Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures

Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures

Alexandria Engineering Journal (2020) xxx, xxx–xxx H O S T E D BY Alexandria University Alexandria Engineering Journal www.elsevier.com/locate/aej ...

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Alexandria Engineering Journal (2020) xxx, xxx–xxx

H O S T E D BY

Alexandria University

Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com

ORIGINAL ARTICLE

Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures M.A. Shousha a,*, A.M. Basha a, M.A. El-enany a, H.M. Moghazy b a b

Civil Engineering Department, Faculty of Engineering, Kafrelsheikh University, Egypt Irrigation Engineering and Hydraulics Department, Faculty of Engineering, Alexanderia University, Egypt

Received 17 December 2019; accepted 8 January 2020

KEYWORDS Seepage characteristics; Grouted vertical barrier; Small hydraulic structures; Sheet pile; Upstream blanket

Abstract This study investigated the effect of using Grouted Vertical Barrier (GVB) on the seepage characteristics (uplift force, seepage rate, and exit hydraulic gradient) under small hydraulic structures. The GVB’s variables, viz., position, depth, width and hydraulic conductivity, were studied experimentally using sand model and numerically employing SEEP/W software. A parametric study investigated several cases of the variables after numerical model verification. The results depicted that the heal and toe ends were the best positions for uplift force and exit gradient, respectively. The maximum reduction in the seepage occurred at both ends. The seepage characteristics swiftly decreased by increasing the GVB’s depth in the pre-mentioned best positions. Upsurge of the GVB’s width sequentially reduced the exit gradient and the seepage rate, whilst negatively impacted the uplift force. Declining the ratio between the hydraulic conductivity of the GVB (K) and the reference soil one (Ko) significantly lowered the seepage until reaching a stationary proportion K/Ko = 1E4. Beyond this, decreasing K/Ko ratio do-nothing. Through regression analysis, three equations were developed to estimate the seepage characteristics affected by GVB’s variables. The indications of comparative studies revealed a better effect of the GVB compared to any of the sheet pile or the upstream blanket. Ó 2020 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction The seepage beneath the small hydraulic structures, being the major factor of the instability for such structures, is an issue of great importance [1,2]. Previous numerical and experimental studies have used different measures to control the seepage * Corresponding author at: Kafrelsheikh, Egypt. E-mail address: [email protected] (M.A. Shousha). Peer review under responsibility of Faculty of Engineering, Alexandria University.

under the hydraulic structures, such as upstream blankets [3], cut off wall [4–6], sheet pile [7] and filters [8]. Grouting is a common technique for increasing the underline soil strength and for decreasing the hydraulic conductivity of the soil [9,10]. Furthermore, grouting was profusely applied to cut down the seepage under dams foundation (e.g. grout curtains) [11,12]. On the other hand, grouting was applied to support underground structure against seepage failure [13,14]. For the seepage problem treatment at the ChaparAbad Dam, Iran, the study suggested the installation of a grout curtain after reviewing many types of water-proofing techniques with respect to cost, feasibility and safety factors

https://doi.org/10.1016/j.aej.2020.01.013 1110-0168 Ó 2020 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: M.A. Shousha et al., Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.01.013

2 [15]. After in-situ tests for the remedial works for the cavity discovered in the earth-fill dam in Korea, cement and chemical grouting were recommended to reduce the soil hydraulic conductivity [16]. The results of this Korean dam study deduced that the permeation application significantly diminished the leakage to 4–50 m3/day compared to an initial stage of 2500 m3/day. The previous studies were concerned with using grouting to control the seepage under foundation of large hydraulic structures only, such as the use of grout curtain under dams. However, none of these studies investigated the effectiveness of using the grouting technique under small hydraulic structures, such as weirs and regulators. Hence, this study was concerned with the strategy of using vertical barrier formed by grouting to resist the seepage flow under small hydraulic structures. The Grouted Vertical Barrier (GVB), main concept of this paper, could be performed in different positions, geometries and hydraulic conductivities using one of the grouting methods, such as (permeation grouting – compaction grouting – jet grouting) [17]. High conductivity of the underlined soil is the most common cause of excess seepage rate [18]. Accordingly, the advantages of diminishing water seepage through GVB became clear due to the very low hydraulic conductivity after grouting. Experimental data proved that the use of injected barrier with water-cement ratio 0.42 reduced saltwater seepage to coastal aquifer by (27–94)% according to its depth [19]. Intuitively, the grouted curtain wall was much more economical than concrete cut-off as a seepage remediation method [20]. Superior to the sheet pile, the GVB was easier in construction for a new or an existing structure, and it increased the underlying soil stability, as well. However, the effectiveness of GVB under weirs and regulators was an issue that needs a comprehensive investigation, especially it’s configuration, geometry and material conductivity. Hence, the objectives of this study were as follows:  Perform an experimental investigating for the effect of position, width and depth of GVB on seepage rate and uplift force under small hydraulic structure.  Verify the numerical results using observed experimental data.  Make a parametric study for a wide range of variable on seepage characteristics under small hydraulic structure.  Carrying out an in-depth study for the GVB variables in the numerical model and determining their effectiveness and significance on the seepage characteristics.  Making a technical comparison between the effect of grouted vertical barrier and a sheet pile.  Obtaining the combined effect of the grouted barrier and upstream blanket, and making a comparative study of their own effect. The results were observed and examined in terms of the total uplift force(F), the seepage rate (q), and the exit hydraulic gradient (I). Security these seepage characteristics represents the stability of the structures [1]. The significant degree and effectiveness of each variable of the GVB on seepage characteristics were examined separately and in accordance with other through statistical analysis. Bases on a regression analysis, three empirical formulas were presented to determine F, q and I under small hydraulic structure in case of an upstream GVB. A comparative study was conducted to evaluate the differential impact of the

M.A. Shousha et al. GVB and the sheet pile on the seepage characteristics under the floor of the structure. Furthermore, a comparison between the influence of the GVB and upstream blanket, and the combined effect of them was investigated, as well. 2. Experimental work Experiments were carried out in an 8 mm thickness Acrylic tank of 1.0 m length, 20 cm width and 75 cm height. This tank is located in the Laboratory of Civil Engineering Department, Kafr El Sheikh University, Egypt. Photo 1 shows the experimental devices, equipment and variables. A weir model was used with a floor length (L) of 40 cm, seepage faces in both upstream (Lus), downstream (Lds), in addition to the porous media depth under the floor (D) of 60 cm. Before the experimental work was conducted, the box tank was fully filled with water and kept for 48 h, and it was observed that no changing in the water level occurred. The contact surface between the acrylic walls and the tank walls was sealed with the rubber glue (silicone) to avoid water leakage. In order to keep both upstream and downstream sides from disturbance, a filter of gravel layer (D50% = 2 mm) was used. Using the constant head permeability test, the hydraulic conductivity of the nature soil was measured as 0.514 * 103m/sec. The grouted vertical barrier was formed by mixing both default sandy soil with a percent of bentonite about 5% by volume, then its hydraulic conductivity was determined from a variable head permeability test as 0.9726 * 1011m/sec. The seepage rate measured utilizing volumetric strategy. Likewise, the uplift head distribution was measured was by piezometric tubes along the floor. At the beginning, the reference case (without GVB) was conducted experimentally. After that, The GVB was formed in the laboratory using a sand bentonite mixture. The independent variables of the GVB were the depth (d), the width (b), and position from the floor to the centre of the GVB (X). The GVB was located at five different positions according to the distance (X) = 0, 10, 20, 30 and 40 cm. For each of the previous positions, the GVB’s depth varies related to the depth (d) = 15, 30 and 45. Furthermore, for each of the prementioned values of (x) and (d), the GVB’s width (b) varies according to (b) = 5, 10 and 15 cm. According to all of the previous scenarios, the water level in the upstream regarded to the surface of sand body was 12 cm which was held steady during each test using an over flow pipe, while the downstream water level was set at the top of the sand surface. A total of 46 experiments were conducted under different conditions according to the grouted barrier depth, width and position. In each experiment, the resulting seepage rate (q) and the uplift force (F) values were determined. These results were prepared to be non-dimensional by dividing the values of F and q on their corresponding values Fo and qo in the reference case (with no GVB), and then the results of relative uplift force F/Fo and relative seepage rate q/qo were explained and discussed. Furthermore, the curves were prepared by nondimensional ratios of the variables (X/L), (b/L) and (d/D). 3. Results and discussion of the experimental work This section focused mainly on making analyses and discussions for results of the uplift force and the seepage rate from

Please cite this article in press as: M.A. Shousha et al., Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.01.013

Effect of using grouted vertical barrier on seepage characteristics experimental observations according to the pre-mentioned tested parameters. 3.1. Effect of GVB on the uplift force In order to signify the effect of GVB’s variables (x, b and d) on the uplift force, a GVB with a certain value of width, depth and conductivity was moved along the floor towards the downstream end, and the uplift pressure heads were recorded. This process was iterated many times in different values of width and depth producing several cases of the GVB. For each of the previous cases, the total uplift force was calculated by integrating the area under the curves of the uplift pressure which shown in Fig. 1. As observed, by moving the GVB from heal towards the toe points, the uplift force steeply increased, so that the highest and lowest values were obtained at both ends, respectively. The graph indicated that all curves were inversely symmetrical around the midpoint (X/L = 0.50). As presented, when the GVB was moved along the upstream half-length of the floor, X/L > 0.50, the ratio F/Fo was less than 100% (positive impact) and ranged between (26–100%) depending on other parameters. On the contrary, the opposite results of the last ones were obtained for

3 X/L > 0.50. When the GVB located at X/L = zero, the effect of the width and depth on the total uplift force (F) was null. Fig. 1 showed that by increasing the GVB depth at the upstream end (from 15 to 30 cm) and (from 30 to 45 cm), The F value decreased by ratios about 15% and 19% respectively, commencing from F/Fo value = 26%, 24% and 21% for b = 5, 10 and 15 cm, in order. In contrast, F value nearly increased by the same ratios of the previous reduction in condition of increasing the GVB depth at the downstream end of the floor. It was clear that the uplift force was slightly affected by increasing the width (b). Whereas, by increasing (b) from 5 to 15 cm, the uplift force was changed by a tiny fracture (less than 5%), in which this effect was a decrease at the upstream and an increase at the downstream. 3.2. Effect of GVB on the seepage rate As presented in Fig. 2, when the GVB was moved along the floor, the seepage rate increased from the heal point reaching its highest value at the middle of the floor, and then it decreased reaching its lowest value at the toe point. This means that heal and toe points were the best positions for a minimum

Fig. 1 Dimensionless diagram for the experimental results of the uplift force versus relative position. (a) the width b = 5 cm, (b) the width b = 10 cm and (c) the width b = 15 cm.

Please cite this article in press as: M.A. Shousha et al., Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.01.013

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Fig. 2 Dimensionless diagram for experimental results of seepage rate versus relative position. (a) the width b = 5 cm, (b) the width b = 10 cm and (c) the width b = 15 cm.

seepage rate value. These results were totally consistent with Khalili Shayan et al. [5]. This may be due to the fact that the seepage path was longer when the GVB was located at heal or toe ends than being located at the middle of the floor because of the GVB’s double side effect. Regarding to Fig. 2 which showed the relative seepage rate q/qo versus the relative position, the maximum difference of the seepage rate between the highest value (at the middle) and the lowest one (at the heal or toe) for the same GVB’s model ranged between (27%); in which smaller differences were reached for the larger depth, and vice versa. Consequently, the GVB position had non-significant effect on the seepage rate. Considering Fig. 2, each group of line graphs in different figures were approximately parallel. This means that the effect of GVB’s depth for any position under the floor was similar regardless the values of other variables. For any width or position, increasing the depth by 15 cm (d/D = 25%) produced a downward tendency ranged from (17% at the ends 22% at the middle). On the contrary, increasing the width by 5 cm (b/L = 12.5%) shifted all line graphs by (1%-3%) downward, also. This lead to the effect of the depth was highly significant, in contrast to the width or the position which were non-significant.

4. Numerical model The current study was performed experimentally using a sand box model. The experimental observation was used to verify the numerical model, and then a parametric study included a wide range of variables was done employing SEEP/W software which depends on the finite element method. The finite element equation [21] for a seepage analysis is: ½KfHg ¼ fQg

ð1Þ

where [K] is a matrix of coefficients related to geometry and materials properties, {H} is a vector of total hydraulic head, and {Q} is a vector of flow quantities. The specified boundary condition in this study was the total effective head {H} at the upstream, which was taken with a constant value to simulate the steady state condition. The left, right and bottom sides were modelled as impermeable boundaries. The numerical model dimension was the same of the experimental model after taking scale 100:1. GeoStudio software version 2012 was characterized by automatics mesh generation algorithms, which sufficiently enabled a well behaved, numerically robust default discretization; However, numerical trials have been run using different mesh sizes to select the ideal mesh size. Fine mesh consisting of elements with

Please cite this article in press as: M.A. Shousha et al., Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.01.013

Effect of using grouted vertical barrier on seepage characteristics

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maximum area of 0.25 m2 is used because a finer mesh does not show significant difference in results. In addition to numerically studying the mentioned variables in the experimental work (X, b, and d) in a wide range, the numerical modelling investigated a new variable effect which is the hydraulic conductivity of the grouted vertical barrier K, Photo 1. The reference soil was taken homogenous and isotropic with two assumed values of hydraulic conductivity to simulates coarse and fine soil types as follows: (Ko) = 1E2 m/s (for coarse soil type) and 1E7 m/s (for fine soil type). All variables were examined in ratios format as follows: the GVB position changed according to the relative position (X/L) = 0.00, 0.25, 0.50, 0.75 and 1.00. The GVB’s depth (d) varied related to relative depth d/D = 0.20, 0.40, 0.60, 0.80 and 1.00. The GVB’s width (b) varied according to relative width b/L = 0.05, 0.25, 0.5, 0.75 and 1.00. The permeability coefficient of the grouted vertical barrier (K) varied according to relative conductivity K/Ko = 1E1, 1E2, 1E3, 1E4 and 1E5. All values of the previous parameters were studied with each other. For each scenario, the seepage rate, the uplift head values, and the exit gradient were determined by the numerical model. 5. Results and discussion of the numerical model 5.1. Verification of numerical model by experimental data Numerical modeling software SEEP/W, used in this study, was widely used for studying the seepage phenomenon under hydraulic structures [5,22–25]. Furthermore, the current study verified the numerical model through experimental observations. The results of the numerical model versus the experimental work results for the total uplift force and the seepage rate is shown in Fig. 3. The correlation coefficient (R2) was used to state the fit as follows: 2 Pn  Xi  X^i R2 ¼ 1  Pi¼1 ð2Þ n  2 i¼1 ðXi  X Þ where Xi = is the observed data from the experimental work, Xi^= the calculated data from the numerical model and X = the average of the observed data. The results in Fig. 3 depict an acceptable agreement among the calculated and the measured results from numerical and experimental models. Based on these outcomes, the investigation continued numerically utilizing the Finite Element method. 5.2. The effects of GVB variables on the uplift force: For several cases of GVB’s variables, relative position (X/L), relative width (b/L), relative depth (d/D) and relative permeability K/Ko), and for two values of the reference soil conductivity (Ko), the total uplift force was calculated by integrating the area under curves of the uplift pressure. The position versus the uplift force for different cases of depth, conductivity and width is shown in Fig. 4. In general, the results were identical to those from the experimental observations. According to the results, it was noticed that the uplift force was affected only by the ratio K/Ko, regardless of the

Fig. 3 Evaluation of Numerical Model for estimating uplift force and seepage. (a) uplift force, (b) seepage discharge.

conductivity value of the reference soil Ko. Therefore, the output value of F for (Ko = 1E2 and K = 1E7) was the same for (Ko = 1E6 and K = 1e11). Adding to that, the correlation between X/L and F/Fo was influenced by the other parameters as follows: For Fig. 4a; when the GVB located at the upstream half length of the floor, the uplift force decreased by increasing the depth or by decreasing either the width or the conductivity. These results were reversed at the half downstream part of the floor. Regarding to Fig. 4b; by plummeting K/Ko, the prementioned trend was obtained until a value of K/Ko = 1E4. Moreover, the variation of F/Fo versus X/L remained constant, even if K/Ko decreased. In addition, the curves of F/Fo versus X/L were approximately typical for K/Ko = 1E3, 1E4 and 1E5. According to the previous analysis, it can be concluded that the best position for the uplift force was at the upstream end of the floor. Therefore, for a GVB located at the upstream end of the floor, a set of curves was prepared to investigate the effect of the d/D, b/L and K/Ko on F/Fo, Fig. 5. As an overall trend, The F/Fo value slumped by increasing the depth or by reducing the width and the conductivity. The main individual and combined influence of these variables can be stated as follows:

Please cite this article in press as: M.A. Shousha et al., Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.01.013

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Fig. 4 Variation of uplift force with relative position. (a) b/L = 0.05, K/Ko = 1E4, (b) d/D = 0.4, b\L = 0.05, and (c) K/Ko = 1E4, d/D = 0.4.

Fig. 5a, shows a slight effect of d/D and b/L in condition of a higher value of the K/Ko, 1E1for example, while as K/Ko decreased  1E2, [Fig. 5b–e], the effect of d/D and b/L became more remarkable. On the one hand, for K/Ko = 1E1, the value of F/Fo decreased by (0–11%) due to the increase of d/D between (0.20–1.00). On the other hand, at K/Ko = 1E5, by soaring the d/D with the previous range, The F/Fo value fell up to (55%). By reducing the K/Ko, the uplift force ratio F/Fo witnessed a downward tendency until it reached a certain value of K/Ko = 1E4. After this value, the uplift force never changed even if K/Ko value declined. This was obvious in Fig. 5d (K/Ko = 1E4) or Fig. 5e (K/Ko = 1E5), where the curves of uplift force were identical for the same cases of b and d, and the curves of K/Ko = 1E3 Fig. 5c were too similar to them. In Fig. 5, increasing b/L ratio produced upward increase in the uplift force except for Fig. 5-1(K/Ko = 1E1) in which with b/L increasing, F/Fo decreased and then it increased again. This result can be more illustrated by Fig. 6, where Fig. 6a showed the uplift head (h) distribution at any distance (X’) from the upstream end of the floor for different b/L ratios. Fig. 6b represented the variation between the width for a GVB located at the upstream end of the floor and the uplift force. By increasing b/L ratio, the area under the curves of the uplift pressure went up. therefore, the uplift force recorded an upward trend. Thereupon, the increasing of the relative width affected negatively, except for the cases of a higher value of relative conductivity K/Ko = 1E1, Fig. 6b. Whereas, by increasing b/L value, F/Fo fell to an extreme value, and then

returned to increase again. This could be due to the use of small GVB’s with high permeability producing a measure of low resistance against the seepage under the floor. This resistance went up by increasing the width leading to F/Fo fall to an extreme value. However, by increasing b/L, the total uplift force raised due to increasing the area under the uplift pressure curves. As shown in Fig. 5 and Fig. 6b, all curves have a value of = 1.00 on the F/Fo axis at b/L = 1.00 for all values of the other variables. This means that the uplift force F was equal to its value in the reference case Fo (no additional effect due to the barrier) in the cases of b/L = 1.00 (the GVB width equal to the total length of the floor). This might be interpreted as: when b/L = 1.00 the GVB acted as a part of the floor, the total uplift force was transmitted through it to the structure floor. 5.3. The effects of GVB variables on seepage rate Fig. 7 presented the results of the seepage rate versus position. As seen, the results were fully compatible with those from the experimental work. It was obvious that at any position, the seepage rate decreased by increasing the depth or width, or by decreasing the conductivity. However, increasing the width had a positive non-significant effect. And it was noticed that had no additional effect due to the decrease of K/Ko at less than 1E4. For a GVB at the upstream end (best position for the minimum seepage discharge and the uplift force), the values of

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Effect of using grouted vertical barrier on seepage characteristics

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Fig. 5 Variation of uplift force with relative depth for GVB at upstream end of the floor. (a) K/Ko = 1E1, (b) K/Ko = 1E2, (c) K/ K0 = 1E3, (d) K/Ko = 1E4, and (e) K/Ko = 1E5.

relative seepage rate q/qo were plotted versus the relative depth for all cases of relative width and conductivity, as shown in Fig. 8. The statistical analysis showed that the main effect of each variable was highly significant. As for the conductivity effect, the seepage rate value (q) depends on both the Ko and the K/Ko ratio. The q value was changed by the same percentage of Ko change. As per Fig. 8 it was obvious that the seepage rate significantly falls by reducing the relative conductivity K/Ko. However, Fig. 8 and Fig. 9 showed also no additional effect, due to the reduce of K/Ko to less than 1E4 (typical). In case of the GVB fully penetrated the porous media under the floor (d/D = 1), the GVB was treated as completely impervious in case of K/Ko  1E4 only.

Increasing the relative width was non-significant in condition of K/Ko  1E3. On the contrary, the relative depth was always highly significant for all K/Ko values. For K/Ko = 1E3, Figs. 8c and 9, the maximum decrease in q/qo ratio between the two cases of b/L = 0.05 and 1.00 (higher and lower value of b/L) was about 10% in average. Conversely to that, the difference in q/qo ratio between the cases of d/D = 0.20 and 0.80 was within (42%). Therefore, it can be deduced that, the relative depth influence was more significant than other parameters, and that the relative width was the least significant one. On the other hand, for cases of K/Ko  1E3, the interaction effect between d/D and b/L was non-significant (P value = 0.61), because the percentage of q/qo decreasing

Please cite this article in press as: M.A. Shousha et al., Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.01.013

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M.A. Shousha et al. due to any increase of d/D is exactly the same for all different cases of b/L. 5.4. The effects of GVB variables on the exit gradient:

Fig. 6 Effect of the width on uplift force. (a) uplift head distribution for several cases of width, (b) variation of uplift force with relative width.

The maximum value of exit gradient (just after the floor downstream end) was plotted versus the relative position X/L as shown in Fig. 10. The exit gradient value decreased by moving the GVB under the floor from heal towards downstream toe until it reached the minimum value at the heal point. For any model of the GVB, the curves of the exit gradient versus position had a progressive slope at the second half of the curve (X/L > 0.50), whilst a tedious one was obtained during the first half length. The maximum difference between the highest and the lowest value of the relative exit gradient I/Io between the upstream end and the middle of the floor did not exceed 2.5%. Conversely, this difference of the I/Io value, between the middle and the downstream end, was nearly one third (up to 35.0%). A main conclusion at this point was that the position effect was highly significant when X/L > 0.5, and the best position for minimum exit gradient was at the downstream end of the floor. Evidently, all curves of X/L versus I/Io have the same trend in all cases. Meanwhile, at any position under the floor, the exit gradient signified a decline with a rising of the depth or width or by decreasing the conductivity. For a GVB barrier at the upstream end, the effect of the relative depth d/D, relative width b/L and relative conductivity K/Ko on exit gradient were investigated, as shown in Fig. 11.

Fig. 7 Variation of seepage rate with relative position. (a) K/Ko = 1E4, b/L = 0.05, (b) d/D = 0.4, K/Ko = 1E4, and (c) d/D = 0.4, b/L = 0.05.

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Effect of using grouted vertical barrier on seepage characteristics

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Fig. 8 Effect of relative depth, width and conductivity on seepage rate for GVB at upstream end of the floor. (a) K/Ko = 1E1), (b) K/Ko = 1E2, (c) K/Ko = 1E3, (d) K/Ko = 1E4 and (e) K/Ko = 1E5.

Considering a relative conductivity, the exit gradient was not affected by changing the Ko value. In another words, the same results were obtained for different models having the same K/Ko ratio, regardless of Ko value. By the same token, declining K/Ko to less than 1E4, did not produce any additional effect. The relative width b/L had a considerable effect on I/Io, especially for higher K/Ko values, 1E1 for example, as there was a difference in the I/Io ratio between cases of b/L = 0.05 and 1.00 within a range of (53–64) %. However, For K/Ko = 1E3 the max difference in I/Io ratio between two cases of b/L = 0.05 and 1.00 was (40.1, 33.8, 26.1, 20.5 and 5.4%) with respect to d/D = 0.20, 0.40, 0.60, 0.80 and 1.00. Regarding the relative, it had a significant effect in case of lower K/Ko ratios. The difference in I/Io ratio between d/D = 0.20 and 1.00 was within a range of (3–13) % in case

of 1E1. Meanwhile, the difference between cases: d/ D = 0.20 and 1.00 was (66.6, 65.8, 58.9, 49.1 and 31.9%) with respect to b/L = 0.05, 0.25, 0.50, 0.75 and 1.00. 6. Regression analysis Through regression analysis, F/Fo, q/qo and I/Io are expressed as a function of d/D, b/L and k/ko for a barrier at the upstream end of the floor. The regression analysis deduces several mathematical models of the independent variables. The criteria used to evaluate the prescient accuracy of the models were as per the following. Firstly, the better model to represent the data is the model that has higher coefficient of determination (R2) as high as possible and significant at the 95% confidence level. Secondly, each variable should have regression coefficient that significantly differ from zero. Table 1 shows

Please cite this article in press as: M.A. Shousha et al., Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.01.013

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M.A. Shousha et al. 1

K/Ko=1E-1 K/Ko=1E-2

0.9

K/Ko=1E-3 K/Ko=1E-4

0.8

q/qo

K/Ko=1E-5 0.7 0.6 0.5 0.4

0

0.2

0.4

0.6

0.8

1

b/L Fig. 9

Variation of seepage rate versus relative width for a GVB at upstream end.

Fig. 10 Variation of exit gradient with relative position. (a) K/Ko = 1E4, b/L = 0.05, (b) d/D = 0.4, b/L = 0.05 and (c) d/D = 0.4, K/Ko = 1E4.

the best-fit models for uplift force, seepage rate and exit gradient according to pre mentioned criteria. Note that ‘‘t” stands for the ‘‘t-test statistic”, which displayed the relative importance of each variable in the model, such as the higher ‘‘t” value, which had the greater contribu-

tion of the independent variables in the model. The best models can be written in equations as follows: F=Fo ¼ 0:4626 þ 0:5962 b=L  0:2258 d=D þ 1:6342 K=Ko ð3Þ

Please cite this article in press as: M.A. Shousha et al., Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.01.013

Effect of using grouted vertical barrier on seepage characteristics

11

Fig. 11 Effect of relative depth, width and conductivity on exit gradient for GVB at upstream end of the floor. (a) K/Ko = 1E1), (b) K/Ko = 1E2, (c) K/Ko = 1E3, (d) K/Ko = 1E4 and (e) K/Ko = 1E5.

Table 1

Results of the best achieved models for uplift force, seepage rate and exit gradient.

Model

Variable

Constant

b/L

d/D

K/Ko

R2

ANOVA (F)

F/Fo

Coefficient t Stat Coefficient t Stat Coefficient t Stat

0.4626 18.372 0.9243 44.107 0.7772 36.662

0.5962 22.858 0.1988 9.159 0.3312 15.083

0.2258 7.207 0.7131 27.354 0.5503 20.87

1.6342 7.206 2.1692 11.494 2.4202 12.677

0.84

208.8(1.17E47)

0.89

321.4(1.91E57)

0.87

274.5 (8.4E54)

q/qo I/Io

q=qo ¼ 0:9243  0:1988 b=L  0:7131 d=D þ 2:1692 K=Ko ð4Þ I=Io ¼ 0:7772  0:3312 b=L  0:5503 d=D þ 2:4202 K=Ko ð5Þ

The deduced coefficient of the determination of the best models for the uplift force (R2) was 0.84, for the seepage rate (R2) was to be equal to 0.89, and for the exit gradient (R2) was to be equal to 0.87. It was observed to be significant at a 95% confidence level, as the significance of the F statistic was less than 0.001. The hypothesis, that each of the coefficients was

Please cite this article in press as: M.A. Shousha et al., Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.01.013

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M.A. Shousha et al.

Fig. 12 Comparative effect of injected barrier and sheet pile on seepage characteristics. (a) Total uplift force, (b) Seepage rate, (c) Exit gradient.

not equal to zero, was accepted at the 95% confidence. The positive sign of the independent variables, which included the relative width for the uplift force and the relative conductivity for all the seepage characteristics, meant that the uplift force increased with relative width. Furthermore, as K/Ko increased, the seepage velocity and then all seepage characteristics increased as expected. However, the negative sign of the other independent variable such as: depth, and the relative width for each of the seepage rate and the exit gradient meant that these independent variables were conversely proportional to the mentioned seepage characteristics. Design engineers can use the previous equations to achieve a specific desired reduction in the seepage characteristics for safe seepage under hydraulic structures.

7. Comparative effect of GVB and sheet pile on the seepage characteristics A comparative numerical study between the effectiveness of a GVB and a sheet pile sheet pile having the same depths and positions presented in Fig. 12. The variables of the GVB was b/L = 0.05 and K/Ko = 1E4 (optimized parameters for minimum uplift force without negative effect on the seepage rate or the exit gradient). The GVB effect was represented by solid line curves and the sheet pile by dotted ones. The curves showed that the difference of means between the effect of the GVB and the sheet pile on reducing the seepage characteristics did not exceed 0.3%. Using the statistical analysis (t-test), it was shown that P-value equalled 0.49, 0.39 m and 0.41 for

Please cite this article in press as: M.A. Shousha et al., Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.01.013

Effect of using grouted vertical barrier on seepage characteristics

13 Fig. 13 shows the reduction in the seepage characteristics (DF/Fo, Dq/qo, DI/Io) due to the separate effect of the GVB and the upstream blanket. The comparison between the two effects signified that the GVB had a great influence on the seepage characteristics compared to that of the blanket’s effect. While the reduction of uplift force, the seepage rate and the exit gradient equalled 78, 64 and 74%, respectively. Concerning d/D = 0.80 and B/Lus = zero, about 59, 50, 53% reduction was obtained for the previous order of d/D = zero and B/ Lus = 0.80. In order to enumerate the combined effect of the GVB and the upstream blanket, the seepage characteristics were plotted versus the relative length of the upstream blanket for different relative depth of the GVB, (Fig. 14a–c). As an overall trend, the seepage characteristics were plunged by increasing the GVB depth or blanket’s length. Regarding the smaller values of B/Lus, the GVB depth had a notable effect on the seepage characteristics. This effect witnessed a dramatic decrease when B/Lus increased. For B/Lus = 0.20, the uplift force, the seepage rate and the exit gradient recorded a decrease of 34, 39 and 43%, respectively. This was because B/Lus elongated from 0.20 to 0.80. These percentages fell to 16, 18 and 21% regarding B/Lus = 0.80. Furthermore, the effect of upstream blanket was more remarkable at the d/D value equal 0.20 than 0.80. 9. Conclusion Experimental work and 2- D numerical analyses were performed to investigate the effect of the GVB on the seepage characteristics under the floor of a hydraulic structure. A competitive study between the GVB and both of the sheet pile and upstream blanket as a seepage control method was conducted. The main findings could be explained as follows:

Fig. 13 Comparative effect of injected barrier and upstream blanket on seepage characteristics. (a) Total uplift force, (b) Seepage rate, (c) Exit gradient.

the uplift force, the seepage rate, and the exit gradient, respectively. In other words, the difference between the effect of the GVB and sheet pile was non-significant. As a results, the GVB was preferable because it was much more cost-effectiveness [20] and it’s construction is easier than sheet pile especially for old constructed hydraulic structures which already exist and need seepage remedial and works. 8. A comparative and a combined effect of the GVB and the upstream blanket on the seepage characteristics In order to investigate the comparative effect between the GVB and the upstream blanket on the seepage characteristics, a study was done using the conducted parameters of a GVB located at upstream end of the floor, where b/L = 0.05, K/Ko = 1E4. The GVB’s depth (d) was modified to be equal to the variation of upstream blanket’s length (B). The tested values for both the relative depth of the GVB(d/D) and the relative length of the upstream blanket (B/Lus) were 0.20, 0.40, 0.60 and 0.80.

SEEP/W software can be used as a trusted tool on determine seepage characteristics under hydraulic structures for a several condition. The effect of the GVB position on the seepage rate was negligible, while this effect was significant on the uplift pressure and somewhat was considerable on the exit gradient. The uplift force increased when the GVB moved towards the downstream end. Therefore, it was better to be located at the upstream end of the floor. The maximum reduction in the uplift force and exit gradient, due to the decrease of relative permeability K/Ko, was obtained at a value of 1E4. Consequently, any decline of K/Ko less than this value had no additional effect on these seepage characteristics. Increasing the relative depth had a considerable effect on reducing the seepage characteristics; for b/L = 0.05 and K/Ko = 1E4, The reduction in the seepage characteristics, due to the variation of the relative depth from 0.2 to 1.0, reached 95% for the uplift force and 100% for the seepage rate and the exit gradient, respectively. Increasing the GVB’s width had a significant negative impact on the uplift force, but it had a slight positive one on the seepage rate and the exit gradient. The GVB was a good tool to control the seepage flow under the floor of a hydraulic structure, and the results revealed better effect of the GVB in reducing the seepage character-

Please cite this article in press as: M.A. Shousha et al., Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.01.013

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M.A. Shousha et al.

Fig. 14 Combined effect of injected barrier and upstream blanket on seepage characteristics. (a) Total uplift force, (b) Seepage rate, (c) Exit gradient.

Photo 1

Seepage tank apparatus and other devices.

Please cite this article in press as: M.A. Shousha et al., Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures, Alexandria Eng. J. (2020), https://doi.org/10.1016/j.aej.2020.01.013

Effect of using grouted vertical barrier on seepage characteristics istics compared to the sheet pile. In addition, the GVB was more economic than the sheet pile. A comparative study was conducted to evaluate the different impact of the GVB and the upstream blanket. The results showed the effectiveness of the GVB in reducing the seepage characteristics by 50% compared to a reduction of 30% by the upstream blanket.

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