1.1 Background
Bridges are a major part of the infrastructure system in developed countries. It has been
estimated that in the USA about 600,000 bridges (Dunker 1993), in the UK about 150,000
bridges (Woodward et al. 1999), in Germany about 120,000 bridges (Der Prüfingenieur 2004)
and in China more then 500,000 road bridges (Yan and Shao 2008) exist. Historical stone arch
bridges still represent a major part of this multitude. It has been estimated that 60 % of all
railway bridges and culverts in Europe are arch bridges (UIC 2005). Recent estimations
regarding the number of historical railway natural stone arch bridges and culverts in Europe lie
between 200,000 (UIC 2005) and 500,000 (Harvey et al. 2007). Also in some regions in
Germany about one third of all road bridges are historical arch bridges (Bothe et al. 2004,
Bartuschka 1995). Dawen & Jinxiang estimate that 70 % of all bridges in China are arch
bridges.
The success of historical natural stone arch bridges - which are often more than 100 years old
- is based on the excellent vertical load bearing behaviour (Proske et al. 2006) and the low cost
of maintenance (Jackson 2004) - not only in mountainous regions. However, changes in loads or
new types of loads (Hannawald et al. (2003) have measured 70 tonne trucks on German
highways under regular traffic conditions and Pircher et al. have measured 100 tonne trucks)
might endanger the safety of such historical structures. Obviously, bridges with an age of more
than 100 years were not designed for motorcars since this mode of transportation has only been
in existence for approximately 110 years. The increase of loads does not only include vertical
loads but also horizontal loads in the longitudinal direction and perpendicular to the longitudinal
direction of these bridges. For example, the weight of inland waterway ships in Germany has
increased dramatically in the last decades, which also corresponds with increasing horizontal
ship impact forces (Proske 2003).
Furthermore some loads from natural processes such as gravitational processes may not have
been considered during the design process of the bridges. Especially in mountain regions this
Historical stone arch bridges under horizontal debris flow impact
Klaudia Ratzinger and Dirk Proske
University of Natural Resources and Applied Life Sciences, Vienna, Austria
ABSTRACT: Many historical arch bridges are situated in Mountain regions. Such historical
bridges may be exposed to several natural hazards such as flash floods with dead wood and
debris flows. For example, in the year 2000 a heavy debris flow destroyed an arch bridge in Log
Pod Mangartom, Slovenia and only recently, in September 2008 an arch bridge was overflowed
by a debris flow. A new launched research project at the University of Natural Resources and
Applied Life Sciences, Vienna tries to combine advanced numerical models of debris flows with
advanced models of historical masonry arch bridges under horizontal loads. The research
project starts with separate finite element modelling of different structural elements of arch
bridges such as spandrel walls, the arch itself, roadway slabs, pavements and foundations under
single and distributed horizontal loads. Furthermore miniaturized tests are planned to investigate
the behaviour of the overall bridge under debris flow impacts. The results will be used to
combine the modelling of the different structural elements considering the interaction during a
horizontal loading. Furthermore this bridge model will then be combined with debris flow
simulation. Also earlier works considering horizontal ship impacts against historical arch
bridges will be used control. The paper will present latest research results.
400 ARCH’10 – 6th International Conference on Arch Bridges
gravitational processes (debris flow impacts (Zhang 1993), rock falls (Erismann and Abele 2001)
and flash floods (Eglit et al. 2007) including water born missiles or avalanches) can cause high
horizontal impact loads.
1.2 Historical Events
In the year 2000, a debris flow destroyed two bridges in Log Pod Mangartom, Slovenia, one of
them was a historical arch bridge. In October 2007 the historical arch bridge in Beniarbeig,
Spain was destroyed by a flash flood. Similarly the Pöppelmann arch bridge in Grimma,
Germany was destroyed in 2002, in 2007 a farm track and public footpath arch bridge over the
River Devon collapsed.
Figure 1: Debris flow impact at the Lattenbach (Proske & Hübl, 2007)
Fig.1 shows an example of the historical arch bridge at the Lattenbach, before and after a debris
flow event, where the bridge is nearly completely filled with debris.
Due to far too expensive solutions or not applicable methods for historical arch bridges it
would be very useful if models were available to estimate the load bearing capacity of historical
masonry arch bridges for horizontal loads perpendicular to the longitudinal direction.
Since intensive research was carried out for the development of models dealing with vertical
loads for historical arch bridges, there is an unsurprising lack of models capable for horizontal
impact forces against the superstructure. This might be mainly based on the assumption that
horizontal loads are not of major concern for this bridge type due to the great death load of such
bridges.
The goal of this investigation is the development of engineering models describing the
behaviour of historical natural stone arch bridges under horizontal forces, mainly debris flow
impacts, focused strongly on the behaviour of the superstructure and based on numerical
simulations using discrete element models and finite element models.
2 INNOVATIVE ASPECT AND GOALS
2.1 Innovative Aspects
The conservation of historical arch bridges is not only an issue of the preservation of cultural
heritage but is also an economic issue since the number of historical bridges in developed
countries is huge (Proske 2009). Compared to vertical load cases no models currently exist for
horizontal loads perpendicular to the longitudinal direction. It is therefore required to develop
new models dealing with these capacious horizontal loads which include all types of
gravitational hazards like avalanches, debris flow, rock falls or flood borne missiles or impacts
from modes of transportation. First works related to the development of debris flow design
impact forces and the behaviour of arch bridges under such an impact have started already 2007
at the Institute of Alpine Mountain Risk Engineering at the University of Natural Resources and
Applied Life Sciences, Vienna (see Fig.2)
Klaudia Ratzinger and Dirk Proske 401
Figure 2 : Examples of the structural behaviour under impacts (left against the pier, right against the arch
itself) (Proske and Hübl 2007)
This investigation and its results regarding debris flow impact will flow into the development of
the new Austrian code of practice Ö-Norm 24801 for the design of structures exposed to debris
flow impacts as well.
2.2 Goal
To develop load bearing behavior models of historical natural stone arch bridges under
horizontal loads perpendicular to the longitudinal direction, a realistic model of debris flow
against solid structures has to be implemented indifferent programs. Separate finite element
modelling of different structural elements of arch bridges such as spandrel walls, the arch itself,
roadway slabs, pavements and foundations under single and distributed horizontal loads are part
of this investigation. Furthermore miniaturized tests are part of the project to investigate the
behaviour of the overall bridge under debris flow impacts. The results will be used to combine
the modelling of the different structural elements considering the interaction during a horizontal
loading. Furthermore this bridge model will then be combined with debris flow simulation. Also
earlier works considering horizontal ship impacts against historical arch bridges will be used.
Therefore three models of historical arch bridges are developed:
(1) Discrete element program model (PFC),
(2) Explicit finite difference program model (FLAC),
(3) Finite element program model (ANSYS, ATENA).
The first and second models are developed to simulate an overall debris flow impact scenario,
whereas the third model is used to investigate details, such as single force against a spandrel
wall, single force against parapets, friction at the arch, single impact force against the arch.
Results from the impact simulation against the superstructure should give an answer, whether
the complete process can be separated into forces acting on the bridge. This reference force
(force-time-function) will then be applied on the finite element models.
The numerical modelling will be accompanied by testing to permit validation of the models.
The tests will be carried out as miniaturized tests (scale about 1:20…50). Already miniaturized
tests of the impact of debris flows against debris flow barriers were already carried out at the
Institute of Mountain Risk Engineering (Proske et al. 2008, Hübl & Holzinger 2003,Fig.3).
Based on this experience, miniaturized arch bridges (span about 40 to 50 cm) will be
constructed and investigated. Also single parts of the arch structure will be investigated in
testing machines, such as behaviour of a pure arch under a horizontal load. Since the machine
cannot be turned, force redirection mechanisms will be used to allow the application of a
standard compression test machine from the University of Natural Resources and Applied Life
Sciences, Vienna.
402 ARCH’10 – 6th International Conference on Arch Bridges
Figure 3 : Side view and view from above of the used debris flow impact measurement test set-up (Hübl
& Holzinger 2003)
3 CALCULATIONS
3.1 Discrete element methods
Discrete element modeling can be done by usingPFC3D (Particle Flow Code 3D) which is used
in analysis, testing and research in any field where the interaction of many discrete objects
exhibiting large-strain and/or fracturing is required. By using the program PFC3D, materials can
be modeled as either bonded (cemented) or granular assemblies of particles.
3.2 Finite element methods
The finite element method (FEM) is one of the most powerful computer methods for solving
partial differential equations applied on complex shapes and with complex boundary conditions.
A mesh made of a complex system of points is programmed containing material and structural
properties defining the reaction of the structure to certain loading conditions. Nodes are
assigned at a certain density throughout the material depending on the anticipated stress levels
of a certain area.
Two types of analysis are commonly used: 2-D modelling and 3-D modelling. 2-D modelling
allows the analysis to be run on a normal computer but tends to yield less accurate results
whereas 3-D modelling shows more accurate results.
For this investigation two FEM programs are used:
(1) ANSYS
(2) ATENA
ANSYS is the leading finite element analysis package for numerically solving a wide variety
of mechanical problems in 2D and 3D. By using ANSYS, the analysis can be done linear and
non-linear, is applicable to static and dynamic structural analysis, heat transfer and fluid
problems as well as acoustic and electromagnetic problems.
The ATENA program is determined for nonlinear finite element analysis of structures, offers
tools specially designed for computer simulation of concrete and reinforced concrete structural
behaviour. Moreover, structures from other materials, such as soils, metals etc. can be treated as
well.
In the first step finite element methods are used to simulate the behaviour of historical natural
stone arch bridges under an impact. Required data for the debris flow models are taken from the
database of the Institute of Mountain Risk Engineering as well from the Austrian Railway
Service (ÖBB).
Klaudia Ratzinger and Dirk Proske 403
The basic requirements for an appropriate assessment of stone arch bridges are:
(1) Choice of a realistic calculation model
(2) Consideration of geometrical and material nonlinearities
(3) Using applicable material models for masonry
(4) Adapted evidence based on the chosen material models.
Therefore, a simplified arch bridge model with various lengths (L), rising of the vault (r) and
thickness of the stone arch (t) was chosen (Fig.4) – first by using a two-dimensional model –
with the purpose to investigate the importance of geometrical properties to their structural
performance and to demonstrate different results. Further models are in process and will be
implemented in the FEM programs as well.
Figure 4 : FE model of a simplified arch bridge (Becke, 2005)
4 CONCLUSIONS
This research project launched by the University of Natural Resources and Applied Life
Sciences, Vienna combines advanced numerical models of debris flows with advanced models
of historical masonry arch bridges under horizontal loads. It started with the implementation of
separate finite element modelling of different structural elements of arch bridges. Furthermore
miniaturized tests will be done in 2010 to investigate the behaviour of the overall bridge under
debris flow impacts. The results will be used to combine the modelling of the different structural
elements considering the interaction during a horizontal loading and the bridge model will be
combined with debris flow simulation.
Last but not least recommendation values for such bridge types should be given by this
investigation that may include further formulas considering for example the adaptation of
masonry stiffness or strength values.
1介绍
1.1背景
桥梁是发达国家的基础设施系统的一个主要部分。在美国估计约有60万座桥(Dunker 1993年),在英国约有15万座桥((Woodward et al 1999年),在德国约12万座桥(Prufingenieur2004年)。在中国超过50万座公路桥梁(Yan and Shao 2008)。历史石拱门任然是这众多桥梁中的主要部分。根据估计,有60%的铁路桥梁在欧洲是拱桥(UIC 2005)。最近的估计,关于在欧洲历史的数量和天然石拱桥铁路桥在20万(UIC 2005年之间)和50万(哈维孙俐。2007年)之间。在德国一些地区也有约三分之一的公路桥梁是历史拱桥((Bothe et al. 2004,Bartuschka 1995)。Dawen & Jinxiang估计, 在中国70%的桥梁是拱桥。
成功的历史自然石拱桥通常都有100多年了,这是基于优秀的垂直承载能力以及低廉的维护成本,并且不仅仅是在山区地区。然而,负载的改变或新的类型的负荷已经开始威胁到这种历史建筑的安全性,在德国高速公路上已有70吨的卡车和100吨的卡车等大型车辆。很明显,设计超过100年的桥当时设计时并没有考虑到汽车这种大约已有110历史的运输工具的变化。外加载荷的增大不仅包括垂直方向的加载,水平荷载作用下对这些桥梁的纵向也有影响。例如, 在德国内陆船的重量在过去的几十年急剧增加,这也符合增长趋势。此外一些自然过程中产生的负荷如重力过程,在设计过程中可能没有没有被考虑。特别是在山区历史石拱桥在泥石流冲击下的水平冲击作用的影响。针对许多历史拱桥都坐落在山区,这样的历史桥梁可能暴露在多种天然危险下,如山洪暴发等。例如,在2000年一场严重的泥石流摧毁了一座拱桥。一项新的研究项目,在自然资源和应用生命科学大学展开,维也纳尝试将先进的数值模型的泥石流与先进的历史砌体拱桥模型在水平荷载作用下相结合。研究项目都有单独的不同结构的有限元建模元素的拱桥承受车辆荷载的作用,例如拱本身,车道和人行道板在集中荷载和分布式水平荷载作用的情况。此外小型化测试计划也在进行调查研究全桥在泥石流作用下的影响情况。这个结果将被用来结合不同结构的造型元素的相互作用中考虑水平加载。此外该桥梁模型还可进行泥石流仿真研究。早期的研究也考虑了横向船对历史拱桥影响的控制。本文将陈述目前的最新研究成果。
400拱拱桥的国际研讨会重力进程、岩石下(1993年Erismann和Abele 2001年),Eglit和山洪学组。(2007年,包括水生成导弹或雪崩)可引起高横向冲击载荷。120历史事件,在2000年,一个泥石流摧毁了两个桥梁在日志圆荚体Mangartom、斯洛文尼亚、之一。他们就是一种历史的拱门大桥。2007年10月Beniarbeig历史拱桥,西班牙毁在突发的洪水。同样Poppelmann拱桥在Grimma,德国在2002年被摧毁了。在2007年,一个农场和公共走道拱桥轨道上河德文郡倒塌了。由于过于昂贵的解决方案,或是不适用的方法,对于历史的拱桥如果模型可用来估计的承载能力将非常有助。砌体拱桥为水平荷载作用下的纵向方向垂直。自从密集的研究进行了模型处理发展垂直,在对历史的拱桥荷载,有明显的缺乏模型对水平力对上部结构的影响的研究。这可能是主要是基于一个假设,即水平荷载作用下主要关心的不是这桥式由于负荷的巨大破坏。这个调查的目的是发展工程模型,来描述历史自然行为的水平力对石拱桥的影响,主要是泥石流的影响、集中的强烈的作用对于上部结构的影响和基于数值利用离散元模拟模型和有限元模型进行分析。
2创新方面和目标
2.1创新方面
保护古城拱桥不仅仅是一个保护的问题,而且是文化遗产的问题,并且也是一个经济问题。巨大数量的历史桥梁在发展。垂直载荷工况相比,目前对于水平荷载作用下的纵向方向的影响分析面的模型还不完善。因此有必要开发新模型处理这些广泛的水平荷载作用,包括所有类型的重力危害,像雪崩、泥石流、岩石承担摔倒或洪水激流等。在这种趋势的影响下,早期的关于影响拱桥的设计在2007年在自然资源和应用生命科学大学已经开始。此调查结果对于泥石流冲击的发展将流入碎片流动的影响。
2.2目标
为了发展研究历史自然石拱桥在水平荷载作用下的纵向方向影响的承载行为模型,于现实,模型的碎屑流对固体结构必须实施无干扰的程序。分开的有限元不同的结构元素的造型,如车辆拱桥的墙壁,拱本身,大板、路面巷道和人行道板在集中力和分布式水平荷载作用部分下的调查。此外小型化测试项目的一部分探讨全桥在泥石流带来的影响下的状况。结果将用于组合
不同结构的造型元素的相互作用过程中考虑水平加载。此外该桥梁模型也会结合泥石流的仿真研究。早期研究也考虑了横向船对历史拱桥的影响。
因此三种模式的历史拱桥是被发展:
(1)离散单元程序模型(全氟化碳的),
(2)显式有限差分程序模型(FLAC),
(3)模型(ANSYS有限元程序,ATENA)。
第一种和第二种模型用来模拟一个全面发展的情形下,泥石流冲击。而第三种模式用于研究细节,比如单缸力对抗作用墙、单武力对抗围墙、摩擦在拱门,单一的冲击力量对拱门的作用。从对上部结构仿真影响结果,可以给出一个答案。完整的过程可以分为有力作用在这座桥,这一提法的作用将被应用于有限元模型。这将伴随数值模拟的验证测试,以允许模型。该测试将被进行规模小型化的测试。已小型化测试泥石流对壁垒的影响。
3计算
3.1离散单元方法
离散单元模型可以通过颗粒流使用它,在任何领域分析、测试和研究许多离散目标的互动
来展示。通过使用该程序PFC3D、材料即可被提取出来作为要么保税(胶结)或颗粒状总成的微粒。
3.2有限元方法
有限元法(FEM)是用最强大的计算机的方法来解决偏微分方程,应用于复杂的形状和复杂的边界条件。网中所构成的复杂系统的积分是程序包含材料和结构定义的反应性能和结构对某些加载条件下的状态。节点指定在一定的密度里,整个资料取决于预期的应力水平。
两种类型的分析常用:二维和三维造型,二维造型的造型允许分析是运行在一个正常的电脑,但往往产生不甚准确的结果,而显示三维造型更精确的结果。
在这个研究有限元程序使用:两个
(1)ANSYS
(2)ATENA
ANSYS有限元分析是在对二维和三维力学问题中最主要的数值包中求解一个
复杂的解。利用ANSYS,做了分析和线性非线性求解,适用于静态和动态结构分析、传热和流体问题以及声学和电磁问题。
确定了ATENA程序的结构的非线性有限元分析,提供了专为计算机模拟工具的混凝土和钢筋混凝土结构模式。此外,结构与其他材料,如土壤、金属等可视为兼容。在第一步有限元方法用于模拟历史自然的作用对石拱桥产生的深远影响。模型所需资料是研究所的数据库的泥石流研究记录。
适当的基本要求是评估石拱桥。
(1)选择一种现实的计算模型
(2)考虑几何、材料非线性的
(3)使用适用的材料模型。
(4)改编的数据的基础上选定材料模型。
因此,一个简化模型和不同长度的拱桥(L),上升的拱顶(r)和厚度的石拱门(t),首先运用二维模型,明确调查的重要性,其结构的几何性质性能,从而显示了不同的结果。并进一步的将过程在有限元数值模拟的基础上实施方案。
4结论
这一研究项目是由自然资源和应用生命科学大学推出的,结合了先进科学,维也纳的泥石流数值模式与先进的模型历史的砌体拱桥在水平荷载作用下的影响。它开始实施分开不同结构的有限元建模元素的拱桥。此外,小型化的测试将在2010年完成,探讨全桥的在泥石流张狂下的影响。结果将用来联合不同结构的造型在考虑相互作用的元素水平加载和桥梁模型将会如何结合泥石流仿真。最后但并非最不重要的推荐值类型应给予这样的桥梁调查,可能包括进一步公式考虑例如改编而成的砌体强度刚度或价值观。