Chapter Two: Design Principle of Dams (Gravity Dam) PDF

CHAPTER TWO DESIGN PRINCIPLE OF DAMS (GRAVITY DAM) By: MOHAMMEDSEID AHMED (MSc) DEC 2025 Gravity Dam A gravity dam has been defined as a structure which is designed in such a way that its own weight resists the external forces. This type of a structure is most durable...

CHAPTER TWO DESIGN PRINCIPLE OF DAMS (GRAVITY DAM) By: MOHAMMEDSEID AHMED (MSc) DEC 2025 Gravity Dam A gravity dam has been defined as a structure which is designed in such a way that its own weight resists the external forces. This type of a structure is most durable and solid, and requires very little maintenance. Force Acting and Load Combination on Gravity Dams  Loads can be classified in terms of applicability or relative importance as primary loads, secondary loads, & Exceptional loads. I. Primary load Identified as those of major importance to all dams irrespective of type.  Water load  Self weight load  Related seepage(uplift) load Force Acting and Load Combination on Gravity Dams II. Secondary load Universally applicable although of lesser magnitude.  Sediment load  wind load  Ice load  Silt load  Thermal and dam (foundation) interaction effect Force Acting and Load Combination on Gravity Dams III. Exceptional loads Earthquakes are the biggest danger to gravity dams That is why, every year and after every major earthquake, they must be tested for cracks, durability, and strength. Are designed on the basis of limited general applicability of occurrence. Tectonic effects, or the inertia loads associated with seismic activity. Primary Loads 1. Water loads (water pressure) Water Pressure (P) is the most major external force acting on such a dam. The horizontal water pressure, exerted by the weight of the water stored on the upstream side on the dam can be estimated from the rule of hydrostatic pressure distribution; which is triangular in shape. There is two cases to estimate water loads, those are when the upstream face is vertical and partially inclined and partially vertical. Case 1: When the upstream face is vertical When the upstream face is vertical, the intensity is zero at the water surface and equal to wH at the base. where is w the unit weight of water and H is the depth of water (MWL). = w *A = (w H*H)/2= ½ w H2 The resultant force due to this external water = ½ w H2, acting at from the base.  Case I1: When the u/s face is partially inclined and vertical and there is a tail water on the d/s When the u/s face is partly vertical and partly inclined, the resulting water force can be resolved into horizontal component () and vertical component (). Force on upstream face Force on downstream face Ph= w *A = (w H*H)/2= ½ w H2 P’h = (w H’*H’)/2= ½ w H’2 Pv1 = w *A1 = w * BC*CD P’v = ½* w =H’*EF Pv2 = w *A2 = ½ w *BC*DA II. Self weight loads  The weight of the dam is the main stabilizing force in gravity dam.  The weight of the dam is equal cross sectional area *the unit weight of the material Case 1: when the upstream face is vertical w1 = c*A1 = c*AB W2 = c*A2 = 1/2c *EC*EF Where: H = Total dam height c = unit weight of concrete II. Self weight loads Case II: When the u/s face is partially inclined and W1 =   partially vertical c-A1 = ½* c*DH*CH W2 = c*A2 = c*H*AB W3 = ½*c*EG*GF Where c is unit weight of concrete III. Uplift (Seepage )loads Water seeping through the pores, cracks and fissures of the foundation material, and water seeping through dam body and then to the bottom through the joints between the body of the dam and its foundation at the base; exert an uplift pressure on the base of the dam.  Cont….  It is a second major external force and must be accounted for in all calculation.  An uplift force virtually reduced the downward weight of the body of the dam and hence acts against the dam stability.  They are four cases to estimate the uplift loads of the given dams Case 1: no drainage gallery is provided and no tail water on the d/s If there is no drainage gallery and tail water at d/s the shape of the uplift pressure is a triangle Pu = Area of triangle Pu = ½* w*H*a  Cont….. Case II: no drainage gallery is provided but there is tail water on the d/s  Pu1 = A1 = w*H’*a Pu2 =A2 =1/2*w*(H-H’)*a  Cont….. Case III: Drainage gallery is Case IV: Drainage gallery is provided and there is tail provided and there is tail water on the d/s water on the d/s Stability Requirement of Gravity Dam The dam as whole should be structurally safe and stable. It should be withstand the stress developed due to imposed loads and the foundation should be strong to carry the loads. Mode of failure of Gravity Dam The dam should be designed such that it is safe against all possible mode of failure, with adequate factor of safety.  The dam may be fail in one or more of the following I. Overturning failure II. Sliding failure III. Tension failure IV. Crushing (Compression )failure I. Overturning failure The overturning failure occur when the resultant of all forces acting on the base passes outside the base of the dam.  If the resultant strikes just the middle third point (e = B/6), a factor of safety 2 is available against overturning.  However, if the resultant strikes outside of the outer middle third (e>B/6), tension crack will occur at the upstream edge (heel).  Factor of safety against over turning, Fo, in terms of moment about the downstream toe of the dam. Fo   M  ve M  ve M  ve inclusive of moment generated by uplift ) Fo > 1.25 may be acceptable, but Fo > 1.5 is desirable. II. Sliding factor Sliding failure occur when the dam slides over its base. The sliding failure is resisted by friction and shear strength of the concrete at upper level and that between foundation rock and concrete at the base. The factor of safety against sliding (Fs)is defined as the ratio of the force resisting sliding to the force leading to cause sliding. Fs µ  Fv  Fh Fs should be greater than 1 Where µ is coefficient of friction between the material and horizontal section and its value is varies b/n 0.65 to 0.75 up on the material used  Cont….. Factor of safety against sliding Fs, estimated using one of the two definition 1. Sliding factor (SF) SF   H V SF should be less than the coefficient of friction i.e SF B/6).  If it is so, the tension develops at the u/s edges (heel)  Hence at the heel, the dam loses contact with the foundation and the effective width is reduced.  This result increase the maximum compressive shear stresses at the toe.  A tension crack does not cause failure of dam but it leads to the failure of dam by crushing or overturning. IV. Failure due to crushing (compression failure) This occur when the compressive stress in the dam and foundation exceeds the safe limits. The vertical stress in the dam and foundation can be determined Eccentricity of the resultant force from the center of the base determined e = B/2 -