pth the sand is
incapable of arching itself, but, for purposes of safety, the writer has
put this at the point, _F_, as noted above, = _D_{X}_, although he
believes that experiments on a large scale would show it to be nearer
0.67._D_{X}_, above which the placing of additional back-fill will
lighten the load on the structure.

We have, then, for _D_{E}_ < _D_{X}_, the weight of the total prism of
the earth plus the water in the voids, plus the added pressure of the
water above the earth prism, that is:

The pressure per square foot at the base of any vertical ordinate =
_V_{P}_

1
_V_{P}_ = _D_{E}_ x 90 + _D_{E}_ x 62--- x 0.40 +
2

1
( _D_{W}_ - _D_{E}_ ) x 62---.
2

To those who may contend that water acting through so shallow a prism of
earth would exert full pressure over the full area of the tunnel, it may
be stated that the water cannot maintain pressure over the whole area
without likewise giving buoyancy to the sand previously assumed to be in
columns, in which case there is the total weight of the water plus the
weight of the prism of earth, less its buoyancy in water, that is

1 1
_V_{P}_ = _D_{W}_ x 62--- + _D_{E}_ x ( 90 - 62--- ),
2 2

which, by comparison with the former method, would appear to be less
safe in its reasoning.

[Illustration: COMBINED EARTH AND WATER PRESSURES. FIG. 12.]

Next is the question of pressure against a wall or braced trench for
materials under Class A. The pressure of sand is first calculated
independently, as shown in Fig. 6. Reducing this to a basis of 100 lb.
for each division of the scale measured horizontally, as shown, gives
the line, _B O_, Fig. 12, measuring the outside limit of pressure due to
the earth, the horizontal distance at any point between this line and
the vertical face equalling the pressure against that face divided by
the tangent of the angle of repose, which in this case is assumed to be
45 deg., equalling unity. If the water pressure line, _C F_, is drawn, it
shows the relative pressure of the water. In order to reduce this to the
scale of 100 lb. horizontal measurement, the line, _C E_, is drawn,
representing the water pressure to scale, that is, so that each
horizontal measurement of the scale gives the pressure