DESIGN OF REINFORCED CONCRETE STRUCTURES| CANTILEVER RETAINING WALL DESIGN STEPS

Figure shows the deflection profile of a cantilever retaining wall

From the figure it is seen that the tension face of stem is near to the back fill, and the main reinforcement should be provided on tension face in vertical direction in stem.

For heel slab the top portion acts as tension face hence main reinforcement is provided on top face of  Heel. For Toe slab bottom portion of the toe slab is the tension face so main reinforcement is provided at bottom in Toe slab.

These are the simple steps for the design of a cantilever retaining wall when the following data has been provided in the question.

DESIGN STEPS

GIVEN DATA : HEIGHT , SBC OF SOIL, ø , µ , Unit weight of soil( ),GRADE OF CONCRETE AND GRADE OF STEEL

STEP 1 :  CO-EFFICIENT OF EARTH PRESSURE

·        Ka =  (1-sin∅)/(1+sin∅)

·        Kp =  (1+sin∅)/(1-sin∅)

STEP 2 : PRELIMINARY DIMENSIONS

·         d_min =  {qo/(γ )} * ((1-sin∅)/(1+sin∅))2

·         Overall Height = Given Height + d_min

·         Base Width B = √(3P/2γ)     where P = 0.5 K_a γ  H²

·         Toe Width = B/3

·         Total Base Width = B + (B/3)

·         Thickness of Base Slab =  H/12   to  H/15

·         Thickness of Stem at Base

M_u = 0.5 K_a  γ h² x (h/3)   x 1.5                                                                                  (i)

M_u = 0.138 f_ck b d²                                                                                                                           (ii)

Comparing (i) & (ii) , value of d is obtained.

D = d + Effective Cover (generally 50mm)

Top width of stem is to be assumed (generally 0.2m).

Also provide shear key of suitable size.

Sliding Force P_ah = 0.5 K_a γH²

Overturning Moment  M_o = 0.5 K_a γ H² x  H/3 

Find  , by using the equation ,    = M_R – M_o

Find eccentricity , e = 

Find Max. Pressure at toe σ_max =    which must < SBC (hence safe)

Find Min. Pressure at Heel σ_min =  which must be > 1.55 (hence safe)

Find Factor Of Safety against overturning = M_R / M_o

Find Factor of Safety against sliding =

STEP 4: DESIGN OF STEM

·         Find factored Bending Moment M_u= 0.5 K_a  h² x   x 1.5

·         Find M_u/Bd²and from SP-16 find p_t  where d = D – Effective cover

·         Find A_st = p_tBd/100

·         Provide suitable dia bars at suitable spacing by the use of Steel Table or SP-16

·         For Distribution Steel, Find Avg. thickness of stem =

·         Find A_st(min) = 0.12% x 1000 x (Avg. thickness of stem)

·         Provide suitable dia bars at suitable spacing

·         On Outer face use 0.06% steel (i.e A_st(min) / 2 )bothways.

·         Check for shear :

Find V_u =0.5 K_a  h² x 1.5

τ_v= V_u/ bd , then find p_t & by use of Table 19 on pg 73 of IS 456 -2000 find τ_c. (If τ_v  < τ_c  hence safe).

 STEP 5 : DESIGN OF HEEL SLAB

·         From Pressure Distribution Below Base diagram find,

·         Pressure at junction of stem with Heel Slab

·         Pressure at junction of stem with toe Slab

·         Total downward pressure on heel slab = weight of backfill + self weight of heel slab

·         Plot diagram showing Net Pressure on heel

·         Find factored shear force and Bending Moment

·         Find M_u/Bd²and from SP-16 find p_t

                                   (where d = Base slab thickness – effective cover)

·         Find A_st = p_tBd/100

Provide suitable dia bars at suitable spacing on top face of heel

·         For Distribution Steel

Find A_st(min) = 0.12% x 1000 x Base Slab thickness

Provide suitable dia bars at suitable spacing on bottom face

·         For crack control use 0.06% steel (i.e A_st(min) / 2 )bothways on bottom face

·         Check for shear :

Find V_u =0.5 K_a  h² x 1.5

τ_v= V_u/ bd , then find p_t & by use of Table 19 on pg 73 of IS 456 -2000 find τ_c. (If τ_v  < τ_c  hence safe).

STEP 6: DESIGN OF TOE SLAB

·         Total downward pressure on toe slab = self weight of toe slab

·         Plot diagram showing Net Pressure on toe

·         Find factored shear force and Bending Moment

·         Find M_u/Bd²and from SP-16 find p_t

                                         (where d = Base slab thickness – effective cover)

·         Find A_st = p_tBd/100

Provide suitable dia bars at suitable spacing.

Half RF of stem anchored in toe will serve as toe RF.

·         For Distribution Steel

Find A_st(min) = 0.12% x 1000 x Base Slab thickness

Provide suitable dia bars at suitable spacing.

STEP 7: DESIGN OF SHEAR KEY

·         Find A_st(min) = 0.12% x 1000 x D where D is width of shear key

·         Total A_st in key = half of main RF in stem + (A_st(min) / 2 value which found  in step 4) 

·         If Total A_st in key > A_st(min)                          (hence O.K)