The aim of this paper is to analyse debris flow impact against rigid and undrained barrier in order to propose a new formulation for the estimation of acting force after the flow impact to safe design protection structures. For this reason, this work concentrates on the flow impact, by performing a series of small scale tests in a specifically created flume. Flow characteristics (flow height and velocity) and applied loads (dynamic and static) on barrier were measured using four ultrasonic devices, four load cells and a contact surface pressure gauge. The results obtained were compared with main existing models and a new equation is proposed. Furthermore, a brief review of the small scale theory was provided to analyse the scale effects that can affect the results.

Every year several gravitational movements, such as debris flows, landslides and avalanches, affect mountainous regions all over the world. Understanding and predicting their interactions with protection structures is a key point for the assessment and the management of risk.

Debris flow impact estimation requires us to analyse and to discuss two key points: the first one is the data availability, deriving from real case observation, to validate the proposed models; the second one is related to the universal applicability of these equations.

Concerning the first point, the difficulties to find available data derived from monitoring of debris flow events force to perform laboratory experiments (Armanini and Scotton, 1992; Huebl and Holzinger, 2003; Canelli et al., 2012) due to the high instrumentation costs.

Furthermore, laboratory tests allow to keep under strict control all the parameters involved and to easily perform several analyses. On the other hand, the question about the scale effects it is not completely solved: many authors raised doubts about the acceptability of the results carried out with these experiments (Iverson, 1997).

The design of mitigation structures requires simple models to predict impact pressure with high reliability; these models should be universally recognized and should include few parameters, easy to estimate. Moreover, material properties and flow characteristics should be considered in the equations. Following these preconditions, an accurate study of the flow behaviour against structures is necessary in order to define European criteria for design of debris flows protection fences.

This paper presents the first results of several laboratory tests performed to reduce the lack of information about impact force prediction.

The possibility to simulate debris flows in laboratory is a controversial argument; even if the similarity theory provides the necessary
support to design models and to extrapolate the data at the real scale, the
scale effects plays an important role in the comprehension of the phenomenon
(Longo, 2011). In particular, while geometric similarity (

These issues were faced starting from an accurate dimensional analysis of
the impact of a saturated mass against a rigid wall. The longitudinal
deformation of this structure is the key parameter that allows us to evaluate
the energy dissipation of the mass. From this point of view, the mean
density of saturated debris

In order to take these relationships into account, the Froude similarity was
applied to the examined experimental tests. The scientific community agrees with
the theory that values obtained from small scale tests are acceptable if the
Froude number of the simulated current is comparable with the real ones
(Hübl et al., 2009; Longo, 2011; Canelli et al., 2012; Scheidl et al., 2013). The open question
deals with the maximum acceptable Froude number for small scale results;
some authors (Hübl et al., 2009) suggest that the maximum acceptable Froude
number for debris flow simulated in laboratory is 3, but it is demonstrated
that debris flow in nature can assume Froude numbers greater than this value
(Costa, 1984). Furthermore, small Froude number means high velocity value
and, simultaneously, high thickness (and vice versa). However, these
conditions do not satisfy the characteristic of the majority of Alpine debris
flows, which are characterized by high velocity (greater than 10 m s

Experiments were performed in a steel flume 4 m long and 0.39 m
wide, in which a rigid barrier was positioned orthogonally at the channel
bottom. The slope is variable between 30 and 35

Scheme of the flume and of the starting mechanism.

2-D and 3-D impact representation registered by Tactilus^{®} pressure sensor.

Four ultrasonic level measurers were mounted along the centre line of the channel at a known distance, decreasing progressively near the barrier. These devices had an acquisition frequency of 1 kHz and were used to evaluate both flow height and impact velocity on the barrier. Four load cells were installed at the plate vertices to measure the normal thrust acting on the barrier.

Flow velocity at the barrier was estimated as the ratio of the distance between last ultrasonic level and the barrier location, and the difference between the time of first arrival of the front flow and the time of impact at the barrier. To observe the trend of the flow rate in the flume, the velocity values were evaluated at each sensor's interval.

A contact surface pressure gauge was used to control the evolution of the
impact load at the barrier. This device, called Tactilus^{®}, is
produced by Sensor Products LLC, and is designed to display a picture of the
pressure distribution, measure and calculate min/max pressure, generate 2-D
and 3-D modelling and region of interest viewing. It is made by a matrix of
32 ^{®} allows
us to check the force values measured using load cells, with the advantage that
in every point of the barriers it is possible to know the corresponding
instant load values. In the experimental tests, this device was also used to
verify the occurrence of vertical wave overpressure. The capability to
record impact pressure in real time allows us to understand and to detect the
most stressed zones of the barrier. In this way, it is possible to verify
the accuracy of the hypotheses done about the behaviour of the current
during the impact.

Main initial properties of the mixture used.

The tests were performed using saturated sand. The main characteristics of the material are listed in Table 1 and its grain-size distributions is shown in Fig. 3. The choice to use sand as the mixture material was made to obtain and easily check the characteristics of the flow. It is well known that the grain size distribution used is not exhaustive and representative of a real debris flow (which is generally made up of a very wide range of grain sizes), but the authors wanted to avoid, at this stage of the study, the formation of over pressures due to the impact of boulders and their interactions inside the mixture. Furthermore, there is the necessity to consider a homogeneous fluid scheme to evaluate the peak thrust.

However, to verify that the simulated currents could be assimilated to debris flows, the six dimensionless parameters recommended by Iverson's theory (Iverson, 1997) were calculated (Table 1). Obviously, the estimated values are referred to the initial conditions. This is a simplification, but it is possible to consider that the Bagnold number, Darcy number and Savage number do not vary considerably during the flow. Therefore, when these values fall into the debris flow region obtained from Iverson's theory, the mixture can be considered as a debris flow.

In this first stage of the study, only rigid and waterproof barrier was used, in order to reduce the possible deformations and consequently to correctly evaluate the force and better understand the dynamics of the impact.

Grain size distribution of the mixture.

Several models were hypothesized to estimate the impact force of debris flow against rigid barrier. In particular, the impact force can be proportional either to hydrostatic pressure or kinetics flow height. Thus, three groups of relations can be used: hydro-static, hydro-dynamic and mixed models.

The equations referred to the first group have the following aspect:

This formula is very popular because it only requires debris density and
flow height and usually flow height is considered equal to channel depth.
The only limit is represented by

Hydro-dynamic models derive from the application of the momentum balance of
the thrust under the hypothesis of homogeneous fluid; impact force can be
evaluated as follows:

The dynamic coefficient is the key point of this relation; it depends on the
flow type, on the formation of a vertical jet-like wave during the impact
and on the barrier type (Canelli et al., 2012). In particular, the drainage
capability of the barrier reduces the magnitude of this coefficient due to
the rapid discharge of the fluid portion through the barrier, preventing the
formation of wave overpressure. Another aspect to take into account while
choosing

In scientific literature, there is a wide range of proposed values for
dynamic coefficient: Hungr et al. (1984) propose

Furthermore, there are others formulations derived from hydro-dynamic
relation. Huebl and Holzinger (2003) relate the Froude number (

Another equation to evaluate the dynamic impact of a debris flow against a
vertical wall is presented by Armanini et al. (2011):

The mixed models consider both the hydro-static and the hydro-dynamic
effects (Cascini et al., 2000; Arattano and Franzi, 2003; Brighenti et al.,
2013); the general equation is the following:

Combining the data obtained using the surface pressure gauge and flow
characteristics (depositional height and velocity), we propose the following
equation to estimate impact force on a rigid wall:

Since static, dynamic, and drag force do not reach their maximum value at the
same time during the debris flow impact,

The sign of the drag force depends on whether the current overflows or not the barrier. On one hand if there is overflow, the sign of the drag force is positive because it induces a deformation at the top of the barrier; on the other hand the sign is negative because the flow produces a friction with the deposited material that reduces the dynamic effects.

Scheme of flow impact and assumed filling process for the calculation of dynamic, static and drag load on the rigid barrier.

This formulation contains both the intrinsic material characteristics,
represented by static internal friction angle

The estimation of the static internal friction angle was done using the tilting box method (Burkalow, 1945); moreover, to verify the value obtained, a back analysis was carried out deriving the internal friction angle from the static force measured by pressure device.

No measurements of bulk density variation were carried out during the impact phase; this value was hypothesized to be constant according to the theory of incompressible fluid.

Flow height and velocity were obtained using ultrasonic devices.

In order to follow the scale principles described in Sect. 2, Eq. (9) has
been normalized by the hydro-static force relative to the impacting front, obtaining

About the filling ratio, it is the ratio between the maximum filling height behind the barrier and the flow height; this number allows us to relate flow thickness to barrier dimension.

When

Analysing the trend of the total impact force in time (Fig. 5), the hypothesized model is confirmed. In fact, it is possible to highlight how the peak force acting on the barrier can be assumed as the sum of two components: one in which static behaviour is predominant and one in which dynamic effects, due to the formation of a vertical jet-like wave, contribute to peak force generation. Furthermore, observing the behaviour of the flow in time, the succession of static and dynamic force is justified because the mobilized volume hits against barrier with consecutive surges.

Total impact force measured at load cells vs. time; the static and the dynamic component are highlighted.

Trend of normalized force measured (points) and predicting model (line)
in function of the Froude number. The labels SS_30

Dimensionless force vs. Froude number for flume inclinations equals
to 30

Linear correlation between filling ratio,

Figure 6 shows the trend of the measured normalized force,

Most of the experimental data fall between the values estimated using Huebl and Holzinger's (2003) equation and Hungr et al.'s (1984) equation with dynamic coefficient equal to 1.5.

In Eq. (10), the only parameter unknown is the dynamic coefficient

Figure 7 represents the trend of the proposed equation compared with the experimental data for different inclination of the flume. In particular, it is possible to notice that the major part of the data falls into a region defined by an upper and a lower limit, evaluated, respectively, using the proposed equation with dynamic coefficients equal to 1.2 and 0.5.

The difference between Fig. 7a and b is the value of filling ratio,
respectively equal to 11 and 9. The fact that the filling ratio is greater
when inclination is greater supports the hypothesis that

According to these observations, the authors want to focus on the trend of the proposed equation: for small Froude number values, relating to the other analysed formulations, it is evident how the static component is predominant compared with the dynamic one. On the other hand, for high values of the Froude number the equation is close to the hydro-dynamic models. This means that if the current has small velocity and, therefore, higher flow height, the peak impact force presents a hydro-static behaviour; on the other hand, with high velocity values and small thickness, the hydro-dynamic components is relevant and it provides the major contribute for the estimation of impact thrust.

Regarding the variation of dynamic coefficient, it is extremely influenced
by the formation of the vertical jet like wave. The fact that

This study has the aim of reviewing the dynamics of debris flow impact against rigid structures and providing a new simple formulation to predict peak thrust.

The equation proposed differs from other formulations because takes into account either flow characteristics, material properties and barrier dimensions. It could easily be used to safely design protection barriers, considering the filling ratio to be the ratio between barrier height and flow thickness.

The model developed has a good capability to predict the forces measured during the laboratory tests. Further studies should be done to verify and, if necessary, to adjust this equation comparing with data obtained from real case events.

The authors would like to acknowledge the Consorzio Triveneto Rocciatori (CTR) for its financial support of part of this project. Edited by: T. Glade Reviewed by: two anonymous referees