORM and Monte Carlo)
Calculated FoS (Mean & characteristic values)
Repeated for range of parameters & CoV
GeoRisk 2017 Denver, 4-6 June 2017
What did we do ?
Footings
Single pile
Retaining walls
4
0
1
2
3
5
6
GeoRisk 2017 Denver, 4-6 June 2017
What did we do ?
Soil Type
• Non-cohesive sand:
• f’k = 32o,
log-normal,
• gk = 20kN/m3, normal,
CoV=0.1
CoV=0.05
• rf,g = 0.2
GeoRisk 2017 Denver, 4-6 June 2017
What did we do ?
Loading:
• Gk
fixed value,
= mean
• Qk
log-normal
CoV = 0.25
• Wk
Gumbel
CoV = 0.50
GeoRisk 2017 Denver, 4-6 June 2017
Why did we do it ?
Why did we do it ?
• Ease of application of RBD methods
• Check reliability of Eurocode compliant designs
• Variation in reliability index with:
– variation in parameters f’ and g
– variation in CoV
• Compare with working stress design
GeoRisk 2017 Denver, 4-6 June 2017
What did we find ?
What did we find ?
b Reliability Ind.
Global FoS
FORM
M/C
Mean
Char
0. Strip vertical load
3.49
3.45
b 5.18
values 3.22.50
– 3.7
1. Square vertical load
3.51
3.46
(<4.86
3.8)
2. Square inclined load
3.69
3.58
3. Pile
3.36
3.35
6.58
2.60
b FORM ~ b M/C
2.76
1.73
4. Gravity wall
3.33
3.3
b 6.88
reasonably3.12
5. Cantilever wall
3.40
3.39
6. Anchored wall
3.24
3.23
constant
all
2.34 for 1.63
types of structure
1.43
1.25
2.40
GeoRisk 2017 Denver, 4-6 June 2017
What did we find ?
What did we find ?
b Reliability Ind.
FORM
0. Strip vertical load
M/C
3.49
3.45
FoS determined
1. Square vertical load
3.51
3.46
using mean values
2. Square inclined load too3.69
3.58
high
3. Pile
3.36
3.35
FoS using charac4. Gravity wall
3.33
3.3
teristic values about
5. Cantilever wall
3.40
3.39
right
6. Anchored wall
3.24
3.23
Global FoS
Mean
Char
5.18
2.50
4.86
2.40
6.58
2.60
2.76
1.73
6.88
3.12
2.34
1.63
1.43
1.25
GeoRisk 2017 Denver, 4-6 June 2017
What did we find ?
1.
2.
3.
4.
FORM gives similar results to Monte Carlo
b values bit low but generally OK
b values consistent for all problem types
FoS highly variable – poor measure
GeoRisk 2017 Denver, 4-6 June 2017
What did we find ?
Characteristic
values:
QHk = 400 kN
FORM design
point values:
QHk = 638 kN
GVk = 3 000 kN +
310 kN
QVk = 2 000 kN
QVk = 1 306 kN
GeoRisk 2017 Denver, 4-6 June 2017
What did we find ?
1.
2.
3.
4.
5.
FORM gives similar results to Monte Carlo
b values bit low but generally OK
b values consistent for all problem types
FoS highly variable – poor measure
DA B* will give different eccentricity to DA1
GeoRisk 2017 Denver, 4-6 June 2017
5.0
29
27
6.0
25
Effect gofAverage
varying
’ and) g
densityf(kN/m
15
17
19
21
23
3
25
f ' Average Friction Angle (deg)
(a) Required footing size L=B (m)
39
3.6
39
7.5
37
7.0
6.5
35
6.0
33
5.5
31
5.0
29
27
4.5
25
15
17
19
21
23
g Average density (kN/m )
(c) Global FoS (using mean values)
25
3
37
3.7
35
33
3.8
31
29
27
3.9
25
15
17
19
21
23
g Average density (kN/m3)
(b) Reliability Index b (r = 0.2)
eg)
f ' Average Friction Angle (deg)
31
39
7.5
25
f ' Average Friction Angle (deg)
f ' Average Fricti
What did we find ?
33
39
2.7
37
2.6
35
2.5
33
2.4
31
2.3
29
2.2
27
2.1
25
15
17
19
21
23
25
g Average density (kN/m3)
(d) Global
FoS
(using
characteristic
GeoRisk
2017
Denver,
4-6 Junevalues)
2017
4.4
11
0.14
4.2
0.12
4.0
EffectCoefficient
of varying
CoV
of Variation g
0.1
0.02
0.18
0.14
0.1
0.06
(a) Required footing size L=B (m)
0.18
10
0.16
9
0.14
8
0.12
7
0.1
Coefficient of Variation f’
0.2
0.02
0.06
0.1
0.14
Coefficient of Variation g
2.8
0.18
0.18
(c) Global FoS (using mean values)
0.2
0.16
3.0
0.14
3.2
3.4
0.12
3.6
0.1
0.02
0.06
0.1
0.14
Coefficient of Variation g
0.18
(b) Reliability Index b (r = 0.2)
Coefficient of Variation f’
What did we find ?
0.2
Coefficient of Variation f’
Coefficient of Vari
0.16
0.18
2.40
0.16
2.45
0.14
2.50
0.12
2.55
0.1
0.02
0.06
0.1
0.14
Coefficient of Variation g
0.2
11
0.18
GeoRisk
Denver,
4-6 June
2017
(d) Global
FoS2017
(using
characteristic
values)
What did we find ?
1.
2.
3.
4.
5.
6.
FORM gives similar results to Monte Carlo
b values bit low but generally OK
b values consistent for all problem types
FoS highly variable – poor measure
DA B* will give different eccentricity to DA1
b values consistent for range of material
properties
7. b values below target for high CoV of
material properties
8. Designing for normal FoS may be unreliable
GeoRisk 2017 Denver, 4-6 June 2017