Week 2 Challenge

Aim:

To Design a Cantilever retaining wall per the given specifications in a detailed manner and

To brief parameters influencing borehole location and its depth of exploration in case of shallow foundation, parameters obtained from geotechnical investigation for foundation design and

To list different types of soil/rock, and criteria for selecting foundation level for the shallow foundation. 

 

Introduction:

Abutments are at the end of the bridge which supports the superstructure and provide vertical and lateral support to the bridge it also acts as a retaining wall to resist lateral movement of soil or earthen fills. Single-span and small bridges are supported only by abutments and the longer bridges require piers to support the unsupported length in between. It also acts as an approach slab for entry to the bridge.

 

Boreholes are drilled to identify various geotechnical parameters of underlying soil strata for the designing and construction of any project. It is drilled via hand-held auger bores, Standard cone penetration drill rigs and drop hammers and reimers. Soil tests in the lab can be conducted to identify another datum as well. 

 

Solution: 

Question No.1: To Design a Cantilever retaining wall per the given specifications in a detailed manner:

 

Given: 

Height of abutment = 4m ( above ground level )

Depth of Foundation = 2m ( below ground level )

Angle of friction Φ = 0.5 

Unit weight of soil Γ = 18 kN/m³

Safe bearing capacity of soil = 200 kN/m²

 

Answer No.1: 

 

Step1: Dimensioning of Retaining wall / Abutment: 

 

Height of abutment = 4 + 2 = 6m

 

Base slab width = 0.4H to 0.7H

 

= 2.4m to 4.2m 

Base slab width = 4m 

 

Max. Toe slab width = B/3 

4/3 = 1.33 m

 

Min. Toe slab width = 0.1 * H 

= 0.6m 

 

Toe Slab width = 1.2m 

 

Thickness of Slab = H/12 to H/10 

= 6/12 to 6/10

= 0.5 to 0.6

 

Thickness of Slab = 0.6m

 

Thickness of Stem near base = 0.1 * H

 

= 0.6m

 

Assume thickness at top of stem as 300mm 

 

Width of heel = 4 - 1.2 - 0.6 

= 2.2m 

 

Step2: Design of Stem: 

 

Maximum working moment = Ka [ Wh³/6]

 

Ka = (1-sinΦ) / (1+sinΦ)

= (1-sin30) / (1+sin30)

= 0.33

 

M = 0.33 [ 18 x 5.4³ / 6 ] 

= 155.88 kNm

 

Factored moment,

= 1.5 x 155.88

= 234 kNm

 

Limiting thickness of stem, d = √ [ Mᵤ / 0.138 fck b ] 

 

= √ 234 x 1000 / 0.138 x 20 x 1 

= 291.17 mm 

 

The assumption made in Step 1 for thickness of stem at top (minimum) is correct. 

 

Step3: Area of Steel Reinforcement:

 

 

Mᵤ/bd² = 233.83 x 10⁶ / 1000 x 600²

 

= 0.649 ≈ 0.65

 

In SP16 pg:48, for Mᵤ/bd² = 0.65 and fy = 500 N/mm²

 

Percentage of reinforcement = 0.156 

Ast = Pt x b x d / 100

 

= 0.156 x 1000 x 600 / 100

= 936 mm²

 

Assume dia of rebar as 16mm, 

ast = π/4 x d²

= 201.061 mm²

 

Spacing, Sᵥ = ast x 1000 / Ast 

= 201.061 x 1000 / 936

= 214mm

 

Provide 16 mm dia rebar as the main reinforcement with a minimum of 200 mm spacing c/c at bottom of the stem and gradually increase the spacing to 300 at top.

 

Distribution reinforcement:

 

Ast = 0.12% x b x d 

 

= 0.12 x 1000 x 600 / 100

= 720 mm²

 

Assume dia of rebar as 10mm,

ast = π/4 x d² 

= 78.53 mm²

 

Spacing, Sᵥ = ast x 1000 / Ast 

= 78.53 x 1000 / 720 

 

= 110 mm²

 

Provide 10 mm dia rebar as the distribution reinforcement with a minimum of 110 mm spacing c/c.

 

Step4: Stability calculations: 

 

Heel projection = Width of base - [ Toe projection + Thickness of stem ] 

= 4 - [ 1.2 + 0.6 ] 

= 2.2

 

Toe projection = width of base slab / 3 

= 4 / 3 

= 1.33

 

Assume toe width as 1.2m 

 

Loads	Magnitude	Distance from a	Moment
Self-weight of Stem: W1= Rectangle portion  = [ 0.3x5.2x25 ]	= 39 kN	= 2.2 + 0.6/2  = 2.5	= 97.5 kNm
Self-weight of Stem: W1= Triangle portion  = [ 0.5x0.3x5.2x25 ]	= 19.5 kN	= 2.2 + 0.6 + 1/3 x 0.3 = 2.9	= 56.55 kNm
Self-weight of Base slab: W2 = 4 x 0.6 x 25	= 60 kN	= 4/2  = 2	= 120 kNm
Self-weight due to back-fill soil: W3 = 2.2 x 5.2 x 18	= 205.92 kN	= 2.2/2  = 1.1	= 226.512 kNm
Moment due to Earth Pressure = Ka [ wh³/6 ] = 0.33 x [ 18 x 5.2³ / 6 ]			= 139.201 kNm
	∑W = 324.42 kN		∑M = 639.763 kNm

 

Z = ∑M/∑W

= 639.763 / 324.42 

= 1.97 m 

 

eccentricity = Z - b/2

= 1.97 - 4/2

= 0.03 m < 0.5 m 

 

Pressure at base Pmax = ∑W/b [ 1 + ( 6 x e / b ) ]

= 324.42 / 4 [ 1 + (6x0.03/4) ]

= 84.75 kN/m²

 

Pressure at base Pmin = ∑W/b [ 1 - ( 6 x e / b ) ]

= 324.42 / 4 [ 1 - (6x0.03/4) ]

= 66.50 kN/m²

 

Pressure at junction of stem with toe slab = (18.25/4) = x /2.8

= 12.775

 

Pressure at junction of stem with heel slab = (18.25/4) = x / 2.2

= 10.037

 

Step 5: Design of Heel slab: 

 

Load	Magnitude	Distance from a	Moment
W3 = 2.2 x 5.2 x 18	= 205.92 kN	= 2.2/2  = 1.1	= 226.512 kNm
Self-weight of heel slab: 2.2 x 0.6 x 25	= 33 kN	= 2.2/2  = 1.1	= 36.3 kNm
Upward Pressure ( abih ) = 66.5 x 2.2	= 146.3 kN	= 2.2/2  = 1.1	= 160.93 kNm (-)
Upward Pressure ( ghi ) = 0.5 x 2.2 x 12.775	= 14.052 kN	= 2/3 x 2.2  =1.466	= 20.6 kNm (-)
	∑W = 399.27 kN		∑M = 81.28 kNm

Maximum moment = 1.5 x 81.28 

= 121.92 kNm

 

Mᵤ/bd² = 121.92 x 10⁶/1000 x 600²

= 0.338 ≈ 0.35

 

In SP16 pg:48, for Mᵤ/bd² = 0.35 and fy = 500 N/mm²

 

Percentage of reinforcement = 0.082

Ast = Pt x b x d / 100

 

= 0.082 x 1000 x 600 / 100

= 492 mm²

 

Assume dia of rebar as 16mm, 

ast = π/4 x d²

= 201.061 mm²

 

Spacing, Sᵥ = ast x 1000 / Ast 

= 201.061 x 1000 / 492

= 408 mm

 

Provide 16 mm dia rebar as the main reinforcement bothways in top and bottom with a minimum of 300 mm spacing c/c.

 

Distribution reinforcement:

 

Ast = 0.12% x b x d 

 

= 0.12 x 1000 x 600 / 100

= 720 mm²

 

Assume dia of rebar as 10mm,

ast = π/4 x d² 

= 78.53 mm²

 

Spacing, Sᵥ = ast x 1000 / Ast 

= 78.53 x 1000 / 720 

 

= 110 mm²

 

Provide 10 mm dia rebar as the distribution reinforcement with a minimum of 110 mm spacing c/c.

 

Step 5: Design of Toe slab: 

 

Load	Magnitude	Distance from a	Moment
Weight of soil above toe slab = 1.2 x 1.4 x 18	= 30.24 kN	= 0.5	= 15.12 kNm
Self-weight of toe slab: 1.2 x 0.6 x 25	= 18 kN	= 0.5	= 9 kNm
Upward Pressure ( cdef ) = 79.275 x 1.2	= 95.13 kN	= 0.5	= 47.565 kNm (-)
Upward Pressure ( efg ) = 0.5 x 1.2 x 5.475	= 3.285 kN	= 1/3 x 1.2  =0.4	= 1.314 kNm (-)
	∑W = 146.65 kN		∑M = 24.75 kNm

Maximum moment = 1.5 x 24.75

= 37.13 kNm

 

Mᵤ/bd² = 37.13 x 10⁶/1000 x 600²

= 0.103 ≈ 0.3 ( Consider the value 0.3 )

 

In SP16 pg:48, for Mᵤ/bd² = 0.3 and fy = 500 N/mm²

 

Percentage of reinforcement = 0.07

Ast = Pt x b x d / 100

 

= 0.07 x 1000 x 600 / 100

= 420 mm²

 

Assume dia of rebar as 16mm, 

ast = π/4 x d²

= 201.061 mm²

 

Spacing, Sᵥ = ast x 1000 / Ast 

= 201.061 x 1000 / 420

= 479 mm

 

Provide 16 mm dia rebar as the main reinforcement bothways in top and bottom with a minimum of 300 mm spacing c/c.

 

Distribution reinforcement:

 

Ast = 0.12% x b x d 

 

= 0.12 x 1000 x 600 / 100

= 720 mm²

 

Assume dia of rebar as 10mm,

ast = π/4 x d² 

= 78.53 mm²

 

Spacing, Sᵥ = ast x 1000 / Ast 

= 78.53 x 1000 / 720 

 

= 110 mm²

 

Provide 10 mm dia rebar as the distribution reinforcement with a minimum of 110 mm spacing c/c.

 

Step 6: Check for safety against sliding: 

 

µ∑W/pH > 1.5

pH = Ka [ WH²/2]

 

µ = 0.5

pH = 0.33 [ 18x6²/2]

= 106.92

 

FOS = 0.5 x 324.42 / 106.92 

1.52 > 1.5 

Hence heel sliding is under permissible limits. 

 

Step 7: Check for safety against overturning: 

 

a = 0.6

FOS against overturning,

Fs = µ∑W/pH + Pp

Pp = Kp x P x a 

Kp = 1 / Ka 

= 1 / 0.33 

= 3

P = 79.275

Pp = 4 x 79.275 x 0.6

Pp = 190.26

 

FOS = 0.5 x 324.42 + 190.26 / 106.92

 

3.29 > 1.5

 

Hence overturning is under permissible limits. 

 

Step 8: Reinforcement detail of Abutment: 

Question No.2: 

To brief parameters influencing borehole location and its depth of exploration in case of shallow foundation, parameters obtained from geotechnical investigation for foundation design and

To list different types of soil/rock, and criteria for selecting foundation level for the shallow foundation. 

 

Solution: 

The bore location is an important factor which helps in determining the geotechnical parameters of a site and its substructure. Boreholes are deep narrow holes dug into the soil at the site to retrieve the samples for lab testing to get a better understanding of the soil strata and their properties. 

 

The location of the boreholes must be carefully planned in a way to reduce the cost of soil investigation at the same time obtain adequate information for designing and constructing any structure. In the case of bridges, usually, it is advised to take soil samples at the point where the pier is deemed to be constructed because the bridge generally spans for more than 30m in urban areas, under such cases the strata are subjective to change from one part of the bridge to another leading to a discrepancy in the obtained soil test reports.  Thus investigating the pier location of the bridges provides adequate data for design and construction. 

 

The depth of the borehole is generally adopted as thrice the width of the foundation. When Standard Penetration tests are conducted the borehole is investigated until a minimum of three and a maximum of five refusal strata ( where the N value is greater than 100 ) or until rock strata are reached. Since shallow foundation is found to be economical, a borehole depth of thrice the width of the foundation shall be adopted. 

 

In the case of abutments as foundations, the borehole depth must be one or twice the height of the wall of the retaining wall. If the layout of the bridge is not finalised at the time of construction, a uniformly spaced grid pattern shall be adopted for the borehole location. Adequate care must be undertaken for the drilling of holes in the vicinity of the earlier dug holes which may cause a collapse of either of the holes, usage of bentonite reduces the effect of collapse. 

 

The type of soil at the site is also an important factor which influences the borehole location and its depth. If the soil at the site is highly compressible and saturated such as clay, black cotton or water table nearer to the ground level, the investigation must continue until it reached a hard stratum because such soils can cause differential settlement.

 

Irrespective of the type of foundation the following parameters are required from the soil investigation about the soil stratum for designing and construction of any structure at a site,  

 

Angle of friction Φ: The Direct shear test on the collected sample during the soil test can be tested on cohesionless soils to understand its failure envelope and its angle of friction. With this basic parameter, many constants can be derived. 

Cohesion and Point of Resistance - The parameter c and adhesion and point of resistance can be obtained from the Standard penetration test in case of c-Φ soils.

Shear strength - Shear strength of clayey soils can be identified in the form of an in-situ undrained manner with the help the of vane shear test. The triaxial shear test can also be used to identify C and Φ  of clayey soils.

Bearing capacity of the soil is important in designing any structure which is obtained after soil tests at the lab and at the site.

Specific gravity, Liquid limit, Plastic limit, and Permeability can also be determined in lab.

 

Types of soils/rock:

 

Clay,

Sand,

Silt,

Sedimentary rock, 

Weathered rock,

Bedrock,

Hardened clay,

Silty clay,

Peat etc. 

 

The founding level of the substructure is dtermined based on the type of strata available at the site, generally, the geotechnical and structural engineers suggest that a borehole to be dug of thrice the width of shallow foundation or three to five refusal strata or bedrock is found.

The standard penetration test is adopted globally to determine the type of strata, depth of each strata, its resistance and the bearing capacity of each layer. With this test, samples can be collected and tested in labs to determine its properties as discussed above. 

Clayey, Black cotton soils are highly compressible thus raft/mat foundation is adopted if the loads are comparatively lesser. 

Cohesionless soils are permeable and cause uplift of foundation called as negative skin friction in case of piles, 

Silt, Sandy silt and peat are weak and have less shear strength which will cause shear failure of strata under heavy loads.

Weathered rock, sedimentary rock and hardened clay are highly resistant to load and can withstand or act as bedrock for piles.

 - Sandy granular soil

 - Clay

 - Silt

 - Black cotton soil

 - Weathered rock

 - Sedimentary rock

 

BOREHOLE / BORELOG REPORT: