Flexible culverts in sloping terrain: Numerical simulation of avalanche load effects

    Flexible culverts in sloping terrain: Numerical simulation of avalanche load effects Amer Wadi, Lars Pettersson, Raid Karoumi PII: DOI: Reference:

S0165-232X(16)00020-3 doi: 10.1016/j.coldregions.2016.01.003 COLTEC 2229

To appear in:

Cold Regions Science and Technology

Received date: Revised date: Accepted date:

21 August 2015 16 December 2015 14 January 2016

Please cite this article as: Wadi, Amer, Pettersson, Lars, Karoumi, Raid, Flexible culverts in sloping terrain: Numerical simulation of avalanche load effects, Cold Regions Science and Technology (2016), doi: 10.1016/j.coldregions.2016.01.003

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(Corresponding Author)

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Amer Wadi

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Flexible culverts in sloping terrain: numerical simulation of avalanche load effects

KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden ViaCon AB, SE-531 02 Lidköping, Sweden

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Email: [email protected]

Prof. Lars Pettersson

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KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden

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Skanska Sweden AB ‒ Major Projects, SE-169 83 Solna, Sweden

Prof. Raid Karoumi

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KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden

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Flexible culverts in sloping terrain: numerical simulation of avalanche load effects Amer Wadi

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Lars Pettersson

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Raid Karoumi

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KTH Royal Institute of Technology, SE-100 44 Stockholm, Sweden ViaCon AB, SE-531 02 Lidköping, Sweden c Skanska Sweden AB ‒ Major Projects, SE-169 83 Solna, Sweden * Corresponding author: [email protected]

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Abstract

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Avalanche protection concrete structures are expensive and their construction period is often influenced by

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the climatological conditions at site, which could result in prolonging the erection process and increase its associated costs. Given the short construction time of flexible culverts, such structures can be a costeffective alternative to traditional protective measures. This article investigates the performance of flexible

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culverts ‒ often referred to as soil–steel composite bridges (SSCB) ‒ when constructed in sloping topography under avalanche loads. A number of 2D finite element models were created to simulate two case

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studies comprised of a pipe arch and a high profile arch. The models were generated to investigate the effect of soil cover depth, the avalanche proximity and the change in soil support conditions around the conduit.

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The aim was to perceive and understand the changes in deformations and sectional forces under defined avalanche loads. The results enable to realise the effect of shallow soil covers in the pronounced change in bending moments due to avalanches. The proximity of avalanche deviation point has a great influence on the structural performance, though increasing the soil cover depth could considerably help in reducing the bending moments resulting from avalanches. It is also found that the downhill soil support configuration has a substantial effect on the flexural response of the structure.

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ACCEPTED MANUSCRIPT Keywords: Flexible culvert; soil–steel composite bridge; Sloping terrain; Finite element model; Avalanche load;

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Snowshed.

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1 Introduction

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Avalanche protection structures are generally required to be built in remote locations, where some parts of the road are exposed to avalanches and rockfalls. The decisions whether to construct such structures are

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often taken on the highest organizational levels and like any other infrastructure project, the decision is mostly influenced by the risks involved, size and frequency of the avalanches, costs to society and the

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required amount of initial investments. Traditional concrete structures are perhaps the first conventional choice when deciding on protection measures for roads against rockfalls and avalanches. The remote

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location of such structures introduces logistical challenges for the efficient mobilization and the supply of

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labour, material and equipment during construction. Concrete casting itself is also considered a main

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challenge when building in this environment.

Avalanche protection galleries are considered direct defence measures for transport roads in the avalanche

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path or deposit zone [1]. In other words, a snowshed can be defined as a roof which is designed to guide the sliding snow across a highway or railway to protect traffic and prevent deep snow deposits on the road [2]. At the beginning of the 19th century, when roads began to replace the ancient pack trails at alpine passes, snowsheds were already an integral part of the road. The old snowsheds were built of wood or stone. The narrow old sheds were relatively inexpensive structures, while modern wide highways require large and costly structures which involve careful studies of location and design [2]. Although avalanche protection galleries provide the best protection against avalanches, they are considered expensive structures and only appropriate when other hedging methods do not provide acceptable security [3]. Thus, in situations where an avalanche deposition zone is very wide, a shed structure would become too long. In such situations, road 3

ACCEPTED MANUSCRIPT closure maybe the only cost effective measure [4]. In contrast, the average estimated construction cost of a conventional concrete snowshed can range between 20 000 and 30 000 Euro per meter length [4–6]. In Switzerland, there exist more than 350 protective galleries, including avalanche galleries and tunnel

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entrances that could be endangered by rockfalls [6]. Similarly, there are around 106 avalanche protection

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galleries (Skredoverbygg) in Norway constituting around 8.2 km in length [7]. According to Norwegian

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avalanche protection plan (2014-2023) for roads [5], new protection galleries will be required on the national roads and the projected cost for those is anticipated to be huge (several hundreds of millions of Norwegian Kroner). Therefore, the urge for an efficient and cost-effective alternative to the traditional

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concrete protection gallery will be highly valued by the stake holders and the tax payers accordingly.

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A soil–steel composite bridge (SSCB) is a structure comprised of corrugated structural steel plates and engineered soil, designed and constructed to induce a beneficial interaction between two material serving its

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ultimate purpose as a bridge or a culvert [8]. Reports have shown that the use of SSCB (also known as

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flexible culverts) has proven to be cost–effective and also environmentally friendly alternative in many cases to traditional concrete structures when built under horizontal or near horizontal ground surface [8–10]. In

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fact, Norwegian document [3] do state that where conditions are favourable for SSCB as avalanche protection, flexible culverts can be cost-effective as an alternative solution [11], where there have been some

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uses of relatively small SSCB in Norway (see Fig. 1) and a few cases were built in hillside locations and have proven to perform successfully [12]. While, the use of flexible culverts may certainly entail technical limits such as the maximum possible surface slopes and spans. These limits are naturally set by the available profile shapes, corrugation size, and the steel and backfill materials, all of which will normally define what is possible with these structures. On the other hand, the cost of avalanche protection flexible structures may vary depending on their size and the involved earthworks. However, one may note that report [11] highlighted a cost saving of 30-50% for a 6 m span protection flexible culvert in comparison to a conventional structure, while the cost for a 9.3 m span protection flexible culvert built in Norway in 1988 was reported of about NOK 45 000 /m [12]. 4

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Fig. 1. A 6.07 m span flexible avalanche protection culvert built in 1983 in Veitastrond, Norway

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[12].

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1.1 Current practice and need

The current design methods for flexible buried structures have design limitations concerning their

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applicability under steep surface slopes. For instance, Swedish design method (SDM) is only applicable for a maximum longitudinal road surface slope of 10% [13,14]. Likewise, and in lieu of a special design, similar

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limitations do exist in AASHTO [15]. Nevertheless, Norwegian documents [16] endorse the use of SDM for avalanche protection provided that the maximum 10% slope is extended to at least three times the span from

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the steel pipe/arch edge. This condition may in some cases increase the construction costs to undesirable limits, making the choice of SSCB in such cases less competitive to other conventional alternatives on the market. On the other hand, there exist design guidelines covering the design of traditional concrete protection structures and how to account for avalanche loadings, where in countries like Norway and Switzerland, design procedure are developed and have been in use by practitioners [3,17]. In US and Canada, engineers rely on the experience and standards developed in Europe for guidelines concerning avalanche defence structures [1]. There are potentially several areas of applications where a flexible buried structure can be a strong competitive alternative when built in sloping terrain, where such structures may function as an avalanche 5

ACCEPTED MANUSCRIPT protection gallery for a given road/path, a culvert under ski slope, or even as a protection canopy for a tunnel entrance [18] (compare Fig. 2). The composite action of flexible buried structures entails more understanding of how such structures may perform under asymmetrical soil conditions. The site topography and limitations induce design and construction challenges of which asymmetrical soil support is one main

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concern that may have performance implications on flexible culverts built in hillside locations. Moreover,

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and in some situations, the lack of a sufficient distance for the backfill material placement on the downhill side can be also another challenging factor for design. These factors combined with the nature of avalanche loading raise the question of how a SSCB would perform under these circumstances. This article aims to

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built in sloping terrain under avalanche loading.

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provide first insights of the different factors and criteria that influence the performance of flexible culverts

Fig. 2. A 9.2 m diameter avalanche protection for mine access tunnel, British Columbia, Canada. (Source: www.ailmining.com)

1.2 Avalanche characteristics Prior to design, the characteristics of the avalanche are assessed by an avalanche expert and they are dependent on the terrain area, local climate and location. Normally, the avalanche expert will assess and communicate with the design engineer about the avalanche characteristics inclusive of avalanche flow height, flow velocity, friction coefficients, flow density and those parameters will be used to quantify the 6

ACCEPTED MANUSCRIPT avalanche load intensity on the affected surfaces [3,17]. The return period of the avalanches shall be considered in the design. For instance, Swiss standard defines an avalanche return period of 30 years as variable actions and with a return period of 300 years as accidental actions [17,19]. Typically, there are several loads to be considered when designing traditional protection galleries inclusive of soil pressure,

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weight of snow deposit, avalanche weight, rockfalls, and the dynamic resultant force resulting for the change

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in direction of avalanche flow (compare Fig. 3).

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gallery. (edited from [3])

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Fig. 3. Some typical load types on a protection

In terms of loading conditions, typically, designer has to check for more than one loading case to decide which one is the dominant for design. These cases can be regarded as the different loading scenarios that

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may exist on site. For example, the roof of the structure might have snow deposit combined with an avalanche sliding on it. Other case might be that the avalanche is sliding directly on the soil. Different cases give different friction coefficients [19,20]. Other cases also exist to account for rockfalls [21]. The Norwegian and the Swiss standards provide guidelines on the different load cases that to be considered for design [3,17].

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ACCEPTED MANUSCRIPT 1.3 Scope and limitations This study is part of a series of investigations aiming to provide knowledge about the behaviour of SSCB in sloping terrain. This investigation is considered as a continuation to the previous work performed on SSCB

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in sloping terrain which was concerning soil loading effects [22]. This article deals primarily with live

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loading effects with special focus on the avalanche loads. The idea of this analysis is to perceive the

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difference factors affecting the overall behaviour and how that relates to avalanche loading themes. Generally, there are different loads and loading cases to be considered when designing for traditional

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avalanche protection galleries and those cases are much dependent on the specific project under study. In particular, the study involves investigations on one of the load cases that may occur on a protection

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structure, which might not necessarily be the worst loading scenario, as the intention was not to ultimately design the structures in this specific study. Therefore, the scope of this article is delimited by assuming

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certain construction and geometrical topography schemes that aim to simulate and realize the influence of

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the some factors on the performance of SSCB under avalanche loading. In particular, the height of cover, deviation point proximity and the condition of soil support around the conduit are factors of concern when

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building SSCB in sloping terrain that this study aims to provide insights of how the different selection of designs affects the performance of flexible culverts under avalanche loading.

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This investigation is mainly based on numerical simulations in predicting the performance of SSCB using finite element program called Plaxis 2D. The study is based on introducing different avalanche loading scenarios to two cases of real structures. In light of that, this study shall be read as introductory guidelines of realizing the feasibility and performance of flexible culverts under avalanche loading. Although the analysis includes two different avalanche load models, the study does not aim to compare the results of the two models, since each model may correspond to different details upon design (i.e. return periods, load factors, evaluation of avalanche characteristics) [3,19]. The two load models were included to highlight their similarities and variances and the fact that different models exist in the field. Slope stability of soil was not part of this particular investigation, though, this issue was highlighted to some extent in an earlier study [22]. 8

ACCEPTED MANUSCRIPT Construction, materials, safety aspects, and environment related issues such as drainage, erosion, durability, and others are not part of this discussion. Indeed, these are important topics and normally discussed for an optimum performance of flexible culverts in general and in sloping terrain in particular.

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2 Case studies

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The performance of SSCB depends greatly on the profile shapes of the structures. The importance lies in the geometrical aspects for each profile and their influence on the structural performance. In general, design methods allow for difference profile shapes and the different design methodologies cover the effect of these

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geometrical parameters [13,15,23]. Therefore, and in order to realise such effects, two case studies were

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chosen for this particular investigation representing to some extent the relative changes of the different geometrical parameters. The case studies were selected having in mind their potential areas of application in

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sloping terrain environment, where they could function as avalanche protection gallery or a culvert under a

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ski slope. The same cases were considered in an earlier study where soil loading effects were investigated [22]. Fig. 4 represents Case I, a so called high profile arch while Case II represents a pipe arch structure. The

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geometry of the two cases is based on two real structures built in Poland. Although these structures were not built as avalanche protection measures [22], this study adopted their geometry as bases for the numerical

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introduction of slopes and avalanche loading. The high profile arch of 11.2 m span (Case I) was originally built in Karpacz city using corrugated steel plates of 200×55×7 mm, and was constructed as a 100 m road tunnel under ski slope. The construction was performed by the cut-and-cover method and the soil cover was ranging from 1 to 2.25 m over the crown along the structure. While, Case II of 8.9 m span was constructed in Poznan city to replace a corroded concrete railway bridge and to carry road traffic inside using 150×50×7 mm corrugated steel plates. The pipe arch was backfilled with sand gravel mix and compacted to 98% standard proctor. Detailed description about construction and instrumentation of these structures can be found in [24,25].

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Fig. 4. Geometry of the studied cases (dimensions are

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in meters).

3 Numerical simulation

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3.1 General

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This investigation is based on a two-dimensional finite element modelling software called Plaxis 2D, where it is used to simulate the cases under study. The construction process of flexible culvert plays an important

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role on its overall performance. Therefore, the backfilling operations were essentially included in the

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analysis, where the software allows the user to access the results at any stage of construction. It is worth mentioning that the assumptions and modelling technique themselves are very similar to the

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authors’ previous work [22], where motivations behind interrelated assumptions are more detailed. Yet,

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some of those assumptions will be presented in the following sections.

3.2 Assumptions and input parameters The principle of plain strain model was utilized and used in the analysis. The soil layers and concrete clusters were modelled using a 15-node triangular element, which provide better results accuracy than 6node triangle elements [26]. The elasto-plasticity Mohr-Coulomb material model was used to model the soil behaviour during the analysis. The interface layer between the soil and steel has the same behaviour of the surrounding soil considering a flexible weaker interface represented in the assumed strength interaction parameter Riner being 0.8 instead of a value of 1.0 for rigid connection. The reduced Rinter is reflected in a reduction for the interface strength parameters (i.e. friction angle and cohesion) and the interface stiffness as 10

ACCEPTED MANUSCRIPT well. This is to account for a realistic friction between soil and steel [27]. A medium mesh size was adopted for all the cases given the convergence of results and calculation time. Geometrical nonlinearity was not included in the analysis.

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The corrugated steel wall is represented by a five node plate element in compatibility with the selection of

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15-node triangle element for the soil. The plate has three degrees of freedom in each node representing two

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translations and one rotation. The corrugation geometry itself was not modelled explicitly, instead it is modelled with equivalent axial stiffness EA and bending stiffness EI. In addition, the plasticity of the steel elements was included by defining maximum axial Np and maximum moment Mp capacities and thus

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governed by a simple interaction equation (1), where Plaxis 2D assumes a linear line between the two capacities [26]. The yield stress for steel is assumed to be 315 MPa for all cases. The concrete foundations

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for Case I is modelled using a linear elastic material model with a unit weight of 24 kN/m 3, an elastic

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modulus of 30 GPa and Poisson’s ratio of 0.2 [22].

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N M   1.0 Np Mp

(1)

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Table 1 lists the main input parameters that were used in the analysis for the two case studies covering the soil and steel materials. Apart from cohesion of native soils (refer to section 3.3), the soil parameters were

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assumed similar to the values used in an earlier work on the same case studies, which were based on a partial calibration process [22]. The elastic modulus values of both native and engineered soils are set to increase linearly with depth from the crown point at 2 MPa/m. The friction angle for both soils is assumed constant throughout the analysis. It is worth to highlight that the corrugation for both cases was changed to corrugation sizes of 380×140×5.5 mm and 200×55×7 mm for Case I and Case II respectively. The reason behind this is that the use of the original corrugation mentioned in section 2 led to calculation termination as the structures were already near yielding before the full application of loads for many of the modelled scenarios. So it was promoted to increase the corrugation size to study the full range of behaviour for the introduced loads, where the aim is to have the steel conduit performing in the elastic range away from the 11

ACCEPTED MANUSCRIPT complexity of post-yielding. It is worth mentioning that the connection of the steel arch structure for Case I is assumed hinged to the concrete foundations.

Parameter/Case

I

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3454

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Backfill 19.3 30 43 1 5 0.30

Native 20 30 38 20 5 0.28

1.74×106 2611 32.6 0.3 Backfill 20 20 36 1 5 0.3

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Table 1. Input parameters for the case studies.

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Native 20 30 38 20 5 0.28

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Axial capacity, Np (kN/m) Moment capacity, Mp (kNm/m) Poisson’s ratio, ν Soil properties Unit weight, ρ (kN/m3) Soil elastic modulus, Es (MPa) Friction angle, θ (degree) Cohesion , c (kN/m2) Dilatancy angle, ψ (degree) Poisson’s ratio, ν

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1.49×106 2240 71.2 0.3

Axial stiffness, EA (kN/m)

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Bending stiffness, EI (kNm2/m)

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Steel plate properties

The backfilling layers were simulated by assuming 30 cm soil thickness lifts for the two cases imitating the

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real construction process. The compactions effects were simulated by having a uniform loading activated on each layer of the backfill and to be deactivated once the next layer is placed, where this accounts for the

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change in horizontal earth pressure and volumetric change during compaction. The uniform load intensity was set to 25 kN/m with a 2 m width starting from a 30 cm offset from the wall conduit. The backfilling layers and their associated compaction loads were simulated simultaneously in a symmetrical way at both sides of the conduit. The same technique was used in [22].

3.3 Model configuration Typically, the construction of an avalanche protection gallery for a road depends on the site conditions and the topography of the road and its surrounding terrain. In particular, when building flexible culverts as protection galleries, the method of construction, the excavation volume and the backfilling requirements 12

ACCEPTED MANUSCRIPT influence the final layout of the completed structure. For instance, the lack of space in some cases for backfill at the downhill side (sea side) may require special consideration in term of soil support conditions and stability. On the other hand, the amount of excavation may depend greatly on the road layout in relation to the surrounding steep terrain. In light of that, there can be different project specific construction methods

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and layout configurations when building flexible culverts for avalanche protection and those are project

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specific.

The layout configurations for the simulations are assumed based on a construction scenario where a certain excavation is performed for the conduit installation. The excavation pit for the backfill soil volume is made

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with a 40° excavation angle created at 3 m bottom distance measured from the conduit both sides, which can

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be said to be in line with the backfilling guidelines in [13]. Though, this might be different in reality on the uphill side and depends on site specific soil investigations. The uphill slope is assumed to have a natural

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slope of 30° and the same angle applies to the backfill slope at the downhill side. In order to avoid soil stability issues during analysis, the shear capacity for all native soils is set by assuming 20 kPa as cohesion

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value, which could represent to some extent the nature of the soil in steep hillside locations. Different factors are investigated in this study including the height of soil cover, the deviation point

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proximity and the adopted load model. The ground surface slopes above the structure were introduced from 10% to 30% (≈ 5.7° to 16.7°) in an interval of 10%. For each case, the height of cover was altered considering 1, 2 and 3 m. The slope rotation point was considered vertically above the crown point so that the slopes are introduced by maintaining the selected height of cover at the crown line (compare Fig. 5 and Fig. 6). Upon design, and in order to avoid the dynamic deviation forces from avalanches, the location of deviating point should be as far as possible from the structure (see section 1.1). Therefore, the effect of the deviation point location was investigated by studying the effect of having the point 18 m away from conduit wall. This distance was selected considering that the deviating forces act maximally over a length of 20 m after the deviating point (see section 3.4). The effect of having a closer deviation point was also studied and 13

ACCEPTED MANUSCRIPT compared by setting the deviation point distance Su to 10 m. Fig. 6 shows the different model configurations for Case I and the same applies when modelling Case II. It is worth to highlight that a short study is also performed to see the effect of having less soil support on the downhill side, where few models for Case I are analysed by adjusting the start point of the downhill slope to start just above the wall conduit line at the

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downhill side. Such effect is studied and compared to represent scenarios where there is lack of space for the

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backfill soil at the downhill side. More details are presented in section 4.

Fig. 5. Case I: (a) modelled pipe arch. (b) connectivity plot (shown for 10% slope and 2

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m cover depth).

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ACCEPTED MANUSCRIPT Fig. 6. Case I model extent and configuration.

3.4 Avalanche loads The study covers the effect of two load models for avalanches being Swiss and Norwegian that have been

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used in different countries and developed to their current format [3,17,19]. Both the Norwegian and Swiss documents [3,17] describe how to quantify the resulting forces from an avalanche when designing protection

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galleries. Basically, the indicative hydrostatic loads from avalanches occur because of the flowing part and act on the gallery roof, or the terrain surface, where flowing avalanches generate a normal load on the terrain

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surface Pn and because of friction on the soil, a tangent Pt load on the terrain surface. In addition, and after a longitudinal gradient change, the deviation of the avalanche flow leads to deviating dynamic forces that are

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represented by equivalent static loads [19]. These deviating forces are characterized into a normal load Fn and a parallel load Ft generated on the terrain surface [1] (compare Fig. 7). The flowing loads Pn and Pt

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depend on the inclination of the terrain surface denoted here with the angle β, while deviation forces Fn and

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Ft depend on the flow velocity Vf and the deviation angle α.

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According to Swiss document [17], the avalanche deviating forces act maximally over a distance of 6 times the flow height of an avalanche ds. Yet, close to the deviating point, the deviating force is magnified by 4 times over a distance of 1.5 times the flow height. On the other hand, the Norwegian document [3] evaluates

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the deviation force to act maximally over a distance of 20 m and the distribution is uniform for the first 10 m and then decent linearly for another 10 m distance. Close to the deviation point, the force is calculated and distributed over a length of 5 m (compare Fig. 7).

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Fig. 7. Sketch showing the distribution of deviation forces for both load models (a) and the equivalent total horizontal

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Fx and vertical Fy calculated components for Plaxis 2D input (b)

For the sake of comparison, the avalanche forces for both load models were evaluated based on the

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following characteristics (avalanche velocity Vs = 35 m/s, flow height ds = 3 m, friction coefficient μs = 0.4,

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and avalanche unit weight γs = 4 kN/m3). These presumed values are selected from some typical range

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values provided in [1,17].

The avalanche forces including hydrostatic and deviation forces are calculated using equations (2-7) [3,17],

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which represent both the Swiss and Norwegian load models. The hydrostatic normal Pn and parallel forces Pt for the avalanche are evaluated similarly for both load

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models using the following formulas:

Pn   s  ds  cos   

(2)

Pt  s  Pn

(3)

While, the deviation normal and parallel forces Fn and Ft are calculated differently for each load model using the following equations:

Swiss load model

Fn 

 s  ds Vs2  sin   6  ds  g

(4)

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Ft  s  Fn

Norwegian load model

Fn 

(5)

2   s  ds Vs2  sin  2  10  12  LL  10    g

 cos  2 

(6)

Ft  s  Fn  Fn tan  2 

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(7)

Where g is the acceleration of gravity (9.81 m/s2) and LL is the surface distribution length after the deviation

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point and it is assumed 20 m since the surface length of ground slope is always larger than the maximum act length being 20 m for all the modelled cases (observe Fig. 6). The above equations calculate the non-

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magnified forces that act away from the deviation point. As mentioned earlier, close to the deviation point, the forces are magnified both in the normal and parallel direction (compare Fig. 7). The magnified forces for

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the Swiss case are evaluated as 4 times the non-magnified forces and distributed over a length of 4.5 m (i.e. 1.5ds). While, the magnified forces for the Norwegian case are calculated similar to equations (6) & (7) but

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instead the force Fn is evaluated based on a distribution length of 5 m (i.e. the denominator in equation (6) is

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replaced by 5g).

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Table 2 summarizes the calculated avalanche forces for both load models with respect to the different deviation angles (i.e. slope surface) and their corresponding total horizontal Fx and vertical Fy components

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(compare Fig. 7 and Fig. 8) that are used for Plaxis input. It is worth to highlight that the presented forces in Table 2 are the non-magnified forces of the load models, the magnified portions are calculated similarly as described earlier.

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Pt

N.LM & N.LM & S.LM S.LM

Fn

Ft

Fy

Fx

N.LM

S.LM

N.LM

S.LM

N.LM

S.LM

N.LM

S.LM

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Pn

Total corresponding force components for Plaxis 2D input (kN/m)

Deviation forces (kN/m)

55.8

47.8

24.7

13.8

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Deviation angle α (surface slope)

Hydrostatic forces (kN/m)

47.4

40.7

13.8

7.6

37.8

33.9

5.9

2.9

11.9

4.8

41.1

34.3

16.4

13.7

18.7° (20%)

11.8

4.7

32.0

26.7

12.8

10.7

13.3° (30%)

11.5

4.6

23.0

19.2

9.2

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24.3° (10%)

7.7

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Table 2. Calculated avalanche forces for the Swiss (S.LM) and Norwegian (N.LM) load models along with their total corresponding vertical Fy and horizontal Fx component for Plaxis 2D input.

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Fig. 9 shows how the loads were applied to the analysed models with respect to deviation point distance from wall conduit. The sum of avalanche hydrostatic and deviation forces are applied starting from the deviation

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point along the surface until its maximum act distance being 18 m and 20 m for the Swiss and Norwegian

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load models respectively. After that maximum act distance, only the hydrostatic avalanche loads are applied.

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It should be noted that this study investigates only the load case of having an avalanche sliding on soil surface with no snow deposit above the structure, where this is one of the cases (i.e. load case 1 in [17]) that

analysis.

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an engineer has to check when performing design (see section 1.2). Other load cases were not included in the

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Fig. 8. Calculated avalanche component forces (Fx,

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Fy) and their distribution along the surface ground slope. (shown for a deviation angle α

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Fig. 9. Plaxis 2D snapshots showing Swiss load model with respect to deviation point distance to the structure. (shown for case II, 10% slope and 2 m soil cover)

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=18.7°)

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4 Results and discussion

The results in this section are presented for all the targeted analysed cases. Yet, some of the cases were not

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able to report their results for the reason that they suffered from calculation termination as the structure was already yielding before reaching the stage of complete loading (see section 3.2).

4.1 Displacements The deflection control of flexible culverts is one of the key parameters to control stresses during the construction process. The presence of a steep surface slope induces asymmetrical soil loading on the conduit and thus promotes asymmetrical displacement. Moreover, the nature of avalanche loading in combination with the soil support condition around the conduit may result in undesired displacements.

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ACCEPTED MANUSCRIPT Fig. 10 to Fig. 13 show the overall deformation shapes for all the modelled cases, where results are presented for the different soil depths, surface slopes and avalanche loads. Fig. 10 and Fig. 12 show that when the deviation point is far away from the conduit (i.e. 18 m), the total deformation due to avalanche loads in

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comparison to soil asymmetrical loading is small, while Fig. 11 and Fig. 13 show a more distinct deformation

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due to avalanche in comparison to soil loading. Though having less deviation angle (i.e. more surface slope)

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will result in less avalanche deviation forces, it can be seen that more asymmetrical soil loading (i.e. 30% in comparison to 10%) influences directly the deformation response of SSCB under avalanche loads, which gives an idea of how important the soil support condition is to the overall performance of flexible culverts. In

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relation to that, Fig. 10 to Fig. 13 show the effect of soil cover where it can be seen that increasing the soil

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depth helps to reduce the deformation effect of avalanche loads even in the cases having close deviation point

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and high deviation angles.

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Fig. 10. Deformation shape of case I for 18 m

Fig. 11. Deformation shape of case I for 10 m

deviation point distance (scaled up 10 times)

deviation point distance (scaled up 10 times)

for different cover depths: (a) 1 m, (b) 2 m,

for different cover depths: (a) 1 m, (b) 2 m,

and (c) 3 m

and (c) 3 m

When an avalanche flexible protection structure is hit by an avalanche, it is of an interest to separate and look at the change of horizontal displacement of the structure. Fig. 14 and Fig. 15 show the total maximum 21

ACCEPTED MANUSCRIPT horizontal displacement Ux presented as percentages of span D for case I and II respectively, where one may note the anticipated amount of increase and change in horizontal deformation upon having closer deviation

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point with respect to different soil covers.

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Fig. 13. Deformation shape of case II for 10 m deviation point distance (scaled up 10 times) for different cover depths: (a) 2 m, and (b) 3 m.

Fig. 12. Deformation shape of case II for 18 m deviation point distance (scaled up 10 times) for different cover depths: (a) 1 m, (b) 2 m, and (c) 3 m

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Fig. 15. Scaled colour map for the total maximum

absolute horizontal displacement Ux presented

displacement

Ux

case II.

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4.2 Sectional forces

horizontal

presented as percentages (%) of span D for

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as percentages (%) of span D for case I.

absolute

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Fig. 14. Scaled colour map for the total maximum

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The total maximum absolute values of normal forces and bending moments were extracted from the

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simulated cases. The idea is to see the trend and scale of forces resulted in the wall conduit under the avalanche loads for the different soil conditions. Fig. 16 shows the total maximum absolute normal forces

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occurring in the wall conduit and they are presented as ratios of axial capacity mentioned in Table 1. The normal forces due to soil tend to increase linearly with increasing the surface slope above the structure irrespective of the cover depth, which coincide to a similar observation presented in [22]. While looking at the cases of 18 m deviation point distance, one might note that the linear increase of normal forces due to soil is still larger than the decrease in the applied avalanche loads and that is with respect to increasing surface slopes (i.e. being a result of having less deviation angles). On the other hand, the overall normal forces inclusive of avalanche loads tend to decrease with respect to increasing surface slopes when looking at the cases of closer deviation point distance (i.e. 10 m), which could be rationally referred that the conduit is now sensing more the decrease in the avalanche forces being a result of having less deviation angle. 24

ACCEPTED MANUSCRIPT Similarly to normal forces, the total maximum absolute bending moments were extracted and presented as ratios of the moment capacity (see Fig. 17). The effect of insufficient soil support (i.e. shallow soil cover and steep surface slope) is more pronounced when looking at the change of bending moments especially for Case

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I (compare Fig. 18). In other words, increasing the height of cover could help considerably in reducing the

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bending moments when having the avalanche deviation point close to structure. On the other hand, Fig. 19

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and Fig. 20 present the change factor for sectional forces when having deviation point close to the structure (i.e. 10 m) in relation to a deviation point distance of 18 m. It can be seen that normal forces are increasing for the two cases when having a closer avalanche deviation (Fig. 19), while Fig. 20 shows that Case I is more

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prone to nearby avalanches than case II in terms of bending moments.

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Fig. 17. Total maximum absolute bending moment

Fig. 16. Total maximum absolute axial force N ratio M ratio for case I and case II

for case I and case II.

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Fig. 18. Bending moment distribution for Cases I and

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II (shown for 2 m soil cover, 20% surface

the Swiss load case).

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slope, 10 m deviation point distance and for

In order to get an idea of the stress level for the analysed cases, Fig. 21 and Fig. 22 show the utilization ratios

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for the stress calculated according to equation (1) for case I and II respectively. The incremental change in stress levels for case I due to the different factors is more distinct than case II, which is mostly referred to the changes occurring to bending moments as noted earlier. It is worth to highlight that the maximum utilization ratio calculated in Fig. 21 and Fig. 22 always correspond to the location where the maximum bending moment occurs in the wall conduit. One might note that for a given slope and unlike case I, increasing the height of cover for Case II (see Fig. 22) does not reduce the stresses in the pipe arch, which could be explained by the profile shape and the way of which sectional forces are distribution especially bending moments for the pipe arch (Case II) in comparison to Case I. (Observe Fig. 17, Fig. 18 and section 4.4).

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Fig. 19. Change factor of total maximum N when

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reducing the deviation point distance from 18

reducing the deviation point distance from 18 m to 10 m.

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m to 10 m.

Fig. 20. Change factor of total maximum M when

Fig. 21. Scaled colour map for maximum utilization ratios for Case I.

Fig. 22. Scaled colour map for maximum utilization ratios for Case II.

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ACCEPTED MANUSCRIPT 4.3 Effect of soil support An investigation has been performed to realise the effect of having less soil support on the downhill side, where this condition simulates in some scenarios the lack of space for the backfill material. The analysis was

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performed by making the downhill slope to start at the same line of the wall conduit instead of the 3 m start

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distance that was used in the original models (compare Fig. 23). For the sake of comparison, the analysis was carried out for a 3 m soil cover for Case I and for the case of deviation point distance of 18 m. Fig. 24 shows the sectional forces ratios for the original models (i.e. sufficient distance of 3 m) in comparison to the case

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having less soil support on the downhill side. For the analysed case, Fig. 24 shows that reducing the soil support at the downhill side slope has almost no influence on normal forces, while it can be seen that the

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reduction of soil support at the downhill side resulted in a substantial increase in bending moments especially due to avalanche loads. The results illustrates the importance of having sufficient soil support conditions at

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the downhill side for an optimum performance of SSCB in sloping terrain and under avalanche loads.

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Fig. 24. A comparison showing the effect of having

Fig. 23. Snapshots showing the adopted model for the

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case of having (b) less soil support at the

total maximum absolute sectional forces performed for Case I.

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downhill side in comparison to (a) original

less soil support at the downhill side on the

modelled case. (shown for Case I, 3 m soil cover

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at 30% surface slope)

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4.4 Effect of steel stiffness

A study has been performed to understand the effect of steel stiffness on the structural performance. This was done by changing the steel corrugation size of Case II to a SuperCor that is similar to the assumed steel stiffness of Case I (see Table 1). Hence, the flexural stiffness EI of this modified case has been raised to about 5 times its previous value. The new modified models of Case II were re-analysed for the deviation point case distance of 18 m. Fig. 25 shows the total maximum sectional forces ratio for the said case, where one may note the distinct variation of moment values due to soil in comparison to the previous case condition illustrated in Fig. 17. Fig. 25 also shows that the change of culvert steel stiffness does not seem to affect much the normal forces when compared to the calculated values in Fig. 16. On the other hand, when 30

ACCEPTED MANUSCRIPT comparing Fig. 26 and Fig. 22, one may note that the utilization ratios due to soil tend to reduce when increasing the steel bending stiffness of Case II. However this reduction is less observable when including the effect of avalanche loads, which might be referred to the substantial increase in bending moments as a

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result of having a less flexible structure.

Fig. 26. Left: scaled colour map for maximum utilization ratios for the modified steel stiffness of Case II. Right: reduction factor of utilization ratios.

Fig. 25. Total maximum absolute sectional forces N &

II.

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M ratio for the modified steel stiffness of Case

5 Summary and conclusions In this study, several FE calculations were carried out for two case studies of flexible culverts and their performance under avalanche loading. The objective was first to highlight the use of SSCB as a conceivable alternative to conventional avalanche protection structures, where the study aimed mainly to provide insights concerning the different factors affecting the performance of flexible culverts under avalanche loads. The 31

ACCEPTED MANUSCRIPT effect of soil cover, avalanche proximity, and the soil support conditions, those were the different aspects that were studied and further discussed. Although this article has a limited nature being primarily based on numerical simulations, it however

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provides first insights on how a flexible culvert would perform under different avalanche load models for

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different soil support conditions. The results show that the normal forces tend to change linearly in response

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to avalanche loads. The effect of insufficient soil support (i.e. shallow soil cover and steep surface slope) is more pronounced in the change of bending moments. The proximity of the avalanche deviation point has a considerable influence on the performance of flexible culvert, although increasing the height of cover could

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largely help in reducing the bending moments from a passing avalanche. The steel stiffness of a flexible

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culvert has an important effect on its structural performance under asymmetrical loads, where a more stiff structure may result in higher bending moments from avalanche loads. The downhill soil support

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configuration has substantial effects on the flexural response of SSCB. The wide modern highways would

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require large protection flexible culverts, where in relation to that, it should be noted that the asymmetrical loadings on open profiles (i.e. arches) should demand a higher flexural capacity for the corrugated plate when

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compared to closed profiles.

While this study has covered several key factors that could affect the performance of flexible culverts under

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avalanche loads, other issues such as construction, durability, geotechnical stability, safety aspects in tunnelling and other project specifics are normally addressed and detailed [2]. For instance, one may refer to the Norwegian experience [3,16,28,29] which provides some guidelines on some of those topics that need to be considered upon the design, construction and operation for this kind of application. The new findings presented in this paper are mainly based on numerical simulations. It would be highly desirable to verify the results with full-scale experiments on a real flexible avalanche protection structure. The further implementation of how to device such findings into a design method is of great interest for future work. In addition, the effect of soil reinforcement is of an interest especially when there is a lack of space at

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ACCEPTED MANUSCRIPT the downhill slope for the backfill material. Rockfalls and soil slope stability are also important interesting topics when designing flexible culverts in sloping terrain.

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6 Acknowledgment

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gratitude to ViaCon AB for financially supporting this research.

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The authors would like to express their thanks to Lars Hansing for his continuous support, and extend their

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ACCEPTED MANUSCRIPT References Gabl K, Gauer P, Granig M, Hofmann R, Kleemayr K, Margreth S, et al. The Technical Avalanche

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[1]

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Protection Handbook. 1st ed. Berlin: Wilhelm Ernst & Sohn, Verlag für Architektur und technische

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[3]

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Snøskred, Håndbok V138). Norway (in Norwegian): 2014.

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[10] Du G. Life Cycle Assessment of Bridges, Model Development and Case Studies [PhD thesis]. KTH

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[13] Pettersson L, Sundquist H. Design of Soil Steel Composite Bridges. 5th ed. Stockholm: KTH Royal

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[18] Brox D, Procter P, Stehem C, Jones A, Chipman S, Hill B, et al. Large Avalanche Protection Canopies

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Egilsstaðir,Iceland: The Association of Chartered Engineers in Iceland; 2008, p. 32–7.

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[21] Ebeltoft R, Larsen JO, S N. Instrumentation of Buried Flexible Culvert Subjected to Rockfall Loading. In: Nadim F, Pöttler R, Einstein H, Klapperich H, Kramer S, editors. Geohazards, USA Eds, ECI

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[26] Plaxis bv. Plaxis 2D Reference Manual. Version 2015.01 2015.

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[28] Norwegian Road Administration (Statens vegvesen). Bridge Engineering, Design of bridges, ferry

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piers and other supporting structures, Handbook N400 (Bruprosjektering, Prosjektering av bruer,

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ferjekaier og andre bærende konstruksjoner, Håndbok N400). Norway (in Norwegian): 2015.

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Norway (in Norwegian): 2014.

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ACCEPTED MANUSCRIPT Highlights

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The performance of flexible culverts is investigated when constructed in sloping terrain under defined avalanche loads. A number of 2D finite element models were created to simulate two case studies. The effect of soil cover, avalanche proximity and soil configuration around the conduit were investigated. The downhill soil support configuration has a substantial effect on the flexural response of the structure. The increase in soil cover depth could considerably help in reducing the bending moments resulting from avalanches.

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