Friedrichswerder Church in Berlin –The Response of the Structure to the Construction Activities Around

SAHC2014 – 9th International Conference on Structural Analysis of Historical Constructions F. Peña & M. Chávez (eds.) Mexico City, Mexico, 14–17 October 2014

FRIEDRICHSWERDER CHURCH IN BERLIN –THE RESPONSE OF THE STRUCTURE TO THE CONSTRUCTION ACTIVITIES AROUND

Wolfram Jaeger, Peter Schoeps, Tammam Bakeer

TU Dresden, 01062 Dresden, Germany [email protected] [email protected]

Jaeger Ingenieure GmbH, 01445 Radebeul, Wichernstr. 12, Germany [email protected]

Keywords: Friedrichswerder Church, finite element modelling, excessive settlement

Abstract. Very close to the Friedrichswerder Church in the centre of Berlin a building project called Kronprinzengärten with a two level underground garage should be realised. The first excavation works have led to excessive settlements at the western side of the church. These settlements produced new cracks or increased the opening of the old cracks, in addition to a partial crumbling of the plaster, mainly in the load bearing walls and the vaulted structure. Due to the new crack situation the building activities were stopped as the overall stability of the church was needed to be evaluated. This has been done with various FEM models at the macro level. The models were built considering the actual geometry, boundary conditions, and material properties of masonry. The whole church was divided into three parts namely: the apse, the bay, and the towers. A plasticity-based nonlinear material model following the Ganz failure surface has been used for masonry material considering the real arrangement of masonry bricks in vaults and walls. Different phases of settlement were applied at the level of the foundation to the FEM models. These include predicted settlements due to the further continuation of the building activities. The continuing makes it necessary to stabilise the soil by grouting. The FEM models were used to capture the internal state, to verify the ultimate limit state using standards rules and to give a statement about the serviceability limit state. The further settlement by continuing of the construction works in the neighbourhood has to be limited by lifting ground injection.

The paper focuses on checking the stability of the church by considering the settlement history over the time. The damage state of the church prior to the beginning of the construction work was readjusted. The crack patterns and widths from FEM models were calculated and compared to the real available data. An estimation of further cracking due to the continuation of construction work was done. Wolfram Jaeger, Peter Schoeps, Tammam Bakeer

1 INTRODUCTION Near to the Friedrichswerder Church in the centre of Berlin a luxury residential project project called Kronprinzengärten with a two level underground garage should be realised. The first excavation works have led to excessive settlements at the western side of the church. These settlements produced new cracks or increased the opening of the old cracks, in addition to a partial crumbling of the plaster, mainly in the load bearing walls and the vaulted structure. Due to the new crack situation the building activities in Kronprinzengärten were stopped as the stability of the church needed to be evaluated.

2 SUBSOIL

2.1 Soil layers and finite element model The geotechnical report of the subsoil in [1] shows that the soil materials of the area of Kronprinzengärten is shown in table 1. Table 1: Layers of soil [1].

Layer No. Elevation of the upper layer surface Soil layers [m AFE] Layer 1: 33.8 Replenishment 1 30.8 2 27.8 Layer 2: 3 26.8 Medium to 4 25.8 coarse sands 5 22.3 6 18.8

The soil layering was assumed to be horizontal over the whole area. The strength parameters and the densities are determined by standard tests whereas the stiffness parameters for the Hardening- Soil model were derived from the information in the geotechnical report [1].

A finite element model has been built in PLAXIS software to check the deformation state after adding the retrofitting measures. Two soil retrofitting measures were considered, (1) A bored pile wall with pile diameter of 0.88 m and spacing every 1.1 m. After installation of the piles, the area in-between will be grouted. A stiffening beam is placed on the top of bored pile wall RO406, 4x20 at +31.40 m and +29.0 m AFE and have an average horizontal distance of 2.5 m. (2) A diaphragm wall with thickness of 80 cm. It consists of double tubular stiffeners RO406, stiffened 2x20 in the height of +31.4 m as well as +29.0 m AFE. The deformation state caused by the excavation and the construction of the new buildings has been checked on the basis of finite element calculations for two typical cross sections in the bored pile and the diaphragm wall area on the eastern side of the excavation area nearby Frie- drichswerder Church.

2 Friedrichswerder Church in Berlin –The Response of the Structure to the Construction Activities around

Figure 1: The finite element model in the final state in the area of the bored pile wall [7]

In the finite element model, the stress-dependent stiffnesses are determined by the following formula:

cos sin = (1) cos + sin ∙ − ∙ is the overlay pressure in / ∙ ∙ = 100 kN/m atmospheric pressure = 0.3 0.5 A historical− pre-loading of on average 200 kN/m was assumed. The reference values used in the FE model for the determination of the stress-dependent stiffness of the hardening-soil- model are given in table 3. With this preload the state of the subsoil is modeled before excavation. The material parameters taken from the geotechnical report are compared with the values used in the FE model in tables 2 and 3.

3 Wolfram Jaeger, Peter Schoeps, Tammam Bakeer

Table 2: Material parameter of soil layer1 (replenishment)

Material parameter Symbol Geotechnical report [1] Finite element model Friction angel 30o 30o 0 kN/m kN cohesion 0.1 m not specified 0 Dilatancy 17 kN/m 17 kN/m Density 9 kN/m 9 kN/m Stiffening modulus / not specified 5 + 1. 7z MN/m Poisson ratio ′ not specified 0.33 Table 3: Material parameter of soil layer2

Material parameter Symbol Geotechnical report [1] Finite element model 1 2 3 4 5 6 1 2 3 4 5 6 Friction angel 35 30 33 35 37 37 35 33 33 35 37 37 Cohesion [kPa] 0 0.1 Dilatancy not specified 5 3 3 5 7 7 18 17 18 18.5 19 19 18 17 18 18.5 19 19 Density 10 9 10 10.5 11 11 10 9 10 10.5 11 11 [kN/m ] ′ / Initial loading 50 25 40 75 80 60 62 62 62 65 65 57 [MN/m] Unloading and 3 × 186 186 186 195 195 171 reloading [MN/m ] Exponent not specified 0.33 0.5 0.5 0.5 0.5 0.3 Secant modulus not specified = [8] Poisson ratio 0.2 0.2 2.2 FEM Results From PLAXIS calculations, the deformation at the foundation of Friedrichswerder Church at level of 31.36 m AFE were determined for each construction phase. The ability to induce deformations on the Friedrichswerder Church through the construction of the diaphragm wall panels was investigated in a separate 3D model by modelling a single panel with distance 3.7 m to FWK. The rotation of the church has been determined by calculating the angular rotation from the maximum settlement difference of a single foundation with base width of 6.1 m.

The construction-related deformation at the foundation back edge is applied in all stages as 55% of the associated deformation at the foundation front edge. This ratio was calculated back from the deformation measurements (foundation and FWK roof) during the construction of the bored pile wall. Table 4 summarizes the expected deformations and rotations in the remaining stages of construction from excavation to the establishment of the new construction. The residual deformations were estimated at 50% of deformation without elevation grouting.

4 Friedrichswerder Church in Berlin –The Response of the Structure to the Construction Activities around

Table 4: The still expected deformations in FWK from the construction phase “soldier pile wall BA I”

Expected horizontal dis- Expected horizontal dis- Settlement placements at the founda- placements at the roof of Variation rotation [mm] tion of FWK in direction FWK in direction of the of the excavation [mm] excavation [mm] Without Eleva- 7aN 6 4 1/2100 18 tion grouting 7bN 6 4 1/2200 18 After elevation 7aN 3 2 1/4200 9 grouting 7bN 3 2 1/4400 9 7aN: In pile wall area (about 30 m in the northern area) 7bN: In the diaphragm wall area (about 40 m in the southern area)

3 THE CHURCH

3.1 Historical background Friedrichswerder Church (Figure 2) was built and designed by the Prussian architect Karl Frie- drich Schinkel from 1824 to 1831 and was the first Neo-Gothic church in the city. It was named for Friedrich Wilhelm – the great elector who served as Duke of Prussia from 1640 -1688. During World War II, the church was severely damaged and rebuilt from 1979 to 1986 and was opened as a branch of the national gallery in 1987 on the occasion of Berlin’s 750-year anniversary cele- bration. Only the façade was resorted true to the original due to high restoration costs. Ten years later, the final restoration of selected details was completed from 1997 to 2000 and the Frie- drichswerder Church became a museum [9]. The church now belongs to Berlin State Museums’.

Figure 2: 3D CAD models of the Friedrichswerder Church

5 Wolfram Jaeger, Peter Schoeps, Tammam Bakeer

3.2 The finite element model Nonlinear analysis was performed based on several FEM models. The models were built considering the actual geometry, boundary conditions, and material properties of masonry. The whole church’s geometry has been divided into three parts: the apse, the bay, and the towers (Figure 3). A plasticity-based nonlinear material model following the Ganz failure surface has been used for masonry material (Figure 4 and Table 5). The orientation of the local coordinate systems of the finite elements was defined to map the real arrangement of masonry bricks in vaults and walls. Different phases of settlement were applied on the level of the foundation to the FEM models. These include predicted settlements due to continuing of the building activities. The continuing makes it necessary to stabilise the soil by grouting. The FEM models were used to capture the internal state, to verify the ultimate limit state using standards rules and to evaluate the serviceability limit state. The safety state of the church has to be evaluated considering the settlements history over the time. i.e. the current state of settlements and the future settlements due to the continuation of construction work according to variant 0a.2 GuD [3].

Z X

FWK (a) (b) (c) Figure 3: Finite element models for (a) the apse, (b) the bay, and (c) the towers

6 Friedrichswerder Church in Berlin –The Response of the Structure to the Construction Activities around

Figure 4: Ganz model of the failure surface of masonry (Law 20 in MultiPlas tool) [2].

Table 5: Input parameters for the material law of masonry

Characteristic values fmx (fk) Uniaxial compression strength perpendicular to the 4.2 N/mm² bed joints. fmy Uniaxial compression strength parallel to the bed 4.2 N/mm² joints ( fmy £ fmx ! ) ftx Tensile strength perpendicular to the bed joints 0.01 N/mm² (» 0,0) (£ C/tan(f) ) fty Tensile strength parallel to the bed joints (= 50 % of 0.16 N/mm² the units’ tensile strength) asy Distance of the head joints (means value) 0.25 m al Distance of the bed joints (mean value) 0.08 m üy Lap length 0,08 m f Friction angle (bed joints) 31° (m = 0,6) c Cohesion (bed joints) 0.08 N/mm²

The damage state of the church prior to the beginning of the construction work was readjusted. The crack patterns and widths from FEM models were calculated and compared to the real available data. An estimation of further damages due to the continuation of construction work was calculated. The modulus of elasticity is taken E = 1100 fk = 4620 N/mm² according to DIN EN 1996-1-1 [11]. The residual strengths were chosen significantly smaller than the maximum strength in order to simulate the unloading of the plasticized or cracked areas and to take into account the load arrangement as far as possible. The material partial safety factor according to DIN EN 1996-1-1 [11] and NA [10] is given as gM = 1.5. Considering a creep factor for long-term loads of z = 0.85 [10], the material safety factor is then:

gM = 1.5 / 0.85 =1.76 (2)

7 Wolfram Jaeger, Peter Schoeps, Tammam Bakeer

Six loading cases were considered for the structural analysis. For every load case the outcome of the previous load cases is used as a starting configuration for the damage and deformations. The calculated load cases are:

L1: Self-weight with restrained foundation supports. L2: The displacement of the foundations in the current state (historical settlement and sub- sidence through pile wall [3]). L3: Additional deformations according to [3]. The whole deformation including the historical deformation: ux = 24 mm (horizontal); uy = -27 mm (vertical); rz = -1/256 rad (rotation). L4: 1.5 times additional deformations. L5: 2.0 times additional deformations. ux = 39 mm (horizontal); uy = -34 mm (vertical); rz = -1/196 rad (rotation). L6: Self-weight increase by a factor of 1.35

In load case 4, the safety factor for the action of settlement which used to calculate the future displacements is taken as gGset = 1.5. In load case 5, the partial safety factor of the settlement has been increased to gGset = 2.0.

Since the application of permanent action on masonry can have a favourable influence on bend- ing elements, therefore, the partial safety factor for permanent action is considered gG = 1.0. However, to consider any possible adverse effect, a partial safety factor of gG = 1.35 has been used for the load case 6. The introduction of material safety factor gM in the model will reduce only the strengths but not the stiffness. However, this approach is on the safe side. The parameters study applied on the bay model showed that the increase of the modulus of elasticity gives more stress concentrations than without material partial safety factor. The second order deformation effects which requires the reducing of the elastic modulus, plays no rule on the bases of massive or curved structure elements.

3.3 FEM Results Figure 5 shows the finite element results for the stresses perpendicular to bed joints. The stresses reach -2.3 N/mm² in compression area and up to 0.01 in the tensile area according to the material parameters. For the direction perpendicular and parallel to bed joints the plastic strains are shown in figures 6 and 7. Thus for all studied load cases the safety state was curried out within the nor- mative predefined security level.

8 Friedrichswerder Church in Berlin –The Response of the Structure to the Construction Activities around

Figure 5: Horizontal deformation [m] due to settlement in Load case 6

9 Wolfram Jaeger, Peter Schoeps, Tammam Bakeer

Figure 6: FE results of the in Load case 6 for stresses perpendicular to bed joints [ N/mm²]

Figure 7: FE results in Load case 6 for the plastic tensile strain perpendicular to bed joints

10 Friedrichswerder Church in Berlin –The Response of the Structure to the Construction Activities around

4 SUMMARY AND CONCLUSION Finite element models were created for the Friedrichswerder Church, the church is divided in- to three models: the bay, the apse, and the entrance to the two towers. The models have simulated under several loading conditions that take into consideration, the history of the construction and the new expected loading conditions due to the construction and excavation works on the Kronprinzengärten project. Since the FE analysis performed nonlinearly, the stresses were redistributed at each cracking state. The crack patterns obtained from nonlinear finite element analysis under current loading condition have a good agreement with the current existing mapped cracks. It was possible for all models under all loading cases to reach a convergent solution. This means, the safety of the structure stability is verified according to the norm-defined safety requirements. For all three models the same settlement values have been used. The model of the apse was calculated using a simplified settlement model, which takes into account also the state of settlements at the end of the excavation and interpolates the foundation deformations accordingly. The overall safety factor determined is actually at load condition 6: g = 1.76 x 2.0 = 3.52 (partial safety factor for the material and for the foundation displacements). The increase in self-weight was not considered. The required safety factor is g = 1.76 x 1.5 = 2.64 ( L 4). The calculations show compression plasticisation near to the crack growth areas. Here the re- duced compressive strength by the partial safety factors is achieved≜ by calculation. The situation can still be considered acceptable. However, this violates the safety factors locally. This refers to the statistically lowest value of strength (5% quantile) and the statistically highest value of the loads (95% or 98% quantile). The first safety measures should be made in form of a cracks injection. This is to avoid interruption of the load flow and therefore avoid possible opening of the existing cracks or formation of new ones. The structural analysis curried out on FWK historical masonry showed the lack of standards to provide a verification procedure for the nonlinear analysis of these constructions. The determination of the safety state is therefore based on the understanding of actions and combinations and their influences on structure elements. The paper showed how to define the possible cases of load combinations based on the type of element and action and how to determine the decisive combinations and the associated partial safety factors. To overcome the errors of human mistakes, such kind of simulation should be checked out independently as well as by comparative calculations, which were done by Dr. Hans Scholz, checking engineer Berlin.

REFERENCES [1] -, Bericht Ergänzende Baugrunduntersuchung für das Bauvorhaben Kronprinzengärten 10117 Berlin-Mitte, Stand 08.09.2010, Fugro Consult GmbH, 2010. [2] Dynardo: MultiPlas – Elasto-plastic material models for ANSYS – General multi-surface plasticity, User’s manual, Weimar, 2011. [3] T. Richter, B. Schädlich, Erläuterungen zu den Varianten; Verformungen FWK. GuD Geo- technik und Dynamik Consult GmbH. Berlin, 2013

11 Wolfram Jaeger, Peter Schoeps, Tammam Bakeer

[4] W. Brameshuber, Eigenschaften von Mauersteinen, Mauermörtel, Mauerwerk und Putzen (Properties of bricks, mortar, masonry and plaster). In: Mauerwerk-Kalender 38, 3–34. Ed. W. Jäger. Ernst & Sohn, Berlin, 2013 [5] H. Gulvanessian, J.-A. Calgaro, M. Holický, Designer´s guide for Eurocode: Basis of structural Design EN 1990. Ice-publishing by Thomas Telford Ltd.: London, 2012 [6] P. Schubert, Attributes of masonry, bricks, masonry mortars and plasters. In: Mauerwerk- Kalender 35, 3–25. Ed. W. Jäger. Ernst & Sohn, Berlin, 2010 [7] T. Richter, B. Schädlich, Bericht: Kronprinzengärten FEM – Verformungsberechnung Ver- bauvarianten 7aN und 7bN. GuD Geotechnik und Dynamik Consult GmbH. Berlin 2014. [8] T. Schanz, Über die Zuverlässigkeit von Setzungsprognosen, Thesis, Wissenschaftliche Zeitschrift der Bauhaus-Universität Weimar, 46. 96-102,2000. [9] W. Gahrig: Unterwegs zu den Hugenotten in Berlin. Historische Spaziergänge. Institut für vergleichende Staat-Kirche-Forschung (Hrsg.), 2., erw., und korr. Aufl., Das Neue Berlin (edition ost), Berlin, 2000 [10] DIN EN 1996-1-1/NA:2012-05: Eurocode 6: Nationaler Anhang – National festgelegte Pa- rameter – Bemessung und Konstruktion von Mauerwerksbauten – Teil 1-1: Allgemeine Re- geln für bewehrtes und unbewehrtes Mauerwerk (National Annex – Nationally determined parameters – Part 1-1: General rules for reinforced and unreinforced masonry structures). [11] DIN EN 1996-1-1:2013-02: Eurocode 6: Bemessung und Konstruktion von Mauerwerks- bauten – Teil 1-1: Allgemeine Regeln für bewehrtes und unbewehrtes Mauerwerk (Design of masonry structures – Part 1-1: General rules for reinforced and unreinforced masonry structures).