Contents preface (VII) introduction 1—37

been considered negative for the most critical condition.

haswater

-tail todue

forceHydrodynamic 1

GRAVITY DAMS

553

Using Eq. (16.19), with p_e = 0, the minor principal stress at the heel σ_1U = σ_yU sec² φ_U – p′ tan² φ_U

• 
  26.11 × 10⁴ × 1.0225 – 96 × 10⁴ × 0.0225
  
• 
  24.54 × 10⁴ N/m²
  

Using Eq (16.22), shear stress at the heel, (τ_yx)_U = (σ_yU – p′) tan φ_U

∴	(τ )	U	= – (26.11 – 96.00) × 10^4	× 0.15
	yx

= 10.48 × 10⁴ N/m²
Further, major principal stress at the heel = p = 96 × 10⁴ N/m² and minor principal stress at the toe = p′ = 9.0 × 10⁴ N/m²
stabilising moment Factor of safety for overturning = _{overturning moment}

	=	(418302.75 + 27091.99 + 1662.88) × 10^4	= 1.84
	(147334.50 + 96183.57) × 10^4
Sliding factor		=		ΣH
	ΣW
	=		472055. × 10^4	= 0.67
		701118. × 10^4

Shear-friction factor of safety (with drains operative),

Fs =	Cb × 1 + µΣW
		ΣH
=	150 × 10^4 × 76.25 × 1 + 07.(701118. × 10^4 )	= 3.46
	472050. × 10^4

(ii) Extreme loading combination (usual loading combination with drains inoperative and the loading due to earthquake):
The inertial and hydrodynamic forces and corresponding moments due to horizontal earthquake have been computed as shown in Table 16.1. The effect of vertical earthquake can be included in stability computations by multiplying the forces by (1 + α_v) and (1 – α_v) for upward and downward accelerations, respectively. Since the computation of hydrodynamic force involves the use of unit weight of water, the hydrodynamic force will also be modified by vertical acceleration due to earthquake. Further, the effect of earthquake on uplift forces is considered negligible. For ‘reservoir full’ condition, the downward earthquake acceleration results in more critical condition. Therefore, the following computations have been worked out for the downward earthquake acceleration only.
Resultant vertical force with downward earthquake acceleration

• 
  (8584.50 + 394.88 + 32.48) × 10⁴ × 0.95 – 2000.68 × 10⁴
  

• 
  6560.59 × 10⁴ N
  

Resultant horizontal force with downward earthquake acceleration

• 
  (4567.50 + 153 + 858.45 + 491.19) × 10⁴
  

• 
  6070.14 × 10⁴ N
  

554 IRRIGATION AND WATER RESOURCES ENGINEERING
Resultant moment about the toe with downward acceleration

• 
  (418302.75 +27091.99 – 147334.50 + 1662.88 – 28183.58
  

– 19321.38) × 10⁴ × 0.95 – 194763.72 × 10⁴

• 
  44843.53 × 10⁴ Nm
  

Now,	y =	ΣM	=	4484353. × 10^4	= 6.835 m
ΣW	656059. × 10^4

Eccentricity, e = 38.125 – 6.835 = 31.29 m
The resultant passes through the downstream side of the centre of the base. The value of e is more than b/6 i.e., 12.71 m. Therefore, there would be tensile stresses around the heel of the dam. The vertical stresses at the toe and heel with downward earthquake acceleration are,

ΣW F

6eI

656059. ×

10^4

F

6 × 3129.I

σyD =

G1

+

J

=

G1

+

J

b

76.25

H

b K

H

76.25 K

= 297.89 × 10^4 N/m^2

ΣW F

6eI

6560.59 × 10^4

F

6 × 3129.I

and

σyU =

G 1

−

J

=

G 1

−

J

b

76.25

H

b K

H

76.25 K

= – 125.81 × 10^4 N/m^2

Factor of safety against overturning

=

(418302.75 + 27091.99 + 1662.88) × 10^4

= 1.15

(147334.50 + 194763.72 + 28183.58 + 19321.38) × 10^4

Sliding factor

=

ΣH

ΣW

(456750. + 153 + 858.45 + 49119.) × 10⁴

• 
  656059. × 10⁴
  

607014.

= _6560.59 = 0.925

Shear-friction factor of safety, F^s = ^{Cb × 1 + µΣW}
ΣH

150 × 10⁴ × 76.25 × 1 + 07. × 656059. × 10⁴

• 
  607014. × 10⁴
  

16029.91 ⁼ 607014. ^{= 2.64}

16.7. FOUNDATION TREATMENT
The foundation of a gravity dam should be firm and free of major faults which, if present, may require costly foundation treatment. The entire loose overburden over the area of the foundation to be occupied by the base of the dam should be removed. The dam itself must be based on the firm material which can withstand the loads imposed by the dam, reservoir, and other appurtenant structures. To consolidate the rock foundation and to make it an effective barrier

GRAVITY DAMS

555

to seepage under the dam, the foundation is often grouted. Grouting consists of filling the cracks and voids in the foundation with grout mixtures (cement-water mixtures) under pressure. The spacing, length, pattern of grout holes, and grouting procedure depend on the height of the structure and the geologic characteristics of the foundation. Grouting operations are carried out from the surface of the excavated foundation or from galleries within the dam or from tunnels driven into the abutments or from other suitable locations, such as the upstream fillet of the dam.

For the purpose of seepage control, a deep grout curtain is constructed near the heel of the dam by drilling deep holes and grouting them under high pressures. These holes, if drilled from a gallery, are identified as ‘A’ holes. Curtain grouting is carried out only after consolidation grouting so that the higher grouting pressure does not cause displacement in the rock or loss of grout through surface cracks. In low dams, galleries are not provided and high-pressure grouting is carried out through curtain holes located in the upstream fillet of the dam before reservoir filling begins. Such grouting holes are identified as ‘C’ holes.
Consolidation grouting to fill voids, fracture zones, and cracks at and below the surface of the excavated foundation is accomplished by drilling and grouting relatively shallow holes. These holes are identified as ‘B’ holes and the grouting is carried out at low pressures.
Water-cement ratios for grout mixes depend on the permeability of the rock foundation and may be around 6 : 1 for consolidation grouting. Pressures for consolidation grouting depend on the strength characteristics of the foundation and may vary over wide range of 70 to 700 kPa. Holes of diameters of approximately 5 cm, spaced at about 5 m intervals, are usually drilled to a depth of about 15 m depending upon the local conditions.
Even after providing a grout curtain some water will percolate through and around the grout curtain. This water, if not removed, may build up very high hydrostatic pressures at the base of the structure. Hence, this water must be suitably drained. This is achieved by drilling one or more lines of holes downstream of the grout curtain. The spacing, depth, diameter, and pattern of these holes would depend on the foundation conditions. Drain holes are drilled only after completion of all foundation grouting. These can be drilled from foundation and drainage galleries within the dam, or from the downstream face of the dam. A suitable system for the collection and safe disposal of the drainage water must also be provided.