# Field Investigation on Hydroabrasion in High-Speed Sediment-Laden Flows at Sediment Bypass Tunnels

^{1}

^{2}

^{*}

## Abstract

**:**

_{v}of different abrasion models for high-strength concrete and granite. The results reveal that these models are useful to estimate spatially averaged abrasion rates. The k

_{v}‑value is about one order of magnitude higher for granite than for high-strength concrete, hence, using material-specific abrasion coefficients enhances the prediction accuracy. Three-dimensional flow structures, i.e., secondary currents occurring both, in the straight and curved sections of the tunnels cause incision channels, while also longitudinally undulating abrasion patterns were observed. Furthermore, hydroabrasion concentrated along joints and protruding edges. The maximum abrasion depths were roughly twice the mean abrasion depths, irrespective of hydraulics, sediment transport conditions and invert material.

## 1. Introduction

_{r}= vertical abrasion rate, Y

_{M}= Young’s modulus of the abraded material, k

_{v}= dimensionless resistance coefficient, also termed abrasion coefficient, f

_{st}= splitting tensile strength of the abraded material, W

_{im}= mean vertical particle impact velocity, L

_{P}= particle hop length, q

_{s}= specific gravimetric bedload transport rate and q

_{s}

^{*}= specific gravimetric bedload transport capacity. The term f

_{st}

^{2}/Y

_{M}is related to the fracture energy required to detach a unit volume from the base material, while k

_{v}accounts for the efficiency of energy transfer from impinging particles to the invert material. The second term of Equation (1) is the flux of kinetic impact energy per unit area and time. The last term in parentheses accounts for the cover effect considering transient alluvial deposits hindering bedload particle impacts and, hence, bedrock incision. The application of particle motion equations, developed from a wide range of data from literature (including fixed and movable beds, and subcritical as well as supercritical flow conditions), has led to the following form of the SAM [21]:

_{s}/ρ = 2.65 = ratio of solid to water density, T* = (θ/θ

_{c}− 1) = excess transport stage, θ = U

^{*2}/((s − 1)gd) = Shields parameter, θ

_{c}= critical Shields parameter, U

^{*}= (g·R

_{h}·S

_{e})

^{1/2}= friction velocity, V

_{s}= particle settling velocity, d = particle diameter, R

_{h}= hydraulic radius and S

_{e}= energy slope. The excess transport stage accounts for the threshold of particle motion, whereas the last term relates to the mode shift from saltation to suspension.

_{v}is yet a challenging issue of ongoing research. The k

_{v}-values were determined for various materials by using a self-developed abrasion mill set-up resulting in the widely accepted value of k

_{v}= 10

^{6}for rock, despite large variations of k

_{v}= 1 × 10

^{6}–9 × 10

^{6}[21,37]. Variations in k

_{v}values are expected since [21] treated Y

_{M}as a constant, i.e., Y

_{M}= 50 GPa, which is a rough simplification regarding the large range of Y

_{M}for rocks and concretes. Moreover, the properties of the impinging sediment, e.g., size, angularity and hardness, and of the abraded material, e.g., Young’s modulus, splitting tensile strength, density, porosity and crystal and clast size, which significantly affect hydroabrasion, are only partly accounted for in the SAM [19,38,39,40,41,42,43,44].

_{v}was determined for a range of materials based on laboratory, field and literature data [21,23,26,32,47]. The authors reported that k

_{v}increases with the invert material’s splitting tensile strength and tends to stabilize at k

_{v}≈ 10

^{5}for hard materials, such as rock and concrete with f

_{st}> 1 MPa.

_{v}. More field data not subjected to potential laboratory scale and model effects are needed to advance knowledge on the governing processes of hydroabrasion and to validate k

_{v}-values [44]. To this end, we investigated hydroabrasion at two Swiss SBTs by testing various concretes and granite under field conditions for a period of 4 and 19 years [48,49]. The hydraulics and sediment transport conditions and hence the hydroabrasion processes in SBTs and high-gradient bedrock rivers are similar. Consequently, the findings of the present investigation also apply to bedrock incision and landscape evolution processes, although the incision rates are generally several orders of magnitude smaller due to considerable lower erosive potential [42].

## 2. Field Sites and Data Acquisition

#### 2.1. Pfaffensprung

^{2}Urner Granite blocks placed in a staggered order without joints (accuracy ± 2 mm) and a 0.3 m thick high-strength concrete section. Although the concrete mixtures are identical (except for steel fibers included in C1, but not in C2 due to their negative effect on the processability) their properties differ due to varying site conditions during construction (Table 2). The quarry provided the compressive strength f

_{c}, splitting tensile strength f

_{st}and elastic Young’s modulus Y

_{M}for granite (Table 2). The compressive strength and density of the high-strength concretes were determined using 28 days old cube (150 mm × 150 mm × 150 mm) and drill core (100 mm × 100 mm) samples. The bending tensile strength f

_{bt}was determined by testing beam samples (120 mm × 120 mm × 360 mm). The compressive strength and the cylindrical compressive strength f

_{c}

_{,}

_{cyl}are related [54], as follows:

_{1}= 1.005 for river gravel aggregate, k

_{2}= 0.95 for silica fume addition, ρ

^{*}= reference concrete density = 2.4 to/m

^{3}and f

^{*}= reference concrete compressive strength = 60 MPa holding for concretes with f

_{c}

_{,}

_{cyl}= 40–160 MPa.

^{8}measurement points, being the limit for data analysis. The first (reference) surface scan was performed after installation of the test fields. The subsequent scans followed every winter during the low flow season. The scan resolution in horizontal and vertical direction was 0.036°. The measurement errors stem from possible shifts of the target bolts, the target-based registration of the TLS scans and the errors of the laser beam. The error of each measurement point is ±3.3 mm and is smaller for abrasion depth calculation over large spatial scales due to averaging.

#### 2.2. Runcahez

_{d}= 110 m

^{3}/s under free-surface flow conditions, it can still bypass a maximum discharge of Q

_{max}= 190 m

^{3}/s under pressurized inflow conditions [57].

_{c}of the tested invert materials was determined from cube samples (120 mm × 120 mm × 120 mm) and the bending tensile strengths f

_{bt}and elastic Young’s modulus Y

_{M}from beam samples (120 mm × 120 mm × 360 mm) [18]. The splitting tensile strength was derived from the bending tensile strength according to Equation (5). Table 2 summarizes the material properties. Note that the roller compacted concrete (RCC) suffered massive abrasion along the tunnel walls due to improper compaction and required a replacement after 1999.

^{3}/s lasting for more than 2.5 h, since no measurement data of the operation are available [48].

_{m}. Therefore, the 19 years data set (considering only the initial measurement in 1996 and the one after 19 years in 2014) was considered as the most significant and representative one and hence, was used herein to compute the abrasion coefficient k

_{v}. For the RCC test field, only the four years data of the properly compacted zone were used (only considering the initial measurement in 1996 and the one after four years in 1999).

## 3. Methods

#### 3.1. Hydraulics

_{e}= S and the hydraulic radius R

_{h}follows from the continuity equation. The river bed roughness k

_{St}follows from the 90-percentile particle diameter of the river bed material d

_{90}[58]:

_{s}and the Reynolds number R = 4UR

_{h}/ν, with ν = kinematic viscosity [59]:

_{s}= 0.003 m, was obtained from back-water calculations for design discharge and respective flow depths and corresponds to typical values for rough concrete [60].

#### 3.2. Bedload Transport and Particle Motion

_{c}[61]. Numerous studies have been conducted on the initiation of bedload transport resulting in a variety of critical Shields number due to different test conditions and definitions of initiation of particle motion [62]. In the present study, θ

_{c}= 0.047 for movable beds in rivers according to [63] and θ

_{c}= 0.005 for SBTs exhibiting planar beds of low relative roughness with k

_{s}<< d according to [45] were selected. At both case study sites, the rivers exhibit an armor layer, protecting the substrate due to its higher resistance against erosion [48]. This was accounted for by adapting θ

_{c}based on the mean grain size of both, the armor layer d

_{m,a}≈ 0.30 m and the substrate d

_{m,s}= d

_{m}[64]:

_{s}

^{*}in the river are applied herein. The first one is a simplification of an implicit probability function for bedload transport [65] and was published by Parker [66]:

_{c}, depending on the bed slope and the angle of repose φ of the sediment particles:

_{90}/d

_{30})

^{0.2}in Equation (13) is weak, so that it can be replaced by 1.05. The last applied equation published by Cheng [68] is based on literature data for S = 0.0013–0.19 [63,69,70] and follows for θ ≥ θ

_{c}:

_{S}according to [73]:

_{r}= 1 = macro roughness factor for moderate roughness. To avoid bedload transport overestimation due to energy dissipation in the rivers, a reduced slope correction S′ (Equation (16)) was used in Equation (13) instead of S

_{e}and a slope corrected Shields parameter θ

_{S}(Equation (17)) instead of θ was used in Equations (12) and (15).

_{s}in the Reuss was computed using the relation q

_{s}/q

_{s}

^{*}= 0.80 according to [74]. This approach was validated based on a former comprehensive study of the bedload transport in the Reuss River including a numerical investigation as well as extensive field surveys [74,75,76].

_{s}/q

_{s}

^{*}= 0.45 according to [18]. The result was validated by means of literature data [18] and morphologic field surveys including gravel excavation volumes [48].

_{s}/d << 0.1 and non-movable planar bed conditions [67]. For SBTs with slopes of S = 0.01–0.04, [23] proposed the following empirical formula for the gravimetric bedload transport capacity:

_{R}and particle hop length L

_{P}are given with [45]:

_{su}can be defined as [78]:

#### 3.3. Hydroabrasion

_{m}(obtained from discrete surface measurements by either a TLS or geodetic levelling) were computed. In a second step, mean abrasion rates A

_{r}were calculated by dividing spatially averaged abrasion depths a

_{m}with the corresponding SBT operation durations T. Furthermore, the 95%-percentile abrasion depths, herein denoted as maximum abrasion depths a

_{max}, were determined. This parameter is assumed to be decisive for design service life analysis and economical investigations of hydraulic structures.

#### 3.4. Model Calibration

_{s}= particle settling velocity according to [79]:

_{v}was calibrated based on the present field data for the (i) SAM assuming a constant Young’s modulus Y

_{M}= 50 GPa, (ii) SAM using the effective Young’s moduli (SAM

^{*}) and (iii) SAMA also accounting for the effective Young’s moduli.

^{3}. The specific gravimetric bedload transport in the SBTs follows from the cumulative bedload mass, the operation duration and the SBT widths with q

_{s}= BL/(b·T). The sediment transport capacity and particle settling velocity in the SBTs follow from Equations (19) and (25) using the averaged hydraulic parameters listed in Table 3, Table 4 and Table 5 for the corresponding period. The invert material properties used for the determination of the abrasion coefficients are given in Table 2.

## 4. Results

#### 4.1. Pfaffensprung

_{SBT}= 32.1 m

^{3}/s, the corresponding mean flow depth, flow velocity and Shields parameter in the SBT were $\overline{h}$ = 0.75 m, $\overline{U}$ = 9.79 m/s and $\overline{\theta}$ = 0.040, respectively.

_{c}′ = 0.049 (Equation (11)), which is in agreement with literature data [63,80,81]. The corresponding critical discharge for initiation of bedload transport amounts to Q

_{c}= 38 m

^{3}/s. The discharge in the river never exceeded the design discharge capacity of the SBT during the observation period from 2012 to 2015, so that the entire bedload mass supplied by the river was assumed to be bypassed (Table 4). Thereby, the transport capacity in the SBT was always considerably larger compared to that of the river so that no depositions in the SBT are expected to have taken place. This is in line with the operator’s experiences confirming no significant accumulations in the reservoir as well as in the SBT. The rolling and suspension probability of the mean particle size d

_{m}are P

_{R}= 0.30 (Equation (20)) and P

_{su}= 0.00 (Equation (22)), respectively. The saltation probability follows with P

_{sal}= 1 − P

_{R}− P

_{su}= 0.70 indicating that saltation was the dominating, rolling the minor transport mode. The corresponding particle hop length amounts to L

_{p}= 2.70 m (Equation (21)).

_{w}= 1.25 ± 0.6 m. Furthermore, a significant abrasion concentration on the orographic right side is visible and clearly shown by the super-elevated longitudinally averaged cross-sectional abrasion profiles in Figure 9. The abrasion depths of both high-strength concretes C1 and C2 were considerably higher after the first year compared to subsequent years. However, the shape of the abrasion profiles observed after the first year of operation were conserved during the following years with a slight trend of amplification.

#### 4.2. Runcahez

_{SBT}= 56 m

^{3}/s. The corresponding mean flow depth, flow velocity and Shields parameter were $\overline{h}$ = 2.0 m, $\overline{U}$ = 7.4 m/s and $\overline{\theta}$ = 0.036, respectively.

_{c}′ = 0.058, which is in agreement with literature data [63,80,81]. The corresponding critical discharge for the initiation of motion is Q

_{c}= 33 m

^{3}/s.

_{s}

^{*}= 0.50 to/s and is thus significantly larger than the corresponding bedload transport capacity of the Rein da Sumvitg River of Q

_{s}

^{*}= 0.08 to/s. As a result, no depositions in the SBT occurred. This was confirmed by the operator’s experiences revealing no depositions in the SBT. Table 5 lists the bypassed bedload masses for the years 1996–1999 and 2000–2014.

_{R}= 0.33 (Equation (20)) and P

_{su}= 0.00 (Equation (22)), respectively. This results in a saltation probability of P

_{sal}= 1 − P

_{R}− P

_{su}= 0.67 indicating that particles were mainly transported in saltation. The computed particle hop length of the mean particle size amounts to L

_{p}= 2.3 m (Equation (21)).

_{w}= 2.5 ± 0.5 m and with two incision channels along the tunnel walls. The temporal evolution of these channels is seen in the longitudinally averaged cross-sectional profiles of the SC test field (Figure 12). The incision channels developed close to the tunnel walls and grew both, in depth and width over time. Furthermore, the abrasion profile is asymmetric. The abrasion depths on the orographic left side are higher than on the right side.

_{max}/a

_{m}= 1.6 and 2.2 at the end of the observation period.

#### 4.3. Abrasion Model Calibration

_{v}-values based on the field data are plotted as a function of the corresponding material splitting tensile strengths in Figure 14. Irrespective of the model, the resulting data scatter is comparable, whereas the results of the SAMA are generally one order of magnitude smaller compared to those of the SAM and SAM

^{*}. Furthermore, a strong material dependency is evident. The k

_{v}-values determined for different types of concrete are similar, except for the polymer concrete (PC) and fluctuate around k

_{v}= 1.3 × 10

^{6}for the SAM, k

_{v}= 8.8 × 10

^{5}for the SAM

^{*}and k

_{v}= 1.9 × 10

^{5}for the SAMA, respectively. The k

_{v}-values of granite are k

_{v}= 1.4 × 10

^{7}for the SAM, k

_{v}= 1.6 × 10

^{7}for the SAM

^{*}and k

_{v}= 2.4 × 10

^{6}for the SAMA, hence being roughly one order of magnitude higher than those of the concretes.

## 5. Discussion

#### 5.1. Abrasion Pattern

_{w}= 2.5 ± 0.5 m roughly scales with the mean computed particle hop length of L

_{P}= 2.28 m, whereas in the Pfaffensprung SBT λ

_{w}= 1.25 ± 0.6 m is approximately half the computed particle hop length of L

_{P}= 2.70 m. The discharge at which the mean particle hop length is L

_{P}= 1.25 m amounts to Q ≈ 12 m

^{3}/s, which was frequently exceeded in the SBT, i.e., for 30 to 90 days per year between 2012 and 2015. A relation between particle motion and abrasion pattern is thus plausible. On the one hand, the observed variations of the abrasion wavelength could stem from the considerably fluctuating hydraulics and sediment transport conditions in the Pfaffensprung SBT (flow depths varying from a few centimeters to some meters and size of particles in motion varying between submillimeter to meter range), causing significant variations in particle hop length. On the other hand, these variations could result from a superposition of different abrasion patterns reducing the observed abrasion wavelength. In order to clarify possible relationships between bedload particle transport mode and abrasion pattern, further systematic investigations are needed. A comparable undulating abrasion pattern was not observed for the granite pavement in the Pfaffensprung SBT, which might be attributed to the fact that abrasion concentrations along the joints are orders of magnitude higher compared to those of the large-area invert and hence make the latter unrecognizable.

_{max}/a

_{m}= 1.6–2.2. This agrees with literature data on mortar abrasion obtained from physical scale model tests of [23]. The detected asymmetric abrasion profiles in the Pfaffensprung and Runcahez SBTs (Figure 9 and Figure 12) are in line with field surveys in other SBTs revealing the formation of an incision channel along the inner side of a bend and further downstream of the bend [48,87,88]. These incisions are attributed to Prandtl’s first type of secondary currents [85]. Such currents cause high bed shear stresses and hence bedload transport concentration at the inner side of the bend leading to an incision channel. This channel, in return, stabilizes the spiral flow and promotes bedload transport concentrations in this topographic depression due to gravity [89], resulting in a self-intensifying process. The effect of Prandtl’s first type of secondary currents is still visible downstream of a bend in the Pfaffensprung SBT, but gradually re-distributes across the tunnel width downstream of the bend.

#### 5.2. Abrasion Model Calibration

_{v}varies significantly for the different abrasion models, as shown in Figure 14, due to different particle trajectories and particle impact equations implied in those models. The k

_{v}-values of the SAMA are generally one order of magnitude smaller than those of the SAM [44]. There is a considerable data scatter in the abrasion coefficient k

_{v}. Accounting for the effective Young’s modulus in the SAM

^{*}did not reduce this data scatter. Instead, other uncertainties and errors dominate the model accuracy, such as (i) the determination of representative hydraulic conditions; (ii) the abrasion measurement errors (±3.3 mm and ±2.0 mm for TLS and geodetic leveling, respectively); (iii) spatial variations of the invert material bending tensile strength (on average = ±10%) and the uncertainty of Equation (5) (±6% according to [51]), both used for computing splitting tensile strength; (iv) the uncertainty of Equation (6) applied for computing invert material Young’s modulus (±5 GPa according to [56]); (v) the uncertainty of representative sediment particle size (assumed to ±20%); and (vi) the estimation error of sediment transport rates (assumed to ±50%). Following error propagation, these uncertainties result in a relative error for k

_{v}of σ

_{r}≈ 87% for the SAM and SAM

^{*}and σ

_{r}≈ 91% for the SAMA on average. Despite this, the present values are in good agreement with literature data for high-strength concrete as well as for granite. For concrete, both k

_{v}= 10

^{6}proposed by [21,37] for the SAM and k

_{v}= 1.9 × 10

^{5}proposed by [44] for the SAMA were confirmed herein with k

_{v}= 1.3 × 10

^{6}and k

_{v}= 1.9 × 10

^{5}, respectively. Furthermore, k

_{v}= 1.4 × 10

^{7}for granite is in line with k

_{v}≈ 10

^{7}proposed by [21,37] for hard rocks such as granite, quartzite and marble. Therefore, the obtained values listed in Table 6 are realistic and can be used in a first step for long-term abrasion prediction of brittle materials.

_{v}-values from the present prototype data and from literature data [21,23,32,36,39,44,47,94] are plotted in Figure 15 for the SAMA as a function of splitting tensile strength. A general trend of increasing k

_{v}with increasing f

_{st}, in agreement with [44], is evident indicating that abrasion rates decrease with increasing splitting tensile strength. However, the stabilization of k

_{v}≈ 10

^{5}for hard materials at f

_{st}> 1 MPa as revealed by [44] is not identified. The data from [36,94] considerably deviate from the general trend. The computed k

_{v}-values of the foams tested by [36] are significantly lower compared to the other materials because of the considerably lower Young’s moduli of Y

_{M}= 3.9–330 MPa and densities ρ

_{c}= 87–960 kg/m

^{3}. Note that the latter is not included in the mechanistic abrasion models, although presumed to also affect hydroabrasion [36,40,41,42]. The field study of [94] was conducted in a weir stilling basin, presumably retaining sediments in a recirculating flow field. As a result, the same sediments repeatedly impacted the invert [95], resulting in a bias of k

_{v}towards lower values. Omitting the k

_{v}-values of [36,94] due to different properties of invert materials and the non-representative test set-up, respectively, significantly reduces the data scatter. Furthermore, Figure 15 displays a certain material-dependency. The highest k

_{v}-values were obtained for rock, followed by concrete and mortar/soft rock. The values for concrete (denoted by circular symbols) are roughly one order of magnitude smaller than those for hard rocks, such as granite, quartzite and marble. This implies that the abrasion resistance of concrete is roughly one order of magnitude lower compared to that of hard rocks. The value for the polymer concrete (PC) is significantly lower (Figure 14) likely due to the polymer matrix, which increases the material ductility. As a result, the mechanistic saltation abrasion model developed for brittle materials is not suitable for predicting the abrasion behavior of such relatively ductile concretes. Therefore, the PC was not considered herein for model calibration.

_{v}-values derived from laboratory and prototype data are in a similar range. This is a promising result indicating that there are no major scale effects and the mechanistic saltation abrasion models are applicable to both, laboratory and prototype scale.

_{v}-values originates not only from measurement errors and input parameter uncertainties, but also from model uncertainties. Hydroabrasion depends on the abrasiveness of the sediment (e.g., hardness and shape [96,97,98,99,100]) on the loading side and on various invert material parameters (e.g., density, porosity, crystal and clast size [36,40,41,42], or the characteristic length introduced by [101]) on the material resistance side. These parameters are either inadequately or not at all accounted for in the models discussed herein, which also contributes to the significant data scatter. Furthermore, the simplification of T

^{*}

^{0.78}≈ T

^{*}

^{0.8}of [44] (in Equation (3)) presumes that the excess transport stage T

^{*}has no effect on abrasion, as already stated by [22,32,47]. A reason for this might be the fact that increasing flow velocity results on the one hand in higher particle impact velocities and increased specific energy transfer, but on the other hand, in lower impact angle and longer particle hop length, which in return reduce the specific energy transfer [44]. This might apply for small excess transport stages. However, the negligence of the excess transport stage in the SAMA might be questioned in particular for high excess transport stages. In SBTs, the excess transport stage can reach T

^{*}≈ 100, so that the term T

^{*}

^{0.78}/T

^{*}

^{0.8}becomes 100

^{−0.02}≈ 0.9. This value and also its effect on the abrasion rate is probably non-negligible. Measurement of the bedload transport through the SBTs, e.g., by using a Swiss plate geophone system, is strongly recommended to reduce the unavoidable uncertainty of bedload transport estimation [14,34,48]. Furthermore, additional comprehensive laboratory studies, as performed by [102] and field studies, as presented herein, are needed to further enhance the model prediction accuracy and to clarify the effects of (i) excess transport stage; (ii) invert material properties other than Young’s modulus and splitting tensile strength; and (iii) sediment properties on the abrasion rate.

## 6. Conclusions and Outlook

_{v}is material-dependent and roughly an order of magnitude higher for granite than for high-strength concrete. (IV) The abrasion resistance of granite with f

_{c}= 240–280 MPa is roughly six times higher than that of high-strength concrete with f

_{c}= 75–110 MPa despite little variations in splitting tensile strength and elastic Young’s modulus.

_{v}-value proposed by [21,37], the application of material-specific k

_{v}-values listed in Table 6 are recommended to enhance the prediction accuracy of the models. The saltation abrasion models are one-dimensional models not able to reproduce the three-dimensional processes of hydroabrasion. To account for that, the local abrasion concentrations can be accounted for with a

_{max}/a

_{m}≈ 2 as a preliminary estimate, while their locations can be derived from the local flow field.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Overview and (

**b**) cross section of the Pfaffensprung SBT (position 46°42′49.8″ N 8°36′36.7″ E) with test field locations 1 and 2 and radar instrumentation for discharge monitoring, position of Figure 2 highlighted red.

**Figure 2.**Measurement installation in Pfaffensprung SBT at test field location 1 during scanning in March 2014, (1) terrestrial laser scanner (TLS), (2) temporary mounted targets and (3) ground water drainage, view in flow direction from high-strength concrete (C1) over granite pavement (G1) to SBT outlet.

**Figure 3.**(

**a**) Overview and (

**b**) cross section of the Runcahez SBT (position 46°40′45.0″ N 8°58′05.7″ E; adapted from [18]).

**Figure 4.**Close-up view of the abraded surface of the Pfaffensprung SBT: (

**a**) high-strength concrete test field C1 after four operational years, (

**b**) high-strength concrete test field C2 after two operational years, (

**c**) granite test field G1 after four operational years showing abrasion concentration at upstream edges and (

**d**) granite test field G1 after four operational years showing abrasion concentration along joints with downstream abrasion shadows.

**Figure 5.**High-resolution abrasion maps of the 10 m long high-strength concrete test field C1 installed at test location 1 in Pfaffensprung SBT after (

**a**) one, (

**b**) two and (

**c**) four operational years (the grey colored areas could not be scanned due to ground water drainage installation).

**Figure 6.**High-resolution abrasion maps of the 20 m long high-strength concrete test field C2 installed at test location 2 in Pfaffensprung SBT after (

**a**) one and (

**b**) two operational years (the grey colored areas could not be scanned due to ground water drainage installation).

**Figure 7.**High-resolution abrasion maps of the 10 m long granite test field G1 installed at test location 1 in Pfaffensprung SBT after (

**a**) one, (

**b**) two and (

**c**) four operational years (blue colored points mark theoretically negative abrasion depths corresponding to detection uncertainty; grey colored areas could not be scanned due to ground water drainage installation).

**Figure 8.**High-resolution abrasion maps of the 20 m long granite test filed G2 installed at test location 2 in Pfaffensprung SBT after (

**a**) one and (

**b**) two operational years (blue colored points mark theoretically negative abrasion depths corresponding to detection uncertainty; grey areas could not be scanned due to ground water drainage installation).

**Figure 9.**Super-elevated longitudinally averaged cross-sectional abrasion profiles of high-strength concrete test fields (

**a**) C1 at test location 1 and (

**b**) C2 at test location 2 installed at Pfaffensprung SBT for the years 2012 to 2015; view in flow direction.

**Figure 10.**(

**a**) Mean and (

**b**) maximum cumulative abrasion depths as a function of cumulative bedload mass at Pfaffensprung SBT for high-strength concrete test fields C1 and C2 and granite test fields G1 and G2 for the years 2012 to 2015.

**Figure 11.**Abrasion depths of the silica fume concrete (SC) test field in Runcahez SBT in (

**a**) 1999 after four years of operation and (

**b**) 2014 after 19 years of operation (circles represent measurement points).

**Figure 12.**Super-elevated, longitudinally averaged cross-sectional abrasion profiles of the silica fume concrete test field (SC) in Runcahez SBT.

**Figure 13.**(

**a**) Mean and (

**b**) maximum cumulative abrasion depths as a function of cumulative bedload mass of invert material test fields in Runcahez SBT.

**Figure 14.**Abrasion coefficient k

_{v}as a function of splitting tensile strength of various SBT invert materials for (

**a**) SAM, (

**b**) SAM

^{*}and (

**c**) SAMA.

**Figure 15.**Abrasion coefficient k

_{v}as a function of splitting tensile strength f

_{st}for the saltation abrasion model modified by [44] (SAMA).

Reservoir | Unit | Pfaffensprung | Runcahez | Lago di Rierna |

Completion | [year] | 1922 | 1962 | 1967 |

Position | 46°42′49.8″ N 8°36′36.7″ E | 46°40′45.0″ N 8°58′05.7″ E | 46°21′38.9″ N 8°55′27.0″ E | |

Volume | [10^{6} m^{3}] | 0.17 | 0.44 | 0.40 |

Capacity Inflow Ratio (CIR^{*}) | [year] | 0.0003 | 0.006 | 0.01 |

River Upstream of Reservoir | Reuss | Rein da Sumvitg | Rierna | |

Mean slope S | [–] | 0.0374 | 0.0365 | 0.10 |

Mean width b | [m] | 18 | 15 | 5 |

Bank slope (idealized) | [–] | 1:1 | 1:1 | 1:1 |

Mean sediment particle size d_{m} | [m] | 0.25 | 0.23 | 0.18 |

90-percentile sediment particle size d_{90} | [m] | 0.68 | 0.53 | 0.75 |

Strickler roughness coefficient k_{St} | [m^{1/3}/s] | 22.5 | 23.5 | 22.1 |

Sediment Bypass Tunnel SBT | Pfaffensprung | Runcahez | Val d’Ambra | |

Completion | [year] | 1922 | 1962 | 1967 |

Length L/acceleration length L_{acc}** | [m] | 282/25 | 572/65 | 512/55 |

Slope S/acceleration slope S_{acc} ** | [–] | 0.03/0.35 | 0.014/0.25 | 0.02/1.0 |

Width b | [m] | 4.4 | 3.8 | 3.6 |

Equivalent sand roughness k_{s} | [mm] | 3 | 3 | 3 |

Design Q_{d}/maximum discharge Q_{max} | [m^{3}/s] | 220/240 | 110/190 | 85 |

General operation duration T | [d/year] | 100–200 | 1–4 | 2.5 |

Observation duration | [year] | 4/2 *** | 19 | 47 |

Tested invert materials | [–] | Concrete, granite | Concrete | Concrete |

Material | f_{c} [MPa] | f_{st} [MPa] | ρ_{c} [to/m^{3}] | Y_{M} [GPa] |
---|---|---|---|---|

Pfaffensprung | ||||

High-strength concrete 1 (C1) | 108 ± 2 | 11.3 ± 0.3 | 2.46 ± 0.03 | 38.6 ± 5.3 |

High-strength concrete 2 (C2) | 78 ± 21 | 11.2 ± 1.1 | 2.45 ± 0.045 | 34.6 ± 11.9 |

Urner Granite 1 and 2 (G1 and G2) | 260 ± 20 | 10 ± 2 | 2.65 ± 0.05 | 59.0 ± 2.7 |

Runcahez | ||||

Silica fume concrete (SC) | 85.9 ± 3.1 | 8.5 ± 2.1 | 2.67 ±0.02 | 54.1 ± 2.8 |

High performance concrete (HPC) | 76.7 ± 2.0 | 7.1 ± 3.0 | 2.98 ±0.02 | 52.7 ± 4.1 |

Steel fiber concrete (SF) | 95.9 ± 2.3 | 8.3 ± 2.0 | 2.73 ± 0.01 | 52.1 ± 2.7 |

Roller compacted concrete (RCC) | 55.7 ± 4.6 | 6.1 ± 1.0 | 2.56 ± 0.05 | 49.7 ± 1.3 |

Polymer concrete (PC) | 66.8 ± 3.0 | 11.7 ± 1.0 | 2.37 ± 0.03 | 16.3 ± 1.3 |

Val d’Ambra | ||||

Concrete | 40 * | 3.4 ** | 2.5 * | 28.1 *** |

**Table 3.**SBT operation conditions and abrasion depths in the Val d’Ambra SBT between 1967 and 2014 [48].

Parameter | Unit | 1967–2014 |
---|---|---|

Mean annual SBT operation duration T | [d/year] | 2.50 |

Mean discharge in SBT $\overline{Q}$_{SBT} | [m^{3}/s] | 42.5 |

Mean flow depth $\overline{h}$ | [m] | 1.60 |

Mean flow velocity $\overline{U}$ | [m/s] | 8.30 |

Mean Shield’s parameter $\overline{\theta}$ | [–] | 0.18 |

Mean annual bedload mass BL | [10^{3} to/year] | 21.0 |

Mean annual abrasion depth a_{m} | [mm/year] | 3.0 |

**Table 4.**Mean annual SBT operation conditions, bedload transport masses and abrasion depths in the Pfaffensprung SBT for the years 2012 to 2015.

Parameter | Unit | 2012 | 2013 | 2014 | 2015 | Average |

SBT operation duration T | [d] | 91 | 61 | 55 | 96 | 76 |

Mean discharge in SBT $\overline{Q}$_{SBT} | [m^{3}/s] | 35.5 | 32.6 | 25.9 | 34.5 | 32.1 |

Mean flow depth $\overline{h}$ | [m] | 0.82 | 0.76 | 0.61 | 0.80 | 0.75 |

Mean flow velocity $\overline{U}$ | [m/s] | 9.8 | 9.8 | 9.7 | 9.8 | 9.8 |

Mean Shield’s parameter $\overline{\theta}$ | [–] | 0.042 | 0.039 | 0.035 | 0.042 | 0.040 |

Bedload mass BL | [10^{3} to/year] | 460 | 370 | 140 | 430 | 350 |

Mean Abrasion Depths a_{m} | 2012 | 2013 | 2014 | 2015 | 2012–2015 | |

High-strength concrete 1 (C1) | [mm] | 15.4 | 9.3 | 1.3 | 5.0 | 31.0 |

High-strength concrete 2 (C2) | [mm] | - | 8.9 | 1.5 | - | 10.4 |

Urner Granite 1 (G1) | [mm] | 2.9 | 0.6 | 0.5 | 1.3 | 5.3 |

Urner Granite 2 (G2) | [mm] | - | 1.4 | 0.6 | - | 2.0 |

**Table 5.**Mean SBT operation conditions, bedload transport masses and abrasion depths in the Runcahez SBT for 1996–1999 and 2000–2014 and the overall average.

Parameter | Unit | 1996–1999 | 2000–2014 | Average |

Mean SBT operation duration T | [d/year] | 1.63 | 1.37 | 1.50 |

Mean discharge in SBT $\overline{Q}$_{SBT} | [m^{3}/s] | 56.4 | 55.7 | 55.9 |

Mean flow depth $\overline{h}$ | [m] | 2.01 | 2.00 | 2.00 |

Mean flow velocity $\overline{U}$ | [m/s] | 7.38 | 7.35 | 7.35 |

Mean Shield’s parameter $\overline{\theta}$ | [–] | 0.036 | 0.036 | 0.036 |

Mean bedload mass BL | [10^{3} to/year] | 10.1 | 10.7 | 10.6 |

Mean Abrasion Depths a_{m} | 1996–1999 | 2000–2014 | 1996–2014 | |

Silica fume concrete (SC) | [mm/year] | 1.6 | 0.7 | 16.8 |

High performance concrete (HPC) | [mm/year] | 1.5 | 0.9 | 20.0 |

Steel fiber concrete (SF) | [mm/year] | 1.0 | 1.2 | 21.9 |

Roller compacted concrete (RCC) | [mm/year] | 1.4 | - | - |

Polymer concrete (PC) | [mm/year] | 0.4 | 1.1 | 27.7 |

k_{v} (10^{6}) | |||
---|---|---|---|

Material | Compressive Strength | SAM | SAMA |

High-strength concrete | f_{c} ≈ 75–110 MPa | 1.3 | 0.19 |

Granite | f_{c} ≈ 240–280 MPa | 14.0 | 2.4 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Müller-Hagmann, M.; Albayrak, I.; Auel, C.; Boes, R.M.
Field Investigation on Hydroabrasion in High-Speed Sediment-Laden Flows at Sediment Bypass Tunnels. *Water* **2020**, *12*, 469.
https://doi.org/10.3390/w12020469

**AMA Style**

Müller-Hagmann M, Albayrak I, Auel C, Boes RM.
Field Investigation on Hydroabrasion in High-Speed Sediment-Laden Flows at Sediment Bypass Tunnels. *Water*. 2020; 12(2):469.
https://doi.org/10.3390/w12020469

**Chicago/Turabian Style**

Müller-Hagmann, Michelle, Ismail Albayrak, Christian Auel, and Robert M. Boes.
2020. "Field Investigation on Hydroabrasion in High-Speed Sediment-Laden Flows at Sediment Bypass Tunnels" *Water* 12, no. 2: 469.
https://doi.org/10.3390/w12020469