Operativity of the Taunsa Barrage, Pakistan: Experimental Investigation on the Subsidiary Weir

Abstract

River barrages ensure water availability for enhanced irrigation and human consumption. Of course, effective and sustainable management of existing barrages requires controlling riverbed erosion through appropriately designed stilling basins with their appurtenances. The present study assesses the stilling basin performance of the Taunsa Barrage, a vital water resources infrastructure built in 1958 in Punjab, Pakistan, and rehabilitated between 2004 and 2008 through the construction of a subsidiary weir (SW) downstream of the main weir. A physical modeling approach was employed, consisting of two distinct phases of laboratory experiments. Phase 1 replicated the Taunsa Barrage before rehabilitation, assessing the need for SW construction under different discharge rates and downstream bed elevations. Phase 2 reproduced the post-rehabilitation conditions, including varying discharge values, heights and positions of the SW, to evaluate the stilling basin design concerning the ability to dissipate flow energy. The results demonstrated (i) inadequate tailwater levels and oscillating hydraulic jump formation under increased discharges in pre-rehabilitation conditions (highlighting the poor performance of the original Taunsa Barrage stilling basin and the need for an SW to address these hydraulic deficiencies), and (ii) that the SW, under the design conditions, achieved optimal head loss for discharge values near the design discharge. However, the head loss efficiency was highly sensitive to variations in the distance and height of the SW due to hydraulic jump pulsations. Moreover, the head loss efficiency rapidly degraded for discharges greater than the design discharge. These findings indicate that the Taunsa barrage stilling basin may lack the capacity to accommodate higher discharges resulting from the interplay between climate change and land use alterations within the upstream Indus River basin. Future research should focus on developing a design that enhances energy dissipation robustness, reducing susceptibility to potential discharge increases.

1. Introduction

1.1. Sustainable Water Management Challenges in Pakistan

Sustainable management of water resources in Pakistan is crucial, as both agriculture and industry heavily depend on reliable water supplies. However, water resources management faces significant challenges, including water shortages driven by population growth, urbanization, and climate change impacts [1]. Inefficient irrigation and outdated distribution infrastructure exacerbate pressure on resources, while limited storage capacity and poorly maintained dams and barrages further complicate management efforts [1]. Additionally, changes in land use and climate profoundly impact surface and groundwater resources, altering river flow patterns and stressing hydrological systems [2]. Changes in climate and weather patterns may significantly alter the intensity and seasonality of river flows, with implications for agriculture, hydropower generation, and other critical sectors [3]. Anticipated changes in climate and land use are likely to further increase river flow extrema [3,4]. These combined factors highlight the urgent need for sustainable water resource management to address projected climate and land use impacts on Pakistan’s agricultural productivity and environmental health, necessitating an attentive assessment of existing hydraulic structures, such as dams and barrages.

1.2. Barrages and Energy Dissipation

Effective design and operation of hydraulic structures play a crucial role in ensuring the stability of downstream systems by mitigating bed erosion. Water flowing down the crest of a barrage gains kinetic energy that must be dissipated before the release into the recipient water body to avoid erosion that could endanger the downstream movable bed and the hydraulic structure itself [5]. The flow energy dissipation can be obtained by converting the supercritical flow to subcritical before releasing it to the recipient water body [6,7,8,9]. To this aim, a wide range of possible energy-dissipating structures is available in technical practice, including the bucket-type energy dissipator and the hydraulic jump-type stilling basin [6,8,10,11].

Two main physical phenomena may influence the design of jump-type stilling basins [12]. First, it is well known that the hydraulic jump position is sensitive to the tailwater level (TWL) [11,13,14,15], implying that appropriate provisions (chute blocks, friction blocks, sills, and downstream dams) must be set to ensure the establishment of the hydraulic jump on the downstream glacis for the desired range of operating discharges. Second, erosion of the river movable bed downstream of the stilling basin is possible due to the reduced contribution of sediment from the water body upstream and the influence of the stilling basin itself on downstream hydrodynamics. Retrogression in the downstream riverbed lowers the TWL [16], leading to a condition where the energy dissipation efficiency of the stilling basin is reduced and the hydraulic jump position is uncertain, or even to the condition where the hydraulic jump formation is not granted because the TWL falls below the minimum value required for jump formation [16,17,18]. In addition, localized erosion immediately downstream of the stilling basin may endanger its stability due to increased uplift pressure and soil piping phenomena. The construction of a subsidiary weir (also called a sub-weir or secondary dam) downstream of the barrage is one of the approaches used to constrain the hydraulic jump position by raising the TWL and preserving the hydraulic structure from failure [12,19]. This also helps reduce the head drop across the barrage and the chances of the apron undermining by uplift pressure [12].

1.3. Problem Statement and Research Goals

The Taunsa Barrage, a flow control structure on the Indus River in the Taunsa district, Pakistan, serves as a crucial component of the country’s irrigation and water management system, feeding four canals (Muzaffargarh, DG Khan, T.P. Link, and Kachhi). Soon after its commissioning in 1958, the Taunsa Barrage started to experience multiple problems, like excessive retrogression of the downstream riverbed, and the ripping of downstream concrete floor and friction blocks [20,21]. These conditions seriously affected the safety of the barrage and reduced the safe discharging capacity to half of the design value [20,21].

Given the above concerns, a feasibility study [20,22] recommended the rehabilitation of the energy dissipation system by removing baffle and friction blocks, adding chute blocks, and constructing a subsidiary weir downstream of the main weir. In compliance with these recommendations, the Irrigation and Power Department (Government of Punjab, Pakistan) planned the construction of a subsidiary weir at approximately 274.3 m downstream of the Taunsa Barrage to almost eliminate the hydraulic jump sweeping and enhance the safe discharging capacity of the barrage [21,22,23,24]. The sub-weir, whose location and crest level were determined after physical model studies carried out by the Irrigation Research Institute (IRI) under the technical supervision of Punjab Barrages Consultants (joint venture of NDC-NESPAK in association with ATKINS Consulting Engineers, UK), was finally constructed in 2008. According to the study conducted by [25], data collected through sounding and probing in the period 2010–2014 (after remodeling) revealed that the retrogression issue persists after the barrage rehabilitation.

Subsequent studies [26,27] with a one-dimensional (1-D) Saint Venant numerical model, namely the HEC-RAS model, claimed that the original TWLs were sufficient to force the formation of a hydraulic jump over the glacis, thus requiring no subsidiary weir. The studies by [26,28] also mentioned that the construction of the subsidiary weir had led to an increased drowning ratio, decreasing the discharging capacity of the barrage. A recent investigation by [29] with a three-dimensional (3-D) Reynolds-averaged Navier–Stokes (RANS) model carried out with a limited number of discharges suggested that both the old and new stilling basin settings were able to ensure the establishment of the hydraulic jump along the glacis for a given TWL. Unfortunately, the geometric configurations used in the 3-D numerical model experiments seem inadequate to represent the real barrage geometry, since the sub-weir was not considered.

The studies mentioned suffer from obvious limitations. 1-D Saint Venant models, where the hydraulic jump is represented with an abrupt flow field discontinuity, cannot take into account the actual hydraulic jump length. For this reason, the 1-D numerical model employed in [26,27] is useful for evaluating the free-surface profile in long river stretches but is insufficient to represent the structure and the actual position of the hydraulic jump in the stilling basin. Moreover, 1-D modeling cannot consider the complicated shape and position of appurtenances like chute and friction blocks in the stilling basin. On the other hand, the 3-D RANS model results in [29] heavily rely on the choice of turbulence model closure and the appropriate roughness calibration, being adversely affected by the incomplete representation of the stilling basin geometry. Moreover, the small number of discharge values considered in [29] was insufficient to draw general conclusions about the stilling basin behaviour. Considerations about the limitations of the cited numerical studies and the observed discrepancies between numerical results and previous experimental studies suggest that the barrage functionality (energy dissipation and safe discharge capacity) should undergo additional investigation.

To settle the controversy about the subsidiary weir functionality of the rehabilitated barrage and address the claims made by preceding studies, we present a physical modeling approach to compare the performance of the Taunsa Barrage before and after its rehabilitation. This objective is achieved by performing multiple laboratory experiments which are characterized by varying discharges, downstream riverbed elevations, and subsidiary weir position and height. The laboratory experiment results highlight the limitations of the original Taunsa Barrage stilling basin and the need for a subsidiary weir to address its hydraulic deficiencies. Under design conditions, the subsidiary weir effectively provides optimal head loss near the design discharge. However, the current design shows limited robustness, suggesting that the stilling basin may not be sufficient to manage potential discharge increases driven by climate change and land use alterations within the upstream Indus River basin.

2. Taunsa Barrage Description

The Taunsa Barrage is a large flow control structure on the Indus River, 39 km southeast of Taunsa Sharif city (Figure 1). The structure is one of the major barrages in Pakistan, serving a territory of 9.5 × 10³ km² for irrigation purposes since 1958. In Figure 2a, a longitudinal strip of the stilling basin, spanning a single bay, is represented to show the barrage condition before rehabilitation. Four rows of trapezoidal and cubic friction blocks were located inside the concrete stilling basin, while a stone apron and concrete blocks protected the riverbed. In Figure 3a, the barrage strip is represented for the condition after rehabilitation in 2008. In this setting, chute blocks are located on the downstream glacis and an end sill delimits the stilling basin. Finally, a subsidiary weir downstream, whose height is H_sw = 2.13 m, is intended to ensure a sufficiently high TWL at the end of the stilling basin. The distance of the secondary weir from the main weir is D_sw = 274.3 m. The main weir height is H_W = 3.35 m.

The barrage, whose design discharge is Q_TB,d = 28,316.85 m³/s (dashed green line in Figure 4), consists of 64 bays, of which 53 are main bays whereas the left and right under-sluices consist of 7 and 4 bays, respectively. Two walls separate the main weir from the under-sluices’ bays. The total width of the barrage between the abutments is W_b = 1415 m, while the total clear waterway, with the exclusion of the two lateral fish ladders, has a width W_w =1170 m. The average clear waterway of a single bay is W_s = W_w/64 = 18.28 m. The design water level (upstream) is H_u = 136.2 m above the mean sea level (AMSL), with a normal operating water level of H_n = 135.8 m. In the original configuration, the elevation of the upstream riverbed, the crest level of the main weir, and the stilling basin level were 128.31 m, 130.45 m, and 126.79 m, respectively (Figure 2b). After remodeling, the stilling basin elevation is now 127.09 m (Figure 3b). The slope of the main weir upstream glacis is 1:4, whereas the downstream glacis is curved with a variable curvature radius. For more details about the barrage and its characteristics, the reader is addressed to the existing literature [21,22,24].

The yearly peak discharges at the Taunsa Barrage from 1958 to 2017 [30] are represented in Figure 4, where the dashed red line shows the reported safe discharging capacity of the barrage before rehabilitation. The inspection of the figure shows that there was a 43% chance that the peak yearly flow rate exceeded the safe discharge capacity before the barrage remodeling. The safe discharge capacity of the barrage was increased to 28,316.85 m³/s after its remodeling (dashed green line in Figure 4). This was demonstrated by the 2010 peak discharge (red bar), which passed the barrage without harming the structure. However, on that occasion the barrage showed additional frailty, although not related to the stilling basing structure, because the flow outflanked the eastern embankment and flooded a 160,000 km² area, causing 2000 victims [31]. Notably, the 2010 peak discharge attained 96% of the design discharge, suggesting that the design discharge could be exuberated in the future.

3. Methodology and Experimental Setup

The laboratory experiments were carried out in a rectangular flume at the Model Tray Hall of the Center of Excellence in Water Resource Engineering (CEWRE) in Lahore, Pakistan, assuming Froude similarity. A schematic layout of the rectangular flume is represented in Figure 5. The total length of the flume was L_f = 9.143 m, while its height and width were H_f = 0.762 m and W_f = 0.522 m, respectively. A free outfall was present at the downstream end of the flume.

It was assumed that the flume width W_f was representative of the average clear water way W_s of a single bay, implying that the geometric scale was λ = W_f/W_s =1:35. Since the unit-width discharge scales with λ^1.5 in the Froude analogy, it follows that the relationship between the discharge Q_m in the model and the discharge Q_TB through the Taunsa barrage total clear way W_w is expressed by

$${\displaystyle \frac{Q_{TB}}{W_w}}={\displaystyle \frac{1}{{\lambda }^{1.5}}}{\displaystyle \frac{Q_m}{W_f}}.$$

(1)

If Q_m,d is the model discharge corresponding to the Taunsa barrage design discharge Q_TB,d, from Equation (1) it follows that Q_TB/Q_TB,d = Q_m/Q_m,d. Where appropriate, we will use the generic symbol Q/Q_d to identify the discharge ratio without specifying if this refers to the river (Q_TB/Q_TB,d) or the laboratory model (Q_m/Q_m,d).

Two distinct groups of runs were performed, as follows. In the first group, Phase 1, the physical model setting reproduced one bay of the Taunsa barrage before rehabilitation, with main weir, friction blocks, and no subsidiary weir. In the second group of runs, Phase 2, the physical model reproduced the barrage conditions after the rehabilitation, with main weir, subsidiary weir, and chute blocks on the downstream glacis. During Phase 2, different positions and heights of the subsidiary weir were also considered.

The discharge through the flume was delivered from the water circulation system, having a constant supply from the tube well, with a discharging capacity of Q_m,max = 0.1133 m³/s. For the discharge measurement, a V-notch equipped with a stilling-well and a point gauge was installed upstream of the main weir. A wire mesh, whose orientation was optimized to be compatible with the desired boundary condition, was installed upstream of the main weir to reduce the turbulence of the water approaching the model. A framed glass was installed near the main weir for improved observation. The water depth upstream of the subsidiary weir (tailwater depth, TWD) was measured with the help of a steel scale. The location of the hydraulic jump was measured from the barrage crest with the help of a steel tape, while the upstream approach velocity was measured with the help of a current meter. A railing was also provided along the model for the smooth movement of a point gauge used to record the flow height.

The two groups of runs are detailed in the following.

Phase 1. The first group of runs was aimed at exploring the performance of the barrage stilling basin before rehabilitation by evaluating the need for a subsidiary weir construction. Acacia wood blocks were located on the flume floor to model the prototype friction blocks. Congruent with the original barrage design, the first two rows of blocks had a trapezoidal shape, while the last two rows were cubical (see Figure 6).

During Phase 1, seven runs were performed with the discharges of

Table 1. Experimental program for Phase 1: discharges.

Run ID	Q/Qd	QTB (m3/s)	Qm (m3/s)
1	1.10	31,148.53	0.067
2	1.00	28,316.85	0.061
3	0.96	27,184.17	0.059
4	0.75	21,237.63	0.046
5	0.50	14,158.42	0.031
6	0.40	11,326.74	0.024
7	0.30	8495.05	0.018

(where the second column represents the discharge ratio Q/Q_d), considering no downstream bed retrogression (see Figure 7a). In these conditions, herein referred to as the Original River Bed (ORB), the prototype riverbed level is equal to 126.79 m. Seven additional runs, referred to as the Retrogressed River Bed (RRB), were performed with the discharges of Table 1, considering a laboratory model with a retrogressed downstream bed (Figure 7b). The retrogression profile (see the detail in Figure 7c) was obtained by averaging the levels from various riverbed profiles downstream of the barrage surveyed by the Irrigation Department of the Government of Punjab in the year 1997 [32]. In the model, the downstream riverbed level is up to 0.074 m lower than the stilling basin level (see Figure 7c) and corresponds to a maximum retrogression of 2.60 m in the prototype.

Phase 2. The second phase of the experiments aimed at reproducing the hydraulic behaviour of the remodeled stilling basin. For this reason, the friction blocks were substituted by chute blocks on the downstream glacis, and the modified geometry was completed by positioning a wooden end sill and a subsidiary weir with height H_m,sw = 0.0599 m at a distance D_m,sw = 7.837 m from the center of the model’s main weir crest (see Figure 8a). The laboratory model for the actual subsidiary weir conditions (herein referred to as SWC), reproduced in Figure 8a, was tested using the discharges of

Table 2. Experimental program for Phase 2 (after remodeling).

Q/Qd	Dm/Dm,sw	Hm/Hm,sw
0.5	0.5	0.60, 0.70, 0.80, 0.90, 1.0, 1.33, 1.66
	0.75	0.60, 0.70, 0.80, 0.90, 1.0, 1.33, 1.66
	1.0	0.60, 0.70, 0.80, 0.90, 1.0, 1.33, 1.66
0.75	0.5	0.60, 0.70, 0.80, 0.90, 1.0, 1.33, 1.66
	0.75	0.60, 0.70, 0.80, 0.90, 1.0, 1.33, 1.66
	1.0	0.60, 0.70, 0.80, 0.90, 1.0, 1.33, 1.66
	1.15	0.60, 0.70, 0.80, 0.90, 1.0, 1.33, 1.66
0.96	1.0	1.0
1.00	0.5	0.60, 0.70, 0.80, 0.90, 1.0, 1.33, 1.66
	0.75	0.60, 0.70, 0.80, 0.90, 1.0, 1.33, 1.66
	1.0	0.60, 0.70, 0.80, 0.90, 1.0, 1.33, 1.66
	1.15	0.60, 0.70, 0.80, 0.90, 1.0, 1.33, 1.66
1.10	1.0	1.0

. Since the lengths in the model scale with λ, one has

$${\displaystyle \frac{D_{m,sw}}{D_{sw}}}={\displaystyle \frac{H_{m,sw}}{H_{sw}}}=\lambda .$$

(2)

In total, 79 experiments were performed by varying the discharge through the flume and the geometry of the subsidiary weir, expressed through its height H_m and distance D_m from the center of the main weir crest (see Figure 8b). These experiments, which differ by the ratios H_m/H_m,sw and D_m/D_m,sw, are intended to improve the energy dissipation mechanism by optimizing the subsidiary weir geometry. The ratios H_m/H_m,sw and D_m/D_m,sw used in the experiments, where H_m/H_m,sw = 1.0 and D_m/D_m,sw = 1.0 correspond to the SWC experimental setting, are reported in Table 2.

4. Results and Discussion

In this section, we present the results of the Phase 1 and Phase 2 experiments. During the discussion, attention is focused on aspects such as the tail water rating curve, the location of the hydraulic jump, and the characterization of the flow energy dissipation mechanism.

4.1. Hydraulic Characterization of the Stilling Basins

4.1.1. Tail Water Rating Curves and Location of the Hydraulic Jump

Tail water levels (TWLs) do not scale with λ because they depend on the reference datum. For this reason, the model stilling basin is characterized using the tailwater depth (TWD) corresponding to different discharges. The prototype TWD and the laboratory model TWD_m scale with λ, like the prototype H_W and the model H_m,w main weir height:

$${\displaystyle \frac{{TWD}_m}{TWD}}={\displaystyle \frac{H_{m,w}}{H_W}}=\lambda .$$

(3)

From Equation (3) it follows that

$${\displaystyle \frac{TWD}{H_W}}={\displaystyle \frac{{TWD}_m}{H_{m,w}}},$$

(4)

meaning that the ratio between tailwater depth and main weir height in the prototype is equal to the corresponding model ratio. The corresponding TWLs in the prototype can be easily computed by adding the stilling basin bed level.

In Figure 9, the experimental values of the ratio TWD/H_W (thick black continuous lines), where H_W is the main weir height in the prototype, are represented as a function of the discharge ratios Q/Q_d of Table 1 in different experimental conditions (ORB, RRB, and SWC). In the same figure, the minimum and maximum tailwater depths for the hydraulic jump formation, as reported in [21], are represented with dashed lines. Tailwater depths smaller than the minimum designed tailwater depth will lead to a sweeping of the hydraulic jump, while tailwater depths greater than the maximum designed tailwater depth will lead to drowning of the hydraulic jump, ultimately reducing the energy dissipation efficiency of the hydraulic jump in both cases. Figure 10 represents the hydraulic jump toe position in the experimental conditions ORB (Figure 10a,b), RRB (Figure 10c,d) and SWC (Figure 10e,f), for Q/Q_d = 0.5 and Q/Q_d = 1.0, respectively.

In Figure 9a, the TWD/H_W experimental values (thick black continuous line) are represented for the ORB condition (Figure 7a). The comparison with the design curve representing the minimum TWD required for the jump formation (thin grey dashed line) shows that the stilling basin setup for the ORB condition is adequate for discharge ratios up to Q/Q_d = 0.75. As the discharge is further increased, the TWD is less than the minimum required value. This observation is further substantiated by the pictures in Figure 10a,b. Figure 10a, where a vertical thin black line indicates the position of the downstream glacis toe, represents the experimental apparatus in the ORB conditions with Q/Q_d = 0.5. The inspection of the figure clearly shows that the hydraulic jump starts well before the downstream glacis toe, ensuring the efficiency of the dissipation mechanism. A different situation is depicted in Figure 10b (Q/Q_d = 1.0), where the hydraulic jump starts to develop at the glacis toe, with efficiency reduction of the energy dissipation mechanism [6,33]. This demonstrates that, even in the ORB condition, the barrage design is unable to cope with the design discharge Q_TB,d.

Figure 9b (thick black continuous line) reports the experimental ratio TWD/H_W for the RRB conditions (Figure 7b). The comparison with the design curve representing the minimum TWD required for the jump formation (thin grey dashed line) shows that the stilling basin setup for the RRB condition is adequate for discharge ratios up to Q/Q_d = 0.50. This value is congruent with what is reported in the literature about the safe discharge reduction to half of the design discharge before remodeling [20,21]. Figure 10c represents the experimental apparatus in the RRB conditions with Q/Q_d = 0.5, showing that the hydraulic jump starts developing just before the toe of the downstream glacis. Figure 10d shows that the hydraulic jump disappears for Q/Q_d = 1.0, while a jet jumping over the front line of friction blocks is formed. This flow configuration is inadequate to guarantee the appropriate amount of energy dissipation.

Figure 9c (thick black continuous line) reports the experimental TWD/H_W values for the SWC setting (Figure 8a). The comparison with the curve of the minimum TWD values required for the hydraulic jump formation (thin grey dashed line) shows that TWDs are adequate for the formation of a hydraulic jump for all the discharge values. The experimental TWD curve is very close to the curve of the maximum TWDs allowed for the hydraulic jump, implying that drowning of the hydraulic jump may occur [21]. This is well visible in Figure 10e,f, corresponding to the discharge ratios Q/Q_d = 0.5 and Q/Q_d = 1.0, respectively.

The location of the hydraulic jump is a parameter affecting the efficiency of the energy dissipation mechanism and the safety of the downstream riverbed. Usually, the desired position of the hydraulic jump toe is the lower one-third of the downstream glacis [12]. The ratio X_HJ/H_W between the hydraulic jump’s toe location X_HJ, measured from the barrage crest, and the main weir height H_W is represented in Figure 11 for the discharge ratios Q/Q_d of Table 1 in the ORB, RRB, and SWC conditions. In the figure, the desired position for the hydraulic jump toe is the region between the two dashed lines, corresponding to the glacis toe (thin black dashed line) and the one-third glacis-length position (thick black dashed line), respectively.

For all the configurations in Figure 11, the jump toe position moves downstream as the discharge increases. This is easily understood when recalling that the upstream total thrust increases with discharge. A closer inspection of Figure 11 (thin black continuous line) shows that the hydraulic jump’s toe is swept from the downstream glacis in the ORB condition when the relative discharge exceeds the value Q/Q_d = 0.75. In the RRB configuration (grey continuous line), the experimental curve lies above the ORB curve in the entire discharge interval and the hydraulic jump is swept from the glacis when the relative discharge exceeds the value Q/Q_d = 0.5. The comparison with the ORB experimental results confirms that the sweeping of the hydraulic jump is further promoted by the retrogression of the downstream riverbed, which causes a decrease in the tailwater stage, reducing the downstream hydraulic thrust. For the SWC condition, the experimental curve (thick black continuous line) is contained between the two limits (dashed lines). This implies that, independent of the discharge through the barrage, the hydraulic jump leans on the downstream glacis because the subsidiary weir efficiently constrains the jump position.

4.1.2. Pulsation and Energy Dissipation of the Hydraulic Jump

The pulsation of the hydraulic jump consists of its quasi-periodic horizontal movement [34,35]. This oscillation can be attributed to inadequate values of the TWD, resulting in the formation of a weak hydraulic jump [36].

Figure 12 represents the dimensionless pulsation period $\tau =T/\sqrt{H_{m,w}/g}$, where g is the gravity acceleration, H_m,w = 0.1072 m is the height of the laboratory model main weir, and T is the pulsation period of the hydraulic jump, as a function of the discharge ratio Q/Q_d (Table 1) in the ORB and RRB cases. A permanent jump with no pulsation (τ = 0) is present for all discharges in the SWC case, and the corresponding data are not reported in Figure 12. The inspection of the figure shows that the pulsation period increases with the discharge increase, resulting in the progressive unstable behaviour of the hydraulic jump itself.

In the RRB case, a stable hydraulic jump is present for Q/Q_d ≤ 0.4, while the hydraulic jump starts pulsating when the discharge ratio exceeds Q/Q_d = 0.4. The pulsation period steadily increases with the discharge, with an abrupt jump for discharge close to the design value (Q/Q_d = 1.0). The ORB case exhibits similar behaviour, but the stable hydraulic jump is present for Q/Q_d ≤ 0.5. The pulsation period in the RRB condition, for given discharge, is always greater than the ORB pulsation period.

The increase in the pulsation period values with the discharge in Figure 12 can be explained by recalling that the upstream total thrust increases with discharge. This causes instability in the hydraulic jump position, leading to excursions of the jump toe whose length and duration increase with the upstream thrust. The duration, and subsequently the period, of these excursions is longer in the RRB condition due to the lower tailwater level, relative to the ORB condition, as already evidenced in Section 4.1.1.

In the following, we evaluate the energy dissipation efficiency using the relative head loss ΔH/H_c where

$$H_c=1.5·{\left({\displaystyle \frac{q^2}{g}}\right)}^{{\displaystyle \frac{1}{3}}}$$

(5)

is the critical head corresponding to the unit-width discharge q and ΔH = H_u − H_d is the total head that is lost through the hydraulic jump. The head is computed as the difference between the total head H = z + h + v²/(2g) immediately upstream (H_u) and downstream (H_d) of the jump, where z is the local bed elevation, h is the flow depth, and v is the depth-averaged velocity.

In Figure 13, the relative head loss ΔH/H_c is plotted as a function of the dimensionless discharge Q/Q_d in the scenarios ORB, RRB, and SWC. The inspection of the figure shows that the relative energy loss decreases with the increase in the dimensionless discharge values in all the scenarios. Furthermore, the relative energy loss in the RRB case (grey continuous line) is reduced with respect to the ORB case (black continuous line with white dots) due to the riverbed retrogression and the consequent decrease of the TWD [12]. The maximum head loss is obtained in the SWC scenario, thanks to the higher TWD obtained with the use of the subsidiary weir.

Even in the SWC case, a considerable drop in the energy loss efficiency is exhibited for discharges greater than the design discharge (Q/Q_d = 1.0). This observation indicates that the design of the rehabilitated stilling basin may exhibit limited flexibility in accommodating a potential increase in discharge through the barrage for a given return period. Such an increase could be caused, for instance, by current climate change and land development (with soil impermeabilization) of the upstream Indus River watershed.

4.2. Sensitivity of the Subsidiary Weir Design

In the present section, the sensitivity of the present subsidiary weir design is evaluated with respect to the head loss efficiency. In Figure 14a, the relative head loss ΔH/H_c is plotted as a function of the relative subsidiary weir height H_m/H_m,sw in the interval [0.6, 1.0] for values of the dimensionless subsidiary weir distance D_m/D_m,sw in the interval [0.5, 1.15] and dimensionless discharge Q/Q_d = 0.5. The energy dissipation corresponding to higher values of the weir height are not represented here because the corresponding hydraulic jump is completely drowned, and the head loss is negligible [35]. The inspection of the plot shows that, for Q/Q_d = 0.5, the energy dissipation rapidly increases with the weir height until a maximum is attained, after which the relative head loss rapidly decreases, meaning that the dissipation efficiency is very sensitive to the weir height. For Q/Q_d = 0.5, the optimum amount of dissipation is obtained with D_m/D_m,sw = 0.5 and H_m/H_m,sw = 0.80. A slightly decreased dissipation is obtained with D_m/D_m,sw = 1.0 and H_m/H_m,sw = 1.0, implying that the present subsidiary weir design supplies a quasi-optimal energy dissipation for Q/Q_d = 0.5.

In Figure 14b, the same quantities are plotted for Q/Q_d = 0.75, H_m/H_m,sw in the interval [0.6, 1.66], and D_m/D_m,sw in the interval [0.5, 1.15]. For Q/Q_d = 0.75 also, the dimensionless head loss ΔH/H_c increases with H_m/H_m,sw until a maximum is attained and rapidly decreases along with increase in the relative subsidiary weir height. The maximum relative head loss is obtained for D_m/D_m,sw = 1.0 and H_m/H_m,sw = 1.0. In other words, the present SWC design appears to be the best possible for Q/Q_d = 0.75.

In Figure 14c, the dimensionless head loss is plotted as a function of the dimensionless subsidiary weir height H_m/H_m,sw in the interval [0.6, 1.66] for values of the dimensionless subsidiary weir distance D_m/D_m,sw in the interval [0.5, 1.15] and dimensionless discharge Q/Q_d = 1.0. Like the cases with Q/Q_d = 0.50 and Q/Q_d = 0.75, the relative head loss is strongly sensitive to the subsidiary weir height, with a maximum relative head loss attained for D_m/D_m,sw = 1.0 and H_m/H_m,sw = 1.0.

In conclusion, Figure 14 shows that the present subsidiary weir design (position and height) leads to quasi-optimum or optimum head loss for the discharge interval considered, with a marked decrease in the dissipation efficiency for changes in the weir height and position. This confirms the scarce robustness of the present design and the difficulties in improving it by acting on the height and position of the subsidiary weir.

5. Conclusions

This study investigates the energy dissipation performance of the stilling basin serving the Taunsa Barrage, built in 1958 in Punjab, Pakistan, and rehabilitated between 2004 and 2008 through the construction of a subsidiary weir downstream of the main weir. Two distinct phases of laboratory experiments were carried out, as follows.

Phase 1 replicated one bay of the Taunsa Barrage before rehabilitation, assessing the need for the subsidiary weir construction under different discharge rates and downstream bed elevations (original and retrogressed riverbed conditions). Phase 2 reproduced the post-rehabilitation conditions, including varying discharge values, heights and positions of the subsidiary weir to optimize its design for enhanced energy dissipation in the stilling basin.

The results of this study revealed the following key findings.

• The pre-rehabilitation conditions exhibited insufficient tailwater levels and the formation of oscillating hydraulic jumps at higher discharges, underscoring the suboptimal performance of the original Taunsa Barrage and the necessity of a subsidiary weir to mitigate these hydraulic issues.
• The subsidiary weir, when operating under design conditions, effectively achieved the desired head loss for discharge values not greater than the design discharge.
• The stilling basin head loss efficiency rapidly dropped for discharge greater than the design values.
• The head loss was highly sensitive to the variations in the position and height of the design subsidiary weir, showing the modest robustness of the present design.

These findings may be partly mitigated by some limitations in the present study. While the laboratory investigation focused on the main bays of the barrage, similar analyses could be extended to encompass the under-sluice bays. Moreover, energy dissipation was measured downstream of the main weir, while future research may consider evaluating dissipation immediately downstream of the subsidiary weir to take into account the actual backwater profile in the downstream reach of the Indus River.

Despite the above limitations, the study addresses the fact that the Taunsa barrage stilling basin seems inadequate to face potential discharge increases through the barrage due to land development of the upstream Indus River watershed or magnified extreme events caused by climate change. On the other hand, the modest robustness of the present design may prevent tackling future discharge increases by intervening on the subsidiary weir height and position. Future research should focus on developing updated hydrologic studies to evaluate potential extreme flows due to climate change and improving the stilling basin design to enhance the robustness of the energy dissipation process against potential discharge increases through the barrage.