Operation of pipe water transmission structure in interaction with subsiding soil

Figure 3. The picture shows a design schematic of a diaphragm for a partially wet soil.

The length of the non-wetted area for a narray of soil with a steady moisture contour can be determined by the formula:

(5)

where B is the width of the water mirror in the associated pool and h is the distance between the lower face of the tip - the diaphragm - and the reservoir bottom.
The wet portion l of the head-base diaphragm's will be measured in centimeters.
ℓ=L–2а=2ℓ₁+ℓ₂-2а
The maximum bending moment in the diaphragm, according to the design approach given in Fig.4.6, is equal to:
(6)

where q₀ is the non-humid component of the diaphragm's base response intensity (n/sm).

The diaphragm of three plates has a moment when l₁ = l,₂= l, but not if
Q₁≠Q₂.

(7)

If the weight difference between the average and extreme plates is small, the formula appears:
(8)

Figure 4. The picture shows how the tip-diaphragm is supported on the moist ground
wedge.

An isosceles trapezium with an upper base equal to the diaphragm thickness can be used to depict the shear area. The height of the trapezoid is equal to h = а /tgβ in line with the designations used in Fig. 4. The trapezium's bottom base is the following size:

where denotes the angle of dispersion of pressures in the soil caused by the action of an extra load. Based on this, the area of the trapezoid will be equal to:




Figure 5. Graphs illustrating the change in the maximum bending moment in the tip of the crossing differential as a function of the parameter "a": 1- according to the formula (8); 2- based on experimental data

With some assumptions, the weight of the plates is viewed as moist loess soil over the whole region of the diaphragm's base. The pressure on the shear regions beneath both edges of the diaphragm corresponds to the difference between the weight of the diaphragm and the entire reaction of the wetted soil. The findings of soil laboratory tests can be used to calculate its value. C = 0.005 - 0.05 MPa for loess low moisture soil.

₍₉₎
where C denotes the particular cohesiveness of natural moisture in

Internal ground friction is ignored since it is a very minor number that contributes to the safety margin. By expressing F_сd with the parameter "a" we may determine the boundary value at which equation (6) will be true.

(10)

o so, we solve the equation for "a" by inserting the beginning data for the tubular differential P 45 + 90, whose operation was investigated throughout the experiment:


в=0,25m;С=40кN/m²;ω=11%;Q₁=50кN;Q₂=40кN;Р_st=25кN/m²;L=9m;
The result is that weget the value a=0.68m.
In Fig. 6, the graphs of the maximum bending moment in the diaphragm of a one-point differential, computed by the formula (7) and estimated on the basis of experimental contact stress diagrams, on the value of the parameter "a" are shown for comparison.
The bulk of experimental points are below the theoretical dependency, as shown in fig. 6: the average difference is 2.4 kNm, which is barely 3% in the area of maximum bending moment values. The experimental points' standard deviation from the straight line is 2.7 kNm.
The cleaving of the soil without moistening under the margins of the tip was determined experimentally at "a" = 0.4 - 0.7 m, which is near enough to the theoretically calculated value of this parameter. The strains on the diaphragm's contact with the base will match to the schematic in Fig.1. g) and the scheme in Fig.1. after cleaving the wedges of soil without moisture.
The inner edge of the differential head is affected by the pressure of the bulk compacted earth. This pressure on the diaphragm is of the following magnitude:
q =φ·ρ·h (11)
where the lateral pressure coefficient is; h– depth from the embankment's surface,
m; - specific bulk soil, kN/m³.
In this scenario, the diaphragm operation design diagram can be depicted as a console of unit widths with embedment at the level of the channel bottom concrete anchoring (Fig. 7).
A significant depth of embedding and the presence of a pipe solidly linked to the diaphragm assure fastening reliability.
The height of the mound, hn (Fig. 6 and 7) corresponds to the length of the console:
h_H =h₁ -h₂- h₃ (12)
Where h₃ is the height of the diaphragm plate portion above the ground level. Take h₃= 0 as an example, which corresponds to the safety margin.