(1) Department of Civil Engineering, KULeuven, Belgium (2) Bjorn Vangenechten, department of architecture, KULeuven, Belgium

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1 THE USE OF 3D-SCANNING IN STRUCTURAL RESTORATION PROJECTS IMPACT OF ACCURATE GEOMETRY ON STRUCTURAL ASSESSMENT: A CASE STUDY ON THE CHURCH OF SAINT-JACOBS AT LEUVEN Luc Schueremans (1) and Bjorn Vangenechten (2) (1) Department of Civil Engineering, KULeuven, Belgium (2) Bjorn Vangenechten, department of architecture, KULeuven, Belgium Abstract Safety and stability of historical structures are of key importance when dealing with a restoration project. The stability of masonry vaults very much depends on its overall geometry and the analysis results strongly depend on the accuracy in which this geometry can be measured in practice. To obtain an accurate estimate of the geometry of the vaults, 3Dlaserscanning was performed. Based on the 3D point cloud, a 3D-model of the vaults allows determining the lines of thrust in the structure as well as the reaction forces (application point and magnitude) at the abutments. This contribution gives a critical appraisal of the process used in the preliminary research phase: gathering the point-clouds, 3D-modelling, structural analysis calculating thrust lines and the consolidation requirements that are obtained. The focus is on the added value of the methodology, its applicability, cost-effectiveness, overall advantages and drawbacks. Keywords 3D laserscanning, masonry vaults, load bearing capacity, point-clouds, 3D-modelling 1. INTRODUCTION The construction of the western tower of the church of Saint Jacobs that is located in the heart of Leuven (B), dates back from During several subsequent building phases, the Romanesque church has been replaced and extended by a church in early Gothic style. The wooden roofs in the central and side naves were replaced with masonry vaults, and flying buttresses were added. The structure itself is located on a former swamp, reclaimed by the monks at the time of construction. The load-bearing capacity of the subsoil is limited, causing large differential settlements. At several occasions in the past, restoration works took place. However, due to the excessive cracks observed, it was decided in 1963 to close the church for 519

2 service, in fear of its structural collapse, to remove the severely cracked masonry vaults of the side naves and to shore up the pillars of the main nave. Additionally, in 2000, the remaining flying buttresses were removed and replaced by tie-rods. The focus of this contribution is on the structural behaviour of the vaults of the main nave that have been constructed in , replacing a wooden barrel vault. The brick masonry vault has a thickness of mm. The ribs are made out of sandstone. The main nave has a span of 8 m and the space within the subsequent columns measures 3.75 m. The central height of the nave is 18.00m. In this type of masonry structures, vertical forces are transmitted by means of vaults towards the walls and foundation system. Since masonry mainly behaves as a non-tension material, lines of thrust have to be found in equilibrium with the actual loading, lying within the cross-section of the vaults. Therefore, the safety is directly related to the geometry itself and the analysis results strongly depend on the accuracy in which this geometry can be measured in practice. Based on an accurate geometric survey, the overall geometry is determined. From the overall geometry, the geometrical safety factor is calculated by means of a limit analysis. As a result, a geometrical safety factor and the horizontal reaction forces at the abutments are obtained. The first is needed to judge the overall structural safety, the latter helps to determine optimal location for the strengthening using additional tie-rods. Therefore, this information is crucial for future consolidation measures, respecting the authenticity of the building and preserving it for the future. 2. ACCURATE GEOMETRIC SURVEY The survey of the vaults was performed using the high precision Leica HDS 3000 laser scanner currently owned by Plowmann Craven & ass. (PCA), a surveying company in the UK [1]. This mid-range scanner uses the time-of-flight principal to measure the distance of a point to the scanner. It has a full field of view (360x270 ) and a guaranteed accuracy of 6mm per point up to a range of 50 meters. Table 1: Technical specifications of laser scanner used in analysis Metrology method Time-of-flight Range 90%; 18% albedo Scan rate Scan resolution Spot size Up to 4000 points/sec Max instantaneous rate Average: dependent on specific scan density and field-of-view From 0-50m : 4mm (FWHH based) 6mm (Gaussian based) Maximum sample density 1.2 mm Field of view Horizontal 360 (maximum) Vertical 270 (maximum) Single point accuracy Position 6 mm Distance 4 mm Angle 60 micro-radians (horizontal & vertical) Modelled surface precision 2mm, one sigma Laser Type Pulsed Colour Green Class 3R (IEC ) 520

3 With its low beam divergence (<6 mm at 50m) it is one of the best mid-range scanners on the market. Although an internal CCD camera gives additional information in the form of RGB values for each measured point, its resolution of only 1MP is a little disappointing. The most important technical specifications of the system are summarized in Tab. 1. Two different scan positions were necessary to capture the whole vault without having any shadows or occlusions. Both scans were made with a vertical scan resolution of 6mm and a horizontal scan resolution of 1 cm as a compromise between level of detail and the computing resources and time needed for data processing. To be able to register both scans, both artificial targets (Leica spherical targets) at the bottom and natural feature points in the vaults themselves were used. The artificial targets were automatically identified and provided a set of well defined tie points. Because the centre of these targets is computed through a least square fitting algorithm, they are less influenced by the position of the scanner then with planar targets (if the scanner direction is nearly aligned with a planar target, its centre can be wrongly detected). The Leica targets are automatically identified and extracted during the acquisition phase by the Cyclone software (Leica Geosystems). Other target points were carefully manually selected and fine scanned for better precision in the registration phase. The Cyclone software aligned both datasets using 4 artificial targets, 6 natural targets and cloud to cloud registration with a final RMS-error of 6mm. Once the point clouds have been acquired, they have to be processed and converted into useable information. Since the required input to the structural calculation phase consists of a number of slices, each slice deployed into a number of 2 dimensional point coordinates, a strategy had to be set up on how to get to these deliverables in the most efficient way. Using the Rapidform software (Inus Technology Inc.) every point cloud was filtered for noise removal, redundant points were removed, a mesh was created and small holes were filled using a curvature based filling algorithm. After this post-processing step, a new coordinate system was defined using the vaults ribbon crossing as the origin and the direction of the axis based on the axis of the transept of the church. Then a point grid, aligned to this new coordinate system, was projected on to the meshed model and the coordinates of these projected points were exported to a dxf-file that can be read by CAD software. As a compromise between manual post-processing time and computation accuracy, the size of the grid was chosen to be 10 cm providing 21 slices for each shell in 1 direction and 39 slices in the other direction. To help automate the point extraction slice by slice and convert their coordinates into a two dimensional frame an ObjectARX (Autodesk) application was written that fits a plane to a number of selected points and exports the coordinates of the points in the plane to a text file. These text files are then used in the structural computation phase to determine the forces inside the vault. 3. SAFETY OF MASONRY ARCHES To evaluate the arch s safety for a given set of parameters, the thrust line method is used [2]. It is a Limit Analysis method using the equations of equilibrium and the resistance characteristics of the materials. In the case of arches, it is supposed that: blocs are infinitely resistant, joints resist infinitely to compression, joints do not resist to traction and 521

4 joints resist infinitely to shear. These hypotheses are certainly restrictive: the material(s) used to construct the arch do not respect them strictly. It was nevertheless shown that - under normal circumstances - they are reasonable [3]. The limits of this theory are discussed elsewhere [4]. Within these boundaries no information related to strength nor stiffness is to be acquired on site using destructive testing. As a result, there is no impact on the historical building. a b c d e Figure 1: laser scanner data processing: a. location of vault, b. meshed model, c. definition of new coordinate system, d. projection of grid onto model, e. final grid points autocad dwg 522

5 The safe theorem for an arch then reads [5, 6]: If a thrust line can be found which is in equilibrium with the external loads and which lies wholly within the masonry, then the structure is safe. This theorem already suggests that more then one solution can be found. Indeed, any thrust line that satisfies the safe theorem requirements, is sufficient to ensure stability. It even does not have to be the actual line of thrust. Figure 2. Arches failure mode and static safety factor α g [4]. Two extreme lines of thrust can be found, in which three hinge points are formed. Because of its degree of static undefinedness, three hinges are required to transform the structure into a static structure. Hinges are formed when the thrust line becomes a tangent line with the intrados or the extrados of the arch. Typical failure modes associated with the limit situations are represented in Fig. 2. In (a) a safe situation is shown. Two extreme lines of thrust are drawn, both having three points in which the thrust line is tangent with the intrados or extrados. As the thickness of the arch decreases (b), the two extremes converge. Finally, when the arch is on the limit between stable and unstable, these two extreme lines of thrust converge to coincident lines. This results in 5 hinges, which transforms the structure into a mechanism of collapse. Given these hypotheses, it can be shown [5] that an arch is stable if a thrust line, remaining entirely inside its shape, can be found. Analytical expressions relating parameters to stability are not available for generic situations. The geometrical factor of safety ( g ) is defined as the minimal multiplicative factor on the arch thickness allowing an internal thrust line to be found. As long as the safety factors exceed one, the structure is in the safe region, the arch is stable. If the safety factor is smaller than one, the structure is in the unsafe region, the arch is unstable. 4. CALIPOUS A LIMIT ANALYSIS FOR ARCHES The manual calculation providing insight in the structural behaviour was extended using a limit analysis software tool developed in the framework of the Master and Ph. D. thesis of Pierre Smars, called Calipous [4]. The Calipous computer program was devised to analyse the stability of masonry arches of complex geometry, possibly subjected to external loads and/or movements of abutments. From the geometrical point of view, an arch is composed of a set of blocks (b i ), Fig. 3, defined as the volume comprised in between two bed joints (j i and j i+1 ). A Joint (j i ) is assumed to have a rectangular shape and is defined by a point on the intrados (u i, v i ), a thickness (t i ), a depth (d i ) and an orientation ( i ). The set of points (u i, v i ) on the intrados have all to lie in a 523

6 vertical plane but the position and orientation of this plane can be arbitrarily set in 3D. If they do not receive a specific value, t i and d i remain constant and the orientation i is set perpendicular to the intrados. Figure 3: schematic view of an arch as defined in the Calipous computer program External loads can be applied on the extrados of the arch (and possibly on its intrados). Forces can be oblique but they have to act in the plane of the arch (F u, F v ). The dead weight of the arch is automatically calculated and is always applied. The specific mass of the blocks is assumed to be constant. Arches made of blocks of different materials can be modeled giving pseudo-depths to the corresponding blocks. The relative eccentricity e i of a thrust line in a joint is the position of the intersection of the resultant of the forces acting on the bed joint of a block and of the plane of the joint relative to the centre of the section: its value is 100% if the thrust line passes by a point on the extrados and -100% if it passes by a point on the intrados. For an admissible thrust line, the eccentricity has to be comprised between -100% and 100% in all the joints, i.e. the line has to stay completely inside the shape of the arch [3, 5]. The basic calculation is the determination of a thrust line passing by three given points. More interestingly, optimisation routines allow the calculation of 'extreme' thrust lines (maximum and minimum) and 'average' thrust line (minimizing the sum of the square of the eccentricities). When a thrust line is calculated, graphical results are sent to a graphic window and text results to a text window, from which they can be exported to DXF and text files. The numerical results are the forces F u and F v at the abutments and, for each of the joints, the value of the normal and tangential forces N i & T i, the relative eccentricity e i, the angle of incidence i and an estimate of the maximum stress i in the joint (assuming that the joints do not resist to tension, that the stress distribution is linear and that the section is rectangular). The program was originally developed in Delphi programming language (Borland). A new C ++ version is under development. 524

7 5. RESULTS FOR THE VAULT OF THE MAIN NAVE OF SAINT-JACOBS CHURCH Based on the geometrical input, accurate values for the minimum and maximum thrust could be calculated, resulting from the vertical proper weight solely. For the overall structural behavior, it is assumed that the main structural elements of the vaults are the cross-ribs. The shells transfer their loads to these ribs. To estimate this load transfer, the shells are split up in small sections, as demonstrated in Fig. 1, c. Each section is assumed to work as an arch. Therefore, following procedure is used in practice: First thin vertical sections are made from the 3D-model with an average thickness of 0.10 cm across the longitudinal and transversal axis of the vault. This results in about 2 times 21 sections in the transversal direction (about 4.00m) and 2 times 39 sections in the longitudinal direction (about 8.00m span of vaults), Fig. 1c. Therefore, a small Matlab subroutine was written to semi-automatically construct the input data files for the Calipous Limit Analysis, accounting for the geometry available from the generated text files as a result from the autocad dwg files, Fig. 1,d; For each of the thin sections, the extreme lines of thrust are calculated (minimum and maximum thrust) as well as resulting reaction forces at the abutments, Fig. 4; The resulting minimum and maximum reaction forces obtained for each of these sections are imposed on the cross-ribs of the vaults as external loading, resulting in two load cases for each of the cross-ribs; The analysis of both cross-ribs result in the reaction forces at the abutments of both cross-ribs as well as the overall geometrical factor of safety. The overall results are outlined in Tab. 2, representing the vertical and horizontal reaction forces for the cross-ribs as well as the geometrical factors of safety. Figure 4: Minimum and Maximum thrust for the example vertical section 1_11 525

8 From this analysis it is clear that the overall geometrical factor of safety, which is larger then unity, demonstrates that the structure is in a safe situation. Because of the symmetry of both cross-ribs, which was also visible from their geometrical layout, the geometrical factors of safety are also comparable. In addition, the horizontal reaction forces are obtained. These reaction forces are used to design appropriate tie-rods, to replace the temporarily tie-rods that were placed when the original flying buttresses were removed in 2006 [7, 8]. The latter were removed since they became unstable due to the large differential vertical settlements in between the main nave and side nave, Fig. 5. Table 2: Horizontal and vertical reaction forces of the cross-ribs at the abutments and geometrical factor of safety. Vertical reaction forces V [kn] Minimum thrust H min [kn] Horizontal reaction forces Maximum thrust Geometrical factor of safety α g H max [kn] Diagonal AB Load case Load case Diagonal CD Load case Load case Legend: Load case 1 and 2 represent the loading obtained from the minimum and maximum thrust from the shell sections that transfer their loading towards the ribs Figure 5: Removal of the flying buttresses dd (left); replacement with temporarily tierods (mid) and geometrical instability of flying buttress (right) 6. DISCUSSION Using terrestrial laser scanner it is possible to create as-built survey documentation in a very time-efficient and accurate way. Although the post-processing of laser scan data still requires a lot of (semi-)manual work and its accuracy is slightly lower then other techniques, it benefits from the fact that it provides a full surface description in stead of measuring only 526

9 specific points as with photogrammetry or total station survey [9,10]. Once a full surface description is available, sections can be easily extracted in any direction and with any spacing required. The use of the gathered data is not restricted to one single application (i.e. structural analysis), but it can also be used for 3D virtual model creation for tourism purposes, heritage archiving, as-built plans, deformation monitoring over time, etc. Since our case study covers a preliminary study, the labor cost is relatively intensive: The capturing of the point-cloud requires half a day of measuring; Building the 3D-model: 1 full day; Retrieving the sections and data-files for Calipous : 1.5 days; Calculating the lines of thrust of the vaults and cross-ribs and analyzing the results: 1 day. Although laser scanning is an evolving technology, data processing and conversion is still a time consuming task. Automation of these procedures is possible to a large extent, but requires user specific algorithms. Therefore, the overall time is believed to be reducible down to 2.5 days. At this time, accuracy is lower then some other techniques, however, for applications that can work with a standard deviation of ± 3 4 mm, recording and processing with the laser scanner are a sound alternative. This accuracy is also to be seen in relation to the object scanned. In this case study the object treated is not a small object with smooth surfaces located in laboratory. The measuring of relatively large objects, several meters; the measuring from a relatively large distance, up to 50 m and the working on site and not in laboratory circumstances, undoubtedly affect the overall accuracy. 7. CONCLUSIONS AND FUTURE RESEARCH In this paper, high precision terrestrial laser scanning was used to provide a full geometrical description of one of the vaults of the church of Saint Jacobs for use in structural analysis. After filtering and converting the raw point cloud data into a three dimensional model, a strategy was set up to convert this model into useable information for the structural calculation phase. Although laser scanning is an evolving technology, it has already proven its usability in many cases [11-15]. Since the complex question formulations for its particular uses are solved only by specific software programs, the use of third party software is vital. Future research focuses on the integration of the methodology within a decision tool or platform. In that, it is meant to integrate the above methodology within a common platform. Therefore, the communication in between the different software tools needs to be provided. The use of the geometrical data for structural analysis objectives of course is only one of the possible applications in case of the preservation of historical buildings. Therefore, the multipurpose use of the data provided by a 3D point cloud or 3D model derived from the data is looked for. An additional goal is to link the uncertainties related to loading, resistance and geometry to objective safety levels [16]. The geometrical safety factor (α g ) obtained from this analysis, is a safety ratio. In that, uncertainty in the analysis related to geometry, material resistance, loading or the calculation model used is not accounted for. Accounting for these uncertainties by means of probability density functions, would allow for an objective treatment of the uncertainties and the calculation of an objective failure probability. The 527

10 procedure is outlined elsewhere [15]. This value can be used as an objective tool in the decision process. ACKNOWLEDGEMENTS The support from Plowmann Craven & ass. (PCA) for the assistance in the survey, from Pierre Smars for the background information on and for use of the Calipous software and from the city of Leuven (B), are gratefully acknowledged. REFERENCES [1] (last visited 21/01/2008); [2] Heyman, J., The stone skeleton, J of Sol Struct. 2 (1966) [3] Heyman, J., The estimation of the strength of masonry arches, Proc Inst Civ Eng 69 (2) (1980) [4] Smars, P., Etudes sur la stabilité des arcs et voûtes, Ph. D. Thesis, KULeuven (2000). [5] Heyman, J., The safety of masonry arches, J Mech Sc 11 (1969) [6] Kooherian, A., Limit analysis of voussoir (segmental) and concrete arches, J Am Concr Inst 24 (4) (1952) [7] Schueremans, L, Van Balen, K., Brosens, K., Van Gemert, D. and Smars P., Church of Saint- James at Leuven (B) structural assessment and consolidation measures, J. Arch Herit, 1 (2007), [8] Smars, P., Schueremans, L. and Van Balen, K., Monitoring the Dismantlement of Four flying Buttresses, Proc SAHC (3) (2006) [9] Van Genechten, B. and Neuckermans, H. Fusing laser scanning and photogrammetry creating close range architectural orthoimages, Proc 10 th EIA (2005) [10] Van Genechten, B. and Neuckermans, H. Fusing laser derived DSM's and matched image edges to create close range ortho-images, Proc VSMM2005 (2005) [11] Alba, M., Fregonese, L., Prandi, F., Scaioni, M. and Valgoi, P. Structural monitoring of a large dam by terrestrial laser scanning, Proc ISPRS (2006) [12] Tsakiri, M., Lichti, D. and Pfeifer, N., Terrestrial laser scanning for deformation monitoring., Proc IAG (2006). [13] Guarnieri, A., Pirotti, F., Pontin, M. and Vettore A. Combined 3D surveying techniques for structural analysis applications, Proc ISPRS (2005). [14] Bonora, V., Colombo, L. and Marana, B., Laser technology for cross-section survey in ancient buildings: a study for S.M.Maggiore in Bergamo, Proc CIPA (2005). [15] Schueremans, L. and Vangenechten, B., The use of 3D-laserscanning in structural restoration projects a case study on the Church of Saint-Jacobs illustrating the possibilities and limitations, Proc OPTIMESS 2007 (2007). [16] Schueremans, L., Probabilistic evaluation of structural unreinforced masonry structures, Ph. D. Thesis, KULeuven,