Block ramps for stream power attenuation in gravel-bed streams: a review

Application of block ramp technique in steep gradient streams for energy dissipation as well as to maintain river stability finds increasing favor amongst researchers and practitioners in river engineering. This paper dwells on a comprehensive state-of-the-art review of flow resistance, energy dissipation,flow characteristics, stability, and drag force on block ramp by various investigators in the past. The forms and equations for each type are thoroughly discussed with the objective of finding the grey areas and gaps. While, more research is warranted further to improve the equations, essential for design analysis. Block ramps can be a promising simple technique to achieve reasonable attenuation of devastating fluvial forces unleashed in gravel-bed streams during cloud bursts.


INTRODUCTION
scour length for uniform and non-uniform sand. Moreover, They found that rock sill performed better than other types of sills for scour minimization. Besides this sediment transport over block ramp has also effect on bed morphology and energy dissipation which was later investigated by Pagliara et al. (a, b).

CLASSIFICATION OF BLOCK RAMP
Depending on the morphological structure and configuration of macro roughness elements, block ramps are classified into two groups, i.e., type A (block carpet) and type B (block cluster). Type A consists of tightly packed blocks covering the entire width of the river. It may be one layer or more than one layer. One layer of blocks interlocked with each other leading to a compact form called as interlocked block ramp. When blocks are arranged in two or more than two layers leading to heavier and more heterogeneous construction then such block ramp is known as dumped blocks. With both types of block ramps, a filter layer should be provided against washout effects (DWA ). Block carpet can be provided up to slope S ¼ 10% (Bezzola ). However, they are investigated up to bed slope S ¼ 40% slope (Robinson et al. ). Type B are characterized by dispersed configuration leading to more natural condition. In this, blocks are either arranged in row and arches (systematic way) or randomly placed. It consists of three types of block ramps. They are Structured blocks, Unstructured blocks and self-structured blocks.
Structured and unstructured blocks are isolated with each other. Structured blocks are characterized by systematic arrangements of blocks in row or staggered form and blocks are isolated with each other leading to more heterogeneous form. The maximum slope for structured block ramp is 6.7% (LUBW ) and maximum slope for unstructured block ramp (UBR) is 3% ( Janisch ). Self-structured blocks ramps get formed due to natural hydraulic load occurring on the ramp after long time. The ramp slope ranges for self-structured block ramp is 5% to 13% (Lange ). The morphological and structural classification of block ramp is shown in Figure 1.

FLOW RESISTANCE
Knowledge of mean velocity is of primary importance in river engineering. Flow velocity can be directly measured by using velocity measuring instrument or using continuity where u * is shear velocity ¼ ffiffiffiffiffiffiffiffi ghS p , Keulegan () proposed k s by using it equivalent to median diameter (D 50 where n a ¼ 0.87(sinα) 0:09 and sin α ¼ bed slope, q ¼ specific discharge, g ¼ acceleration due gravity.
Whatever approach used to derive flow resistance Equation, It is found that flow resistance equation is more reliable on type of flow condition for which depth of flow or hydraulic radius is larger compared to bed roughness. given geometrical and hydraulic conditions. Hence, Equation (7) is not valid for larger value of block concentration (Г >30%-35%).  (7) and finally, they proposed the following relation.
The flow resistance Equation (9)  Some of the widely used flow resistance equations for block ramp is briefly presented in Table 1 with their application range.

ENERGY DISSIPATION ON BLOCK RAMPS
The energy head at the ramp head is H 1 ¼ H þ1.5 h c , where 1.5 h c is the specific energy at a critical depth (at the head of a ramp), and at toe is H 2 ¼ h þ q 2 /(2gh 2 ), specific energy at toe. So, the relative energy dissipation is given as ΔH r ¼ ΔH/ the toe of a smooth ramp chute as, where ΔH r is relative energy dissipation, h u ¼ uniform flow They found that the form of Equation (16), however, doesn't fit the experimental data well, especially for smooth ramp, and finally, they suggested the following relationship.  Figure 4(a), they ¼ 2:21 ln(h=d 84 ) þ 6:00 (11) It is applicable for block ramps of type A with dumped blocks. Valid for bed slope 2.8% < S< 33% and median rock diameter 52 D 50 278 (mm) Derived for crossbar block ramps with boulder height of crossbars as D B . It is valid for relative submergences 1.5 < h/D B < 4 and for tested ramp slopes 2% < S < 10% also found that relative energy dissipation decreases with an increase in slope keeping roughness constant. So, Energy dissipation is also a function of the slope of ramp. Figure 4 shows relative energy dissipation as a function of h c /H obtained by various investigators.
Pagliara & Chiavaccini (b) extended the energy dissipation mechanism to structured and unstructured block ramps, and proposed a relation same as Equation (17) in which block concentration Γ was introduced.  used for ramps without boulders by substuting Г ¼ 0, Here E and F are two parameters that are functions of arrangement and roughness of blocks which are given in Tables 3 and 4.
where, L R is length of ramp, a 1 , a 2 , a 3 are coefficient whose values are tabulated below and rest of all are same as discussed above.The above Equation is applicable for They are h c /H, ramp scale roughness and the ramp submergence condition. The effect of ramp slope can be considered negligible for relative energy dissipation for same scale roughness and ramp submergence condition (L j /L R ) as shown in Figure 6.
Which is valid for range: 0< L j /L R < 0.7, 0.1 < h c /H<        So, there is variability in both turbulence intensity as well as time averaged velocity which is positive in terms of hydraulic heterogeneity and ecological aspects.
Though the time-averaged velocity were found to be heterogeneously distributed throughout the length of the ramp but the double averaged (averaged both in time and space) velocity u profile is found to be almost uniform distribution as shown in Figure 9.  buyout and gravity force) acting on sediment particle resting on streamwise bed slope given by, where, τ cθ is the critical shear stress on the sloping bed of angle θ, τ co ¼ critical shear stress on horizontal bed and ϕ is friction angle of sediment. However, mountain stream is characterized by low value of relative submergence and steep bed slope of large scale roughness. So, Shields approach is not suitable for mountain streams.
Later on Aguirre-Pe & Fuentes () put forth their concept that critical shear stress doesn't represent the condition for initiation of sediment motion in steep macroroughness stream(S! 0:005 and h/d 10). Aguirre-Pe et al.
() suggested a relationship for sediment entrainment in terms of critical particle densimetric Froude number given as, Which is valid for 0.02 < S < 0.065 ; 0.02< h/d 50 < 30 But for field engineers it would be worth to express failure criteria in terms of critical specific design discharge rather than critical particle densimetric Froude number.
Whittaker & Jäggi () investigated stability of block carpet type block ramp with different block diameter, bed material, characteristics grain size, bed slope and different ramp length.
They suggested a relationship between critical specific discharge q cr , bed slope S and block diameter D 65 for the determination of stability of block ramps of block carpet (type A) with dumped blocks.
where S ¼ bed slope, G ¼ specific gravity of block ¼ ρ s ρ w ¼ 2.65 and D 65 ¼ block diameter for which 65% of mixture is finer, ρ s is density of block and ρ w is density of water.
Hartung and Scheuerlein, 66 suggested a relationship for block ramp type A with interlocked blocks in terms of critical velocity u cr : where u cr ¼ critical flow velocity, D B ¼ equivalent block diameter and other terms are same as defined above.
where, D 50 ¼ is the median size of blocks, S ¼ slope of ramp. In this experiment, the investigated chutes were made of layers of thickness 2D 50 placed over geotextile as filter medium.
According to Aberle () the stability of block cluster type is determined with q cr ¼ 0:062 S À 1:11 It has the same structure as Equation (25) where q c is critical failure discharge of reinforced chutes and q co is one for base chutes and Γ is block concentration as discussed above. Pagliara & Chiavaccini (2007)  They combined experimental results with Equation (7) (flow resistance estimation for block ramp with protruding boulders) and definition of densimetric Froude number, obtained following relation for critical particle densimetric Froude number as, where a 1 depends on blocks disposition : a 1 ¼ -2.2 for rows, a 1 ¼ -2.0 for random, a 1 ¼ -2.6 for arc and a 1 ¼ -2.6 and À2.8 for two different reinforced arc types configurations.
The dependency of Equation (30)  17. Generally in mountain river, characteristics size of river bed material is taken as d xx ¼ d 90 (Janisch et al. 2007 where q d Ã ¼ Dimensionless specific discharge, They also parametrized dimensionless specific discharge with D/d 90, Г, D, and q which is given as,   Figure 11(a).
The configuration was chosen in a such a way to experience boulder interaction process to determine forces and drag coefficients. They related drag coefficient with Reynolds number. The variation of drag coefficient versus Reynolds number is shown in Figure 11(b).
For single boulder cube, C d shows quasilinear dependency on the Reynolds number as shown in Figure 12  represented by Equation (36). It shows coefficient of drag C d increases for decrease in Reynolds number.
Similarly, it follows for single cylindrical boulder shape but having lower drag coefficient than cube shape. In this case, For three cubical boulders in different rows, the upstream boulder gets lower value of C d due to backwater effect offered by downstream boulders.
C d ¼ À3:5 × 10 À6 R þ 1:6 (38) But for six boulder arranged in different row as shown in Figure 11(a) it shows, C d varies in a quadratic fashion with Reynolds number.
C d ¼ À3:4 × 10 À 11 R 2 þ 8:0 × 10 À6 R þ 1:4 (39) C d ¼ À4:9 × 10 À 11 R 2 þ 1:2 × 10 À5 R þ 0:8 Equation (39) and (40) is for downstream outer and middle boulder in third row respectively. The variations of C d and R, both are shown in Figure 11(b). The drag coefficient for outer boulder of third row is higher than middle one boulder of same row. It is due to fact that the upstream boulder bifurcates main flow towards downstream outer boulder causing to increase in drag coefficient of outer boulder and decrease in drag coefficient for middle boulder.
The interaction process decreases drag coefficient of upstream boulder. Interaction process becomes negligible When the distance between each boulder is increased causing to reduce drag coefficient as represented by Equation (41).

FURTHER RESEARCH NEEDS
A comprehensive review is presented on experimental studies relating to different configurations of block ramps covering various design aspects such as flow resistance, energy dissipation, stability and drag coefficient of block ramp as well as its flow characteristics done by various investigators in the past. The forms and equations for estimating each of these aspects are also presented in detail.
While more research is warranted for further improving the equations essential for design analysis. The major grey areas and gaps which could enhance the future research are as follows.
• 3-Dimensional turbulence burst analysis using modified 3-D Reynolds Stress approach using all the three fluctuating instantaneous velocity components u 0 , v 0 , w 0 around blocks to improve the understanding on internal mechanism of turbulent flow structure which is primarily responsible for energy dissipation. Present reported research on turbulent analysis is based on 2-D Reynolds stress concept, where as in reality turbulent bursts occurrence is 3-Dimensional. The positive end product from this research foray will significantly enhance the prediction of residual energy from block ramps much more realistically leading to their better design.
• Even though block ramp technology is used mostly in mountainous torrents carrying highly non-uniform bed and suspended sediment load in episodic transport mode, hardly any research is reported on this vital issue. In this respect, innovative research design is awaited for a skillful interaction between the fluvial processes of 3-Dimensional turbulent bursts on ejection and sweep attributes with sediment transport modes of entrainment, transport and deposition for episodic flow regime.
• Since block ramp application in primarily hilly torrents is made in a highly turbulent flow conditions with rapidly varied unsteady flow regime, the present day formulations are based on assumption of steady flow condition. This steady flow assumption superimposed on 2-D Reynolds stress simplification has obviously introduces probably great deal of error with regard to actual energy loss estimation in the design of block ramps.

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