Calculations for Reinforced Title
Hand Calculations for modular block wall of height 10.75 m
Reference
BS 00!"1#$010
%ate # %esigned b&# Checked b& # '((ro)ed b& # %esign *n(ut +arameters Reinforced Soil Data
'ngle of *nternal friction ᶲ1 -nit wt
1
,$ ° 1.5 k/cu.m
Retained Backfill Soil Data
,0 °
'ngle of *nternal friction ᶲ$ -nit wt
1.5 k/cu.m
Foundation Soil Data
Cohesion
0 k+a
'ngle of *nternal riction ᶲ,
,02
-nit wt
1.5 k/cu.m
Crash Barrier Data
Stri( load due to crash barrier 3
15.45 k+a
i)e oad 3l
$, k+a
i)e oad should be considered as (er (ro)isions of *RC#7"$014 6ater table is considered below the influence one. 8eneral Shear ailure is considered.
COMPUTATO! OF "#T"R 10.75 m H*8H 6' B ST'T*C '/'S*S
Coefficient of acti$e earth %ressure (k a)&
or reinforced soil#
ka 9 :l"si :l"sin nᶲ;:l< ;:l
kal
9
0.,07
6all batter
ᶿ=
or retained backfill soil#
1
ᶲ
9
32
4.$,
ka$
0.,,,
9
=echanical wall height H 9
10.75
m
ength of reinforcement 9
7.!0
m
=inimum embedment de(th
1
m
-nit weight of foundation soil >f
1
kN/m3
oundation (ro(erties #
Su''ar of %artial factors to e used
+artial factors
to be a((lied tan0? Soil material factors #
to be a((lied C to be a((lied Cu Sliding across surface of reinforcement :fs;
Soilreinforcement interaction factors
+ullout resistance of reinforcement :f(; oundation bearing ca(acit& # to be a((lied +artial factors of safet&
Sliding along base of the structure or an& horiontal surface where there is soil"soil contact
Partial load factors for load co'inations associated *ith *alls
A
@ffects
=ass of the reinforced soil bod& :ffs; =ass of the backfill on to( of the reinforced soil wall :ffs; @arth (ressure behind the structu:ffs; Traffic load# An reinforced soil b:f; Behind reinforced soil block
:f;
1.5
51
*RC#S+#10$"$014 C'S@ #'
A'%S Self weight of Reinforced Soil 6all e)er >9 iDHDDff5 9 1.5D10.75D7.!D1.5
k/m
9
$$!7.1 k/m
Stri( load due to Crash Barrier >$
'rm
9 3 F bDfts
E*
9
,.
width of the Stri( oad >$
9 15.5D1.!D1.5
k/m
9
,7.0 k/m
b9
1.!
E$
9
0.
E,
9
,.
3l
D H D ffs
>ertical load due to i)e oad
>,
9 3l F Dffs 9 $,D7.!D1.5
k/m
"
$!$.$ k/m
Resultant >ertical oad R) 9 >1<>$<>, 9
$5!!.45 k/m
Horiontal orces
@arth (ressure behind reinforced soil block +i " 1$ D ka$
D)$ D H$Dffs
9 0.5D0.,,,D1.5D10.75D10.75D1.5 9
5,4.$$ k/m
@arth +ressure due to i)e oad #
+$ 9 ka$ D
9 0.,,,D$,D10.75D1.5 "
1$,.5! k/m
Check for Sliding along the base
C'S@GB or long term stabilit& where there is soil to soil contact at the base of
the structure fsRh R):tan0?(fms;<:CDfms; Rh
is the horiontal factored disturbing force
R)
is the )ertical factored resultant force
0?(
is the (eak angle of shearing resistance under effecti)e stress c
fms
is the (artial materials factor a((lied to tan0?(I C?IC-
fs
is the (artial factor against base sliding
is the effecti)e base width for sliding
Sliding force :Rh;
9
Resisting force
9
:R) D tanA?(;fms
9
!.J1 k/m
:+i<+$;
7J.,4
9
!57.7 k/m
!.J1
Hence structure is safe in sliding stabilit&
5$
*RCGS+G 10$"$014
Check for Bearing ailure A)erturning =oment =o 9 :+* D H, < +$ D H$;
C'S@ #'
9
$57.4 k/"mm
Resisting =oment =r 9 :>* D $ <c$ F >$<>,D$; 9
J!41., K/"mm @ccentricit& :e; of resultant load R) about the centre line of the
base of width :=r"=0;
e9
$ " *:>1<>$<>,
9
,.
70!$. $5!!.4!
9
,.0"
9
1.04 m
$.75$
Bearing (ressure r due to =e&erhof distribution r
9
R) "$e
is the reinforcement length at the base of the wall R)
is the resultant of all factored )ertical loads 9
$5!!.4! 5.504
9 r
uit fms
4!!.$J k/m
< D %m
fms is (artial material factor a((lied to uIt -ltimate bearing ca(acit& of foundation soil
uit 9 Lcf for c( 9 ,02
/c
9 ,0.14
/
9 1.4
/&
9 $$.40 "$e 9 5.50
uit 9 /< 0.5 :"$e; &f /& 9 1440.0
k/m$ r
1047.14 k/m$
45!.$J
1047.14
Hence foundation is safe against bearing ca(acit& failure
5,
*RCiS+G 10$"$014
CA=+-T'T*A= A */T@R/' ST'B**T AR 10.75 m H*8H 6' B ST'T*C '/'S*S
Check for Ru(ture or reinforced soil#
kal
9
0.,07
0
r1
,$ 2 or retained backfill soil #
ka$
9
0I,,,
H
10.55 m
7.!0 m oundation +ro(erties
%m
9
1m
r
1 k/m,
A'%S Self weight of Reinforced soil wall
> 9 >iDHD 9
14,.,, k/m
>ertical load due to stri( load 3F b >$
9
$4.7$ k/m
>ertical load due to li)e load >
9 3M F 174. k/m
Horiontal orces +a 9 1$ D ka$D)$D H$ 9
,4,.0$ k/m
4; @.+ due to +$ 9 ka$ D 3I D H
Check for internal Sliding
Calculation for bottom la&er of 8eogrid or long term stabilit& where the contact at the base of the structure
fsRh R):a1Dtan0?(fmN;<:CID7fms;
Rh
is the horiontal factored disturbing force
R)
is the )ertical factored resultant force
0?(
is the (eak angle of shearing resis
fms
is the (artial materials facto 0?(I C?IC-
fs
is the (artial factor against base sliding
?
is the effecti)e base width for sliding Rh
9
9
1.,
: +F<+;D ffs !,5.0 k/m
R)
9
:)F < )$; 150.05 k/m $!.5,
54
4.57
*RC#S+#10$"$014 =A=@/TS A)erturning =oment =o
9
=o
9
:+i D H,Dffs < +$ D H$ Dffs; $44J.1 k/"mm
ffs Resisting moment =r 9 :>F D $ <c$ F >$<>,D$;Dffs =r
9
J41.0 K/"mm @ccentricit&I e 9
@le)ation of 8eogrid a&er @l
9
0.$ m
@$
9
0.1 m
S)O
9
0.5D:@$"@1;<@1 0.505 m
o)
9 R) :"$e;
9
T(
44!.4$ k/m$ 9 kai D o) D S)
9
!J.$, k/m Considering the crash barrier as a stri( load and
where
Ts
9
:ka D S) D ff D SO %
%
9
::h
calculating Ts for the bottom most 8rid la&er Ka
0.,07
S)
0.505 m
ff 9
55 *RCGS+G10$"$014
1.5
S
9
$4.7, K/m
%
9
!.75 m
Ts
9
0.,! K/m
T
P T6 < Tsi
T
9
70.07 K/m
8eogrid T&(e Q$
8eogrid T&(e Q1 Tult:k+a;
40.0
!0.0
Strength Reduction factors %urabilit& :Rd; *nstallation damage:Rd; :based on t&(e of soil; Cree( :Rcr;
1.1
: >aries based on tem( of soil;
T design :k+a;
9T-Mt:RdFRidFRc
or T&(e Q!
#
1.51 $0.J4
T%9
Tult:RdDRidDRcr;
9
7.5, k/m
,1.41
fn9T%T 1.1 1.1
from Table J
Check for +ullout *nclination of failure surface w.r.t horiontal @le)ation from bottom wall batter :w;
! 9 45 < 0# 9 45 < ,$$ 9
@l
9
0.$0, m
4.$,2
@. e 9
h @ F Tan:co; TanLi;
@ffecti)e ength
e
9
7.47 m Tt
+erimeter of the th la&er#
OO n C
cohesion of the soil
90 K/m$
ffs
1.5
from Table 11
fn
1.,
from Table 11
1.1
from Table J
$ 1
A.K
5! 1RC#S+# 10$"$014
from Table 11
(
9
0.5
h
9
10.55 m
ff
9
f(
f(
1.5 from Table 11 + D (D eD:f $.4
Case '
Check for Connection Strength
The ultimate connection strength TuMtconn :n; at each geos&nthetic reinforcement shall be calculated as
Tultconn :n;
acs
U'w:n;tan'cs wher e T -Mtconn:n; 9 ultimate con acs 9 a((aren 'cs 9 a((are
acs I 'cs 6w:n;
shall be consi 9
:H"@;DuD6u
Connection calculations for bottom most 8rid # H9 &u
wall height 9
10.15 m
%ensit& of (lain concrete
9
6V 9 Block unit width front to back
9
wLn;
7$.1 K/m
acs
1J.71 K/m
'cs
,0
1 ultconn :n; rom Case '
!1.77 K/m TI
70.07 K/m
's T is greater than T-Mtconn:n; a secondar& reinforcement of 1.0m length is (ro)ided at an ele)ation of 0.!0Jm 9
Therefore 5Ufor the bottom most la&er for connection
T
9
70.07D0.40!0.505 5!., T
5!.,
K/m U TuMtconn :n; !1.
Soil Wall (Static)
° °
i.e 10.15 m <0.! m road crust
-ltimate limit state
Ser)eciabilit& limit state
combinations
B
C
1.5
m
1.5
uuuuuuu
m m
a; @Fternal anti infernal stabilit&
m
:Critical
case for sliding;
onditions
A.K
;
! 1.$7 A.K
/c < /< 0.5 :"$e; &f /&W
A.K
9
1.5 K/m,
e)er 'rm
where
E*
9
,. m
b
9
1.! m
E$
9
0. m
E,
9
,. m
0.4 k/m
tance under effecti)e stress conditions
A.K
9
1.5 from Table
$"
1$ of BS 00!"1 #
$010
:=r"=0; *:>1<>$<>,;D1.5 ,.
70,1.J $5$4.$
,.0"
$.7!
1.014 m
!
1.$7 A.K
irst la&er from bottom Second la&er from bottom
:for bottom grid; calculating the tension due to the st 1.!m
b
9
1.! m
d
9
0. m
where Crash barrier area :'; 9 0.Jm$ %ensit& of Con
where h 9
$5 K/m,
S
9 'D&c
:10.75"0.$;
for bottom grid
8eogrid %ata 8eogrid T&(e Q,
8eogrid T&(e 8eogrid T&(e Q4 Q5
0.0
100.0
1$0.0
1.15
1.15
1.15
8eogrid T&(e Q! 150.0
1.1 1.51 41.
5$.,5
f BS# 00!
!$.$
7.5,
A.K
lliX C t r"."O Mfr.
of BSG 00!"1 # $010 of BSG 00!" a? tan f BSG 00!"1 ms
of BS# 00!"1 # $010 where a1 9
0.
of BS# 00!
sD>lDh;TDfn 6here f( 9 1., from Table 11 of BS# 00!"1# $010
nection strength t minimum connection strength between geogrid reinforcement and block unit t angle of friction for connection of geogrid reinforcement and block unit ered from T&(e Q! grid to block connection re(ort
$4 K/m 0.,05 m
@i
9
0.$0, m
0.$0,<::0.!0J"0.$0,O$; 0.40! m
A.K
