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Nonlinear numerical evaluation of the bearing capacity

3 May, 2021 11 min reading
Based on the thesis by: Jacopo Scacco, PHD Student at Politecnico di Milano

Nonlinear numerical evaluation of the bearing capacity

The main aim of this thesis, by the author Jacopo Scacco, is the FEM modeling and the subsequent evaluation of the bearing capacity of St. Jacob Church in the Broumov Region, with particular attention on the influence of the shallow footing and their degradation.


Nonlinear numerical evaluation of the bearing capacity


Broumov Region


Broumov Region is a harmonious, ecologically and aesthetically balanced landscape and it is unique in the Czech Republic, for its position, morphology, settlement of civilizations, and architecture. Located on the border between Czech Republic and Poland, the region is characterized by a huge diversity, from mountains and valley to meadows and grassland, with strange bizarre 'rock-towns' making the area even more exceptional.


The group of Baroque churches in the Broumov Region represents a perfect example of a combination between architecture and rural landscape. This peculiar heritage site requires specialized analysis to preserve its uniqueness. St. Jacob Church, the one investigated in this thesis, was the first one to be built in the region by Christoph and Kilian Dientzenhofer.



St. Jacob Church


Architectural Overview


The church of St. Jacob Greater was built in the years 1720 – 1723 on the site of the older wooden gothic church, designed by Christian and concluded by Kilian Dientzenhofer. The Church is located in the village of Ruprechtice, in the north part of the Broumov region. The location of the church, on a slight hill, was probably selected in order to create a sort of main entrance to the village (Fig. 3.2), at the corner of the roads coming from the city of Mezmesti and Broumov (7 km distant).


Fig. 3.2 – View of the façade from the main road; Aerial view (Google Maps)


The monumental and austere façade, with an orientation at SW consists of two levels: 

  • The first very simple, flat, and characterized by the portal and the arch window along with the principal axe, with a small opening and relevant arches at the sides.
  • The second level is a sort of shaped gable with a curve cornice, smoothly linked to the level below by two spirals. 


In the previous works of Christian, it is possible to find a similarity of this kind of façade in the complex of Broumov monastery (Fig. 3.3).


Fig. 3.3 – Main façade of St. Jacob; Façade in the complex of the Broumov Monastery


As it is typical of Baroque, the main façade is not anymore a natural continuation of the internal distribution.


Material Overview

After the geometric and architectonic description, it is important to define the material features of the building:



1 – Stones


The church was built, as the rural nature of the project required, with the stones available in the surrounding area. Broumov region is rich in quarries, with a high prevalence of sandstones. There is evidence, since the beginning of the 18th century, of quarries located in Bozanov and Vernerovice. The first one provided a huge amount of material for constructions overall the Czech Republic, having very good physical-mechanical properties, especially:

  • Strength;
  • frost resistance;
  • absorbency and abrasion resistance.

Taking into account that porosities could vary in a range from 0 to 35%, it is easy to find the reason for such differential deterioration for stones subjected to the same external actions.



2 – Rendering


From the point of view of the external render covering the surface of the external walls, two different typologies can be detected:

  • The first one, very thin, made of lime mortar, applied on the 'frame' of each wall;
  • The second one, thicker, covering the central part of each wall, made of large sand aggregates.



3 – Roof and ceiling


The roof and the ceiling are made completely of timber. The ceiling, arranged with timber boards, is covered by gypsum and lime plaster. The structure is made basically by prunes, covered by two different materials: stone tiles and metal sheets.

Fig. 3.5 – 3D Drawing roof (Facelli,2014)


Soil Overview

Despite the Broumov region is mainly characterized by sedimentary sandstone and rhyolite (Palaeozoic era), the church is founded on a relatively recent soil region (Mesozoic era), made of soft clay and loamy clay, with fluvial origin.



Damage Overview

The damages observed during the visual inspection are linked to a lack of maintenance of the church since the Second World War. Several damages experienced by the churches are strictly related to:

  • problems of water penetration;
  • high moisture content in the walls
  • the phenomena of rising capillarity.

The most severe consequences of this situation are the formation of biological colonization on the interior enclosure walls and the loss of plaster's integrity and the stones as well.


Externally, the thinner render results to be loss in almost the totality of the surface, leaving the stones subjected to external actions. The ticker render, as well, is missing in a different location, is characterized by phenomena of detachment and bulging. This kind of damages are peculiar of the churches investigated, the one discussed in this thesis, St. Jacob, but also St. Anna and St. Barbara (Fig. 3.10)

Fig. 3.10 – Deterioration of the render in St. Jacob Church (Left); St. Anna (Central); St. Barbara (Right)




The reason for this common situation has, as mentioned, to be related to the presence of water, coming from the soil and the roof for the poor condition of the gutters (Fig. 3.11). As it is noticeable from the picture, the soil, in correspondence of not working gutters, appears deteriorated and could have a role in settlement phenomena.



Fig. 3.11 – Deteriorated soil; Detail of the gutters


This scenario involved phenomena of efflorescence, leading to plaster detachment, and phenomena of freeze-thaw cycles of the stones. As already discussed above, the differential degradation of stones spread all over the walls' surface with the use of stones of different features (Fig. 3.12). It's also possible to find the same kind of damage in St. Barbara and St. Anna.


Fig. 3.12 – Differential deterioration in St. Jacob (Left); St. Barbara (Central); St. Anna (Right)


The high level of moisture, along with lack of ventilation, had a negative impact also in the interior of the Church, involving peeling, discoloration, and biological colonization on the surface of the walls. The walls most affected are the ones oriented to NW, being under the shadow of the trees and subjected directly to the sunlight from the opposite windows, ensuring the ideal situation for the biological growth (Fig. 3.13)


Fig. 3.13 – Rising dampness and Biological colonization on the internal walls


The situation in St. Jacob is slightly better than St. Barbara and St. Anna, regarding the damages of rainwater, as it is built upon a slight hill, avoiding the accumulation of water on a single side of the church. 

Along with the problems related to the moisture, during the survey, several cracks were detected in the walls and the ceiling. The cracks of the ceiling have to be related to the false vault system used in the Broumov group of churches. The cracks occurred, in fact, along the above main trusses, caused by the long-term action and deformation of timber elements (Fig. 3.15). This is similar to St. Barbara.


Fig. 3.15 – Cracking pattern in the ceiling of St. Jacob (Dienztenhofer Adventures); Cracks in the ceiling of St. Barbara


The majority of cracks on the walls do not represent source of wonder. Some of these are related to:

  • some concentration of stress due to local punctual load;
  • discontinuity of the shape;
  • normal behaviour of arches under self-load or could be the first signs of other phenomena;
  • the level of moisture and salt concentration in the stones below;
  • soil settlements phenomena.



Detailed identification of the damages observed during the inspection is provided in the tables below. For any kind of damages an example is showed: 



Bearing Capacity of the Enclosure Walls

Among Broumov's churches, this aspect represents an important uncertain coming from the peculiar typology of the walls. In fact, the not regular arrangement of the stones and the use of different materials does not allow an easy application of standards. So, it is necessary a more sophisticated analysis using micro modelling. Afterward, the goal is the application of the derived properties in the 3D model. 


To carry out this task, it is fundamental detailed information of the geometry and material properties. Taking advantage of the current situation of render's deterioration, it was possible to collect two different portions of the walls, identifying the textures. The locations, in the main façade and in the NW longitudinal wall, were selected as the most representative of the church in terms of arrangement and stone used.


Fig. 4.2 – Walls investigated


Material Properties for Modelling

The modelling of the walls was carried out through the software ATENA 2D, analyzing separately the models of the longitudinal wall and the sectional walls. The constitutive model selected has been the 'Non-linear cementitious 2'. In this model, it is settled for tensile behavior an exponential opening law, where is necessary to set directly the fracture energy in tension.


For compression, the strain at the peak stress has to be defined, along with the critical displacement wd that defines the slope of the linearly descending brunch after peak stress.

The definition of the material properties involved several considerations regarding:

  • The compressive strength
  • The modulus of Young
  • The restant sandstones
  • The definition of the compressive softening
  • The critical displacement
  • The mortar;

Two different approaches were carried out, studying the capacity of the longitudinal and transversal sections of the walls separately.


Soil Interaction

The poor condition of the soil is the source of concern for the future stability of the church. For this reason, it is necessary to make an effort to get reliable results about the interaction between the soil and the church. 



In the definition of the total deformation of the subsoil, it is fundamental to determine which portion of the subsoil is actually subjected to the load of the structure in a relevant way.



The analysis of the influence of the soil on the structure started from the definition of the basic characteristic of the soil under the church.



An analysis with the FEM software 2D 'GEO5' was carried out in order to have sensitivity in terms of displacement that the church experienced and in terms of depth influence.



For the further 3D analysis it has been necessary a conversion of the properties of the subsoil in springs constant.




The 3D analysis was done using FEM software DIANA, enable to model the nonlinear behavior of masonry and the cracks distribution.



The geometric model in DIANA was done after a slight simplification of the reality, taking away the small details that could have led to mesh issues.


As the purpose was the investigation of the global behavior of the church and the evolution of possible settlements, it was neglected, in the model, the small sacristy beyond the church.


Fig. 6.1 – Façade drawing of St. Jacob (Facelli, 2014); 3D Model in DIANA



The decision of which material properties used for masonry is always a difficult task. In this case, the analysis carried out by means of micro modelling have contributed to reducing the several uncertain, acquiring more sensitivity in the definition of the parameters.



At first, a simple elastic analysis was carried out, to check banal mistakes in the mesh and in the material properties and to make a comparison in terms of settlements with the result obtained with GEO5.


Fig. 6.5 – Vertical displacement results




A set of nonlinear analysis was carried out with the purpose to identify the distribution of cracks as a result of differential settlements.

The several uncertain that characterize this case study made necessary an analysis not focused on a fixed situation, but imposing different situations based on different hypothesis.



1° Scenario

The first scenario involves settlements at the NW corner of the church, where actually the visual inspection detected the worst condition around the church, highlighted in red in the picture below.



2° Scenario

In the second scenario, all the backside of the church is involved, as highlighted in the picture.



3° Scenario

In the third scenario, a new location was investigated. Along with the location in the NW corner, also the SW corner was subjected to displacement as the presence of a not well working gutter.



4° Scenario

The last scenario proposed is the most extreme one, prefiguring settlements in all the locations interested by the presence of not good working gutters. The final result is a combination of the second and third scenarios, involving finally also the main façade.




– The different approaches, used in the thesis, allowed to reduce the high level of uncertainty, or at least to understand where it would be better concentrating efforts.

– The first part of the thesis revealed the most severe problem is represented by the high level of moisture in the walls involving different damages, from biological colonization on the surface of the wall to the deterioration of the stones.

– From the micro modelling analysis, the values obtained, compared with reliable standards, are typical of a medium-good quality masonry. This allowed overcoming the concerns about the capacity of the wall compared to the load applied, six times less than the strength.

– The overall soil settlement was found utilizing elastic analysis with GEO5 and DIANA, obtaining results around 2-3 cm of vertical displacement. Afterward, different scenarios of the church subjected to differential settlements clarified that vertical differential settlements are not responsible for the current cracking pattern.

– From the subsequent analysis carried out, it appears more probable a problem related to horizontal displacements, due to past works on site.

– Based on the assumption done, from the structural point of view, the enclosure walls do not show serious problems enable to affect the stability.



Future Recommendations

Due to the historical importance of the building, not invasive, compatible, and durable interventions are suggested.

Walls Features

For first it is necessary to obtain more information about the geometry and the materials of the enclosure walls. At the moment, the properties of the infill are totally unknown, along with the one of the mortar. An easy and cheap way to collect this information could be the use of an endoscopy camera. This test will help to realize if the filling is made of small size stones, rubble masonry, or even poorer material.

A double flat jack could provide both compressive strength and Young's modulus. However, in the peculiar arrangement of stones, it would be difficult to identify two horizontal layers where to insert the flat jacks. So, it is suggested to use elastic wave methods as sonic tests, impact echo tests, and tomography tests. Carrying out direct and indirect sonic tests, in different locations, would allow obtaining reliable results in terms of elastic modulus. 

Along with the material properties, also the internal geometric features should be investigated. The endoscopy investigation could even help in determining the thickness of the leaves. However, impact echo tests would be ideal to detect the internal shapes of stones and the eventual presence of interlocking. Sonic tomography tests can give precious information about the presence of detachment in external leaves.



Cracks and soil monitoring

The vertical crack in the niches located at north has been related to the horizontal movement of the soil, due to works carried out during the '40. However, to validate this theory, it would be useful to make a monitoring of an eventual extension of the crack. This could be checked by applying a plaster mark on the crack. However, it could be easily broken by the effect of temperature changing that in the Broumov region is high. So, it is suggested the application of a crack meter for a period of time would allow to filter out the environmental effects. For this reason, the application also of sensors for temperature and humidity is necessary.

Monitoring of the soil settlements is a fundamental step for ensuring the future stability of the church. The best spot to be controlled should be the one at the back of the church, where the soil in correspondence of the sacristy seems more deteriorated. 


General interventions

As the concentration of waters around the church is the source of concern, it is necessary to carry out an inspection to establish the effective efficacy of the drainage system built in 1937, and eventually to plan maintenance of that. At the same time, the gutters that do not work properly have to be fixed, avoiding the concentration of rainy water around the shallow foundation of the church.


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