Out-of-plane collapse of walls is perhaps one of the most common modes of failure of masonry structures during earthquakes. Depending on the restraint conditions, walls can fail by developing a hinge along their height, thereby resulting in the formation of a two-block out-of-plane collapse mechanism. Equations of motion derived for this mechanism thus far have modelled the cracked wall as a single-degree-of-freedom (SDOF) system made up of two rigid bodies. However, most of these formulations assume that the interfaces between the blocks themselves, as well as between the blocks and the supports, are rigid. Alternatively, equations of motion have also been derived for two-block systems with flexible interfaces, which model the system as having four degrees of freedom, which is considerably more complicated than the SDOF model. Neither of these formulations account for the finite compressive strength of the interfaces, upon the exceedance of which crushing occurs, thus further reducing the dynamic resistance of the structure. This paper presents the derivation of an equation of motion for a cracked wall section taking into account the presence of flexible interfaces as well as crushing effects. Using as a case-study a typical multi-story spanning masonry wall, the importance of considering crushing during out-of-plane collapse is then quantified for a range of interface properties and loading conditions.

Building monitoring and protection are important components of underground projects in urban areas. Typically the procedures applied for the assessment of settlement-induced damage to buildings are based on simplified assumptions that do not take into account soil–structure interaction. Assessment methods based on the relative stiffness between the structure and the soil exist, but they are rarely applied in practice due to concerns about the accuracy and reliability. The primary aim of this work is to use the large amount of monitoring data provided by the Crossrail project in London to improve understanding of building performance and existing damage assessment methods. The paper gives an initial overview of the available monitoring data by presenting four representative case studies for load-bearing masonry buildings on shallow foundations. Structural data are then used to evaluate the consistency of predictions produced by different relative stiffness formulations. The results show the effect of building stiffness on the soil surface settlements and clarify the effects of various assumptions made during prediction. The conclusions highlight opportunities to improve prediction procedures and the need for more detailed monitoring data for future tunnelling projects.

Structural monitoring of surface building displacements is a significant component of the total financial investment for underground construction projects in urban areas. While traditional monitoring requires in-situ (terrestrial) measurements and trigger levels based on preliminary evaluation of vulnerable structures, very recent advances in Interferometric Synthetic Aperture Radar (InSAR) techniques enable remote monitoring over extensive areas, providing rapid, semi-automatic, and dense measurements with millimetre accuracy. Despite the well-established use of InSAR in geophysical applications, only a few studies are currently available on the use of satellite-based monitoring for the assessment of building deformations and structural damage. The aim of this project is to investigate the potential of InSAR monitoring data as an input to post-tunnelling damage assessment procedures. First, InSAR-based measurements of building displacements, induced by the excavation of Crossrail tunnels in London, were acquired and processed. Then, following the definition of a step-by-step procedure, the satellite-based building displacements were used to evaluate structural deformation parameters typically used in extensive damage assessment procedures. Results show that the number of available measures per single building can enable the estimation of deformation parameters, a capability that is not economically feasible for large scale projects using traditional monitoring systems. The comparison with greenfield predictions offers new insight into the effect of soil-structure interaction and demonstrates the suitability of InSAR monitoring for post-tunnelling damage assessment of structures. The outcome of this work can have a significant economic impact on the construction industry and can advance the knowledge of building and infrastructure response to ground subsidence.

The potential damage caused by tunnel excavations to surface buildings can be effectively investigated by centrifuge testing. However, for practical reasons only a limited number of geometrical configurations can be tested in a geotechnical centrifuge. Therefore, numerical modelling provides an essential tool to generalise the laboratory results. This paper illustrates the performance of a 2D finite element model of masonry buildings subjected to tunnelling in sand. The results of the first series of centrifuge tests performed on complex 3D printed masonry structures and presented in the companionpaper were used for the model validation. The model includes nonlinear constitutive laws for both the soil and the building. Differently than previous works, this paper focuses on the accurate simulation of the building response by using structural parameters specifically defined for the assessment of building deformations. The results provide insights into the effect of different building positions relative to the tunnel on the structural response. The validated model can be used to investigate the effect of different building conditions on the soil-structure interaction mechanism.

Failure of masonry structures generally occurs via specific collapse mechanisms which have been well documented. Using rocking dynamics, equations of motion have been derived for a number of different failure mechanisms ranging from the simple overturning of a single block to more complicated mechanisms. However, most of the equations of motion derived thus far assume that the structures can be modelled as rigid bodies rocking on rigid interfaces with an infinite compressive strength—which is not always the case. In fact, crushing of masonry—commonly observed in larger scale constructions and vertically restrained walls—can lead to a reduction in the dynamic capacity of these structures. This paper rederives the rocking equation of motion to account for the influence of flexible interfaces, characterized by a specific interface stiffness as well as finite compressive strength. The interface now includes a continually shifting rotation point, the location of which depends not only on the material properties of the interface but also on its geometry. Expressions have thus also been derived for interfaces of different geometries, and parametric studies conducted to gauge their influence on dynamic response. The new interface formulations are also implemented within a new analytical modelling tool that provides a novel approach to the dynamic analysis of masonry collapse mechanisms. Finally, this tool is exemplified, along with the importance of the interface formulation, by evaluating the collapse of the Dharahara Tower in Kathmandu, which was almost completely destroyed during the 2015 Gorkha earthquake.

Understanding the building response to tunnelling-induced settlements is an important aspect of urban tunnelling in soft ground. Previous centrifuge modelling research demonstrated significant potential to study this tunnel-soil-structure interaction problem. However, these recent studies were limited by simplified building models, which might result in uncertainties when interpreting the building performance to tunnelling subsidence. This paper presents an experimental modelling procedure and the results of a series of centrifuge tests, involving relatively complex surface structures subjected to tunnelling in sand. Powder-based three-dimensional (3D) printing was adopted to fabricate building models with realistic layouts, facade openings and foundations. The 3D printed material had a Young's modulus and a brittle response similar to historic masonry. Modelling effects and boundary conditions are quantified. The good agreement between the experimentally obtained results and previous research demonstrates that the soil-structure interaction during tunnel excavation is well replicated. The experimental procedure provides a framework to quantify how building features affect the response of buildings to tunnelling subsidence.

Current procedures for the assessment of buildings response to tunnelling take into account the effect of soil-structure interaction through the definition of the building stiffness relative to the soil stiffness. Limitations of these procedures are uncertainties in the evaluation of structural parameters and inconsistent results between different methods. In this paper, three existing formulations of the Relative Stiffness Method (RSM) have been critically evaluated by analysing the governing factors in the building stiffness calculation and their effect on the structural damage assessment. The results of a sensitivity study on building height, eccentricity, opening ratio, tunnel depth, soil and masonry stiffness, and trough width parameter quantified the effect of these factors on the considered RSMs. The application of different RSMs to a real masonry building adjacent to the Jubilee Line tunnel excavation underlined the significant effect of window openings, façade stiffness and neutral axis position on the building stiffness calculation and deformation prediction. These results highlight the need for a consistent and robust damage assessment procedure.

This paper presents a new CAD-interfaced analytical tool for the nonlinear dynamic analysis of masonry collapse mechanisms. Utilizing rocking dynamics, the tool derives and solves equations of motion for a broad range of collapse mechanisms, for any user-defined structural geometry. Using as a starting point a digital drawing of the structure in Rhino (a typical CAD software), the tool computes the kinematic constants defining these equations of motion, which are then exported to MATLAB and solved for either pulse-response to generate overturning spectra, or full time-histories. The use of the tool is demonstrated by comparing its predictions to results from experimental shake-table tests, as well as against field observations from the 2015 Gorkha earthquake, while its predictive abilities are illustrated using as case-studies the Casa Grande Ruins National Monument in the United States, as well as the Church of San Leonardo Limosino in Italy, which sustained some damage during the 2012 Emilia earthquake sequence.

Spaceborne multi-temporal interferometric synthetic aperture radar (MT-InSAR) is a monitoring technique capable of extracting line of sight (LOS) cumulative surface displacement measurements with millimeter accuracy. Several improvements in the techniques and datasets quality led to more effective, near real time assessment and response, and a greater ability of constraining dynamically changing physical processes. Using examples of the COSMO-SkyMed (CSK) system, we present a methodology that bridges the gaps between MT-InSAR and the relative stiffness method for tunnel-induced subsidence damage assessment. The results allow quantification of the effect of the building on the settlement profile. As expected the greenfield deformation assessment tends to provide a conservative estimate in the majority of cases (~71% of the analyzed buildings), overestimating tensile strains up to 50%. With this work we show how these two techniques in the field of remote sensing and structural engineering can be synergistically used to complement and replace the traditional ground based analysis by providing an extended coverage and a temporally dense set of data.

In urban tunnelling projects, surface buildings interact with tunnelling-induced ground movements. Understanding this interaction aids when predicting the behaviour of buildings above tunnelling works. However, much uncertainty still exists about the impact of structures on tunnelling subsidence and thus current design practice is widely based on empirical methods that neglect this soil-structure interaction. To refine current modelling assumptions and reduce uncertainty, more detailed knowledge of the influence of buildings on tunnelling-induced ground displacements is needed. This paper presents results from an experimental investigation that seeks to provide a more thorough understanding of this soil-structure interaction problem using more realistic surface structures. In particular, it focuses on the effect of surface structures on the ground surface and subsurface soil displacements. Three centrifuge tests with building models placed in different regions of the tunnelling-induced settlement trough were compared to a greenfield case. The ground model consisted of a dense, dry sand and the building was 3D printed. Results showed how the structure alters the vertical and horizontal soil displacements associated with tunnel excavation. Soil deformation mechanisms were notably influenced by the position of the building model relative to the tunnel, causing different magnitudes of vertical and horizontal ground movements above and next to the tunnel, widening of the surface and subsurface settlement troughs and localised failure beneath building corners.

The interaction mechanisms between surface structures and tunnelling-induced ground movements were investigated through centrifuge testing. Although numerous studies have considered this soil-structure interaction problem, previous experiments have neglected important building characteristics and field data inherently contain numerous uncertainties related to the soil, the structure and the tunnelling procedure. Consequently, the interpretation of results and validation of computational models can be problematic. In this study, tunnelling beneath three-dimensional printed structural models with varying building characteristics (i.e. Position, length and facade openings) was simulated in a centrifuge. The experimental results demonstrate that tunnelling induces soil displacements at the surface and subsurface that are notably altered due to nearby structures. Specifically, different amounts of vertical and horizontal ground movements, soil dilation and widening of settlement troughs were observed. Building distortions and horizontal building strains were also affected by the relative position of the building to the tunnel, the building length and the area of facade openings. The experimental results provide important data for the evaluation of current design methods and verification of computational models.

This paper studies damage to a few specific monuments in the Kathmandu Valley that were either partially or completely destroyed during the 2015 Gorkha earthquake. Three of these structures—namely, the Basantapur Column, the Dharahara Tower, and the Narayan Temple—were modeled both analytically using rocking dynamics and computationally using discrete element modeling (DEM). The results emphasize the importance of large low frequency content within the ground motion, demonstrating that the Dharahara Tower could have collapsed due to the primary long-period ground motion pulse alone. In addition, comparison of analytical and computational modeling to the observed response enables evaluation of structural behavior, including discussion of the importance of elastic amplification and column embedment on performance during the earthquake.

Accurate simulation of the building response to soil settlements is useful for the risk assessment of underground excavations in urban areas. Two-dimensional numerical models with coupling between the soil and structure offer a relatively flexible means of investigation for large scale projects, as complete 3D simulation is time consuming. However, the material parameters of the 2D building models need to be adjusted to reproduce the correct building stiffness relative to the soil. Furthermore, 2D models neglect potential torsional effects,which can be relevant during the tunnel advance and due to building orientation with respect to the tunnel. In this work, the responses of 2D and 3D models are compared to evaluate the effect of the dimensional assumption on the accuracy of the prediction of cracking in masonry structures. First, a 2D finite element simulation, which includes both the soil and the structure, is compared to the results of a centrifuge test on a scaled 3D structure subjected to tunnelling in sand. The assumptions employed to calculate the stiffness of the "equivalent" 2D model are highlighted and discussed. Second, a semi-coupled model, where the soil is not modelled directly but the soil displacements are directly applied to an interface which accounts for the soilstructure interaction, is presented. Finally, a 3D semi-coupled model of the structure is used to investigate the 3D boundary effect in the centrifuge sand box. In all simulations, a cracking model is used to account for the structural damage experimentally observed. Comparison of the 3D model and experimental results demonstrates the ability of the model to reproduce the torsional building response.The modelling of cracking in the masonry makes it possible to assess the development of structural damage and its influence on the building response. The comparison between the 2D and 3D results enables quantification of the impact of 2D simplification on the final prediction.

Tunnelling in urban areas requires a careful estimation of the consequence of soil settlements on existing buildings. In this paper the interaction between the excavation of a tunnel in sand and surface structures is investigated. A two dimensional finite element model is presented and validated through comparison with centrifuge test results, both with and without structures. The model is then used to perform a sensitivity study on the effect of building weight on soil movements and structural deformations. The results of the validation indicate that assuming a no-tension interface between the soil and the structure is essential to capture the soil-structure interaction that was experimentally observed. The parametric analyses show that the relation between the building stiffness and the tunnelling-induced deformations depends on the building weight.

Large displacement response of stone masonry structures often involves the opening and closing of dry joints, or hinging behaviour. Discrete element modelling (DEM) is often used to model large displacement response as it inherently captures the interaction of discrete bodies, and allows for joint contact recognition in a more efficient manner than many finite element modelling procedures. Modelling such behaviour can be computationally demanding and the problem becomes more complicated when reinforcing, often in the form of post-tensioning, is applied to prevent collapse. This paper evaluates the ability of DEM to accurately capture the behaviour of reinforced masonry as observed in an experimental study conducted at the University of Porto. The DEM software 3DEC was used to model the response of the post-tensioned arch when subjected to gravity and a superimposed dead load, and this response was evaluated for varying levels of pre-stress in the arch. A reasonably good correlation was observed between the experimental and DEM results, and the differences that do exist are discussed.

Tunnelling in urban areas continues to increase and has highlighted the need for a better understanding of the impact of tunnel excavations on existing buildings. This paper considers the influence of surface structures on ground displacements caused by tunnelling in sand through finite element modelling and centrifuge testing. First, the importance of modelling assumptions is evaluated by comparing centrifuge modelling results to finite element modelling results for various soil constitutive models: both a Young's modulus that linearly increases with depth and a power law relation between the soil stiffness and stresses are considered. Second, the most effective soil constitutive model was used to perform a sensitivity study on the effect of different factors governing the structural response. In particular, the effect of the building stiffness and weight on the modification of soil displacements is investigated by introducing a simple surface structure. The use of a no-tension interface between the building and the soil was found to be essential to investigate the effect of weight on gap formation between the soil and the structure, as observed during the experimental tests. Results show the importance of considering the relation between the building weight and the relative stiffness between the building and the soil when assessing the structural response.