Comparative study for designing the horizontal thrust blocks in pipelines for water and sewage networks

A

Area of pipe

A_b

Bearing area required (ft²)

b

Width of the block calculated block width (ft)

d

Internal pipe diameter

e

Soil pressure at the bottom of the block

e’

Soil pressure at section x

Fe

Pressure force at the bottom of the block

Fe’

Pressure force at section x

h

Height of the block

I

The second moment of area about the neutral axis z

Kp

Passive pressure

M(x-x)

Moment about section x

P

Hydrostatic test pressure

Sb

Bearing strength (lb/ft₂)

Sf

Safety factor

T

Thrust force (lbf)

y

The perpendicular distance to the neutral axis

σ

Normal stress

θ

Degree of bent pipe

γc

Concrete density

γ

Soil density

φ

Friction angle

Pipelines are a traditional way of transferring the water between the zones on the city plan. A layout has crossing lines, a change in direction produces an unbalanced thrust force. Thrust forces could cause the elbows to separate from the pipe or cause damage to the soil around them. A thrust block is typically used to provide resistance for thrust forces by transferring them to the soil in such a way that the resultant stress is less than the soil's bearing strength. In ECDIPWSN, the thrust blocks are in the form of L sections, while in AWWA the thrust blocks are truncated pyramids. According to EPCOR (2021), prior to any acceptance of testing activities for concrete thrust blocks, the concrete must be cured for a minimum of 3 days in the case of high early strength concrete or 7 days in the case of normal/sulphate-resistant concrete. Based on the WSSC (2019), 1 ft is the minimum depth of filling over the thrust block Dipra (2016) stated that a standard Proctor density of at least 90% must be achieved between the bearing surface and the undisturbed soil.

For all materials and applications of pipes, Jeyapalan & Rajah (2007) presented their thrust block design based on the fundamental principles of fluid mechanics and geotechnical engineering. The researchers concluded that, when calculating the length of the pipe with joints restrained on each end, the type of pipe material does not matter. According to the Abu Ghdaib et al. (2011) investigation, an anchor block for a pipeline crossing state lines can be reduced significantly in size. Using analysis of a large-diameter hydrocarbon pipeline and an anchor block at a remote launching/receiving station, the team monitored the pipeline in the field. As a result of field monitoring, the researchers concluded that the pipe anchor block system's size could be reduced. Genetic algorithms were used to optimize the bearing area of thrust blocks by Anwar et al. (2012). The design equation was used to calculate the bearing area, which then distributed among the width and height. Based on their findings, the height of the blocks must vary between one and two times the width of the blocks for any soil, and vice versa for hard clay. To estimate the performance of a traditional approach in ensuring economic design for Nigerian applications, a genetic algorithm was used to simulate the design of a thrust block on some Nigerian soils by Anwar et al. (2013). They concluded that a block's width should be between one and two times its height for optimum efficiency.

A thrust block was manually designed by Gupta & Hussain (2018) for the proposed palatable water supply line-1 in the state of Uttarakhand for the town of Berinag, part of Pithoragarh district, located in India. Anchor blocks and penstock pipes were designed by Moni et al. (2018) for several locations at different heads, and analyzed according to water hammer impacts. Model experiments were carried out on a buried pipe model in a model ground by Araki & Hirakawa (2019) with a constant load simulated thrust applied laterally with an increase in hydraulic gradient step by step decreasing the internal effective stress. On the ground, gabion models were arranged at different widths according to the thrust direction. Researchers found that the gabions stabilized the pipe even when the effective pressure of the surrounding ground decreased significantly, and that the width of the gabions affected their behavior in the ground. The study of thrust blocks installed in Bidhnoo Block, Kanpur District, India, was conducted on six types of poorly graded soil by Mishra & Kumar (2019). The goal of the research was to find the optimum area of a thrust block.

This research has more than one aim. The first aim was specific to AWWA, to find the proportion between height and width of the soil contact area. Another aim for ECDIPWSN, was based on determining the proportions among the six dimensions that make up the thrust block. The third aim was to compare the two codes regarding concrete quantities and analyze how the pipe level affects concrete quantities.

Mishra & Kumar (2019) presented a design of a thrust block located in sandy silt soil, with a bearing capacity of 143.6 kN/m², the results of this study are shown in Table 1.

By solving the design equations, one can calculate the minimum bearing area, but the issue is how to divide the area into width and height (b and h). The bearing area dimensions can be varied and give the same bearing area (Ab) but different volumes. For the optimal design, the block width should differ between one and two times the height and vice versa according to Anwar et al. (2013). As shown in Figure 2, we put the proportion of the (h/b) from half to two to attain the optimum volume. According to Figure 2, the optimum thrust block volume is at h = 2b.

The thrust block in Figure 3 had six dimensions (b1, b2, c1, c2, h1 and h2), and the minimum dimensions of h1 and b2 was the same pipe diameter. Three main factors determine the optimum dimensions (safety factor against sliding, overturning, and minimum volume). We made two assumptions in order to determine the optimal dimensions. The first assumption is that the minimum dimension equals the diameter of the pipe. The second assumption is to change one dimension without changing the others.

Figure 4(a) shows the impact of thrust block dimensions on the safety factor against sliding. Dimensions (b1, b2, and c2) have a small effect and can be neglected, dimension (c1) has a moderate effect, whereas dimensions (h1 and h2) have a large effect. By increasing dimension value, the gap between the effects of (b1, b2, and c2) and the effects of (h1 and h2) widened.

Figure 4(b) illustrates how thrust block dimensions affect the safety factor against overturning. Compared to dimensions (b1, b2, c1, and h2), dimension (c2) had an insignificant effect, and dimension (h1) was the most crucial in terms of determining the safety factor against overturning. The gap between the effect of (h1) and the other dimensions widened as the dimension value increased.

We proceeded to the second step of the paper, which is the comparison between the two methods after which we determined the optimal ratio of the dimension to the other dimensions. According to the ECDIPWSN, the same data (diameter of pipe and thrust force) are analyzed in Table 2. The ECDIPWSN method takes into account the pipe level, so we examined 10 levels of pipe between −1 m and −10 m.

In Figure 6, the thrust block volume decreased as the diameter of the pipe decreased, as well as when the digging depth increased, because the soil pressure is linearly proportional to the digging depth. Additionally, the volume of the thrust block created by the AWWA method is smaller than that created by the ECDIPWSN method when the excavation depth ranged from 1 to 6 m, and they were similar at between 7 and 8 m, but larger at more than 8 m.

Thrust blocks are among the most essential underground structures. Any pipe network project should include thrust blocks, especially at bends, whether horizontal or vertical. Thrust blocks are designed to resist thrust forces. Many codes refer to the thrust block as AWWA and ECDIPWSN. In this study, we aimed to find the minimum cost of the thrust block by finding the minimum volume of it.

Our research had three objectives; the first was to determine the ratio between area dimensions of a thrust block designed using the (AWWA) method, which revealed that h = 2b. The second objective was to obtain the ratios among the dimensions of the thrust block designed by the ECDIPWSN method, which concluded that h1: h2: c1: c2: b1: b2 as 0.89:0.89:1.0:0.43:0.43:0.43. From a point of view of optimal volume, a comparison between the two methods is the third objective. Results of the study discovered the volume of the thrust block created by the AWWA method was smaller than the volume created by the ECDIPWSN method when excavation depth was low but was larger when excavation depth was large.

I would like to express my gratitude to ALLAH for giving me the will to accomplish this work. My special thanks go to Dr Moustafa Samir Darweesh, Assistant Professor in Civil Engineering Department, Faculty of Engineering, Assiut University, Egypt, for his great and sincere help and valuable guidance during the period of this work.

All relevant data are included in the paper or its Supplementary Information.