Valutazione della possibilità di utilizzo di programmi di elaborazione gratuiti per la correlazione digitale di immagini

Negli ultimi anni la tecnica di misura della correlazione digitale di immagini (“Digital Image Correlation” = DIC) sta trovando numerose applicazioni nell’ambito della meccanica sperimentale come valida alternativa per misure di campi di deformazione su componenti strutturali soggetti a carichi statici e dinamici. Misurare deformazioni in provini troppo piccoli, troppo grandi, teneri o caldi, è un tipico scenario in cui diventano necessarie le tecniche senza contatto in quanto l’applicazione di estensimetri risulta inefficiente. L’obiettivo di questo lavoro consta nel valutare l’applicabilità e l’accuratezza di programmi di elaborazione gratuiti per la correlazione digitale di immagini evidenziandone il metodo di utilizzo e l’autenticità dei risultati verificati attraverso prove in laboratorio. Tali programmi, per praticità e gratuità, nel campo bidimensionale, possono considerarsi una valida alternativa a programmi commerciali di elevato costo. Nonostante ciò, presentano alcune criticità e limitazioni che emergeranno dalle attente sperimentazioni effettuate. Verrà così definita la corretta e necessaria preparazione del set up sperimentale antecedente la prova e il campo di applicabilità a cui si prestano tali programmi per un preciso ed autentico rilevamento delle deformazioni subite da un corpo sottoposto a sollecitazioni, al pari di un comune estensimetro.

Ottimizzazione dei parametri di acquisizione ed elaborazione per l'analisi di segmenti ossei tramite correlazione di immagini digitali

La Correlazione digitale d’immagini (digital image correlation, DIC) è una tecnica di misura delle deformazioni e degli spostamenti, relativamente nuova, che permette di fare misure a tutto campo di tipo non invasivo. In questa tesi di Laurea Magistrale in Ingegneria Meccanica si è proceduto alla sua ottimizzazione e validazione per un’applicazione di tipo biomeccanico (distribuzione di deformazioni in segmenti ossei). Sono stati indagati i parametri di post-processo, di pre-acquisizione e di preparazione del provino. Per la validazione dello strumento sono stati confrontati i risultati ottenuti da provini di forma semplice con quelli teorici, così da avere una stima di quanto il dato misurato si discosti da quello reale. Infine, quanto appreso prima, è stato applicato a una vertebra umana, oltrepassando il limite, finora presente, di misure puntuali con estensimentri.

High-speed Imaging of a Bulk Metallic Glass During Uniaxial Compression

High-speed imaging directly correlates the propagation of a particular shear band with mechanical measurements during uniaxial compression of a bulk metallic glass. Imaging shows shear occurs simultaneously over the entire shear plane, and load data, synced and time-stamped to the same clock as the camera, reveal that shear sliding is coincident with the load drop of each serration. Digital image correlation agrees with these results. These data demonstrate that shear band sliding occurs with velocities on the order of millimeters per second. Fracture occurs much more rapidly than the shear banding events, thereby readily leading to melting on fracture surfaces.

Development of a balanced experimental–computational approach to understanding the mechanics of proximal femur fractures

The majority of people who sustain hip fractures after a fall to the side would not have been identified using current screening techniques such as areal bone mineral density. Identifying them, however, is essential so that appropriate pharmacological or lifestyle interventions can be implemented. A protocol, demonstrated on a single specimen, is introduced, comprising the following components; in vitro biofidelic drop tower testing of a proximal femur; high-speed image analysis through digital image correlation; detailed accounting of the energy present during the drop tower test; organ level finite element simulations of the drop tower test; micro level finite element simulations of critical volumes of interest in the trabecular bone. Fracture in the femoral specimen initiated in the superior part of the neck. Measured fracture load was 3760 N, compared to 4871 N predicted based on the finite element analysis. Digital image correlation showed compressive surface strains as high as 7.1% prior to fracture. Voxel level results were consistent with high-speed video data and helped identify hidden local structural weaknesses. We found using a drop tower test protocol that a femoral neck fracture can be created with a fall velocity and energy representative of a sideways fall from standing. Additionally, we found that the nested explicit finite element method used allowed us to identify local structural weaknesses associated with femur fracture initiation.

Spalling uniaxial strength of Al2O3 at high strain rates

In this article research into the uniaxial tensile strength of Al2O3 monolithic ceramic is presented. The experimental procedure of the spalling of long bars is investigated from different approaches. This method is used to obtain the tensile strength at high strain rates under uniaxial conditions. Different methodologies proposed by several authors are used to obtain the tensile strength. The hypotheses needed for the experimental set-up are also checked, and the requirements of the set-up and the variables are also studied by means of numerical simulations. The research shows that the shape of the projectile is crucial to achieve successfully tests results. An experimental campaign has been carried out including high speed video and a digital image correlation system to obtain the tensile strength of alumina. Finally, a comparison of the test results provided by three different methods proposed by different authors is presented. The tensile strength obtained from the three such methods on the same specimens provides contrasting results. Mean values vary from one method to another but the trends are similar for two of the methods. The third method gives less scatter, though the mean values obtained are lower and do not follow the same trend as the other methods for the different specimens.

Fracture propagation and stress corrosion in the case of dissimilar laser hybrid welded joints

The paper addresses the fracture propagation and stress corrosion behaviour of laser hybrid welds achieved between low carbon steel and stainless steel thin sheets. The crack propagation within these overmatched in strength welds was investigated by crack tip opening displacement (CTOD) on CT specimens notched transverse to the weld. A Digital Image Correlation System was used to qualify and estimate the initial crack length obtained by fatigue. The results are associated with the fractographic examinations of various regions of laser hybrid joints. Stress corrosion behaviour of the joint is also discussed.

Análisis de metodologías para la medida de la resistencia a tracción por spalling

En el presente trabajo se presenta un estudio teórico y experimental de la determinación de la resistencia a tracción de materiales frágiles a partir de la técnica experimental de spalling. Se utilizan diferentes metodologías propuestas por varios autores para determinar la resistencia a tracción por spalling y se lleva a cabo un estudio mediante simulaciones numéricas de las diversas variables que influyen en este tipo de ensayos. Además, se realiza una campaña experimental de ensayos a una alúmina del 99,5% de pureza cuyos resultados son utilizados para la determinación de la resistencia a tracción de este material a partir de tres métodos diferentes propuestos por varios autores. Se expone el estudio y comparación de los resultados experimentales obtenidos de resistencia a tracción de la alúmina empleando técnicas de fotografía a alta velocidad y un sistema de correlación digital de imágenes. Los resultados muestran que la resistencia a tracción obtenida difiere en función de las diferentes metodologías propuestas.A theoretical and experimental study of the tensile strength of brittle materials using the experimental procedure of spalling of long bars is presented in this article. Different methodologies proposed by several authors are used to obtain the tensile strength of Al2O3 monolithic ceramic. The hypotheses needed for the experimental set-up are also checked, and the requirements of the set-up and the variables are also studied by means of numerical simulations. An experimental campaign has been carried out including high speed video and a digital image correlation system to obtain the tensile strength of alumina. Finally, a comparison of the test results provided by three different methods proposed by different authors are presented. The tensile strength obtained from three different methods on the same specimens provides different results.

Effect of strain and magnetic field on the critical current and electric resistance of the joints between HTS coated conductors

Engineering of devices and systems such as magnets, fault current limiters or cables, based on High Temperature Superconducting wires requires a deep characterization of the possible degradation of their properties by handling at room temperature as well as during the service life thus establishing the limits for building up functional devices and systems. In the present work we report our study regarding the mechanical behavior of spliced joints between commercial HTS coated conductors based on YBCO at room temperature and service temperature, 77 K. Tensile tests under axial stress and the evolution of the critical current and the electric resistance of the joints have been measured. The complete strain contour for the tape and the joint has been obtained by using Digital Image Correlation. Also, tensile tests under external magnetic field have been performed and the effect of the applied field on the critical current and the electric resistance of the joints has been studied. Finally, a preliminary numerical study by means of Finite Element Method (FEM) of the mechanical behavior of the joints between commercial HTS is presented.

Effect of strain and magnetic field on the critical current and electric resistance of the joints between HTS coated conductors

Engineering of devices and systems such as magnets, fault current limiters or cables, based on High Temperature Superconducting wires requires a deep characterization of the possible degradation of their properties by handling at room temperature as well as during the service life thus establishing the limits for building up functional devices and systems. In the present work we report our study regarding the mechanical behavior of spliced joints between commercial HTS coated conductors based on YBCO at room temperature and service temperature, 77 K. Tensile tests under axial stress and the evolution of the critical current and the electric resistance of the joints have been measured. The complete strain contour for the tape and the joints has been obtained by using Digital Image Correlation. Also, tensile tests under external magnetic field have been performed and the effect of the applied field on the critical current and the electric resistance of the joints has been studied. Additionally, fatigue tests under constant cyclic stress and loading-unloading ramps have been carried out in order to evaluate the electromechanical behavior of the joints and the effect of maximum applied stress on the critical current. Finally, a preliminary numerical study by means of the Finite Element Method (FEM) of the electromechanical behavior of the joints between commercial HTS is presented.

Mechanical behavior of 2G REBCO HTS at 77 and 300 K

El gran esfuerzo realizado durante la última década con el fin de integrar los diferentes materiales superconductores en el campo de los sistemas eléctricos y en otras aplicaciones tecnológicas ha dado lugar a un campo de investigación amplio y prometedor. El comportamiento eléctrico de los Superconductores de Alta Temperatura (SAT) crítica (masivo y cintas) depende de diferentes parámetros desde su fabricación hasta la aplicación final con imanes o cables. Sin embargo, las aplicaciones prácticas de estos materiales están fuertemente vinculadas con su comportamiento mecánico tanto a temperatura ambiente (manipulación durante fabricación o instalación) como a temperaturas criogénicas (condiciones de servicio). En esta tesis se ha estudiado el comportamiento mecánico de materiales masivos y cintas de alta temperatura crítica a 300 y 77 K (utilizando nitrógeno líquido). Se han obtenido la resistencia en flexión, la tenacidad de fractura y la resistencia a tracción a la temperatura de servicio y a 300 K. Adicionalmente, se ha medido la dureza mediante el ensayo Vickers y nanoindentación. El módulo Young se midió mediante tres métodos diferentes: 1) nanoindentación, 2) ensayos de flexión en tres puntos y 3) resonancia vibracional mediante grindosonic. Para cada condición de ensayo, se han analizado detalladamente las superficies de fractura y los micromecanismos de fallo. Las propiedades mecánicas de los materiales se han comparado con el fin de entender la influencia de las técnicas de procesado y de las características microestructurales de los monocristales en su comportamiento mecánico. Se ha estudiado el comportamiento electromecánico de cintas comerciales superconductoras de YBCO mediante ensayos de tracción y fatiga a 77 y 300 K. El campo completo de deformaciones en la superficie del material se ha obtenido utilizando Correlación Digital de Imágenes (DIC, por sus siglas en inglés) a 300 K. Además, se realizaron ensayos de fragmentación in situ dentro de un microscopio electrónico con el fin de estudiar la fractura de la capa superconductora y determinar la resistencia a cortante de la intercara entre el substrato y la capa cerámica. Se ha conseguido ver el proceso de la fragmentación aplicando tensión axial y finalmente, se han implementado simulaciones mediante elementos finitos para reproducir la delaminación y el fenómeno de la fragmentación. Por último, se han preparado uniones soldadas entre las capas de cobre de dos cintas superconductoras. Se ha medido la resistencia eléctrica de las uniones con el fin de evaluar el metal de soldadura y el proceso. Asimismo, se ha llevado a cabo la caracterización mecánica de las uniones mediante ensayos "single lap shear" a 300 y 77 K. El efecto del campo magnético se ha estudiado aplicando campo externo hasta 1 T perpendicular o paralelo a la cinta-unión a la temperatura de servicio (77 K). Finalmente, la distribución de tensiones en cada una de las capas de la cinta se estudió mediante simulaciones de elementos finitos, teniendo en cuenta las capas de la cinta mecánicamente más representativas (Cu-Hastelloy-Cu) que influyen en su comportamiento mecánico. The strong effort that has been made in the last years to integrate the different superconducting materials in the field of electrical power systems and other technological applications led to a wide and promising research field. The electrical behavior of High Temperature Superconducting (HTS) materials (bulk and coated conductors) depends on different parameters since their processing until their final application as magnets or cables. However, practical applications of such materials are strongly related with their mechanical performance at room temperature (handling) as well as at cryogenic temperatures (service conditions). In this thesis, the mechanical behavior of HTS bulk and coated conductors was investigated at 300 and 77 K (by immersion in liquid nitrogen). The flexural strength, the fracture toughness and the tensile strength were obtained at service temperature as well as at 300 K. Furthermore, their hardness was determined by Vickers measurements and nanoindentation and the Young's modulus was measured by three different techniques: 1) nanoindentation, 2) three-point bending tests and 3) vibrational resonance with a grindosonic device. The fracture and deformation micromechanics have been also carefully analyzed for each testing condition. The comparison between the studied materials has been performed in order to understand the influence of the main sintering methods and the microstructural characteristics of the single grains on the macroscopic mechanical behavior. The electromechanical behavior of commercial YBCO coated conductors was studied. The mechanical behavior of the tapes was studied under tensile and fatigue tests at 77 and 300 K. The complete strain field on the surface of the sample was obtained by applying Digital Image Correlation (DIC) at 300 K. Addionally, in situ fragmentation tests inside a Scanning Electron Microscope (SEM) were carried out in order to study the fragmentation of the superconducting layer and determine the interfacial shear strength between substrate and ceramic layer. The fragmentation process upon loading of the YBCO layer has been observed and finally, Finite Element Simulations were employed to reproduce delamination and fragmentation phenomena. Finally, joints between the stabilizing Cu sides of two coated conductors have been prepared. The electrical resistivity of the joints was measured for the purpose of qualifying the soldering material and evaluating the soldering process. Additionally, mechanical characterization under single lap shear tests at 300 and 77 K has been carried out. The effect of the applied magnetic field has been studied by applying external magnetic field up to 1 T perpendicular and parallel to the tape-joint at service temperature (77 K). Finally, finite element simulations were employed to study the distribution of the stresses in earch layer, taking into account the three mechanically relevant layers of the coated conductor (Cu-Hastelloy-Cu) that affect its mechanical behavior

La estabilidad del frente de excavación de un túnel en terrenos heterogéneos o con un criterio de rotura no-lineal

El frente de un túnel puede colapsar si la presión aplicada sobre el es inferior a un valor limite denominado presión “critica” o “de colapso”. En este trabajo se desarrolla y presenta un mecanismo de rotura rotacional generado punto a punto para el cálculo de la presión de colapso del frente de túneles excavados en terrenos estratificados o en materiales que siguen un criterio de rotura nolineal. La solución propuesta es una solución de contorno superior en el marco del Análisis Límite y supone una generalización del mecanismo de rotura mas reciente existente en la bibliografía. La presencia de un terreno estratificado o con un criterio de rotura no-lineal implica una variabilidad espacial de las propiedades resistentes. Debido a esto, se generaliza el mecanismo desarrollado por Mollon et al. (2011b) para suelos, de tal forma que se puedan considerar valores locales del ángulo de rozamiento y de la cohesión. Además, la estratificación del terreno permite una rotura parcial del frente, por lo que se implementa esta posibilidad en el mecanismo, siendo la primera solución que emplea un mecanismo de rotura que se ajusta a la estratigrafía del terreno. Por otro lado, la presencia de un material con un criterio de rotura no-lineal exige introducir en el modelo, como variable de estudio, el estado tensional en el frente, el cual se somete al mismo proceso de optimización que las variables geométricas del mecanismo. Se emplea un modelo numérico 3D para validar las predicciones del mecanismo de Análisis Limite, demostrando que proporciona, con un esfuerzo computacional significativamente reducido, buenas predicciones de la presión critica, del tipo de rotura (global o parcial) en terrenos estratificados y de la geometría de fallo. El mecanismo validado se utiliza para realizar diferentes estudios paramétricos sobre la influencia de la estratigrafía en la presión de colapso. Igualmente, se emplea para elaborar cuadros de diseño de la presión de colapso para túneles ejecutados con tuneladora en macizos rocosos de mala calidad y para analizar la influencia en la estabilidad del frente del método constructivo. Asimismo, se lleva a cabo un estudio de fiabilidad de la estabilidad del frente de un túnel excavado en un macizo rocoso altamente fracturado. A partir de el se analiza como afectan las diferentes hipótesis acerca de los tipos de distribución y de las estructuras de correlación a los resultados de fiabilidad. Se investiga también la sensibilidad de los índices de fiabilidad a los cambios en las variables aleatorias, identificando las mas relevantes para el diseño. Por ultimo, se lleva a cabo un estudio experimental mediante un modelo de laboratorio a escala reducida. El modelo representa medio túnel, lo cual permite registrar el movimiento del material mediante una técnica de correlación de imágenes fotográficas. El ensayo se realiza con una arena seca y se controla por deformaciones mediante un pistón que simula el frente. Los resultados obtenidos se comparan con las estimaciones de la solución de Análisis Límite, obteniéndose un ajuste razonable, de acuerdo a la literatura, tanto en la geometría de rotura como en la presión de colapso. A tunnel face may collapse if the applied support pressure is lower than a limit value called the ‘critical’ or ‘collapse’ pressure. In this work, an advanced rotational failure mechanism generated ‘‘point-by-point” is developed to compute the collapse pressure for tunnel faces in layered (or stratified) grounds or in materials that follow a non-linear failure criterion. The proposed solution is an upper bound solution in the framework of limit analysis which extends the most advanced face failure mechanism in the literature. The excavation of the tunnel in a layered ground or in materials with a non-linear failure criterion may lead to a spatial variability of the strength properties. Because of this, the rotational mechanism recently proposed by Mollon et al. (2011b) for Mohr-Coulomb soils is generalized so that it can consider local values of the friction angle and of the cohesion. For layered soils, the mechanism needs to be extended to consider the possibility for partial collapse. The proposed methodology is the first solution with a partial collapse mechanism that can fit to the stratification. Similarly, the use of a nonlinear failure criterion introduces the need to introduce new parameters in the optimization problem to consider the distribution of normal stresses along the failure surface. A 3D numerical model is employed to validate the predictions of the limit analysis mechanism, demonstrating that it provides, with a significantly reduced computational effort, good predictions of critical pressure, of the type of collapse (global or partial) in layered soils, and of its geometry. The mechanism is then employed to conduct parametric studies of the influence of several geometrical and mechanical parameters on face stability of tunnels in layered soils. Similarly, the methodology has been further employed to develop simple design charts that provide the face collapse pressure of tunnels driven by TBM in low quality rock masses and to study the influence of the construction method. Finally, a reliability analysis of the stability of a tunnel face driven in a highly fractured rock mass is performed. The objective is to analyze how different assumptions about distributions types and correlation structures affect the reliability results. In addition, the sensitivity of the reliability index to changes in the random variables is studied, identifying the most relevant variables for engineering design. Finally, an experimental study is carried out using a small-scale laboratory model. The problem is modeled in half, cutting through the tunnel axis vertically, so that displacements of soil particles can be recorded by a digital image correlation technique. The tests were performed with dry sand and displacements are controlled by a piston that supports the soil. The results of the model are compared with the predictions of the Limit Analysis mechanism. A reasonable agreement, according to literature, is obtained between the shapes of the failure surfaces and between the collapse pressures observed in the model tests and computed with the analytical solution.

Mechanical behavior and deformation micromechanisms of polypropylene nonwoven fabrics as a function of temperature and strain rate

The mechanical behavior and the deformation and failure micromechanisms of a thermally-bonded polypropylene nonwoven fabric were studied as a function of temperature and strain rate. Mechanical tests were carried out from 248 K (below the glass transition temperature) up to 383 K at strain rates in the range ≈10−3 s−1 to 10−1 s−1. In addition, individual fibers extracted from the nonwoven fabric were tested under the same conditions. Micromechanisms of deformation and failure at the fiber level were ascertained by means of mechanical tests within the scanning electron microscope while the strain distribution at the macroscopic level upon loading was determined by means of digital image correlation. It was found that the nonwoven behavior was mainly controlled by the properties of the fibers and of the interfiber bonds. Fiber properties determined the nonlinear behavior before the peak load while the interfiber bonds controlled the localization of damage after the peak load. The influence of these properties on the strength, ductility and energy absorbed during deformation is discussed from the experimental observations.

Análisis de media de diferencia entre imágenes y su posterior implementación usando Matlab

El proyecto consta de dos partes principales y dos anexos. La primera es teórica, en ella realizamos; a modo de introducción, un estudio sobre el tratamiento digital de la imagen, desarrollando las principales técnicas de tratamiento y análisis de imágenes que pudimos estudiar durante la carrera. Una vez desgranado el análisis nos centraremos en la correlación digital de imagen, su evolución y distintas técnicas, donde nos centramos en la correlación cruzada normalizada que usamos posteriormente para la correlación de imágenes con Matlab. La segunda parte consiste en la implementación de un sencillo programa mediante Matlab en el que podremos evaluar y analizar las diferencias entre dos o más imágenes, pudiendo observar gráficamente la desviación en milímetros entre varias imágenes y su dirección con vectores. Posteriormente analizamos los resultados obtenidos y proponemos posibles mejoras para futuros proyectos de correlación de imágenes digitales. Por último, incluimos un par de anexos en los que incluimos un tutorial para automatizar acciones con Adobe Photoshop para facilitar el pretratamiento de fotografías antes de analizarlas con el script y una posible práctica de laboratorio para futuros alumnos de la escuela utilizando nuestro script de Matlab. ABSTRACT. The project involves two main parts and two annexes. The first is theoretical, it performed; by way of introduction, a study on digital image processing, developing the main treatment techniques and image analysis we were able to study along our career. Once shelled analysis we will focus on digital image correlation, evolution and different techniques, where we focus on normalized cross-correlation which we use later for the correlation of images with Matlab. The second part is the implementation of a simple program using Matlab where we can evaluate and analyze the differences between two or more images and can graphically see the deviation in millimeters between various images and their direction vectors. Then we analyze the results and propose possible improvements for future projects correlation of digital images. Finally, we have a couple of annexes in which we include a tutorial to automate actions with Adobe Photoshop to facilitate pretreatment photographs before analyzing the script and a possible lab for future school students using our Matlab script.

Measurements of stress-optic coefficient and Young's modulus in PMMA fibers drawn under different conditions

We have systematically measured the differential stress-optic coefficient, ΔC, and Young's modulus, E, in a number of PMMA fibers drawn with different stress, ranging from 2 up to 27 MPa. Effect of temperature annealing on those parameters was also investigated. ΔC was determined in transverse illumination by measuring the dependence of birefringence on additional axial stress applied to the fiber. Our results show that ΔC in PMMA fibers has a negative sign and ranges from -4.5 to -1.5×10-12 Pa -1 depending on the drawing stress. Increase of the drawing stress results in greater initial fiber birefringence and lower ΔC. The dependence of ΔC and initial birefringence upon drawing stress is nonlinear and gradually saturates for higher drawing stress. Moreover, we find that ΔC is linearly proportional to initial fiber birefringence and that annealing the fiber has no impact on the slope of this dependence. On the other hand, no clear dependence was observed between the fiber drawing stress and the Young's modulus of the fibers as measured using microscopic digital image correlation with the fibers tensioned using an Instron tension tester. © 2010 SPIE.

Nonlinear soil-structure interaction for buried pressure pipes under differential ground motion

Pipelines extend thousands of kilometers across wide geographic areas as a network to provide essential services for modern life. It is inevitable that pipelines must pass through unfavorable ground conditions, which are susceptible to natural disasters. This thesis investigates the behaviour of buried pressure pipelines experiencing ground distortions induced by normal faulting. A recent large database of physical modelling observations on buried pipes of different stiffness relative to the surrounding soil subjected to normal faults provided a unique opportunity to calibrate numerical tools. Three-dimensional finite element models were developed to enable the complex soil-structure interaction phenomena to be further understood, especially on the subjects of gap formation beneath the pipe and the trench effect associated with the interaction between backfill and native soils. Benchmarked numerical tools were then used to perform parametric analysis regarding project geometry, backfill material, relative pipe-soil stiffness and pipe diameter. Seismic loading produces a soil displacement profile that can be expressed by isoil, the distance between the peak curvature and the point of contraflexure. A simplified design framework based on this length scale (i.e., the Kappa method) was developed, which features estimates of longitudinal bending moments of buried pipes using a characteristic length, ipipe, the distance from peak to zero curvature. Recent studies indicated that empirical soil springs that were calibrated against rigid pipes are not suitable for analyzing flexible pipes, since they lead to excessive conservatism (for design). A large-scale split-box normal fault simulator was therefore assembled to produce experimental data for flexible PVC pipe responses to a normal fault. Digital image correlation (DIC) was employed to analyze the soil displacement field, and both optical fibres and conventional strain gauges were used to measure pipe strains. A refinement to the Kappa method was introduced to enable the calculation of axial strains as a function of pipe elongation induced by flexure and an approximation of the longitudinal ground deformations. A closed-form Winkler solution of flexural response was also derived to account for the distributed normal fault pattern. Finally, these two analytical solutions were evaluated against the pipe responses observed in the large-scale laboratory tests.