CHAPTER 14

DESIGN EXAMPLE

 

14.1 DESIGN EXAMPLE

1. Design Conditions

a) Configuration of GRS-RW

Height

= 5.1 m

Excavation stage on slope

= 1 stage

The design cross-section is shown in Figure 14.1.

b) Properties of Backfill Soil

Unit weight

= 19 kN/m3

Internal friction angle

= 30o

c) Ground Conditions

Soil

Layer #

Depth

(m)

Soil

Type

Saturated Unit Weight (kN/m3)

Bulk Unit Weight

(kN/m3)

Cohesion

(kPa)

Internal Friction Angle

(o)

1

> 3

clay

18

18

100

0

2

0 - 3

clay

18

18

50

0

 

d) Geosynthetic

Length of embedment, l

2.0 m

Vertical spacing, D

0.3 m

Vertical spacing for full-length geosynthetic layer, D

1.5 m

Angle of repose to determine full-length geosynthetic, f

30o

Spring constant, ks

200 kN/m

Design standard strength, Tk

30 kN/m

 

 

 

Dead

Live1

Earthquake

Reduction Factor, a

a j= 0.62

a i= 0.62

a e= 0.62

Design Rupture Strength, T (kN/m)

Taj= 18

Tai= 27

Tae= 27

Factor of Safety against Pullout, Ft

2.0

1.5

1.25

1 considers wind load for the sound wall

2 value given as example, differs with type of material

Coefficient of horizontal subgrade reaction, Kh = 90 kN/m3 (for a sound wall of area 5.1 m2)

e) Facing

Configuration

thickness at the crest

= 0.6 m

thickness at the base (design ground surface)

= 0.855

slope along the front

= 1:0.05

slope along the back

= 1:0

Type of structure: reinforced concrete

unit weight, g

= 25 kN/m3

elastic modulus, E

= 2500 MPa

Concrete: allowable stresses

standard design strength, s ck

= 24 MPa

allowable flexural-compressive

strength (reinforced), s ca

= 4.5 MPa

allowable flexural-compressive

strength (unreinforced), s ca

= 8.0 MPa

allowable flexural tensile strength, s ta

= 0.225 MPa

allowable shear strength, t a

= 0.39 MPa

Steel reinforcement: allowable stress (SD 294)

allowable tensile strength

= 180 MPa

 

For allowable stresses under combined loading conditions, the following coefficients are used.

Loading State

Coefficient

Combination of Load

Dead

1.0

dead weight + surcharge + earth pressure + dead weight of sound wall

Live

1.25

dead weight + earthquake earth pressure + dead weight of sound wall + wind load (both directions)

Earthquake

1.5

dead weight + earthquake earth pressure + dead weight of sound wall

 

f) Factors of Safety (after construction)

Stability

Method of Analysis

Type of Analysis

Dead Load

Live Load

Earthquake

External

Fellenius Method

circular surface

1.3

1.3

1.0

Internal

Two-wedge

sliding, over-turning

2.0

1.5

1.25

 

2. Loading Conditions

a) Combination of Load (after construction)

 

Loading State

Dead

Live

Earthquake

Backfill, Foundation

Dead weight

x

x

x

 

Earthquake load

 

 

x

Facing

Dead weight

x

x

x

 

Earthquake load

 

 

x

Sound Wall

Dead weight

x

x

x

 

Wind load

 

x1

 

Surcharge

 

x

x

 

1 wind load is considered to act on both directions (outwards, inwards).

b) Dead Weight

c) Earthquake Inertia Force

External stability analysis (backfill, ground)

Horizontal seismic coefficient, KH= 0.15

Internal stability analysis (backfill)

Horizontal seismic coefficient, KH= 0.15

Design earthquake coefficient, KH = n 1n 2k o

where KH: design horizontal seismic coefficient

k o: standard design seismic coefficient = 0.15

n 1: regional correction factor = 1.0

n 2: ground correction factor = 1.0

d) Surcharge Load

 

Dead

Live

Earthquake

Width of Surcharge

Surcharge (kN/m)

10

10

0.0

15 m

 

e) Loading acting on Crest of Facing

External Load

Dead

Live (outwards)

Live (inwards)

Earthquake

Vertical load, Pv (kN/m)

0.0

0.0

0.0

0.0

Horizontal load, Ph (kN/m)

0.0

4.5

-4.5

0.0

Moment, Pm (kN.m/m)

0.0

6.75

-6.75

0.0

 

calculation of wind loads (dead)

Height of sound wall, H

= 3.0 m

Distance between wall column, a

= 4.0 m

Wind pressure, p

= 1.5 kPa (wind speed = 45 m/s)

Horizontal load, Ph

= p.H = 1.5´ 3 = 4.5 kN

Moment, Pm

= 0.5.H.Ph = 0.5´ 3.0´ 4.5 = 6.75 kN.m

 

f) Earth Pressure

Using two-part wedge method.

3. Results of Internal Stability Analysis (factors of safety)

Loading State

Overturning

Sliding

Required

Dead

2.633

2.206

2.0

Live (outwards)

2.932

2.919

1.5

Live (inwards)

4.476

3.283

1.5

Earthquake

2.368

1.579

1.25

The internal stability is satisfied against different failure modes.

4. Facing Structural Analysis

a) Finite Element Model

A finite element analysis is conducted by modeling facing as beam element and geosynthetic as spring. The combined earth pressure (the larger resultant obtained from direct sliding or overturning analyses is selected), dead weight of facing, earthquake inertia force, external load acting at the facing crest are applied (see Figure 14.2).

b) Forces acting in the Section

Loading State

Bending Moment, Mmax (kN.m)

Shear Force, Qmax (kN)

Dead

3.10

6.51

Live (outwards)

-9.37

-6.22

Live (inwards)

10.49

7.76

Earthquake

4.06

-10.56

sign convention with reference to Figure 14.1

moment: clockwise positive (tension in front of facing),

shear force (positive acting towards the left)

c) Stress Analysis

The axial force is neglected in stress analysis (conservative)

i) Flexural failure analysis (unreinforced)

s b = M/z

where s b : bending stress, M: bending moment, Z: section modulus.

Z is determined using a thickness of 60 cm; Z= bh2/6= 1.0´ 0.62/6 = 0.06 m2

maximum bending moment, Mmax = 10.49 kN.m

so, s b= 17.48 kPa < 28.1 kPa (=22.5´ 1.25)

ii) Shear failure analysis

t = Q/A

where t : shear stress, Q: shear force, A: cross sectional area

maximum shear force, Qmax= 10.56 kN

t = 10.56 kN/0.6 = 17.6 kPa < 58.5 kPa (= 39´ 1.5)

iii) Steel reinforcement

tensile stress:

compressive stress:

compressive stress: s c= 2M/ bx(d-x/3)

where

n: elastic modulus ratio = 15

b: width =100 cm

d: effective height = 55 cm

As : area of steel reinforcement = 1.267´ (100¸ 30) = 4.22 cm2

s s = 47.4 MPa < 270 MPa (=180´ 1.5)

s c = 0.517 MPa < 10 MPa (= 8´ 1.25)

t = 0.0176 MPa < 0.585 MPa (=0.39´ 1.5)

5. External Stability Analysis

The results of analysis using Fellenius Method is shown in the Table below. The required factors of safety are satisfied.

Loading State

Factor of Safety

Required Factor of Safety

Dead

1.667

1.3

Live (outwards)

1.697

1.3

Live (inwards)

1.693

1.3

Earthquake

1.380

1.0

 

The above-presented design example was analyzed using a computer program. The consolidation and external sliding analyses have to be conducted separately.

 

 

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