(工事中) Example of stability analysis of concrete gravity dam

(24 March 2021)

Design conditions of dam (1)

Items	Values
Dam type	Concrete gravity
Seismic coefficient	k=0.15
Dam height	H=155.0 m
ELT (dam top level)	EL.675.0
FSL (full supply level)	EL.670.0
MOL (minimum operation level)	EL.630.0
USL (upstream sedimentation level)	EL.615.0
DWL (downstream water level)	EL.540.0
DSL (downstream sedimentation level)	EL.540.0
ELB (dam foundation level)	EL.520.0
tw (dam top width)	10.0 m

(note) DWL and DSL are set to the same level as the riverbed level.

Design conditions of dam (2)

Items	Values
Unit weight of concrete	23.5 kN/m3
Unit weight of water	10.0 kN/m3
Unit weight of sedimenrtation (submarged)	12.0 kN/m3
Sedimentation pressure coefficient	0.5
Uplift coefficient (at drainage hole)	0.2
Foundation rock class	CH
Cohesion of foundation rock	C= 3.2MPa
Internal friction angle of foundation rock	phi= 50 degrees
Allowable bearing capacity	qu=4.396 MPa

f:id:damyarou:20210324111252j:plain

Design strength parameters for CH class-rock

Shear strength (average of CH upper limit and CM upper limit)

$\begin{equation} \tau=3.2 + \sigma\cdot\tan 50 ^\circ (MPa) \end{equation}$

Uniaxial compressive strength of rock mass

$\begin{equation} \sigma_c=\cfrac{2\cdot c\cdot \cos\phi}{1-\sin\phi}=\cfrac{2\cdot 3.2\cdot \cos 50}{1-\sin 50}=17.584 (MPa) \end{equation}$

Allowable bearing capacity (safety factor pf 4.0)

$\begin{equation} q_a=17.584 / 4.0 = 4.396 (MPa) \end{equation}$

Stability requirements

Items	requirements
Requirement for overturning	100% of base in compression for all load combinations including the case of earthquake (resultant within middle third)
Requirement for sliding	Required safety factor for sliding shall be greater than or equal to 4.0 for all load combinations including the case of earthquake
Requirement for bearing stress	Maximum vertical stress at dam foundation shall be less than allowable bearing capacity of foundation rock for all load combinations including the case of eartquake

Study cases

Case	Reservoir water level	seismic coefficient	section
1	FSL (EL.670.0)	k=0.15	non-overflow section
2	FSL (EL.670.0)	k=0.15	overflow section

(note) in the actual design, wave due to wind and wave due to earthquake shall be considered. However, they are ignored in this study because of simple calculation.