There are three types of installation or construction conditions for underground conduits, viz.:
(i) Trench condition,
(ii) Embankment condition, and
(iii) Tunnel condition.
ADVERTISEMENTS:
Trench condition exists when the conduit is installed in a relatively narrow trench (not wider than twice the external diameter of the conduit) cut in undisturbed soil and then covered with earth backfill up to the original ground surface.
Embankment Condition Prevails under Two Circumstances:
(i) When the conduit is covered with fill above the original ground surface; or
(ii) When the trench in undisturbed ground is so wide that trench wall friction does not affect the load on the conduit.
ADVERTISEMENTS:
Depending upon the position of the top of the conduit in relation to the original ground surface, the embankment condition is further classified as:
(a) Positive projecting condition,
(b) Zero projecting condition,
(c) Negative projecting condition, and
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(d) Imperfect trench condition
Tunnel condition exists when the conduit is placed by means of jacking or tunnelling. Such a condition arises when conduit is to be placed more than 9 to 12 m deep or when the surface obstructions are such that it is difficult to install the conduit by the conventional procedure of excavation and backfilling.
In this case the general method is to excavate the tunnel, to support the earth by suitable means and then to lay the conduit. The space between the conduit and the tunnel is finally filled up with compacted earth or concrete grout. If the length of the tunnel is short say 6 to 10 m the entire circular section can be constructed as one unit. For longer tunnels construction may be in segments with refilling proceeding simultaneously.
Type # 1. Loads on Conduits in Trench Condition:
Such a condition exists in most of the cases. The sewers or conduits are laid in trenches or ditches excavated in natural or undisturbed soil and then covered by refilling the trench to the original ground level.
ADVERTISEMENTS:
The vertical dead load to which a conduit is subjected under trench conditions is the resultant of two major forces. The first component is the weight of the prism of soil within the trench above the top of the conduit and the second is due to the friction or shearing forces generated between the prism of soil in the trench and the sides of the trench produced by settlement of backfill. The resultant load on the horizontal plane at the top of the pipe within the trench is equal to the weight of the backfill minus the upward shearing forces.
The load on rigid conduits in trench condition is given by the Marston’s formula as-
Wc =CdwB2d … (5.4)
Where
ADVERTISEMENTS:
Wc = load on the conduit per unit length;
w = unit weight of backfill soil;
Bd = width of the trench at the top of the conduit; and
Cd = load coefficient which is a function of the ratio of height of fill to width of trench (H/Bd) and the friction coefficient μ’ between the backfill and the sides of the trench.
The load on flexible conduits in trench condition is given by the following formula:
Wc = Cd w Bc Bd … (5.5)
In which
Bc = outside width (diameter) of the conduit; and other terms are same as indicated above.
The unit weights of common backfill materials (w) encountered are given in Table 5.1
The value of load coefficient Cd is given by the following equation:
In which
K = Rankine’s ratio of lateral pressure to vertical pressure;
μ’ = coefficient of friction between the backfill and the sides of the trench;
H = height of fill above the top of the conduit; and
Bd = width of the trench at the top of the conduit.
For the various backfill materials under commonly encountered soil conditions the values of Kμ’ are as indicated below:
(a) For granular materials without cohesion minimum value of Kμ’ = 0.1924.
(b) For sand and gravel maximum value of Kμ’ = 0.165.
(c) For completely saturated top soil maximum value of Kμ’= 0.150.
(d) For ordinary clay maximum value of Kμ’ = 0.130.
(e) For saturated clay maximum value of Kμ’ = 0.110.
The values of load coefficient Cd for the above noted backfill materials as obtained by equation 5.6 for different values of (H/Bd) are given in Table 5.2.
Influence of Width of Trench:
It has been experimentally seen that when the width of trench excavated is not more than twice the external width (diameter) of the conduit, the assumption made in the trench condition of loading holds good. If the width of the trench goes beyond three times the outside dimension, it is necessary to apply the embankment condition of loading. In the transition width from Bd = 2Bc to Bd = 3Bc computation of load by both the procedures will give the same results.
Type # 2. Loads on Conduits in Embankment Condition:
(a) Positive Projecting Conduits:
A conduit is said to be laid as a positive projecting conduit when the top of the conduit is projecting above the natural ground into the overlying embankment.
The load on the positive projecting conduit is equal to the weight of the prism of soil directly above the structure plus or minus vertical shearing forces which act in a vertical plane extending upward into the embankment from the sides of the conduit.
These vertical shearing forces ordinarily do not extend to the top of the embankment but terminate in a horizontal plane at some elevation above the top of the conduit known as the plane of equal settlement. The magnitude and direction of relative movement between the interior and exterior earth prisms depend on the settlement ratio rsd which is defined below.
Where, /
Sm = Compression of side prism of soil of height pBc;
P = projection ratio, which is the ratio of the height of the top of the conduit above the adjacent natural ground surface (initial) or the bottom of a wide trench to the outside width (diameter) of the conduit;
Bc = outside width (diameter) of the conduit;
Sg = settlement of natural ground adjacent to the conduit;
Sf = settlement of the bottom of the conduit; and
dc = deflection of the conduit or shortening of its vertical height under the load.
The various elements of the settlement ratio indicated above are shown in Fig. 5.7.
As shown in Fig. 5.7 the critical plane is a horizontal plane tangential to the top of the conduit. If the critical plane settles more than the top of the conduit, i.e., if (Sm + Sg) is more than (Sf + dc), the settlement ratio rsd is positive. The exterior prisms thus move downwards relative to the interior prism and hence the shearing forces act in the downward direction.
The load on the conduit is therefore equal to the weight of the prism of soil directly above the conduit plus shear force. On the other hand if the critical plane settles less than the top of the conduit, i.e., if (Sm + Sg) is less than (Sf + dc), the settlement ratio rsd is negative.
The interior prism thus moves downwards relative to the exterior prisms and hence the shearing forces act in the upward direction. The load on the conduit is therefore equal to the weight of the prism of soil directly above the conduit minus shear force.
The settlement ratio rsd, therefore, indicates the direction and magnitude of the relative settlement of the prism of earth directly above and adjoining the conduit.
The product rsd x p gives the relative height of the plane of equal settlement and hence the magnitude of the shear component of the load. When (rsd x p) = 0, the plane of equal settlement coincides with the critical plane and there are no shearing forces and the load is equal to the weight of the central prism. It is not practicable to predetermine the value of rsd However, recommended design values of rsd based on actual experience are given in Table 5.3.
The load on positive projecting conduits (both rigid and flexible) is given by the Marston’s formula as-
Wc = Cc w B2c … (5.8)
Where
Wc = load on the conduit per unit length;
w = unit weight of backfill material;
Bc = outside width (diameter) of the conduit; and
Cc = load coefficient.
The load coefficient Cc is a function of the product of the settlement ratio and the projection ratio (i.e., rSd x p) and the ratio of the height of fill above the top of the conduit to the outside width (diameter) of the conduit (i.e., H/Bc). It is also influenced by the coefficient of internal friction (μ) of the backfill material and the Rankine’s ratio of lateral pressure to vertical pressure (K). Suggested values of the product K x μ for positive and negative settlement ratios are 0.19 and 0.13 respectively. The values of the load coefficient Cc can be obtained from Fig. 5.8.
For positive projecting conduits the following four conditions may prevail:
(i) Complete projection condition
(ii) Incomplete projection condition
(iii) Complete trench condition
(iv) Incomplete trench condition
The condition corresponding to positive values of settlement ratio is termed as projection condition, and that corresponding to negative values of settlement ratio is termed as trench condition. Further depending on the position of plane of equal settlement the projection as well as trench conditions may be complete or incomplete.
Above the plane of equal settlement, the interior and exterior prisms settle equally and hence no shearing forces are generated above this plane. If the embankment is sufficiently high (i.e.. H> Hr) the plane of equal settlement lies within the embankment. This condition is then termed as incomplete projection condition and incomplete trench condition as the case may be.
However, if the embankment is not of sufficient height (i.e., H < Hr) the plane of equal settlement does not lie within the embankment, and such a condition is termed as complete projection condition and complete trench condition as the case may be. The range of the values of the product rsd x p for all the four conditions of positive projecting conduits are indicated in Fig. 5.8.
(b) Negative Projecting Conduits:
A conduit is said to be laid in a negative projecting condition when it is laid in a trench which is narrow with respect to the size of the conduit and shallow with respect to the depth of cover. Further the native material of the trench is of sufficient strength so that the trench shape can be maintained dependably during the placing of the embankment, the top of the conduit being below the natural ground surface and the trench is refilled with loose material and the embankment is constructed above.
Thus in this case the prism of soil above the conduit is loose and of greater depth as compared to the adjoining embankment. As such the interior prism settles more than the prism over the adjoining areas thereby generating upward shearing forces which reduce the load on the conduit.
In this case critical plane passes through the top of the trench. The settlement ratio rsd for the negative projecting conduit is given by the expression-
Where
Sg = settlement of natural ground adjacent to the trench;
Sd = compression of the backfill in the trench within the height p’Bd,
P’ = projection ratio of negative projecting conduit, which is the ratio of the vertical distance from the natural ground surface down to the top of the conduit to the width of the trench;
Bd = width of the trench;
Sf = settlement of the bottom of the conduit; and
dc = deflection of the conduit or shortening of its vertical height under the load.
The various elements of the settlement ratio indicated above are shown in Fig. 5.10. Exact determination of the settlement ratio is difficult. However, for design purposes the recommended value of rsd is – 0.3.
The settlement ratio for a negative projecting conduit is always negative because the settlement of the critical plane is more than the settlement of the natural ground. Hence the product rsd x p’ is also negative.
The load on negative projecting conduits is given by the Marston’s formula as
Wc = CnwB2d … (5.10)
Where
Wc = load on the conduit per unit length;
w = unit weight of backfill material;
Bd = width of the trench; and
Cn = load coefficient
The load coefficient Cn is a function of the ratio of the height of fill above the top of the conduit to the width of trench (i.e., H/Bd), projection ratio p’ and the settlement ratio rsd. The values of Cn may be obtained from Fig. 5.11 which gives the values of Cn for various values of (H/Bd), rsd and p’.
(c) Imperfect Trench Conduit:
An imperfect trench conduit is employed to minimise the load on a conduit under embankments of unusual heights. In this case the conduit is first installed as a positive projecting conduit. The embankment is then built up to some height above the top of the conduit and thoroughly compacted as it is placed.
A trench of the same width as the conduit is excavated directly over it down to or near its top. This trench is refilled with loose compressible material and the rest of the embankment is completed in a normal manner.
Marston recommended the use of the layers of hay, straw, corn-stalk, etc., in between the layers of loose soil filled in the trench, in order to increase the compressibility of this prism of soil and thus decrease the load on the conduit.
The load on conduits installed in imperfect trench condition is given by the Marston’s formula as-
Wc = CnwB2c … (5.11)
where
Wc = load on the conduit per unit length;
w = unit weight of backfill material;
Bc = outside width (diameter) of the conduit; and
Cn = load coefficient.
Since imperfect trench conduit is somewhat similar to negative projecting conduit, the values of Cn for imperfect trench conduits may also be obtained from Fig. 5.11 by taking Bd = Bc on the assumption that the trench fill is not wider than the conduit.
Type # 3. Loads on Conduits in Tunnel Condition:
The vertical load acting on the tunnel supports and eventually the conduit in the tunnel is the resultant of the two major forces viz., the weight of the overhead prism of soil within the width of the tunnel excavation and the shearing forces generated between the interior prism and the adjacent material due to friction and cohesion of the soil.
The load on conduits installed in tunnel condition is given by the Marston’s formula as-
Wc = Ct Bt (wBt-2c) … (5.12)
Where;
Wc = load on the conduit or tunnel support per unit length;
w = unit weight of soil above the tunnel;
Bt = maximum width of the tunnel excavation;
c = coefficient of cohesion (or unit cohesive strength) of soil above the tunnel; and
Ct = load coefficient.
The load coefficient Ct is a function of the ratio of the distance from the natural ground surface to the top of the tunnel to the maximum width of tunnel excavation (i.e., H/Bt) and the coefficient of internal friction of the material of the tunnel.
When the coefficient of cohesion c is zero, equation 5.12 reduces to the same form as equation 5.4 applicable for rigid conduits in trench condition. The recommended values of coefficient of cohesion c for different types of soil are given in Table 5.4.
The values of load coefficient Ct may be obtained from Fig. 5.14 which gives the values of Ct for various values of (H/Bt) and different soil conditions.
Effect of Submergence:
Sewers may be laid in trenches or under embankment in areas which may be temporarily or permanently submerged in water. The fill load in such cases will be reduced and it will correspond to the buoyant weight of the fill material. However, if the effect of submergence is ignored an additional factor of safely is provided, but it may be necessary to check whether the conduit is subjected to floatation.
Under submergence, the minimum height of the fill material that will be required to prevent floatation ignoring the frictional forces in the fill can be determined from the following equation:
In which;
Hmin = minimum height of fill material;
Bc = outside width (diameter) of the conduit;
ws = unit weight of saturated soil;
wo = unit weight of water; and
W = weight of the empty conduit per unit length.
Wherever sufficient height of fill material is not available, anti-floatation blocks should be provided.