Standardized Stress Model for Design of ... - J-STAGE

International Journal of Erosion Control Engineering Vol. 10, No. 1, 2017

47

Original Article

Standardized Stress Model for Design of Torrential

Barriers under Impact by Debris Flow (According to

Austrian Standard Regulation 24801)

Johannes HUEBL1, Georg NAGL

1, Jürgen SUDA2 and Florian RUDOLF-MIKLAU3

1 Institute of Mountain Risk Engineering, University of Natural Resources and Life Sciences, Vienna

(Peter Jordanstrasse 82, 1190 Vienna, Austria) 2 alpinfra engineering + consulting GmbH, Lützowgasse 14/1.; 1140 Vienna (Austria)

3 Federal Ministry for Agriculture, Forestry, Environment and Water Management, Vienna (Austria)

[email protected]

Torrential checkdams with energy dissipating, filtering or deflecting function for debris flows are expected

to be subject to extreme dynamic stress that requires the application of high safety standard for design,

construction and maintenance. The standardized procedure for checkdam design has been developed from

comparative calculations of common debris flow models from engineering practice and calibrated by

impact measurements of debris flow laboratory experiments and data available from literature. The model

is based on a combined static- dynamic stress approach, additional impacts by single objects like boulders

are included. The dynamic area of the dynamic component is derived from a characteristic wetted cross

section area of debris flow corresponding to the design event, which can be found at a characteristic cross

section upstream of the checkdam. The static load is based on a hydrostatic fluid assumption and calculated

analogously to water pressure (with debris flow density) and acts upon total construction height. The

dynamic component is calculated according to the momentum equation and acts uniformly distributed on

the dynamic impact area right below the overflow section up to a height of maximum 4 meters. The

maximum local impact of a single boulder is defined to act on an area of 0.7 x 0.7 meter with 1MN. This

new regulation shall guide practitioners for more objectives and save design of checkdams impacted by

debris flows.

Key words: debris flow, impact force, Austrian standard

1. INTRODUCTION

The design of structural mitigation measures

against debris flows is a challenging task for

engineers. In a first step the relevant mass wasting

process has itself to be determined. Subsequently

process based parameters like density, flow velocity

and depth have to be transferred into a model that

represents loading conditions. Additionally the

granular composition of debris flows varies over

time. Nevertheless, it is essential to develop a

practical standardized stress model for the design of

torrential barriers under the impact of debris flows.

The design of the barriers has to follow its

function (ONR24800) that may affect the initiation,

the transport or deposition of debris flows. The

interaction with the structures can be described by

following functional types:

Stabilization and consolidation

Energy dissipation

Deflection

Usually structures of the above mentioned functions

are combined in a so called functional chain [Kettl,

1984].

To harmonize the design of technical structures

the so-called Eurocode was launched. Based on this

concept the ONR Series 2480xx was established,

encompassing torrential processes, snow avalanches

and rock fall. Within this series two regulations

(ONR24801 & ONR24802) specifies the load model

for debris flows based on results of field

experiments, miniaturized flume experiments and

back-analysis

2. EXPERIMENTAL MEASUREMENTS

AND FIELD OBSERVATION

mailto:[email protected]


48

Table 1 Empirical coefficient for impact models, comparison of different k factor for selected impact models

Hydraulic Model Study k Notes

Hydrostatic Model

ghkp

density of debris flow

³m

kg

h flow depth m

g acceleration of gravity

²s

m

k empirical factor /

[Lichtenhahn, 1973] k value between 7-10

2.8-4.4

Based on recalculations

[Armanini, 1997] k= 5

5

Theoretical analysis of dynamic impact by

experimental investigations made by

[Armanini and Scotton, 1993]

[Scotton and Deganutti, 1997] k=2.5-7.5

2.5-7.5

Small scale debris flow model test

Modified hydrodynamic

Model


³m

kg


²s

m

v velocity

s

m

[Hübl and Holzinger, 2003]

6.0)(8.05.4 ghvp

7.5

Evaluation of model test to the

dependence of Froude number and

pressure.

Combined Models

c = volume weight of

concentration

Q = Discharge

[Kherkheulidze, 1967]

²)5(1.0 vhcP 1

Total pressure in tons/square meter.

averaged over the depth; water load

momentum and static pressure being taken

into account

[Arattano and Franzi, 2003]

²2

1ghQvF

1.4-1.7

with reference to [Armanini and Scotton,

1993]

There are only a few data published on full size

debris flows impact loads. In Japan observations at

Mt. Yakedake showed a dynamic pressure of 6

tons, estimated from pressure marks on a steel plate

of a size of 15 x 15 cm [Suwa et al., 1973]. At the

Jiangjia River, China, monitoring activities started

in 1973 [Hu et al., 2006; Cui et al., 2005]. Hu et al.

[2011] recorded impact loads of 38 surges with a

flow depth of less than 2 meters and mean

velocities up to 12 m/s. The pressure was then

divided in a fluid and grain impact part. Fluid

pressure attained values up to 100 kN/m², the

estimated grain impact loads reached values an

order of magnitude higher. In Switzerland real scale

tests were performed on a steep slope with a release

volume of 50 m³ [Bugnion et al., 2012 a, b]. Two

sensors of different size measured the impact force.

Additionally velocity, density and flow depth were

recorded. Full size debris flow tests were carried

out in Austria in order to estimate impact forces on

obstacles [Hübl et al., 2009; König, 2006]. To gain

an insight in grain impact loads, additional free-fall

studies with different sized cubes were conducted.

Concrete cubes of 100 and 300 kg weight were

released from 1 to 6 m height. To measure the

impact force, 15 load cells got fixed on a tread bar,

which were arranged grid wise. Another method to

estimate impact forces is the back analysis of

events, if adequate data are available. Based on

back calculation of debris flow volume, peak

discharge and mobility values for impact pressure

were assessed, using the hydrostatic and

hydrodynamic pressure equation. Hungr et al.

[1984] calculated the forces on a destroyed

pre-stressed bridge beam by the November 1983

Charles Creek event. The size of the design boulder

for impact calculations should be equal to the

corresponding flow depth. In Italy, the Sarno event

(May 5-6, 1998) was investigated by [Zanchetta et

al., 2004]. A common method to study the behavior

and the physical properties of debris flows are

miniaturized flume experiments. The most

significant drawback of this kind of tests are

possible scaling errors [Yu, 1992; Armanini and

Scotton, 1993; Scotton and Trivellato, 1995;

Armanini, 1997; Iverson, 1997; Arattano and

Franzi, 2003; Hübl and Holzinger, 2003; Huang et

al., 2007; Tiberghien et al., 2007; Iverson et al.,

2010; Scheidl et al., 2013].

3. HYDRAULIC MODELS FOR IMPACT

CALCUALTION

Several formulas for impact forces calculation

can be found in literature. Hydraulic and solid

collision models are used to represent the

interaction of debris flows with control structures


49

Table 2 Hydrodynamic models Hydraulic Model Study k Notes

Hydrodynamic Model 2vap


³m

kg


2s

m

v velocity

s

m

A Area ²m

[Watanabe and Ikeya, 1981] 2a for laminar and fine grained

4

Field measurements of Mt.

Sakurajima

[Egli, 2000] 42a

4-8

after [GEO, 2000]; with density

1800-2200

³m

kg

[Zhang, 1993] 53a

6-10 after [Zhang and Yuan, 1985;Zhang

et al.,1990]

[Wendeler, 2008] 27.0 a

1.4-4.0 Full scale tests at the Illgraben

Switzerland

[Bugnion et al., 2012a,b] 8.04.0 a with max of 2

0.8-1.6

Real scale tests with a release

volume of 50 m³;velocity vary

between 2 and 13 m/s

[Hungr et al., 1984]

1a 1.5 A

3

Load area should be range over an

area as wide the design debris flow

reach, but 1.5 greater height

[Mizuyama, 1979] 1a

2

Separated the debris flow pressure

into fluid and boulder impact force

[Armanini and Scotton, 1993] 2.245.0 a

0.9-4.4

[VanDine, 1996] 1.5 A

1.5A Recommend the momentum

equation after [Hungr et al.,1984]

and Hertz equations

[Tiberghien et al., 2007]

13.5

[Lo, 2000] 3a

6

[Du et al., 1987] 3a

6

[Hübl et al., 2009]. Furthermore the hydraulic

models can be distinguished between hydrostatic,

hydrodynamic and combined models (Table 1).

Transferring the hydrodynamic to hydrostatic

models can be carried out by the application of the

Bernoulli energy line. This results in an empirical

factor k, assuming Froude number is 1,

)1(2

1 2vahgk

where is density, g is gravitational acceleration, v

is mean flow velocity, h is flow depth, and a and k

are coefficients (see Table 1 and 2).

4. COLLISON MODELS

The point impact load due to boulders carried in

the flow may be more important for the design of

certain structural elements [Hungr et al., 1984].

Most collision models for boulder impacts are based

on the Hertz equation [Hertz, 1881]. Timoshenko

and Goodier, [1970] propose this approach

especially for inflexible structures. VanDine [1996]

and Hungr et al. [1984] recommended the Hertz

equation too, but due to deformation and associated

energy loss Hungr et al. [1984] proposed a reduction

factor of 0.1. Lo [2000] and Sun et al. [2005] pursue

this proposition.

4.1 Hertz equation The Hertz equation was reformulated by [Zhang

et al., 1996] for the calculation of boulder impact

load FHertz:

)2(5,1 nKFCHertz

Kc is a dimensionless reduction factor, α and n can

be calculated by Eqs. (3) and (6), respectively

)3(4

54,0

2

n

vmbb

where, mb is boulder mass [kg] and vb the impact

velocity in [m/s];


50

Fig. 1 Comparison of Impact force by Hertz to the force of stiffness method from different length of a simple supported beam

Table 3 Geometric and material data

Spherical intender

Diameter 0.5 m

Material Concrete

Concrete strength Characteristic cube

strength 30 N/mm²

E Modulus 31,000 N/mm²

Density 2500 kg/m³

Beam 0.3 x 0.2m and

0.5 x 0.5m

Length 3-6m

Cross section 0.3m x 0.2m and

0.5m x 0.5m

Concrete strength Characteristic cube

strength 30 N/mm²

E Modulus 31,000 N/mm²

Density 2500 kg/m³

)4(1

B

B

B

Ek

)5(1 2

b

b

b

Ek

where bis the poisson ratio for the boulder,Bis

the poisson ratio for the barrier both equal to 0.2, Eb

is the modulus of elasticity for the boulder, and EB

for the barrier (both equal to 31,000 [N/mm²].

)6(

3

4 5,0

Bb

b

kk

rn

with br as the radius of the elastic sphere.

4.2 Flexible stiffness method

For flexible elements, Hungr et al. [1984] and

also the Chinese standard [MLR, 2006] recommend

to calculate the impact force by the stiffness

method. For a simple beam [Kramer, 2007] the

force to reach the equivalent maximum static

deflection Fstiff can be calculated by Eq. (7).

)7(gmVgmFStiff

Where m is the mass [kg], g gravitational

acceleration [m/s²], l length of beam [m],

)8(2

1stat

s

hV

h is the fall height [m] and sstat is the deflection

from dead load [m].

)9(48

³

IE

lgms

stat

Eq. (9) describes the stiffness of a simple supported

beam with E modulus of elasticity [N/mm²] and I

area moment of inertia [m4].

Figure 1 shows dimensionless reduction factor

of stiff members by comparing the impact force of

Hertz to the stiffness method. The parameters for

comparison of the two different methods are

described in Table 3.

4.3 Design models of different countries

Kwan [2012] gives an overview of the state of

art knowledge in different countries on the design

of impact loads on torrential check dams. It’s based

on literature review. The summary of original

recommendation is given in Table 4.

5. DESIGN MODEL OF AUSTRIAN

STANDARD ONR 24801

The newly developed Austrian Standard

ONR24801 provides a standardized model for

construction of debris flow barriers, which has been


51

Table 4 Compression of design practice of different countries

[Kwan, 2012]

Design Practice Dynamic Pressure Boulder impact

load

Hongkong

[Lo, 2000]

2vp

3

Hertz equation with

load reduction factor

0.1

British Columbia

[VanDine, 1996]

2vp

1

Hertz equation and

reference to [Hungr

et al. 1984]

China

[MLR, 2006]

2vp

1 for

cirular

structure

33.1 for

rectangular

structure

Flexural Stiffness

equation

Japan

[NILIM, 2007]

2vp

1

Modified Hertz

equation, load

reduction factor less

than 0.1

Taiwan

[SWCB,2005]

2vp

1

Modified Hertz

equation, load

reduction factor of

0.2-0.5. Separate

consideration of

dynamic pressure and

boulder impact

Fig. 2 Distinction between load and process model

developed from field and miniaturized experiments

[Scheidl et al., 2013; Hübl and Holzinger, 2003;

Proske et al., 2008] and also from engineering

practice from the Austrian torrent control service.

The proposed method should enable practitioners to

properly design debris flow countermeasures with

the restriction that usually only a few data are

available. Naturally, simplifications and

assumptions are necessary. Therefore, the process

“debris flow” and the interaction with the structure

itself are divided (Fig. 2). At the interface the

parameters of the process have to be transferred to

impact parameters that act on a specified load area.

Basis of design is the load distribution and the force

size of the stress model.

5.1 Load area

Fig. 3 Cross section area projected to the impact area on the

barrier for calculation

Fig. 4 Cross-section of a wide barrier

After a debris flow event the most obvious

evidences are flow marks on both sides of the

channel. Hence, the cross sectional area of past

debris flows is the only parameter that can be

measured directly in ungauged catchments. This

cross section area stands for the magnitude of

design event. For the calculation of the impact area

on the structure, the cross sectional area of the

design event of this upstream reference

cross-section (AQM) is projected to the barrier

(AQdyn). Both areas have to be the same size, the

projected impact area is localized just below the

discharge section of the barrier (Fig. 3).

The design impact area AQdyn is approximated

by a rectangle, with a height of 2-4 m, depending

on the type of debris flow. For muddy debris flows

the height hdyn assumed to be 2 m, for coarse

grained debris flows 4 m.

)10(dyndynQdyn bhA

with

mhmdyn

42

)11(QMQdyn

AA

If the width of the barrier (bGes) is more than three

times of bdyn, several load cases for variable impact

areas (AQdyn) have to be shifted to more distal parts

of the barrier (Fig. 4).

5.2 Characteristic properties

Relevant process parameters, like velocity and

density, have to be estimated. To overcome

extensive calculations, a range of possible values of

density and velocity are given for different types of

alpine debris flow according to ONR 24800. The

recommended data are derived from measured or

observed alpine debris flows (Table 5).


52

Table 5 Characteristic values for processes of debris flows

Channel

process Debris flood

Debris flow

stony muddy

Density (ρ)

[kg/m³] 1300-1700 1700-2000 2000-2300

Velocity

(v) [m/s] 3-5 3-6 5-10

Fig. 5 Stress combination model for debris flow

5.3 Calculation of debris flow impact

The design model is based on a combined static

and dynamic load, resulting from the momentum

equation. It is supposed that the highest impact

force results from the initial contact of the debris

flow with the barrier structure. Sediment behind the

barrier may dampen the impact of the process and

reduce the dynamic pressure on the structure. The

stress model is composed of the following

components:

Dynamic debris flow pressure (pdyn)

Static debris pressure (pst)

Imposed load (pa)

Equivalent static load for the impact of a

single component (eg. tree trunk, large

boulder), (Fe) (Fig. 5).

The debris flow impact model is based on the

following equations, which represent the

momentum equation for fluvial water pressure.

)12(²vpdyn

)13(hgpst

According to the Eurocode 1990, the characteristic

value of action should correspond to the upper

values with an intended probability of not being

exceeded during some specific reference period in

time. The design value Pd of an action P can be

expressed by

)14(stdynGd

PPP

)15(Qdyn

d

d

A

Pp

With

Pd as the design value of action [kN]

pd as the design value of pressure [kN/m²]

Table 6 Partial factor of safety G, for Limit State of STR

(Internal failure or excessive deformation of the structure or

structural member) for the design situations of BS1 (persistent

conditions), BS2 (transient conditions) and BS3 (accidental

conditions)

Limit

state

Duration Ultimate limit state

BS1 BS2 BS3

STR Permanent unfavourable 1.35 1.20 1.00

favourable 1.00 1.00 1.00

Variable unfavourable 1.50 1.30 1.00

favourable 0 0 0

Table 7 Static equivalent load

Process Static load FE Impact area

[kN] [m]

Coarse grained

debris flow 1000 0.7 x 0.7

Fig. 6 Energy dissipating function type

G is a partial safety factor for the action which

takes account of the possibility of unfavourable

deviations of the values from the representative

values (Table 6).

The partial factor depends on the classification by

their variation of time (design situation):

Persistent design situation (e.g. debris flow)

Transient design situation (e.g. avalanche,

shrinking)

Accidental design situation (e.g. earthquake,

rock fall)

5.4 Single boulder impact

Furthermore, the impact of a single component

has to be taken into account for Ultimate Limit

State assessment. The impact area has to be

localized at an adverse position on the barrier

(Table 7).

5.5 Adaption for compound barriers For compound barriers ONR 24801

recommends an adapted arrangement of the impact


53

Fig. 7 Comparison of published dynamic impact pressures with calculated pressures from ONR 24801 without boulder impact, with

design values (partial factor of safety G = 1.35) and characteristic values.

Fig. 8 Impact force by Hertz equation with reduction factor Kc = 0.1


54

area. The influence width be has to be adjusted

according to the following rules, where bl is the

width of the slit.

mb

bmb l

el

22

mbmbel

12

6. COMPARISIONS AND CONCLUSIONS

To test the ONR Standard, the results of the

calculations with different debris flow densities

were compared with published data sets [Hu et al.,

2011; Proske et al., 2008]. Most authors only

mention maximum pressure and do not distinguish

between dynamic and grain impact pressure.

Therefore it is difficult to compare the results of the

ONR approach with published data. Only Hu et al.

[2011] divide their data into different impact

components. The calculated characteristic values of

the dynamic pressure based on the ONR method

correspond well with the published data for

dynamic pressure of Hu et al. [2011]. Our proposed

design values represent the uncertainty of the data

and imply the factor of safety for unfavorable

situations (Fig. 7). The maximum reported forces

are covered by considering the single boulder

impact approach.

Applying the Hertz method with a reduction

factor Kc of 0.1 indicates that a boulder impact with

a mass of 1300 kg and an impact velocity of 9 m/s

(or with a mass of 10000 kg and an impact velocity

of 3 m/s) does not exceed the design value

according to ONR24801 (Fig. 8).

The comparison reveals that the results of the

ONR Standard fit well to the published data.

Though our proposed method represents a very

practical approach, it is based on physical principles.

Within the next years adaptions will be applied due

to gained experience and new scientific results.

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Received: 8 July, 2015

Accepted: 2 March, 2016

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