In domes and cylindrical structures, it is possible to distinguish in an experimental model, a latitudinal band in the form of a ring loaded from the inside.
The main goal of the research was to assess the effectiveness of peripheral strengthening using various techniques. For this purpose, 6 models (R1, R5, R6, R7, R8 and R9) of masonry rings were made, with loading applied from the inside by means of a dedicated hydraulic system. A complex stress state was induced using a 4-point loading scheme. Six different composite systems were used to strengthen the rings. The parameters of: geometry, construction materials, loading system and measuring instrumentation were the same for all six models.
2.1 Geometry and static scheme of the models
An example of a model prepared for experimental testing is presented in figure 2. Critical dimensions, measuring instrumentation and loading system are described below.
Models of masonry rings were built to a technical scale with geometrical parameters as detailed below
- axial diameter of the ring: d = 300 cm,
- internal radius: ri = 133.25 cm,
- outer radius: re = 166.75 cm,
- cross section: A = 250 x 335 mm = 83 750 mm2,
- height: h = 25 cm.
The right brick bonds were selected to achieve maximum cross-sectional attachment and to minimize joint thickness. The joints between the bricks had a thickness in the range: 5 ÷ 20 mm. Using appropriate brick elements, a repeatable bond was obtained. Thus the rings had 8 symmetrical axes. Stable temperature conditions prevailed in the laboratory hall during preparation and testing of the models with the air temperature in the range of 18 ÷ 22oC, and air humidity ranging between 45% ÷ 55%.
The models were built on a base covered with PE foil to minimize the influence of friction. The friction coefficient of the brick substrate against the base had been calculated on the basis of a ramp test, yielding a value equal to μ = 0.43.
Figure 3 shows a diagram of the test stand, along with the arrangement of the sensors. The “F1” and “F2” detectors are strain gauges that register pressure on the structure. “P” detectors registered pressure in the loading system. Additionally a pressure gauge was installed at the hydraulic pump. Meters marked with the letter “d” were inductive displacement sensors (LVDT) recording the change in the diameter of the ring. The symbol “u” denotes inductive displacement sensors (LVDT) recording displacements of masonry structure points.
The design of the ring loading system was purposefully light and mobile. Its central part was made of a steel body composed of four double-acting hydraulic jacks with a stroke of 50 mm and a maximum working pressure of 20 MPa. The system ensured concentrated forces of 150 kN on each pressure unit were obtained and transmitted to the model through 6 elastomer discs.
The loading system transmitted force into four points (points 1, 2, 3, 4). This loading pattern resulted in a complex (unfavorable) stress state in the circumferential direction. The static solution of the ring (internal forces) is presented in figure 4. The resulting state of stress in the structure was designed to simulate the unfavorable forces occurring in the support zones of domes, which result from disturbances in support continuity (pendentives, pillars, columns).
2.3 Bricks, mortar and masonry properties
One of the objectives of the research was to determine the material characteristics of the masonry, from which the rings models were made. This is why the bending and compression strength of the bricks and mortar was tested, and why the compression and shear strength of the masonry fragments was examined.
The compressive strength tests of the bricks were carried out in accordance with standard PN-EN 772-1 [13]. The mean value was equal to 11.75 MPa, standard deviation was 2.88 MPa and a coefficient of variation was calculated at 24.5%. A lime mortar with a grain size of 0 ÷ 2 mm was used in the construction of the models. The mortar was characterized by a high plasticity, low shrinkage (due to the longer setting time) and high adhesion to the substrate. These features are also characteristic for historical mortars. Bending and compression strength tests were carried out on 18 samples, 14, 21 and 28 days after forming, in accordance with the procedure described in PN-EN 1015 standard, [11]. The average value for the compressive and shear strength of the lime mortar is similar to the results obtained in testing of historical mortars by Matysek, [9] and Domasłowski et al. [10], which confirms the validity of its use in reconstructions and experimental testing of historic structures.
In addition to tests of individual materials, an examination was carried out of the entire structure of masonry elements. The value of the average compressive strength of the brickwork was converted into a characteristic value, and then compared to the characteristic value calculated according to the Eurocode formula (taking into account specific parts of the masonry). The experimental value was found to be more than three times higher. Table 1 summarizes the key results of all the tests conducted.
2.4 Strengthening methods
The following systems were used to strengthen the rings:
- R1: single CFRP strip attached to the masonry by a two-component epoxy composition;
- R5: single layered carbon fibre wrap on epoxy resin;
- R6: two layers of glass fibre mesh embedded in a mineral matrix;
- R7: four layers of B-FRCM system based on basalt fibre mesh embedded in a mineral matrix;
- R8: three layers of carbon fibre mesh embedded in a mineral matrix;
- R9: three layers of P.B.O. fibre mesh embedded in a mineral matrix.
Figure 5 shows all the reinforcing materials used. Most of them were covered additionally with a top layer of matrix. Table 2 summarizes the mechanical properties of the reinforcing materials. The data are based on the technical sheets of the individual products.