geosynthetics engineering: in theory and …...α m = maximum wall acceleration coefficient at...

GEOSYNTHETICS ENGINEERING: IN THEORY AND PRACTICE

Prof. J. N. Mandal

Department of civil engineering, IIT Bombay, Powai , Mumbai 400076, India. Tel.022-25767328email: [email protected]

Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay


Module - 6LECTURE - 27

Geosynthetics for reinforced soil retaining walls

Mechanically stabilized segmental reinforced soil wall

Geosynthetic reinforced soil wall system

Major components of reinforced soil system

Precast concrete modular blocks or panel facings andconnections Design of geosynthetics reinforced soil retaining wall

(Partly covered)

Recap of previous lecture…..


Step 4: Determine design factor of safety (FS) based onmode of failures

The geosynthetic reinforced soil wall is designed based onlimit equilibrium method of analysis. The two limit statesare:

(i) Ultimate limit state: actual failure (collapse) of thereinforced soil wall.

(ii) Serviceability limit states: excessive deformation and/orsettlement of reinforced soil walls.

Check the settlement criteria of reinforced soilstructure using conventional methods.


External stability:


• Sliding: Factor of safety (FS) ≥ 1.5

• Overturning: FS ≥ 2.0

• Bearing capacity: FS ≥ 2.5

• Overall (Deep-seated) stability: FS ≥ 1.3

• Seismic stability: FS ≥ 1.1 or 75 % of all static FS

Estimate settlement using conventional settlementanalysis


Check external wall stability with a uniformsurcharge load (Ultimate Limit state)

Reinforced soil wall with uniform surcharge loadProf. J. N. Mandal, Department of Civil Engineering, IIT Bombay

Rankine’s failure surface


Rankine’s distribution of lateral earth pressureWs = surcharge pressure

Wq = Weight of surcharge load = Ws. L

Wr = Weight of reinforced soil = γr. H. L

Pb = Lateral soil pressure from backfill

Pq = Lateral pressure due to surcharge load Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay

µ = tanδ = Co-efficient of shearing resistance betweensoil and reinforcement.

δ = Angle of shearing resistance between soil andreinforcement.

Ca = Adhesion between soil and reinforcement.


Factor of safety against sliding

ForcesDrivingorizontalHForcessistingReorizontalH

FSsliding

2babb H..K

21P H.W.KP sabq

Total driving force = Pb + Pq

Kab = tan2(450-Φb/2) = Coefficient of active earthpressure of backfill soil behind reinforced zone


Total Resisting force = µ. (Wr + Wq) + Ca.L = μ. (γr. H. L + Ws. L) + Ca. L

5.1)WH.5.0(H.KL.C)LWL.H..(FS

sbab

asrsliding


Factor of safety against overturning

2H.P

3H.PM qbov

2L.W

2L.WM qrr

Overturning Moment about the toe (Mov),

Resisting moment about the toe (Mr),

2H.W.K

6H..KM

2

sab

3

babov

2L.W

2L.H.M

2

s

2

rR 2L).L.WL.H.(M srR

0.2

LH)W3H..(K

)H.W(3FS 2

sbab

rsgoverturnin

MomentgOverturninMomentsistingRe

FS goverturnin


Factor of safety against bearing capacity

Meyerhof’s stress distribution for ground bearing pressureEccentricity (e) = Lbottom/2 – x' = Mov / V

x' = (Mr – Mov)/ V; V = total vertical load = Wq + Wr

If e ≤ L/6, no tension will develop beneath the footing.

From Mayerhof’s distribution, the acting length (L') = L – 2eProf. J. N. Mandal, Department of Civil Engineering, IIT Bombay

Two types of bearing capacity failures:

General shear:

e2LWW rq

maxv

Le21

WH. srmaxv

2

sr

sbab

srmaxv

LH

)WH.(3)W3H.(K

1

)WH.(

The maximum vertical stress, σvmax

qr

qbov

WW2H.P

3H.P

VMe

6

L)WH.(L6

)W3H.(H.Kesr

sb2

ab


Ultimate bearing capacity of soil (qult),

N'L5.0Ncq fcfult

Nc, Nγ = dimensionless bearing capacity factors

L' = L – 2e

5.2qFSmaxv

ultcapacitybearing


• Local shear:If the subsoil is poor, the bearing capacity is to beincreased. Three layers of geogrids or geocell mattresscan be provided beneath the foundation for groundimprovement.

Three layer of geogrids Geocell as a mattress foundation


• Slip failure / overall (deep-seated) stability: For deep-seated (overall) stability, use rotational slipmethod by classical slope stability analysis. The failuresurface will pass completely outside the reinforced soilmass.

Computer program is available to solve this problem.

Factor of safety against overall stability ≥ 1.3.

Particularly in case of an unstable hillside, the potentialcompound failure may occur.

The overall or global stability should not be avoided.


EXTERNAL STABILITY FOR SEISMIC LOADING

The conservative pseudo-static Mononobe-Okabeanalysis is recommended by AASHTO and FHWAguidelines for the seismic design of geosyntheticmechanically stabilized earth walls.

Apart from the static thrust, a seismic thrust ordynamic horizontal thrust (PAE) is also acting on thereinforced soil walls during an earthquake


Dynamic horizontal thrust acting on the reinforced soil walls during an earthquake.


αm = maximum wall acceleration coefficient at centroid ofwall mass,γb = unit weight of backfill,H = height of reinforced soil wall, andαo = maximum ground acceleration coefficient.

For example, αo = 0.04 for zone III (IS: 1893-1984).

H 0.375 P 2bmAE

oom ) -(1.45

(Seed and Whitman, 1970)

(Segrestin and Bastic, 1988)

The dynamic force (PAE) acts at a distance of 0.6H fromthe base of the wall.


The horizontal inertia force PIR is defined as,

mIR MP

M = mass of active zone of reinforced wall withbase width of 0.5H.

γr = Unit weight of reinforced zone,L = length of reinforcement,H = Height of reinforced soil wall

HLP rmIR (Seed and Mitchell, 1981)

50% of seismic thrust PIR is to be considered. Thereduction in PIR is due to the fact that two forces areunlikely to peak simultaneously.


Add all of the forces to determine the total horizontalactive force due to seismic loading:

• Horizontal component of active earth pressure due tothe retained back fill.

• Horizontal active earth pressure due to the surcharge.

• Seismic thrust (PAE), and

• 50 % horizontal inertia force PIR.


a) Check for Sliding due to seismic loading:

• Calculate resisting force (same of static condition)

• Calculate total active horizontal force including the totalhorizontal force due to seismic loading.

• Check dynamic factor of safety = 0.75 x static factor ofsafety.

75.0x5.1forcehorizontalactiveTotal

forcesistingReFOS seismicSliding


b) Check for overturning due to seismic loading:

• Calculate resisting moment (same of static condition)

• Calculate total driving moment.

- Horizontal force PIR is acting at the centre of gravity ofthe reinforced zone

- Dynamic horizontal thrust (PAE) is acting at a distance of0.6H from the base of the reinforced soil.

0.2x75.0momentdrivingTotalmomentresistingTotal

seismicforFOSov


Step 5: Check internal stability of geosyntheticreinforced soil wall (Ultimate limit state)

Allowable tensile strength of geosynthetic and thegeosynthetic-soil friction parameters play a very importantrole.

The wide width test of geosynthetic should be conductedaccording to ASTM or other test standards to determinethe ultimate tensile strength (Tult) of geosynthetics.

factorreductionCumulativeTT ult

allowable

Calculate the long term design strength (LTDS)= Treqd ≤ Tallowable


Internal stability:

Internal stability design of geosynthetic reinforced soil wall

Spacing of geosynthetic reinforcement Anchorage length of the geosynthetic reinforcement Connection strength between the geosynthetic

reinforcement and wall panels


a) Determine maximum developed tensile strength (Treqd)and vertical spacing (Sv)

Basic concept of evaluating the required tensile strength


Treqd. = k. σv. Sv = σh Sv

The maximum tensile force without considering any shearbetween the slices and the facing can be expressed as,


For geogrid, Treqd = Sv σh/ Cr

Cr = Coverage ratio = width of reinforcement (w)/ center-to-center horizontal spacing between two reinforcement (Sh)

Determination of coverage ratioCr = 1 (reinforcement is continuous and covers 100 % inplan view)

Cr = 0.6 (reinforcement covers 60 percent in plan view)Prof. J. N. Mandal, Department of Civil Engineering, IIT Bombay

Now, σh = σhs + σhq

σhs = soil pressure = γr H Karσhq = surcharge pressure = Kar q

So, total horizontal earth pressure, σh = γr H Kar + Kar .q

2

45tanK r2ar

ϕr = coefficient of friction in reinforced soil zone

Kar = coefficient of active earth pressure in reinforcedsoil zone

H = height of wall


Generally, the vertical spacing of the reinforcement isbetween 0.2 m to 0.8 m for mechanically stabilized earthwalls i.e. reinforced soil wall.

For geosynthetic wrapped face wall, the verticalspacing varies between 0.2 m to 0.5 m.

For modular block wall-face, vertical spacing is twicethe width of the modular block or 0.8 m whichever is less(AASHTO Standard Specifications for Bridges, 1996,with 1997 Interims).


b) Determine the embedded length (Le) of geosyntheticreinforcement

rrviepullhv C'.tan.C.L.2FS..S 'tan.C.C.2

FS..SL

rirv

pullhve

FSpull = factor of safety against pull-out failureCr = coverage ratio Ci = Interaction coefficient determined from pullout test


Please let us hear from you

Any question?


Prof. J. N. Mandal

Department of civil engineering, IIT Bombay, Powai , Mumbai 400076, India. Tel.022-25767328email: [email protected]


geosynthetics engineering: in theory and …...α m = maximum wall acceleration coefficient at...

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