Shock and Vibration

Volume 2016 (2016), Article ID 7871089, 15 pages

http://dx.doi.org/10.1155/2016/7871089

## Development of a Vehicle-Bridge-Soil Dynamic Interaction Model for Scour Damage Modelling

^{1}School of Civil, Structural and Environmental Engineering, University College Dublin, Newstead, Belfield, Dublin 4, Ireland^{2}School of Planning, Architecture and Civil Engineering, Queen’s University Belfast, University Road, Belfast BT7 1NN, UK

Received 1 July 2015; Revised 19 August 2015; Accepted 23 August 2015

Academic Editor: Ruqiang Yan

Copyright © 2016 L. J. Prendergast et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Damage detection in bridges using vibration-based methods is an area of growing research interest. Improved assessment methodologies combined with state-of-the-art sensor technology are rapidly making these approaches applicable for real-world structures. Applying these techniques to the detection and monitoring of scour around bridge foundations has remained challenging; however this area has gained attraction in recent years. Several authors have investigated a range of methods but there is still significant work required to achieve a rounded and widely applicable methodology to detect and monitor scour. This paper presents a novel Vehicle-Bridge-Soil Dynamic Interaction (VBSDI) model which can be used to simulate the effect of scour on an integral bridge. The model outputs dynamic signals which can be analysed to determine modal parameters and the variation of these parameters with respect to scour can be examined. The key novelty of this model is that it is the first numerical model for simulating scour that combines a realistic vehicle loading model with a robust foundation soil response model. This paper provides a description of the model development and explains the mathematical theory underlying the model. Finally a case study application of the model using typical bridge, soil, and vehicle properties is provided.

#### 1. Introduction

##### 1.1. Motivation for Modelling Damage in Civil Engineering Structures

Farrar and Worden [1] give a very useful overview of the area of structural health monitoring (SHM). They point out that the motivation for governments and private companies implementing this technology is due to the economic and potentially lifesaving impact it can have. Dimarogonas [2] points out that online damage detection/monitoring started in the early 1970s when power companies started looking at developing ways of identifying defects in rotating shafts while machinery was in use. To date this kind of condition monitoring of rotating machinery has been the most successful application of SHM and it is almost entirely non-model based [1]. Effectively these machines have quite a narrow range of operating behaviours so anomalies are relatively easy to identify. As there were many of these machines in service, over time it was thus possible to develop databases that allowed specific types of damage (e.g., chipped gear teeth or damaged bearings) to be identified from particular features of the machine’s vibration signature. This concept of looking for damage-sensitive features in a response signal is central to SHM. Typically an SHM algorithm works by seeking a damage feature in a response signal or by identifying a change in some characteristic of the structure when it is damaged, for example, natural frequency, mode shapes, or damping. For rotating machinery these damage features could be identified relatively easily through experiments or by correlating monitoring data with subsequent servicing records. The first instance of applying the SHM philosophy to large scale civil engineering structures was in the 1970s and 80s when the oil industry began attempting to apply this technology to offshore platforms. In comparison to damage arising in rotating machines, this time the structures were large and multiple damage locations/severities were possible so the nature of the damage features was typically unknown. Therefore, it was necessary to simulate candidate damage scenarios using numerical models, in order to, for example, observe how that damage affected the frequency of the platform. The idea behind this was that if this frequency was subsequently observed in the field it could be correlated to a given damage scenario. In general the challenges of applying vibration-based SHM to offshore platforms are significant as factors such as variations in the mass of the structure due to changes in the mass of the storage tanks and changes in the amount of marine growth on the structure can prove problematic.

The development of SHM tools for bridge engineering faces the same challenges as the oil industry in that it is very rare that one can take a full size test piece and apply damage for the purpose of developing monitoring tools. In fact it is practically unheard of in bridge engineering, as the structures themselves are just too valuable/important to interfere with. Therefore when researchers wish to try and develop a new SHM algorithm to detect a particular type of defect in the structure, the first task is to try and understand how damage affects the response of the structure. To establish this, their options (broadly speaking) are to use a computer model [3] and/or a laboratory experiment using a scaled model of the structure [4]. Occasionally it will be possible to test at full scale when a bridge is due to be retrofitted, for example, a scoured but retrofitted bridge in Italy; see [5]. However, in many cases the first option is a computer model to undertake simulations of candidate damage scenarios. The challenge, therefore, is to develop a model that outputs realistic results. A numerical model that outputs signals that are representative of those likely to be encountered on the real structure is a very useful tool when trying to develop new SHM algorithms. This paper aims to develop just such a model, as, by including vehicle-bridge interaction and soil-structure interaction, every effort is made to make the loading (applied to the bridge) and the (soil) boundary conditions of the model as realistic as possible. It should be noted that the aim of this paper is not to develop a new SHM technique for scour detection but to present the basis of a model to make it easy for others to test emerging SHM techniques by allowing them to generate realistic bridge response signals occurring due to foundation scour. Section 1.2 gives some examples of numerical models developed to simulate damage in beam-like structures, where the model outputs (e.g., acceleration, velocity, or displacement signals) were subsequently used as inputs to damage detection algorithms. This section also provides a discussion on previous works focussed on modelling scour damage.

##### 1.2. Modelling Structural Damage for SHM Algorithm Development

Over the past two decades several authors have prepared models of damaged structures with a view to developing SHM algorithms to detect this type of damage. A particular focus has been given to models which represent localised damage in a structure (e.g., cracking or section loss). Ostachowicz and Krawczak [6] describe the different methods commonly used to model structural stiffness loss due to damage. Friswell and Penny [7] give a very useful overview on crack modelling for SHM. They point out that approaches for modelling cracks in beam type structures typically fall into three categories: local stiffness reduction [8], discrete spring models [9], and complex models in two or three dimensions. They compare the three approaches and broadly speaking they conclude that, for structural health monitoring which utilises low frequency vibration, simple models of crack flexibility based on beam elements are adequate.

Other authors have developed models to simulate the response signals of damaged beam structures to moving loads and then used the signals from these models as inputs to SHM algorithms. A number of authors have simulated the structure as having a localised loss in stiffness and then calculated the response to a moving point force [10]. Hester and González [11] modelled a similar type of damage; however they modelled the moving load as a sprung vehicle to incorporate vehicle-bridge interaction effects, that is, to make the simulated response signals as realistic as possible. This is important when numerically testing the versatility of a new SHM algorithm before applying it to a real structure. Others have postulated that the occurrence of damage will affect the damping of the bridge and prepared numerical models to simulate this by analysing the vehicle acceleration signals output from the model [12]; that is, this is an indirect monitoring approach as the vehicle response passing over a damaged bridge is used to detect the damage feature.

In terms of scour modelling, several authors have investigated the effect of scour on the static and dynamic properties of bridges using numerical methods. The principle underlying these approaches is that, during scour, loss of soil contact occurs which leads to higher applied stress over the area of soil remaining in contact with the foundation. This, coupled with the nonlinear stiffness of soils, leads to lower operational system stiffness [13]. Therefore scour presence should be detectable as a change in the dynamic properties of the structure. Ju [14] developed a 3D FE model of a bridge incorporating soil-structure and fluid-structure interaction to assess the magnitude of the change in natural frequency of the bridge with increasing scour. They validated the bridge natural frequencies from the model against a full-scale field experiment and then used the numerical model to study various scour conditions and how it affected the bridge’s natural frequency. They concluded that scour causes a reduction in bridge natural frequency but the magnitude of the frequency change with scour is affected by varying foundation geometry and layering in foundation soils. Chen et al. [15] developed a full FE model of a cable-stayed bridge with a pylon and a pier. They updated the model properties to obtain a match to modal data obtained from the actual structure. They then used known data about the pylon foundation condition to obtain representative soil stiffness (matching the stiffness of the actual soil). The numerical model was then used to update the scour depth around the pier until the predicted frequency data matched the observed data. In this case, the numerical model was used to ascertain the actual scour condition around the real pier and this paper serves as a successful real-life application of a vibration-based scour detection method. Klinga and Alipour [16] developed a numerical model to assess the effect of scour on various static and dynamic performance features of a bridge. They used their model to perform pushover analyses, buckling analyses, and modal analyses under extreme scour conditions to assess the effect of scour on the various bridge elements such as the piles and columns. They present a number of case studies of affected performance features due to scour.

Unlike authors working in the area of bridge damage via cracking and so forth, for the purpose of scour detection, many authors have developed models to specifically perform a single task only, that is, to establish the depth of scour around a foundation element or assess the change in bridge performance under scoured conditions. No authors to date have developed a model capable of rapidly modelling a variety of bridge scour scenarios with the flexibility to test emerging SHM techniques. This paper aims to develop a numerical model that can generate dynamic signals (displacement, velocity, and acceleration) from a bridge under a variety of input loading/scour scenarios in order to allow users to develop and/or test SHM algorithms. Because of the increasing popularity of integral bridges, the structure modelled in this paper is a two-span integral bridge. Details about this type of bridge are given in Section 2.1. Section 1.3 summarises the aims of the model presented in this paper.

##### 1.3. Generic Algorithm for Modelling Integral Bridge Scour

###### 1.3.1. Method

In order to develop a representative vehicle-bridge interaction model for the purpose of simulating the effect of scour on the dynamic response of an integral bridge, a number of key assumptions are made. In the first instance, to aid in the rapid generation of dynamic data, the integral bridge is assumed to act as a 2D frame system. The reason behind this is twofold: (i) it is assumed that the dynamic movements of interest for scour on an integral bridge predominately take place in the longitudinal direction (it is acknowledged that this assumption may not hold true for other bridge types; e.g., [15] found that for a cable-stayed bridge the first horizontal flexural and second torsional mode of the pylon were the most sensitive to scour) and (ii) 3D numerical modelling is very user and computationally costly and the resulting signals of interest are not expected to vary significantly from those in a 2D system. For these reasons, transverse and torsional motion of the integral bridge is neglected. The benefit of a 2D frame system is that a variety of representative bridges can be rapidly modelled, as the user only has to specify a relatively small number of parameters (bridge element structural and geometric properties, vehicle parameters such as axle spacing and mass). For the purpose of generating signals to test emerging SHM concepts, this is deemed adequate.

Scour can be modelled around both the central pier and the left and right abutments of the bridge and is considered as the increase in effective length of the bridge pier/abutments corresponding to a decrease in bed elevation level. The stiffness of the soil can be varied to be representative of soils from loose to dense in situ conditions that are typical of the range of ground conditions encountered in riverine environments. The foundation scour model used in this paper is derived from previously validated work undertaken by the authors (see Section 1.3.2). The method for modelling the various bridge elements, namely, deck, abutments, pier, and soil, is discussed in detail in Section 2.

###### 1.3.2. Validation of Scour Model

The greatest uncertainty with regard to bridge input parameters relates to the soil stiffness. It is imperative to specify soil properties that adequately reflect the boundary stiffness effects of the soil likely to be encountered in the field for the purpose of accurate scour modelling. The method for deriving soil stiffness for scour evaluation comes from an experimental investigation undertaken by [17]. In this work, the authors measured the change in the natural frequency of a full-scale pile to manually induced scour. The field measurements were compared to numerical models developed using a Winkler spring-beam methodology (see Section 2.3). Two different methods were used to estimate the soil stiffness; the first derived soil stiffness based on the shear modulus of the soil obtained from the Multichannel Analysis of Surface Waves (MASW) (see [18]); the second method used estimates of shear modulus from a correlation to measured Cone Penetration Test (CPT) tip resistance () data measured at the experimental site. The results of the frequency change with scour are reproduced in Figure 1.