FLOOD03746

• County: Boulder
• Basin: South Platte
• Title: Human Stability in a High Flood Hazard Zone
• Date: 8/1/1989
• Prepared For: CWCB
• Prepared By: David Love & Associates
• Floodplain - Doc Type: Educational/Technical/Reference Information

Abt, Wittler, Taylor, and Love

BACKGROUND

In order to assess the hazard to human life resulting
from flood waters, an analysis was conducted to deter-
mine when a body would topple into the :flow. The anal-
ysis was conducted using a simplified ri!:id body mono-
lith composed of a rectangular block with broad face
and upper limbs as shown in Fig. 1 (David J. Love and
Associates, Inc" 1987). The monolith configuration is
considered an extremely conservative E.stimate of the
body structure with respect to flood exposure. It was
assumed that the results of the monolith analysis were
representative of the lower limit of human stability.

I
I
I
I
I
I
I

~: '
Width
Thicknes~

Figure 1. Idealized Body Monolith.

During a flood event, the monolith is subjected to a
variety of forces to include the weight of the monolith,
W, buoyancy, B, the dynamic force due to velocity, P,
surface friction, F'r, the hydrostatic upstream force, F u,
and the hydrostatic downstream force, Fd. The rota-
tional stability of the monolith is the r,esultant of the
forces acting at the downstream bottom edge of the
monolith. The rotation or toppling occurs when the

WATER RESOURCES BULLETIN

force of the oncoming flow exceeds the moment due to
the resultant weight of the monolith, Summing mo-
ments about the downstream bottom edge of the mono-
lith results in the expression

lMOOge = ((W - B) x (lt2 thickness)} - [P ,. (lt2d)) = 0 (2)

as d is the depth of flow and where

B = (thickness) x (width) x (d) x Yw

(3)

as Yw is the unit weight of water and

P = (Cd) x (p) x (Vl/2) x An x Sr

(4)

as Cd is a coefficient of drag, p is the density of water, V
is the average flow velocity, An is the area normal to
flow, and Sris a safety factor.
Solving Eq, 2 results in a unique toppling hazard
envelope. Figure 2 presents the toppling hazard enve-
lope for a monolith weighing 120 lbs, five feet in height.
It is observed in Fig. 2 that an infinite number of flow
velocities and depths can result in the toppling of the
120 lb monolith. The product numbers resulting at in-
stability of the 120 lb monolith range from approxi-
mately L 75 to 6.0. Toppling envelope curves can be de-
veloped for monoliths of different weights, The analysis
assumes that the monolith is standin~' upright and is
placed on a firm and/or stable found'ltion. Also, the
analysis assumes that the velocity distribution is uni-
form in the channel.

Hazard Envelope

10
~
.,
Q.
...
-
,., 5
-
u
0
~
00

Monolith
Test
Resu Its

Area of
Instobl'/ity

2
Depth (ft)

3

4

Figure 2. Toppling Hazard Envelope Curve for 1:1. 120 lb Monolith.

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