Until the engineer can say with certainty that his calculations are reasonably based on facts, he is forced to admit that his design must be lacking, either in the elements of safety, on the one hand, or of economy, on the other, and, until he can give to his client a full measure of both these factors in fair proportion, he cannot justly claim that his profession has reached its full development.

Table 1 gives approximate calculations of pressures on two types of tunnels and on two heights of sheeted faces or walls, due to four varying classes of materials.

TABLE 1.—­PRESSURES ON TYPICAL STRUCTURES UNDER VARYING ASSUMED CONDITIONS.

[Illustration:  Key to Table of Pressures, etc.]

h = exterior height, l = exterior width,

    { [delta] = depth of cover, that is,
    { D{E}_ = earth, and D{W}_ = water depth,

[phi] = angle of repose, and, for tunnels D{W}_ > D{E}_ a depth

l           [phi]
= ----- ( 45 deg. + ------- )
2              2

W{E}_ = weight of 1 cu. ft. of earth = 90 lb.; W{W}_ = weight of 1 cu. ft. of water = 621/2 lb.

Conditions:  1 = normal sand, 2 = dry sand, 3 = supersaturated firm sand with 40% of voids, 4 = supersaturated semi-aqueous material, 60% aqueous, that is, 60% water and aqueous material.

_______________________________________________________

|        |        |        |            |
Combined   |        |        |        |            |
assumed   |  h   |  l   | [phi]  |   D{E}_  |
conditions. |        |        |        |            |
______________|________|________|________|____________|
|        |        |        |            |
I_{1}    |   20   |   30   |   45 deg.  |     40     |
I_{2}    |   20   |   30   |   30 deg.  |     40     |
II_{1}    |   15   |   15   |   45 deg.  |     40     |
II_{2}    |   15   |   15   |   30 deg.  |     40     |
III_{1}    |   15   |        |   45 deg.  |     15     |
III_{2}    |   15   |        |   30 deg.  |     15     |
IV_{1}    |   30   |        |   45 deg.  |     30     |
IV_{2}    |   30   |        |   30 deg.  |     30     |
______________|________|________|________|____________|
>
_______________________________________________________

_____________
|        |        |        |            |            |
Combined   |        |        |        |            |            |
assumed   |  h   |  l   | [phi]  |  D{E}_   |   D{W}_  |
conditions. |        |        |        |            |            |
______________|________|________|________|____________|_____

_______|
|        |        |        |            |            |
I_{3}    |   20   |   30   |   50 deg.  |     40     |     60     |
I_{4}    |   20   |   30   |   40 deg.  |     40     |     60     |
II_{3}    |   15   |   15   |   50 deg.  |     40     |     60     |
II_{4}    |   15   |   15   |   40 deg.  |     40     |     60     |
III_{3}    |   15   |        |   50 deg.  |     15     |     15     |
III_{4}    |   15   |        |   40 deg.  |     15     |     15     |
IV_{3}    |   30   |        |   50 deg.  |     30     |     30     |
IV_{4}    |   30   |        |   40 deg.  |     30     |     30     |
______________|________|________|________|____________|____________|
APPROXIMATE PRESSURES ON TUNNELS, PER SQUARE FOOT.