# Evaluation of the Performance of Unreinforced Stone Masonry Greek “Basilica” Churches When Subjected to Seismic Forces and Foundation Settlement

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Summary of Observed Case Studies

#### 2.1. Foundation Settlement

#### 2.2. Damage due to Strong Earthquake Ground Motion

## 3. Simplified Numerical Evaluation Process Assuming Non-Failing Masonry Wall Inter-Connections

**S**for each masonry structural element. These stress demand values (

_{Ed}**S**) are next utilized together with corresponding capacity values

_{Ed}**S**obtained on the basis of assumed strength values for the stone masonry for the studied churches. A set of such assumed strength values are listed in Table 2. In order to utilize current provisions for the design of masonry structural elements the numerically obtained deformation and stress demands for each masonry structural element is uncoupled into its in-plane and out-of-plane part. One of the main difficulties in assessing the capacity values for old stone masonry construction is the lack of experimentally verified strength values. In order to partially overcome this difficulty a number of specimens (Table 1 column 1) were built employing irregular stones with a cubic compressive strength of 60 MPa and low strength mortar with a mean cubic compressive strength equal to 0.85 MPa. The mortar joints were relatively thick (approximately 25 mm). These specimens were approximately 370 mm by 270 mm in plan and 270 mm height. Each specimen was placed in a testing rig hosting a vertical jack with a load cell and a flat sliding bearing resting at the top surface of each specimen; each specimen had its bottom part securely fixed as shown in Figure 10a,b. In addition, a horizontal actuator was securely attached at the top part of each specimen in order to apply a horizontal load in a gradually increasing manner, keeping at the same time the vertical load constant at a predetermined level. The aim of this experimental setup was to force each specimen to fail in an almost horizontal sliding mode at an equivalent mortar joint located between its top and bottom part, as is shown in Figure 10b. The final objective of this experimental sequence was to be able to quantify the shear strength against the sliding mode of failure (

_{Rd}**f**) through the parameters included in a “Mohr-Coulomb” shear strength criterion as is expressed by Equation (1). The shear strength of the stone masonry when the normal stress is zero is denoted by

_{vk}**f**. The compressive axial stress acting on the bed joint is denoted by

_{vko}**σ**and

_{n}**μ**is an assumed value for the static coefficient of friction.

**f**

_{vk}= f_{vko}+ μ σ_{n}**σ**) applied during testing (Table 1 column 3). Employing formula 1 with values

_{n}**f**= 0.12 MPa and

_{vko}**μ**= 0.45 the predicted sliding shear strength values are found, listed in Table 1 column 4. Reasonably good agreement is obtained between measured and predicted sliding shear strength, as is indicated by the relevant ratio of measured over predicted sliding shear strength with values listed in column 5 of the same Table.

**σ**) acting simultaneously, is also employed by Euro-Code 6 [20]. In this case, the value of the static friction coefficient is assumed to be equal to 0.4. The strength values listed in Table 2 are based on the Euro-Code 6 shear strength envelope, assuming values of

_{n}**f**= 0.16 MPa and of

_{vko}**μ**= 0.4 (Table 2, column 1). Similarly, low strength values were assumed for the tensile strength normal (

**f**) and parallel (

_{xk1}**f**) to an equivalent horizontal joint (Table 2, column 2). The shear capacity defined in this way corresponds to the mechanism resisting the sliding mode of failure. Tomazevic [21] proposed a procedure, developed by Turnsek and Cacovic [22], towards estimating the shear capacity corresponding to the mechanism resisting the diagonal tension mode of failure for a masonry structural element having a height (h) and a length (l). In this case the shear strength (

_{xk2}**τ**) is given by the following relationship.

_{max}**R**=

_{i}**S**/

_{Rdi}**S**> 1

_{Edi}**R**=

_{i}**S**/

_{Rdi}**S**< 1

_{Edi}**S**represents the demand posed for each masonry structural element as it results from the simplified numerical simulation;

_{Edi}**S**is the corresponding capacity value which is obtained on the basis of assumed strength values for the stone masonry (Table 2). Note that no safety coefficients are used in estimating the capacity values at this stage of the evaluation process. Inequality 3 signifies safe structural performance. Inequality 4 denotes that the predicted structural performance exceeds a certain limit state thus signifying the development of structural damage corresponding to the specific limit state that is exceeded. These corresponding capacity over demand ratio (

_{Rdi}**R**) values are used in this simplified numerical evaluation process; a ratio (

_{i}**R**) value smaller than 1 indicates that a distinct limit state has been reached leading to the corresponding failure mode. The following five common structural damage scenarios are stated corresponding to five distinct relevant limit-states through the relevant ratio values (

_{i}**R**/

_{i}= S_{Rdi}**S**). Scenario (

_{Edi}**a**) addresses the in-plane shear limit state which corresponds to a sliding failure mode through the value of the ratio (

_{1}**R**); scenario (

_{τsli}**a**) addresses the in-plane shear limit state corresponding to a diagonal tension failure mode (

_{2}**R**). Scenario (

_{τdia}**b**) corresponds to a compressive mode of failure (

**R**) whereas scenario (

_{ς}**c**) corresponds to the in-plane tensile limit state (

**R**). Finally, scenario (

_{σ}**d**) corresponds to the out-of-plane tensile limit state (

**R**). Both scenario (

_{M}**c**) and scenario (

**d**) use the

**f**strength value, listed in Table 2 column 2.

_{xk1}**a**)

_{1}**R**= shear strength/shear stress demand.

_{τsli}**R**< 1 signifies in-plane sliding shear mode of failure

_{τsli}**a**)

_{2}**R**= shear strength/shear stress demand.

_{τdia}**R**< 1 signifies in-plane diagonal tension mode of failure.

_{τdia}**b**)

**R**= compressive strength/compression stress demand.

_{ς}**R**< 1 signifies in-plane compression mode of failure.

_{ς}**c**)

**R**= tensile strength/tensile stress demand.

_{σ}**R**< 1 signifies tensile mode of failure normal to bed joint (in-plane)

_{σ}**d**)

**R**= tensile strength/tensile stress demand from out-of-plane flexure.

_{M}**R**< 1 signifies out-of-plane tensile mode of failure normal to bed joint at the extreme fibre.

_{M}**R**,

_{τsli}**R**< 1) predict the corresponding limit state condition. As can be seen, this methodology is based on combining numerical stress demands resulting from elastic analyses with limit-state strength values. An alternative approach is to incorporate these limit-state strength values in a non-linear push-over type of analysis [29]. As was shown in this study by Manos et al. [29] the above linear-elastic approach is a reasonable approximation of the actual behaviour and of predicting regions of structural damage, being both less complex and time consuming than the corresponding non-linear approach. Manos et al. [30,31] developed a relevant expert system for assessing the various resisting capacities of vertical masonry structural elements.

_{τdia}, R_{ς}, R_{σ}, R_{M}## 4. Results from Distinct Case Studies and Discussion

#### 4.1. Numerical Simulation of the “Basilica” Church of Assumption of the Virgin Mary at Dilofo-Voio-Kozani

#### 4.2. Numerical Simulation of the Dynamic and Earthquake Response of “Basilica” Churches

**R**ratio values. These ratio values for either the sliding shear (

_{τ}, R_{σ}, R_{M}**R**,) or the diagonal tension (

_{τsli}**R**) are indicated with the common ratio value

_{τdia}**R**Ratio

_{τ}.**R**values, indicating in-plane compressive limit-state, are not shown as this mode of failure is not reached anywhere in this church.

_{ς}**R**ratio values. It can be seen that all these ratio values are smaller than one (

_{τ}, R_{σ}, R_{M}**R**< 1) in numerous locations, indicating that the corresponding limit state has been reached at all these locations of the structure that the relevant ratio value is linked with. For clarity the whole structure is deconstructed part by part in these figures in four walls that form its 3-D stone masonry shell. The East transverse wall is placed at the top left corner of Figure 16 whereas the West transverse wall at the bottom left corner. The South longitudinal wall is placed at the top right corner of Figure 16 whereas the North longitudinal wall at the bottom right corner.

_{τ}, R_{σ}, R_{M}**R**ratio values are well below one (

_{M}**R**< 1) mainly for both North and South longitudinal walls indicating that these walls for this church reached a widespread out-of-plane flexural limit state.

_{M}**R**<1,

_{σ}**R**< 1) whereas at the top part of these walls the development of the out-of-plane flexure limit state prevails (

_{τ}**R**< 1).

_{M}## 5. Numerical Simulations of the Seismic Performance Including Non-Linear Response Mechanisms

#### 5.1. Foundation Uplift

#### 5.2. Non-Linear Response Simulating the Detachment of the Masonry Walls from the Roof Level as well as at Their Corner Interconnection

## 6. Observed Structural Performance for a Long Period Range

## 7. Conclusions

**R**). These are derived using the numerically predicted demands as well as capacities based on assumed strength properties of the masonry for distinct failure modes which correspond to in-plane shear, compression or tension as well as out-of-plane flexure limit states.

_{τ}, R_{ς}, R_{σ}, R_{M}## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**(

**a**) The Basilica structural system with the interior colonnade of the central nave; (

**b**) The Basilica structural system with the peripheral longitudinal and transverse walls.

**Figure 3.**(

**a**) Heavy damage of the East wall. South-East view; (

**b**) Heavy damage of the North wall. North-West view; (

**c**) Heavy damage of the vaulting superstructure.

**Figure 4.**The “Basilica” church of Profitis Ilias at Siatista – Kozani (

**a**) Longitudinal cross-section; (

**b**) Wooden shoring of South longitudinal wall.

**Figure 10.**(

**a**). Short stone masonry specimen subjected to sliding shear; (

**b**) Sliding mode of failure of short stone masonry specimen.

**Figure 11.**Non-deformable foundation (

**a**) distribution of maximum tensile stresses South-East view (

**b**) distribution of maximum tensile stresses North-East view. The scale at the far right of each plott indicates that the colours used to represent stress values in this numerical representation of the structure are ranging from 0.1 MPa to −0.1 MPa. Yellow colour indicates stress values excedding 0.1MPa.

**Figure 12.**Deformable foundation (

**a**) distribution of maximum tensile stresses South-East view (

**b**) distribution of maximum tensile stresses North-East view. The scale at the far right of each plott indicates that the colours used to represent stress values in this numerical representation of the structure are ranging from 0.1 MPa to −0.1 MPa. Yellow colour indicates stress values excedding 0.3 MPa.

**Figure 14.**The numerical simulation of the “Basilica” church of St. Marina in Soullaroi in Kefalonia. (

**a**) Longitudinal direction; (

**b**) Transverse direction.

**Figure 15.**Constant ductility response spectral curves of the Chavriata record, Kefalonia 2014 earthquake together with the relevant Euro-Code 8 design spectral curves: (

**a**) N-S component (

**b**) E-W component.

**Figure 16.**Summary results of the evaluation process in terms of

**Rτ**,

**Rσ**,

**R**ratio values, for moderately deformable foundation (axial stiffness value of supporting links equal to 24.5 KN/mm).

_{M}**Figure 19.**(

**a**) Non-linear links to simulate uplifting of the structure at the soil-foundation interface; (

**b**) Non-linear links to simulate detachment between the roof and the masonry walls or between vertical walls at the corners.

**Figure 20.**(

**a**) Push-over in the East-West direction (Ey), foundation uplift; (

**b**) Push-over in the North-South direction (Ex), foundation uplift.

**Figure 21.**(

**a**) Push-over in the East-West direction (Ey)—detachment of the West wall; (

**b**) Push-over in the North-South direction (Ex)—detachment of the North wall.

**Figure 22.**Images of total destruction to old masonry construction in Argostoli, Kefalonia island during the 1953 earthquake sequence.

Code Name of Tested Specimen | Measured Value f_{vk} (Mpa) | Applied Level of Normal Stress σ_{n} (Mpa) | Predicted f_{vk} (Mpa) | Ratio Measured f_{vk}/Predicted f_{vk} |
---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) |

Sample 1 | 0.396 | 0.53 | 0.359 | 1.103 |

Sample 2 | 0.41 | 0.61 | 0.395 | 1.038 |

Sample 3 | 0.305 | 0.46 | 0.327 | 0.933 |

Sample 4α | 0.20 | 0.30 | 0.255 | 0.784 |

Sample 4β | 0.375 | 0.54 | 0.363 | 1.033 |

Shear Strength f_{vko} for Zero (σ_{n}) Normal Stress (MPa) | Tensile Strength Normal (f_{xk1})/Parallel (f_{xk2}) to Bed-Joint (MPa) | Compressive Strength f_{k} (MPa) | Young’s Modulus E (MPa) | Poisson’s Ratio |
---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) |

0.16 | 0.15/0.60 | 3.50 | 1000 | 0.2 |

**Table 3.**Base shear Values (KN) based on the Chavriata response spectra (which is the most demanding).

Studied Church/Soil Conditions | N-S (Transverse x-x) | E-W (Longitudinal y-y) |
---|---|---|

St. Marina Soullaroi/Hard Soil | 5229 | 8397 |

St. Marina Soullaroi/Soft Soil | 5803 | 8828 |

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**MDPI and ACS Style**

Manos, G.C.; Kotoulas, L.; Kozikopoulos, E.
Evaluation of the Performance of Unreinforced Stone Masonry Greek “Basilica” Churches When Subjected to Seismic Forces and Foundation Settlement. *Buildings* **2019**, *9*, 106.
https://doi.org/10.3390/buildings9050106

**AMA Style**

Manos GC, Kotoulas L, Kozikopoulos E.
Evaluation of the Performance of Unreinforced Stone Masonry Greek “Basilica” Churches When Subjected to Seismic Forces and Foundation Settlement. *Buildings*. 2019; 9(5):106.
https://doi.org/10.3390/buildings9050106

**Chicago/Turabian Style**

Manos, George C., Lambros Kotoulas, and Evangelos Kozikopoulos.
2019. "Evaluation of the Performance of Unreinforced Stone Masonry Greek “Basilica” Churches When Subjected to Seismic Forces and Foundation Settlement" *Buildings* 9, no. 5: 106.
https://doi.org/10.3390/buildings9050106