Microsoft Word - numero_51_art_23_2542 G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 288 Focussed on Fracture and Damage Detection in Masonry Structures Comparison of Two Parameters Models for clay brick masonry confined by FRP Giancarlo Ramaglia, Gian Piero Lignola, Andrea Prota University of Naples, Federico II, Department of Structures for Engineering and Architecture, Via Claudio 21, Naples, 80125, Italy giancarlo.ramaglia@unina.it, glignola@unina.it, aprota@unina.it ABSTRACT. Masonry elements are often confined in order to improve their structural capacity. Generalized methods to assess the behavior of confined masonry columns are usually derived from concrete confinement models. However, concrete and masonry present several crucial differences due to their physical and mechanical properties. The recent scientific researches provided relevant information on the experimental behavior of confined masonry columns. In this paper, the Stassi D’Alia failure criterion, recently particularized by the authors to assess the axial capacity of confined solid clay brick masonry, has been discussed remarking its potential as a solid mechanics model. The model has been validated by means of comparisons with 67 relevant experimental results available in the scientific literature. The tested specimens made of solid clay bricks were strengthened with several types of strengthening systems. In order to assess the potential of the confined model, the comparison included also other four available mechanical models based on classical failure criteria available in the scientific literature. The reliability of the confinement models was remarked by assessing some relevant statistical parameters. KEYWORDS. Mechanical approach; Masonry; Confinement; Experimental tests. Citation: Ramaglia, G., Lignola, G.P., Prota, A., Comparison of Two Parameters Models for clay brick masonry confined by FRP, Frattura ed Integrità Strutturale, 51 (2020) 288-312. Received: 14.06.2019 Accepted: 26.11.2019 Published: 01.01.2020 Copyright: © 2020 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. INTRODUCTION odern strengthening strategies can be performed to improve the structural capacity of several types of structures [1, 2]. For masonry buildings strengthening strategies can be applied to improve different aspects [3, 4]. In particular, intervention strategies can be used to improve both the load capacity [5, 6] and the ductility capacity [7]. Many innovative materials were used in strengthening applications of real structures and heritage buildings since many years [8]. The effectiveness of these systems was demonstrated in many research programs by means of static [9, 10] and dynamic [11, 12] tests. The benefits due to the confinement effects represent a key aspect in the engineering applications. Confinement can be applied by means of wraps made of composite materials [13, 14]. This strengthening M http://www.gruppofrattura.it/VA/51/2542.mp4 G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 289 strategy limits or prevents the lateral deformations and increases the axial capacity of the structural member. The increasing of the lateral compression in axially loaded elements provides a three-dimensional stress state. This stress state is beneficial to increase the load capacity of the confined structural member as demonstrated by the classical failure criteria of building materials [15, 16]. In the practical applications, the confinement is used either to confine individual structural elements or entire buildings, or parts of them. The attention focuses on masonry columns where confinement methods accounting for masonry peculiarities are not available in the technical literature. Several models can be used to assess the confinement impact due to the intervention strategies [17]. Many available confinement models were developed using semi-empirical approaches and were usually derived from concrete [18] or from the classical failure criterions. Confinement models developed for concrete and extended to the masonry have some drawbacks due to the strong variability of the masonries. For this reason a model for all types of masonries is extremely difficult to develop. In this background, the confinement models based on failure criteria appear to be the best approaches to assess the axial capacity of strengthened masonry columns. These models allow to assess the impact of many properties of masonry constituents on the structural performance. Therefore, confinement models able to assess the axial capacity of masonry columns represent important targets. In this paper, a confinement model, recently particularized by the authors [15] from the failure criterion of Stassi-D’Alia [19, 20] to assess the axial capacity of strengthened masonry, has been discussed remarking its potential as a solid mechanics model. This model was developed according to a failure criterion accounting for the main mechanical parameters representative of the masonry. In order to assess the reliability of the proposed model, other available mechanical models [21] have been used too, to predict the axial capacity of strengthened masonry elements actually tested. The theoretical results of several models have been compared with the experimental results. Finally, in order to confirm the potential of the proposed mechanical model a statistical analysis has been carried out. CONFINEMENT MODELS he present paper focuses on confinement models based on a mechanical approach. In particular, the stress state in each point of the material must respect the failure criterion. The failure criterion is based on the definition of boundaries of the failure surface. It can be expressed based on several mechanical parameters representative of materials. This is preferable to assess the impact of several mechanical parameters on the structural behavior of strengthened masonry elements. Furthermore, these models can be easily implemented in Finite Element Modeling (FEM), [22, 23]. The confinement models available in the scientific literature were developed on a failure criterion based on mechanical parameters representative of the confined material. The maximum compressive strength can be assessed by changing the confinement effect (i.e. the lateral or confining stress). For a generic point of the material, the stress state is provided by three components, 1 , 2 and 3 along the principal axes, 1, 2, and 3 respectively. The axes 1 and 2 define the main plane where the lateral stresses act (i.e. plane of the cross-section). This internal stress state is due to the confinement effect and depends on the confinement technique. The axis 3 defines the direction where the maximum stress 3 increases according to the failure condition (i.e. longitudinal axis of the member). The failure criterion has been applied on masonry elements, therefore in the direction 3 the stress increases up to the compressive strength, 0mf (unconfined masonry) and mcf (confined masonry). Conversely, the 1 and 2 represent the internal stresses provided by the confinement system (under uniform lateral stress 1 2  ). The envelope of the main stress, 3 while changing the lateral stress, 1 and, 2 provides the confinement curve of the masonry member. The confinement curve of masonry depends on the compressive and tensile strengths, 0mf and mtf respectively. The tensile strength can be expressed in normalized form as the tensile and the compressive strength ratio, 0mt mf f  . This value characterizes the mechanical behavior of the masonry materials. The masonry is made of two main constituents: bricks and mortar and can be modelled according to several approaches: micro or macro-modelling approaches. For this analysis, modelling the masonry, as a whole, appears to be the favorite approach due to the detailed level of analysis. In fact, in order to assess the confinement properties of a masonry element, it can be modelled by using an average behavior between the constituents. For the masonry, the tensile strength is generally governed by the mechanical properties of the mortar. Therefore, the tensile strength of masonry, mtf can be assumed equal to the tensile strength of mortar. Is a normal practice to express the tensile strength as function of the compressive strength of masonry. The tensile strength of masonry as whole can be assumed equal to 10% of its compressive strength for lime mortar and 20% for cementitious T G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 290 mortars according to experimental results [24, 25]. Conversely, the compressive strength of masonry, 0mf is generally assessed by means of compressive tests performed on masonry specimens. The mechanical model based on failure criterion allows to assess the confinement curve under a non-uniform stress state 1 2  typically developed in non- axisymmetric confined elements. For these elements, two main lateral stresses can be identified 1 ,minlf  and 2 ,maxlf  . The values, ,minlf and ,maxlf depend on the confinement system used for the strengthening strategy. The confinement model depends on these parameters. In fact, for finite element modeling where lateral stresses are usually non-uniform, a mechanical model is essential to account for non-uniform stresses and it can be easily implemented. In the following section, the classical failure criterions were used to derive confinement models. Drucker-Prager model The Drucker-Prager model [26] provides the boundaries of the failure surface D Pf  as function on the internal stress state, 1 , 2 , 3 and on the strengths of material ( 0mf and mtf ):             1 2 2 3 1 3 1 2 3 1 2 3 0 0 0 2 , , 3 3 1 D P m m mf f f f                          (1) The entire failure surface can be normalized to the compressive strength of masonry 0mf . The lateral stresses are the same, 1 2 lf   assuming an axisymmetric confinement, where the value, lf depends on the strengthening system used. The equation of the failure surface (1) D Pf  according to Drucker-Prager model can be written in normalized form, D Pf  , as follows:        2 1 3 1 1 3 1 1 2 3 0 0 1 2 22 , 3 1 3 1 3 l mc D P m m f f f f f                           (2) Fig. 1 shows the three-dimensional failure surface assuming the value  changing from 0 up to 1 with a step of 0.2. Figure 1: Failure surface according to a Drucker-Prager model assuming  changing from 0 until to 1 with a step of 0.2. G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 291 In the Eqn. (1) the confinement effect is provided by the lateral stresses 1 2  ; while, 3 represents the axial stress applied on the masonry columns. The confinement curve is provided by the maximum 3 related to the lateral stress state 1 2  (i.e. the confinement effect). In particular, the Eqn. (2) provides a second order equation in the unknown parameter, 3 . In order to obtain the confinement curve, only the compressive component must be considered for the analysis: 3 1 3 1 2           (3) The Eqn. (3) can be used to assess the confinement curve of strengthened masonry columns. It represents one solution (maximum compressive stress) of the algebraic Eqn. (2). The second solution regards the negative value of the stress 3 (i.e. tensile stress), useless for this discussion. Stassi-D’Alia model The Stassi-D’Alia model [19, 20] provides the boundaries of the failure surface, S Df  with the following equation:       2 2 2 2 1 2 3 0 1 2 3 1 2 3 1 2 2 3 1 3 0 0, , 1S D m m mf f f f                             (4) The Eqn. (4), assuming an axisymmetric confinement, can be rewritten in normalized form as follow:   2 2 1 2 3 1 1 3 3 1 3 0 0 , 2 1 2l mc S D m m f f f f f                           (5) Fig. 2 shows the three-dimensional failure surface assuming the value,  changing from 0 up to 1 with a step of 0.2. Figure 2: Failure surface according to a Stassi-D’Alia model assuming  changing from 0 up to 1 with a step of 0.2. G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 292 The Eqn. (5) is an algebraic second order equation in the unknown parameter, 3 . The positive solution of the previous equation provides the maximum compressive strength, 3 for different lateral stress states 1 2  :  2 3 1 1 1 1 1 2 1 2 12 12 2               (6) The envelope of the 3 points to change the internal lateral stress state 1 2  represents the confinement curve. Henky-Von Mises model Henky-Von Mises model [27, 28] was developed for homogeneous materials with compressive strength, 0mf equal to the tensile strength, mtf (i.e. 1  ). This assumption is certainly not justified for the masonry, where 1  , but it is interesting in order to assess the drawbacks of the other models. This model provides the boundaries of the failure surface by means of the following equation:      2 2 2 2 1 2 3 1 2 3 0 1 2 2 3 1 3 0 0, ,H VM m m mf f f f                   (7) The Eqn. (7), expressed in normalized form and under an uniform lateral stress state, becomes: 2 2 1 2 3 1 1 3 3 0 0 , 1 2l mc H VM m m f f f f f                     (8) Fig. 3 shows the three-dimensional failure surface model independent on  . Figure 3: Failure surface according to a Henky-Von Mises model independent on  . The solution of the Eqn. (8) for confinement is represented by the positive stress, 3 : 3 11   (9) G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 293 Mohr-Coulomb model Mohr-Coulomb model [29, 30] provides the boundaries of the failure surface by means of the intersection of six planes: 1 2 1 2 2 3 2 3 3 1 3 1 sin cos 2 2 sin cos 2 2 sin cos 2 2 c c c                                                 (10) where:  is the friction angle and c is the cohesion of material. These mechanical parameters can be expressed as function of the compressive and tensile strengths. The failure surface can be normalized to the compressive strength of masonry, 0mf . Not all planes must be considered to describe the confinement curve of the strengthened masonry elements. In particular, the firsts two equations of the algebraic system (10) can be neglected since they do not contain the axial stress, 3 . The remaining Eqns. (10) provide solutions grouped two by two. Therefore, only two equations are sufficient to describe the boundaries of the failure surface. These equations can be rewritten according to a uniform lateral stress state and in normalized form as follows: 2 3 2 3 1 2 3 0 0 3 1 3 1 1 2 3 0 0 1 ' , 2 2 1 1 1 '' , 2 2 1 1 l mc M C m m l mc M C m m f f f f f f f f f f                                                         (11) Fig. 4 shows the three-dimensional failure surface assuming the value,  changing from 0 up to 1 with a step of 0.5. Figure 4: Failure surfaces according to a Mohr-Coulomb model assuming  changing from 0 up to 1 with a step of 0.5. In order to assess the confinement performance, the solution of the (11) must be focused on the compressive stress only, as follows: 3 1 1 1     (12) CONFINING STRESS ESTIMATION he experimental results have been compared with the theoretical predictions. The confinement curve provides the confined masonry strength, cmf while changing the confining stress, lf due to the passive confinement. The confining stress, lf can be assessed by using several formulations [31, 32]. In this paper, two approaches T G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 294 have been adopted to calculate the confining stress, lf . The effective confining stress (namely ,l efff ) depends on additional parameters not involving the characteristics of the composite system. Semi-empirical formulations available in the scientific literature provide this stress as a function of key efficiency parameters. According to classical formulation [31] the effective confining stress, ,l efff under passive confinement, can be assessed as follow: , 1 2l eff l eff f f effff f k E k        (13) where, fE is the Young’s modulus of the fiber, f is the ultimate design strain of the fiber (for the following experimental comparisons, it is equal to the average ultimate strain, without any safety factor) and f is the confinement volumetric ratio of the strengthening system. The calculation of f depends on the characteristics of the strengthened cross section: 4 f f f f t b D p      for circular wrapped cross-section (14)   4 max , f f f f t b b d p      for rectangular cross-section (15) where, ft is the thickness of the confined layer, fb is the width of the wrap, fp is the spacing between the wraps, D is the diameter of the circular cross-section, b and d are the dimensions of the rectangular cross-section. The coefficient, effk depends on efficiency of the strengthening system; it can be assumed as follow: eff h vk k k k   (16) where the three coefficients, hk , vk and k can be easily assessed according to the formulations reported in the CNR guidelines [31]. They depend on geometrical and mechanical parameters; hk is the coefficient of horizontal efficiency: '2 '2 1 3h m b d k A     (17) where the dimensions 'b and 'd provide the sizes of the effectively confined core (external dimensions minus the radii of the rounded corners), and mA is the area of the gross cross-section and assumes unitary value also for circular confined columns. The coefficient vk represents the vertical efficiency that assumes unitary value for continuous wrapping systems ( f fb p ). The coefficient k is the efficiency due to the inclination of the fibers. In the present paper, the strengthening was carried out without inclination of fibers, justifying the assumption of 1k  . A second approach [32] has been used to estimate the lateral stress, ,l efff on the confined members, as follows: , 2l eff l eff f f f eff b d f f k t E k b d          (18) For circular confined cross-sections, the dimensions, b and d assume the value of the diameter, D . The coefficient, effk can be calculated with the same previous formulations [31]. G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 295 EXPERIMENTAL RESULTS everal experimental programs, taken from the technical literature, have been considered. The reliability of the confinement models previously discussed has been checked by comparison between the theoretical predictions and experimental results. Experimental tests were carried out on masonry specimens strengthened with several types of strengthening systems. The attention focused on masonry columns made of solid and cored clay bricks tested under pure axial load (a total of 67 tests were collected). The axial capacity of these masonries was improved with several strengthening strategies. Present work focused on strengthening systems made of organic matrix (i.e. epoxy-resin) and different types of fibers (basalt, carbon and glass) namely Basalt Fiber Reinforced Polymer (BFRP), Carbon Fiber Reinforced Polymer (CFRP) and Glass Fiber Reinforced Polymer (GFRP) respectively. The masonry columns considered in the experimental programs are characterized by rectangular and circular cross-sections with different scale factors. The experimental programs were conducted by using different techniques. In experimental tests, the confinement on a masonry specimen can be provided by means of active or passive systems. The active confinement is applied in the laboratory by means of specific machines. Under uniform axial load, the increasing of the axial load provides a transverse (restrained by the wrapping) dilatation producing a passive confinement. Therefore, the efficiency of the passive confinement is strongly influenced by the characteristics of the masonry substrate and the strengthening system. For masonry columns passively confined, the failure condition is generally due to the failure of the wraps. In following section a synthetic description was provided of the experimental programs used for the comparison between the experimental results and the numerical predictions. Additional information on the specimens and experimental results were reported in the appendixes A and B. In Faella et al. [33], fiftyfour masonry specimens with different texture, dimensions and constituents were tested under pure axial load. A pozzolan based mortar was used for all masonry specimens (Tab. 1.A). The specimens were strengthened by using several types of strengthening systems having mechanical characteristics shown in Tab. 1.A. Seventeen masonry specimens made of two types of solid clay bricks were considered for the theoretical and numerical comparison. The two types of masonries present mass densities equal to 1650 kg/m3 and 1700 kg/m3 respectively and different dimensions as shown in Tab. 1.B. They were wrapped with different number of plies (one or two) and different types of GFRP (namely type a and type b as shown in Tab. 1.A). The density and thickness of fibers are equal to 900 g/m2 and 0.23 mm/ply respectively. In Di Ludovico et al. [34] eighteen passive confinement tests were performed on scaled and not scaled down masonry columns. Only the experimental results on clay brick masonry (Tab. 2.A) have been included in the present analysis. The tests were performed under pure axial load on masonry columns strengthened with several types of composites (Tab. 2.A). Six tests were carried out on square clay masonry columns with dimensions shown in Tab. 3.B. For this group the clay brick presents sizes of 55×115.5×255 mm3, while the thickness of joints was reduced at 12 mm due to the scale effects. The masonry had a mass density equal to 1700 kg/m3. The specimens were strengthened by using uniform wrapping with synthetic fibers (GFRP and BFRP composite systems). The confinement tests were carried out according to displacement control with rate of 0.005 mm per second. The failure mode was due to the composite for the entire set of specimens. Three of the six specimens were wrapped with one ply of composite based on Glass fiber (GFRP) having density and thickness of fiber equal to 900 g/m2 and 0.48 mm/ply respectively. Three specimens were wrapped with one ply of strengthening system based on basalt fibers (BFRP) having mass density and thickness equal to 254 g/m2 and 0.24 mm/ply respectively. Further information were reported in the Tab. 2. A. In Alecci et al. [35] tri-axial compression tests were performed on nineteen specimens. Three of the nineteen specimens made of pressed clay bricks (Tab. 3.A) of 65×30×14 mm3 dimensions were tested using passively confinement. Then cylindrical specimens with diameter of 54 mm were obtained from elements of 250×120×50 mm3. They were cut in 14 mm thick slices and successively divided in two semicircular shaped bricks. The joints were made of lime mortar with reducing granulometry to respect the scale factor. The final cylindrical specimens had height of 85 mm and reduced thickness of joints of 2.5 mm due to the scale factor (Tab. 5.B). The specimens were wrapped with CFRP (Tab. 3.A) composite characterize by different volumetric ratio of fiber (Tab. 5.B). It was obtained fixed the type of composite and changing the equivalent thickness as shown in Tab. 5.B. The unconfined compressive strength was assessed by means of direct test (Tab. 3.A). The failure mode occurs by means of the progressive increasing of the axial load with a load rate equal to 0.2 MPa per second. These conditions were the same for each specimen and the failure mode occurred due to cracking of the composite system. In Bieker et al. (2002) [36] eight masonry specimens were tested under pure axial load. Two types of masonry (solid and hollow bricks) were considered to perform the confinement tests. The solid clay brick had dimensions of 71×115×240 S G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 296 mm3 and 113×115×240 mm3 for the solid and hollow masonry respectively. The masonries present mass density of 2000 kg/m3 and 900 kg/m3 for solid and hollow bricks respectively. The masonry was prepared using two types of mortar: calcium mortar (namely type a) and cement mortar (namely type b). Brick and mortar were coupled in order to get a realistic representation of the existing masonries. The specimens were wrapped using two types of strengthening systems based on synthetic fiber (carbon and glass) and epoxy-resin. The carbon was applied using sheets having a mass density of 230 g/m2. Conversely, the glass fiber was applied using an unidirectional fiber system with a mass density of 430 g/m2. The wrapping was applied by means of one or two plies of CFRP, and two and three plies of GFRP with resin interlayers. The mechanical characteristics and the geometries of specimens were shown in Tabs. 4.A and 7.B respectively. In Rao et al. [37] seventyeight specimens were involved in the experimental investigation. The attention focused on standard specimens made of solid and cored clay bricks (Tab. 5.A). The mortar joint thickness changed between 10 and 12 mm (Tab. 9.B). The specimens were wrapped by CFRP and GFRP having 200 g/m2 and 200-360 g/m2 respectively (Tab. 5.A). One ply of CFRP and GFRP (Tab. 5.A) was wrapped around the specimens. The failure of specimens occured at increasing axial load, under displacement control at rate of 0.01mm per second. In Corradi et. al. [38] twentyfour masonry columns made of solid clay brick were tested under pure axial load. Two types of masonry were considered for the experimental program (Tab. 6.A). The geometrical characteristics were reported in the Tab. 11.B. The attention focused on four masonry specimens strengthened using several strengthening systems (Tab. 6.A). The solid clay bricks with dimensions of 245×120×55 mm3 were used to assembly the masonry specimens. The mortar used was composed of Portland cement and hydraulic lime. The thickness of mortar was fixed to 8-10 mm. The specimens were wrapped with strengthening systems made of organic matrix (epoxy resin) and synthetic fiber with different mechanical properties (Tab. 6.A). Two types of fibers were considered for the passive confinement: carbon with high tensile strength (CFRP-HT) and carbon fiber with very high modulus (CFRP-VHM). In Krevaikas et al. [39] fortytwo masonry specimens made of solid clay brick were tested (Tab. 7.A) by means of pure axial load tests. For the analysis, six specimens were considered to compare the numerical results with the theoretical previsions. The brick element had dimensions of 55×40×115 mm3 coupled with a mortar cement and lime based. The specimens were prepared according to several scale factors (1:1, 1.5:1 and 2:1) providing specimens with dimensions 115×115×340 mm3, 172.5×115×340 mm3 and 130×115×340 mm3. The thickness of mortar was fixed to 10 mm for all specimens. Two types of strengthening systems were considered: GFRP and CFRP (Tab. 7.A). The specimens were wrapped with one, two and three plies of unidirectional CFRP sheets or with five plies of unidirectional GFRP system (Tab. 13.B). The fiber system was applied on the substrate using epoxy-resin. In Aiello et al. (2009) [40] thirtythree masonry specimens were tested under pure axial load. For the present study one specimen was considered due to the similarity with previous experimental programs (Tab. 8.A). The specimen was made of solid clay bricks having dimensions shown in Tab. 15.B. It was prepared starting from blocks with dimensions of 100×150×30 mm3. A mortar lime and cement based was used for the masonry specimen. It was wrapped with GFRP system with one plie and epoxy-resin (Tab. 8.A). The further information on the mechanical properties of constituents used in the past experimental programs previously outlined were reported in the Appendix A, from Tab. 1.A to Tab. 8.A. The geometrical characteristics of the specimens (cross-section, b×h and height, h), characteristics of strengthening systems (type of fiber, number of layers, nl, equivalent thickness, teq) and the experimental results in terms of unconfined, 0mf and confined compressive, mcf strengths, are reported in Appendix B. The confined compressive strength, mcf can be normalized to the unconfined compressive strength, 0mf , as shown in Appendix B. For each specimen, the effective confining stress, ,l efff has been assessed according to the two approaches previously discussed (Eqns. 13 and 18). The effective confining stress, ,l efff has been expressed in normalized form as shown in the Appendix B, from Tab. 1.B to Tab. 16.B. The additional results of the experimental tests are available in the original papers [33-40]. STATISTICAL PARAMETERS FOR THE COMPARISON OF RESULTS he reliability of the mechanical models previously discussed has been tested by comparing the theoretical previsions with the experimental results. Some statistical parameters have been chosen to assess the reliability of the available confinement models. The comparison has been performed by means of some statistical parameters. The absolute approximation provides first information on the local reliability of the confinement models and it can be calculated as follow: T G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 297 exp,i , exp,i th if f e f   (19) where, exp,if and ,ithf represent the experimental and theoretical values for the generic specimen, i respectively. In particular they represent the compressive strength of the confined masonry specimen derived by the experimental and theoretical results. They are generally normalized to the unconfined compressive strength of the masonry specimen. However, the approximation parameter provides local information without considering the entire sample. Therefore it cannot be used to assess the performance of mechanical models. Three statistical parameters can be used to assess the entire sample of the experimental results: the mean absolute percentage error (MAPE), mean square error (MSE) and coefficient of determination (R2). These statistical parameters allow to compare the theoretical prediction with the experimental results on the entire statistical sample. The statistical parameters can be calculated as follow: exp,i , 1 exp,i n th i i f f f MAPE n     (20)   2 exp,i , 1 n th i i f f MSE n     (21)  2 exp,i , 2 1 , 1 1 n th i i n th i i f f R f                  (22) where, n is the number of specimens for each confinement test. The prediction models provide reliable results when: 2 0 0 1 MAPE MSE R    THEORETICAL AND EXPERIMENTAL COMPARISON RESULTS he reliability of mechanical models previously derived by the available failure criteria has been discussed in the following section, by comparing the experimental results with the theoretical previsions. The analysis was carried out in terms of direct comparison between the experimental and theoretical results and in terms of confinement curves. A first step has been carried out by comparing the confined compressive strength, mcf normalized to the unconfined compressive strength, 0mf , experimentally evaluated with the same ratio calculated using the theoretical models. No specific information is provided in original papers on tensile strength of masonry as a whole. Tensile strength is preferably retrieved by direct or indirect experimental tests [41] or correlations with other mechanical properties [40]. Compressive strength of the mortar only was reported and the tensile strength of masonry is assumed equal to 10% of compressive strength for lime mortar and 20% for cementitious mortars. The values of 𝛼 assumed for each experimental program are shown in Tab. 1. The direct comparison between the experimental results and the theoretical previsions is a useful tool to assess the response of the model on the entire experimental sample. It can be performed on a diagram where in the horizontal axIs is shown the normalized confined compressive strengths, theoretically assessed; while on the vertical axis is reported the T G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 298 same value experimentally assessed. On this diagram, the ideal line is represented by a linear function with unitary angular coefficient. The points located at left of the ideal line (dashed grey line of following figures) correspond to theoretical values lower than the experimental results. Therefore, if the sample points shift at left of the ideal line, the theoretical model provides conservative results. Experimental program 𝛼[-] Faella et al. (2011) -0.1 Di Ludovico et. al. (2010) -0.1 Alecci et al. (2009) -0.1 Bieker et al. (2002) -0.1(solid clay), -0.2(cored clay) Nanjunda Rao et al. (2014) -0.2 Corradi et al. (2007) -0.2 Krevaikas et al. (2005) -0.2 Aiello et al. (2009) -0.2 Table 1: Value of the normalized tensile strength of masonry,  for the experimental programs. (a) (b) Figure 5: Comparison between experimental results and Stassi-D’Alia model: a) experimental and theoretical results comparison, b) confinement curve comparison for α =-0.1 (red solid line) and α =-0.2 (red dashed line). G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 299 Another important information can be assessed with the confinement curves. They provide the confined compressive strength while changing the effective confining stress, normalized to the unconfined compressive strength. The theoretical confinement curves are shown for two values of the normalized tensile strength of masonry, α fixed at -0.1 (dashed line) and -0.2 (solid line) according to the experimentally calculated values. Fig. 5 a) shows the comparison between the Stassi- D’Alia model and the experimental results; while the Fig. 5 b) shows the theoretical confinement curves with the several experimental points. The effective confining stress has been evaluated according to the approaches previously discussed (Eqns. 13 and 18, howsoever it is remarked that in the case of square cross sections the results are equal). Comparing this model with the experimental sample, the good fitting of the theoretical results with the experimental results is clear. In particular, the Stassi-D’Alia model provides reliable results for the entire experimental sample without excessive overestimation of the theoretical previsions (Fig. 5 a). The theoretical results confirm that the confinement curve is weakly influenced by the tensile strength of masonry. It is interesting to note that the mechanical model reasonably predicts the axial capacity for the entire range of the lateral stress field. The same approach has been carried out for other theoretical models. Fig. 6 a) shows the comparison between the Drucker-Prager model and the experimental results; while Fig. 6 b) shows the theoretical confinement curves with the experimental points. (a) (b) Figure 6: Comparison between experimental results and Drucker-Prager models: a) experimental and theoretical results comparison, b) confinement curve comparison for α =-0.1 (blue solid line) and α =-0.2 (blue dashed line). This model strongly overestimates the experimental results as shown in Fig. 6 a). In particular, this effect is very clear for high values of the confining stress. In fact, for low confining stresses, , 0 0.2l eff mf f  the mechanical model provides reliable results if compared with the experimental tests. However, a great number of tests were carried out at high G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 300 confining stress values. Therefore, on the entire experimental sample the model provides a weak estimation of the axial capacity of masonry columns wrapped with composites. Furthermore, it results strongly influenced by the tensile strength of masonry providing confinement curves strongly different while changing the tensile strength of masonry. Fig. 7 a) shows the comparison between the Hencky-Von Mises model and the experimental results; while Fig. 7 b) shows the comparison between the theoretical confinement curves and the experimental points. (a) (b) Figure 7: Comparison between experimental results and Hencky-Von Mises models: a) experimental and theoretical results comparison, b) confinement curve comparison independent on α. This model does not depend on the normalized tensile strength of confined material, α. The theoretical and experimental comparison shows a clear underestimation of the experimental values. This effect is clear for the entire confining stress field. The Fig. 8 a) shows the comparison between the Mohr-Coulomb model with the experimental results; while Fig. 8 b) shows the comparison between the theoretical confinement curves with the experimental points. This theoretical model is strongly influenced by the normalized tensile strength of masonry, α. Furthermore, an overestimation of the experimental results is clear for the entire experimental example sample. Also for low values of the effective confining stresses the experimental results are not so well fitted by the theoretical results (Fig. 8 a). In order to confirm previous qualitative dissertation, the statistical parameters: MAPE, MSE and R2 have been calculated for the mechanical models. They are shown in Tabs. 2 and 3 for the comparison between the experimental and theoretical results. The effective confining stress, ,l efff has been calculated according to the previous Eqns. (13) and (18). The statistical parameters calculated according to Eqns. (13) and (18) are shown in Tab. 26 and 27 respectively. G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 301 (a) (b) Figure 8: Comparison between experimental results and Mohr-Coulomb models: a) experimental and theoretical results comparison, b) confinement curve comparison for α =-0.1 (black solid line) and α =-0.2 (black dashed line). Statistical parameter Stassi- D’Alia Drucker-Prager Henky-Von Mises Mohr-Coulomb MAPE 0.225 1.324 0.289 0.855 MSE 0.328 12.481 0.535 5.075 R2 0.820 -1.86 0.603 -0.512 Table 2: Statistical parameters to comparison the theoretical and the experimental results, with a confined lateral stresses, ,l efff calculated according to Eqn. (13). Statistical parameter Stassi- D’Alia Drucker-Prager Henky-Von Mises Mohr-Coulomb MAPE 0.243 1.375 0.280 0.887 MSE 0.311 13.342 0.496 5.419 R2 0.833 -1.954 0.800 -0.563 Table 3: Statistical parameters to comparison the theoretical and the experimental results, with a confined lateral stresses, ,l efff calculated according to Eqn. (18). G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 302 The assessment of the statistical parameters confirms the reliability of the Stassi-D’Alia model compared to others. It is interesting to note that the model is weakly depended on the formulation - eqs. (13) versus (18) - used for the effective confining stress, ,l efff (Fig. 9). Hence, the statistical results confirmed the Stassi-D-Alia model to be the best analytical tool to assess the axial capacity of confined clay brick masonry. (a) (b) (c) Figure 9: Statistical parameters changing the calculation approach of the effective confining stress, ,l efff : a) MAPE, b) MSE and c) R2. CONCLUSIONS our confinement models were derived by the classical failure criterions available in the scientific literature. These models were used to assess the axial capacity of masonry specimens made of solid clay brick and strengthened with several types of strengthening systems (GFRP, CFRP and BFRP). They were carried out to assess the increase of the axial capacity due to the wrapping interventions. These models are fully based on mechanical parameters representative of the materials: tensile and compressive strengths of masonry and the effective confining stress. The reliability of the mechanical models was assessed by comparison with relevant experimental programs. The strength values are derived by 67 experimental test results. They allow to apply the mechanical model to the masonry specimens actually tested. The effect of confinement is strongly related to the effective confining stress. It was evaluated according to two main approaches available in the literature. Between the several mechanical models the Stassi D’Alia was proposed to assess the axial capacity of confined masonry columns. The reliability of this model was demonstrated by comparing the theoretical values with the experimental results. In order to confirm the potential of this model, the comparison was carried out considering also the other mechanical models. The comparison confirmed the Stassi-D’Alia model to be the best approach to assess the axial capacity of masonry columns made of solid clay brick and strengthened with innovative composite systems. It was remarked both by direct comparison of experimental results with the numerical previsions and by statistical parameters. In particular, the Stassi-D’Alia model provided good fitting for the entire range of the effective confining stresses. The model indicates that the axial capacity of the strengthened masonry is not much influenced by the tensile strength of masonry, despite the model is potentially able to account for such variations if more refined values are F G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 303 known. The weak influence of the tensile strength of masonry on the axial capacity of the strengthened masonry element is clear, by the experimental results also. It is due to the prevailing confinement effect if compared to that of tensile strength of masonry. The Drucker-Prager model strongly overestimates the experimental results. This effect is very clear for high values of the confining stress, while, for low confining stresses, the mechanical model provides reliable results. However, a great number of tests were carried out at high confining stress values. Therefore, on the entire experimental sample the model provides a weak estimation of the axial capacity of masonry columns wrapped with composites. Furthermore, it results strongly influenced by the tensile strength of masonry providing confinement curves strongly different to change the tensile strength of masonry. The Henchy-Von Mises model does not depend on the normalized tensile strength of confined material. The theoretical and experimental comparison showed a strong underestimation of the experimental values. This effect is clear for the entire confining stress field. The Mohr-Coulomb provides a clear overestimation of the experimental results for the entire experimental sample. 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[41] ASTM E519M-15 (2015) Standard Test Method for Diagonal Tension (Shear) in Masonry 23 Assemblages, ASTM International, West Conshohocken, PA. G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 305 APPENDIX A echanical properties of constituents in terms of compressive strength, f, tensile strength, ft, tensile strain, εt and Young’s modulus, E. These parameters refer to the experimental programs used for theoretical and numerical comparison. Element f [MPa] ft [MPa] εt [-] E [GPa] Mortar 1.03 - - - Epoxy resin (type a) 30 30 - 3 Epoxy resin (type b) 25 25 - 3.1 GFRP (type a) 2560 - 0.032 80.7 GFRP (type b) 1600 - 0.025 65 Table 1.A: Mechanical properties of constituents for the experimental tests [33]. Element f [MPa] ft [MPa] εt [-] E [GPa] Mortar 6.9 1.71 - - Brick 22.71 - - - Epoxy resin - 40 0.0018 3 BFRP - 1814 0.019 91 GFRP - 1371 0.021 69 Table 2.A: Mechanical properties of constituents for the experimental tests [34]. Element f [MPa] ft [MPa] E [MPa] Mortar 2.1 - 577 Brick 15.7 - 3058 Unconfined masonry 13.6 - - Resin - 50 3000 Carbon - 3430 230000 Table 3.A: Mechanical properties of constituents for the experimental tests [35]. Element f [MPa] ft [MPa] εt [-] E [GPa] Solid clay brick 20 - - - Hollow clay brick 12 - - - Calcium mortar (type a) 1 - - - Cementitious mortar (type b) 5.1 - - - Epoxy resin - 30 - 3.8 CFRP - 3500 0.015 230 GFRP - 2250 0.031 70 Table 4.A: Mechanical properties of constituents for the experimental tests [36]. M G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 306 Element f [MPa] ft [MPa] εt [-] E [GPa] Clay brick 7.65 - 0.0064 1.96 Cement mortar 7.0 - 0.0018 11.2 CFRP-Gr200 - 230 0.015 25.1 GFRP-Gr200 - 110 0.031 10.6 GFRP-Gr360 - 175 0.031 11.6 Table 5.A: Mechanical properties of constituents for the experimental tests [37]. Element f [MPa] ft [MPa] εt [-] E [GPa] Clay brick, series 1 20.78 - - - Clay brick, series 2 27.45 - - - Cement mortar 10 3.36 - - CFRP-HT - 3338 0.00799 417.6 CFRP-VHM - 1955 0.00307 637.2 Table 6.A: Mechanical properties of constituents for the experimental tests [38]. Element f [MPa] ft [MPa] εt [-] E [GPa] Brick 23.5 - - - Mortar 2.23 - - - CFRP - 3500 0.015 230 GFRP - 2000 0.029 70 Table 7.A: Mechanical properties of constituents for the experimental tests [39]. Element f [MPa] ft [MPa] εt [-] E [GPa] Brick 23.5 - - - Mortar 2.23 - - - CFRP - 3500 0.015 230 GFRP - 2000 0.029 70 Table 8.A: Mechanical properties of constituents for the experimental tests [40]. APPENDIX B eometrical characteristics of the specimens (cross-section, b×d and height, h), type of fiber, number of layers, nl, equivalent thickness, teq, unconfined compressive strength, 0mf and confined compressive strength, mcf , normalized confined compressive strength, 0/mc mf f , effective confining stress, ,l efff , normalized effective confining stress, , 0/l eff mf f calculated according to Eqns. (13) and (18). G G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 307 ID specimen b [mm] d [mm] h [mm] Type of fiber [-] nl [-] teq [mm] fmc [MPa] fm0 [MPa] fmc/fmc0 [-] S1 250 250 500 GFRP (type a) 1 0.48 19.29 13.71 1.407 S2 250 250 250 GFRP (type a) 1 0.48 26.23 13.98 1.876 S3 250 250 250 GFRP (type a) 1 0.48 21.21 13.98 1.518 S4 250 250 250 GFRP (type a) 2 0.96 35.18 13.98 2.517 S5 250 250 250 GFRP (type a) 2 0.96 30.52 13.98 2.184 S6 380 383 492 GFRP (type b) 1 0.23 12.03 8.3 1.426 S7 387 375 485 GFRP (type b) 1 0.23 12.79 8.3 1.518 S8 377 380 488 GFRP (type b) 1 0.23 14.15 8.3 1.678 S9 383 378 486 GFRP (type b) 2 0.46 14.52 8.43 1.723 S10 377 378 481 GFRP (type b) 2 0.46 16.01 8.43 1.899 S11 383 374 492 GFRP (type b) 2 0.46 12.64 8.43 1.499 S12 250 248 470 GFRP (type b) 1 0.23 17.65 11.12 1.588 S13 250 249 470 GFRP (type b) 1 0.23 16.27 11.12 1.463 S14 250 247 470 GFRP (type b) 1 0.23 15.94 11.12 1.434 S15 248 247 462 GFRP (type b) 2 0.46 19.10 11.12 1.718 S16 245 248 471 GFRP (type b) 2 0.46 20.57 11.12 1.850 S17 246 251 473 GFRP (type b) 2 0.46 21.45 11.12 1.929 Table 1.B: Geometrical characteristics and experimental results [33]. ID specimen keff [-] fl,(eq.13) [MPa] fl,eff,(eq.13) [MPa] (fl,eff/ fm0), (eq.13) [MPa] fl, (eq.18) [MPa] fl,eff, (eq.18) [MPa] (fl,eff/ fm0), (eq.18) [MPa] S1 0.38 9.830 3.782 0.276 9.830 3.782 0.276 S2 0.38 9.830 3.782 0.271 9.830 3.782 0.271 S3 0.38 9.830 3.782 0.271 9.830 3.782 0.271 S4 0.38 19.661 7.565 0.541 19.661 7.565 0.541 S5 0.38 19.661 7.565 0.541 19.661 7.565 0.541 S6 0.42 1.922 0.799 0.095 1.929 0.802 0.095 S7 0.42 1.902 0.790 0.094 1.932 0.803 0.095 S8 0.42 1.937 0.806 0.096 1.945 0.809 0.096 S9 0.42 3.843 1.598 0.190 3.869 1.609 0.191 S10 0.42 3.894 1.622 0.192 3.899 1.624 0.193 S11 0.42 3.843 1.599 0.190 3.890 1.619 0.192 S12 0.46 2.944 1.342 0.121 2.956 1.347 0.121 S13 0.46 2.944 1.341 0.121 2.950 1.344 0.121 S14 0.46 2.944 1.342 0.121 2.962 1.350 0.121 S15 0.46 5.935 2.709 0.244 5.947 2.715 0.244 S16 0.46 5.935 2.712 0.244 5.972 2.728 0.245 S17 0.46 5.865 2.673 0.240 5.924 2.701 0.243 Table 2.B: Effective confining stress calculated according to Eqns. (13) and (18) for the experimental program, [33]. G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 308 ID specimen b [mm] d [mm] h [mm] Type of fiber [-] nl [-] teq [mm] fmc [MPa] fm0 [MPa] fmc/fmc0 [-] S18 264 265 560 Glass 1 0.48 9.97 6.22 1.604 S19 267 265 560 Glass 1 0.48 8.53 6.22 1.372 S20 266 265 560 Glass 1 0.48 11.29 6.22 1.817 S21 266 266 560 Basalt 1 0.24 10.40 6.22 1.673 S22 265 264 560 Basalt 1 0.24 9.82 6.22 1.580 S23 265 264 560 Basalt 1 0.24 10.20 6.22 1.640 Table 3.B: Geometrical characteristics and experimental results [34]. ID specimen keff [-] fl,(eq.13) [MPa] fl,eff,(eq.13) [MPa] (fl,eff/ fm0), (eq.13) [MPa] fl, (eq.18) [MPa] fl,eff, (eq.18) [MPa] (fl,eff/ fm0), (eq.18) [MPa] S18 2.48 5.80 2.48 0.399 5.81 2.48 0.399 S19 2.46 5.75 2.46 0.395 5.77 2.47 0.397 S20 2.47 5.77 2.47 0.397 5.79 2.47 0.398 S21 1.40 3.27 1.40 0.225 3.27 1.40 0.225 S22 1.40 3.29 1.40 0.226 3.29 1.41 0.226 S23 1.40 3.29 1.40 0.226 3.29 1.41 0.226 Table 4.B: Effective confining stress calculated according to Eqns. (13) and (18) for the experimental program, [34]. ID specimen b [mm] d [mm] h [mm] Type of fiber [-] nl [-] teq [mm] fmc [MPa] fm0 [MPa] fmc/fmc0 [-] S24 54 54 85 Carbon 0.125 0.0206 20.63 13.58 1.519 S25 54 54 85 Carbon 0.25 0.0413 27.38 13.58 2.016 S26 54 54 85 Carbon 0.167 0.0275 22.80 13.58 1.679 Table 5.B: Geometrical characteristics and experimental results [35]. ID specimen keff [-] fl,(eq.13) [MPa] fl,eff,(eq.13) [MPa] (fl,eff/ fm0), (eq.13) [MPa] fl, (eq.18) [MPa] fl,eff, (eq.18) [MPa] (fl,eff/ fm0), (eq.18) [MPa] S24 0.15 2.62 0.40 0.0292 2.62 0.40 0.0292 S25 0.15 5.24 0.79 0.0583 5.24 0.79 0.0583 S26 0.15 3.49 0.53 0.0389 3.49 0.53 0.0389 Table 6.B: Effective confining stress calculated according to Eqns. (13) and (18) for the experimental program [35]. ID specimen b [mm] d [mm] h [mm] Type of fiber [-] nl [-] teq [mm] fmc [MPa] fm0 [MPa] fmc/fmc0 [-] S27 240 240 500 Carbon 1 0.131 13.374 5.295 2.526 S28 240 240 500 Carbon 2 0.262 14.922 5.295 2.818 S29 240 240 500 Glass 2 0.34 12.142 5.295 2.293 S30 240 240 500 Glass 3 0.51 13.215 5.295 2.496 S31 240 240 500 Carbon 1 0.131 4.751 3.299 1.440 S32 240 240 500 Carbon 2 0.262 5.279 3.299 1.600 S33 240 240 500 Glass 2 0.34 5.930 3.299 1.798 S34 240 240 500 Glass 3 0.51 5.948 3.299 1.803 Table 7.B: Geometrical characteristics and experimental results [36]. G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 309 ID specimen keff [-] fl,(eq.13) [MPa] fl,eff,(eq.13) [MPa] (fl,eff/ fm0), (eq.13) [MPa] fl, (eq.18) [MPa] fl,eff, (eq.18) [MPa] (fl,eff/ fm0), (eq.18) [MPa] S27 0.48 3.77 1.82 0.343 3.77 1.82 0.343 S28 0.48 7.53 3.64 0.687 7.53 3.64 0.687 S29 0.48 6.15 2.97 0.560 6.15 2.97 0.560 S30 0.48 9.22 4.45 0.841 9.22 4.45 0.841 S31 0.48 3.77 1.82 0.551 3.77 1.82 0.551 S32 0.48 7.53 3.64 1.102 7.53 3.64 1.102 S33 0.48 6.15 2.97 0.900 6.15 2.97 0.900 S34 0.48 9.22 4.45 1.349 9.22 4.45 1.349 Table 8.B: Effective confining stress calculated according to Eqns. (13) and (18) for the experimental program [36]. ID specimen b [mm] d [mm] h [mm] Type of fiber [-] nl [-] teq [mm] fmc [MPa] fm0 [MPa] fmc/fmc0 [-] S35 225 105 415 Glass 1 0.467 8.08 5.60 1.443 S36 225 105 415 Glass 1 0.242 8.02 5.60 1.432 S37 225 105 415 Glass 1 0.274 6.95 5.60 1.241 S38 225 105 415 Carbon 1 0.371 6.61 5.60 1.180 S39 150 105 320 Glass 1 0.369 7.27 3.68 1.976 S40 150 105 300 Glass 1 0.370 5.95 1.78 3.343 S41 150 105 300 Glass 1 0.223 4.80 1.54 3.117 S42 245 105 460 Glass 1 0.347 9.19 6.15 1.494 S43 245 105 460 Glass 1 0.200 9.75 6.15 1.585 S44 245 105 460 Carbon 1 0.412 8.14 6.15 1.324 S45 225 222 420 Glass 1 0.316 7.73 4.62 1.673 S46 225 222 420 Glass 1 0.443 7.50 4.62 1.623 S47 225 249 460 Glass 1 0.675 8.26 4.32 1.912 S48 225 249 460 Glass 1 0.467 8.00 4.32 1.852 Table 9.B: Geometrical characteristics and experimental results [37]. G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 310 ID specimen keff [-] fl,(eq.13) [MPa] fl,eff,(eq.13) [MPa] (fl,eff/ fm0), (eq.13) [MPa] fl, (eq.18) [MPa] fl,eff, (eq.18) [MPa] (fl,eff/ fm0), (eq.18) [MPa] S35 0.29 0.47 0.14 0.025 0.73 0.22 0.039 S36 0.29 1.31 0.39 0.069 2.06 0.61 0.108 S37 0.29 0.24 0.07 0.012 0.37 0.11 0.020 S38 0.29 0.56 0.17 0.030 0.88 0.26 0.046 S39 0.48 0.86 0.41 0.112 1.05 0.50 0.136 S40 0.48 0.86 0.41 0.231 1.05 0.50 0.281 S41 0.48 0.86 0.41 0.268 1.05 0.50 0.326 S42 0.24 0.32 0.08 0.012 0.53 0.13 0.021 S43 0.24 0.89 0.21 0.035 1.49 0.36 0.058 S44 0.24 0.38 0.09 0.015 0.63 0.15 0.024 S45 0.44 0.64 0.28 0.062 0.65 0.29 0.062 S46 0.44 0.89 0.39 0.085 0.89 0.40 0.086 S47 0.43 0.62 0.27 0.063 0.66 0.29 0.066 S48 0.43 1.71 0.74 0.172 1.80 0.78 0.181 Table 10.B: Effective confining stress calculated according to Eqn. (13) and (18) for the experimental program, [37]. ID specimen b [mm] d [mm] h [mm] Type of fiber [-] nl [-] teq [mm] fmc [MPa] fm0 [MPa] fmc/fmc0 [-] S49 245 250 500 Carbon-HT 2 0.330 24.39 14.63 1.667 S50 245 250 500 Carbon-VHM 2 0.286 22.37 14.63 1.529 S51 245 250 500 Carbon-HT 2 0.330 29.99 14.63 2.050 S52 245 250 500 Carbon-VHM 2 0.286 26.84 14.63 1.835 Table 11.B: Geometrical characteristics and experimental results [38]. ID specimen keff [-] fl,(eq.13) [MPa] fl,eff,(eq.13) [MPa] (fl,eff/ fm0), (eq.13) [MPa] fl, (eq.18) [MPa] fl,eff, (eq.18) [MPa] (fl,eff/ fm0), (eq.18) [MPa] S49 0.33 8.944 0.204 0.204 9.04 3.01 0.206 S50 0.33 4.473 0.102 0.102 4.52 1.51 0.103 S51 0.44 8.944 0.267 0.267 9.04 3.94 0.270 S52 0.44 4.473 0.134 0.134 4.52 1.97 0.135 Table 12.B: Effective confining stress calculated according to Eqn. (13) and (18) for the experimental program, [38]. G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 311 ID specimen b [mm] d [mm] h [mm] Type of fiber [-] nl [-] teq [mm] fmc [MPa] fm0 [MPa] fmc/fmc0 [-] S53 115 115 340 Carbon 1 0.117 13.63 12.07 1.129 S54 115 115 340 Carbon 2 0.234 16.92 12.07 1.402 S55 115 115 340 Carbon 3 0.351 25.42 12.07 2.106 S56 115 115 340 Glass 5 0.750 40.00 12.07 3.314 S57 115 115 340 Carbon 1 0.117 16.87 12.07 1.398 S58 115 115 340 Carbon 2 0.234 23.91 12.07 1.981 S59 115 115 340 Carbon 3 0.351 34.69 12.07 2.874 S60 115 115 340 Glass 5 0.750 44.87 12.07 3.717 S61 172.5 115 340 Carbon 2 0.234 11.90 6.65 1.789 S62 172.5 115 340 Carbon 3 0.351 17.29 6.65 2.600 S63 172.5 115 340 Glass 5 0.750 24.37 6.65 3.665 S64 230 115 340 Carbon 2 0.234 11.79 6.21 1.899 S65 230 115 340 Carbon 3 0.351 12.00 6.21 1.932 S66 230 115 340 Glass 5 0.750 17.81 6.21 2.868 Table 13.B: Geometrical characteristics and experimental results [39]. ID specimen keff [-] fl,(eq.13) [MPa] fl,eff,(eq.13) [MPa] (fl,eff/ fm0), (eq.13) [MPa] fl, (eq.18) [MPa] fl,eff, (eq.18) [MPa] (fl,eff/ fm0), (eq.18) [MPa] S53 0.44 7.02 3.09 0.256 7.02 3.09 0.256 S54 0.44 14.24 6.28 0.520 14.24 6.28 0.520 S55 0.44 21.37 9.41 0.780 21.37 9.41 0.780 S56 0.44 26.09 11.49 0.952 26.09 11.49 0.952 S57 0.53 7.12 3.80 0.314 7.12 3.80 0.314 S58 0.53 14.24 7.59 0.629 14.24 7.59 0.629 S59 0.53 21.37 11.39 0.943 21.37 11.39 0.943 S60 0.53 26.09 13.90 1.152 26.09 13.90 1.152 S61 0.37 9.50 3.50 0.526 11.87 4.37 0.657 S62 0.37 14.24 5.25 0.789 17.80 6.56 0.986 S63 0.37 17.39 6.41 0.963 21.74 8.01 1.204 S64 0.25 7.12 1.77 0.285 10.68 2.66 0.428 S65 0.25 10.68 2.66 0.428 16.02 3.98 0.642 S66 0.25 13.04 3.24 0.522 19.57 4.87 0.783 Table 14.B: Effective confining stress calculated according to Eqn. (13) and (18) for the experimental program, [39]. G. Ramaglia et alii, Frattura ed Integrità Strutturale, 51 (2020) 288-312; DOI: 10.3221/IGF-ESIS.51.23 312 ID specimen b [mm] d [mm] h [mm] Type of fiber [-] nl [-] teq [mm] fmc [MPa] fm0 [MPa] fmc/fmc0 [-] S67 250 250 500 Glass 1 0.48 19.65 13.72 1.432 Table 15.B: Geometrical characteristics and experimental results [40]. ID specimen keff [-] fl,(eq.13) [MPa] fl,eff,(eq.13) [MPa] (fl,eff/ fm0), (eq.13) [MPa] fl, (eq.18) [MPa] fl,eff, (eq.18) [MPa] (fl,eff/ fm0), (eq.18) [MPa] S67 0.38 6.16 2.37 0.173 6.16 2.37 0.173 Table 16.B: Effective confining stress calculated according to Eqns. 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