Behavior of precast ferrocement thin walls under cyclic loading : an experimental and analytical study

Thin ferrocement walls are the structural elements that comprise the earthquake resistant system of housing built with this material. This article presents the results drawn from an experimental campaign carried out over full-scale precast ferrocement thin walls, which were assessed under cyclic loading conditions. The tests assessed the strength of the walls, their hysteretic behavior, ductility, energy dissipation, equivalent damping, their coefficient of energy dissipation and their characteristic failure mode when subjected to cyclic loading conditions. Finally, an analytical model that modeled the nonlinear dynamic behavior exhibited by ferrocement walls was implemented; its feasibility and potential use in earthquake resistant design of ferrocement walls was evaluated.

Seismic demand determines the material and type of the structural systems used in housing construction.Earthquakes prompt the need for research of innovative systems with better cost-effectiveness and better seismic performance than current systems.Ferrocement-based structural systems have demonstrated high resistance (Naaman, 2000;Bedoya-Ruiz, 2005), low seismic fragility (Bedoya-Ruiz et al., 2005), and environmental sustainability (Bedoya-Ruiz, 2011).These systems usually are comprised of precast thin walls, which are assembled in different configurations according to the constructive system of the dwelling (Naaman, 2000;Castro, 1979;Gokhale, 1983;Olvera, 1998;Wainshtok-Rivas, 1994;Abdullah, 1995;Machado, 1998).
Typical dimensions of precast ferrocement walls range between 500 and 1000 mm in width, 2000 to 2400 mm in height and 10 to 50 mm in thickness.The strength of the walls is provided by a set of meshes and sometimes reinforced by bars embedded in a highstrength mortar.Homes built using precast ferrocement thin walls have been constructed in the Malay Archipelago, Sumatra Islands, Sri Lanka, New Guinea, Mexico, India, Thailand, Cuba, USA, Brazil and Colombia.
The first recorded applications date back to the early 1940s, when Nervi (1956) proposed the use of ferrocement for the construction of fishing boats.Later, Castro (1979) and Olvera (1998) built one and two-story houses with ferrocement walls in Mexico. In India, in 1983, Gokhale (1983), documented a system for housing construction called "Catone".In 1998, Wainshtok-Rivas (1994) described the first ferrocement constructions made in Cuba in 1986.Naaman (2000) published the results of his investigations developed on ferrocement houses at the University of Michigan.He explored the advantages of ferrocement from an industrialized viewpoint, in order to enable the development and dissemination of the benefits of using this material.Bedoya-Ruiz (2005) published, on the experimental and analytical research carried out on walls and ferrocement houses.
There have been some methodologies for the earthquake resistant design of houses, based on precast ferrocement thin walls using static analysis.For example, Bedoya-Ruiz (2002) and Wainshtok-Rivas (2004) developed an approach to earthquake resistant design of ferrocement houses using the Method of Equivalent Horizontal Force (MEHF), in order to obtain seismic forces for areas of moderate to high seismic activity.Recently, Bedoya-Ruiz et al. (2010) proposed a nonlinear dynamical model to evaluate the vulnerability of ferrocement houses.This model was in accordance with the experimental behavior exhibited by the structures when subjected to cyclic loading conditions, while allowing several damage scenarios for zones with different seismic activity.This article treats the seismic behavior of precast ferrocement thin walls subjected to cyclic loading conditions.A nonlinear dynamical model for earthquake resistant design of ferrocement homes built in areas of moderate to high seismic hazard is presented.
The plan of this study was as follows: first, laboratory tests on fullscale walls were carried out in order to evaluate the hysteretic behavior, strength, energy dissipation capacity, damping and failure modes of precast ferrocement thin walls when subjected to cyclic loading conditions.Then, a nonlinear dynamical model that is able to simulate the behavior exhibited by ferrocement walls under cyclic loading conditions was proposed.The Bouc-Wen-Baber-Noori (BWBN) model of hysteresis (Bouc, 1967;Baber and Wen, 1981) was used here.Finally, an evaluation of the performance of the walls when subjected to random external excitations using the proposed nonlinear dynamical model was performed.

Test specimens
Several ferrocement thin walls were built and tested as depicted below.

Description of the materials
Each wall was constructed using mortar, wire mesh and steel bars.The mortar was made with Portland cement type I (CEM I), sand screened with a No. 7 sieve (approx.2mm), water and superplasticizer using the following proportions by weight: sand-cement ratio 1:2, water-cement ratio 0.40, superplasticizer 1% of cement weight.The superplasticizer was used in order to improve the workability and penetrability of the mortar through the meshes.The reinforcement distributed in the cementitious matrix consisted of six hexagonal mesh layers with an opening of 31.75 mm (this mesh was placed longitudinally); and two #2 bars at the ends of the wall.The specific surface of the reinforcement was 0.0314 mm 2 /mm 3 and its volume fraction was 0.39%.
The compressive strength of the mortar (′  ) after 28 days was 33 MPa, and its Young modulus (  ) was 11050 MPa; the yield resistance (  ) of the hexagonal mesh was 282 MPa, and its Young modulus (  ) was 81 GPa.Finally, the yield resistance of the #2 bars was 420 MPa.

Test setup and load history.
The geometry of each of the 12 specimens is sketched in Fig. 1; an overview of the test set up is also shown in Fig. 1.

Figure 1. Test setup and dimensions (in mm)
The walls were anchored to very rigid foundation beams in order to provide lateral support.Then, each "wall-foundation beam" system was anchored to a reaction floor with steel screws as illustrated in Fig. 2. In order to constrain the walls to in-plane-displacements, lateral bracing was employed.The lateral displacement induced by the hydraulic actuator was measured using LVDTs placed at the top of the walls.

Figure 2. Actual configuration
Each precast ferrocement thin wall was subjected to the cyclic loading pattern shown in Fig. 3, where ∆  is the ultimate displacement corresponding to the failure limit state.

Test results
The results drawn from the tests are summarized in the following sections.

Hysteretic behavior and strength.
In order to compute the structural parameters of the precast ferrocement thin walls, the specimens were subjected to cyclic loads that simulate seismic action; the hysteresis response curves drawn from the tests were used to assess the ultimate strength and the ductility of the system.
Fig. 4 shows one of the hysteresis cycles drawn from the cyclic tests carried out on the precast ferrocement thin walls.Fig. 5 shows the envelope corresponding to the same hysteresis loops.The positive and negative envelopes are similar; therefore, the average is computed and used for subsequent calculations.
The envelopes drawn from the cyclic tests showed a maximum average lateral load capacity of 13 kN.Using the ASTM E2126-11 norm (ASTM, 2011), and the envelopes of the hysteresis loops, structural parameters the ferrocement thin walls were computed as shown in Table 1.Energy dissipation and damping.
Current structural designs are based on fragility analysis, which aims to dissipate the energy transmitted by external dynamical forces by means of the hysteretic response; in this way, the safety margin of the structural elements is increased and the sudden failure of the material is avoided.In order to achieve this control in ferrocement structures, the walls should have the capacity to dissipate the energy when subjected to cyclic loading conditions.One way to quantify the amount of dissipated energy when a structure is subjected to time-varying loads is by computing the area enclosed by the hysteresis loops (see Fig. 4).
Another way to evaluate the capacity of the material in terms of energy dissipation is by means of the so-called equivalent viscous damping ratio (  ), which is defined as (Priestley, 1996;Chopra, 2006): where   stands for the energy dissipated by the structural element in the -th loading cycle and (  )  is the elastic potential energy stored by an equivalent linear elastic system when the maximum displacement in the -th cycle is reached in static conditions.
The dissipated energy in the -th cycle   can be computed from the measured hysteresis loops.The elastic potential energy stored by an equivalent linear system (  )  is given by the area under the load vs. displacement curve obtained in the cyclic tests.It is given by the area under a right triangle whose base equals the maximum positive displacement measured in the model (∆  )  and whose height (  )  is the average peak load of the analyzed cycle, i.e.: where |.| represents the absolute value, (  )  and (  )  represent the maximum and minimum values that the load reaches in the -th cycle.With these data, the energy (  )  can be computed as: Table 2 shows the energy   and (  )  , the drifts and the equivalent viscous damping computed for each drift level.Fig. 6 shows the accumulated dissipated energy as a function of the drift.Fig. 7 shows the equivalent viscous damping as a function of the drift.The system achieves higher energy dissipation with an increase in the displacements.Furthermore, the equivalent viscous damping is above the usual values for concrete-based systems.Similarly, and according to Priestley (2003), for wall systems, the damping ratio can be computed according to: where  is the ductility ratio computed above.According to the ductility ratio shown in Table 1 and from the cyclic tests performed on the ferrocement walls, the equivalent viscous damping ratio is 17.98%, this value is within the behavior shown in Fig. 7.
All walls exhibited loss of energy.However, the rounded shape of the hysteresis curves and the area enclosed by those loops suggest that the system has good energy dissipation capacity, as this increases with the drift.The shape of the hysteresis loops effectively determines the ability of these walls to dissipate energy when they are subjected to loads beyond its linear range.On the other hand, a small degree of pinching can be observed in the center of the hysteresis loops due to opening and closing of cracks generated in the surface of the walls, which affects the ability of the system to dissipate energy.These effects will be considered in the nonlinear dynamical model that will be proposed below.

Coefficient of energy dissipation capacity.
The coefficient of energy dissipation capacity (  ) is a design-oriented concept, which aims to approximate the nonlinear behavior of structural systems when subjected to seismic loads.It is used in most of the earthquake resistant design codes, in order to reduce the magnitude of the loads assessed from an elastic viewpoint.
In order to determine   , we used the model proposed by Takada et al. (1988), which is independent of the period of the structure: where  is an adjustment factor, which represents the degree of deviation of the   vs.  relation from the equal energy expression √2 − 1. Results drawn from Monte-Carlo simulations indicate that the average value of  is between 1.05 -1.34 (see Miranda andBertero, 1994 andTakada et al., 1988 for further details about the Monte-Carlo simulation).Taking  = 1.05, we have that   = 2.38, and taking  = 1.34, we have that   = 3.04; these values of   are similar to those used by Wainshtok-Rivas ( 2004) for earthquake resistant design of dwellings based on precast ferrocement thin walls in Cuba.Fig. 8 shows the precast ferrocement thin walls after the tests.The main source of energy dissipation of the walls was due to yielding of the flexural reinforcement in areas where plastic hinges appeared.In general, these zones are located at the base of the wall.The observed crack pattern suggests a predominant failure due to sliding-shear.Initially, the overall behavior was flexural and most of the shear force at the base of the wall was transmitted by bending to the compressive zone.There were also cracks in the compressive area.Later, the increase in the cyclic action led to yielding of the meshes.Several cracks appeared on the surface of the walls and their width and length increased at the base of the wall.It must be pointed out that during the cyclic test, there were no fragile failure modes of the ferrocement walls.

Analytical model
The Bouc-Wen-Baber-Noori (BWBN) model of hysteresis (Baber and Wen, 1981;Baber and Noori, 1985) is very popular in the field of structural dynamics because it models not only degradation of the material, but also pinching effect.It has been used in an ample range of applications such as vibration of concrete structures (Kunnath et al., 1997), wood joints (Foliente, 1995;Ajavakom et al., 2008), among others.
Let us consider a single-degree-of-freedom (SDOF) system with hysteretic restoring force and viscous damping, described by the differential equation with initial conditions (0) =  0 and (0) =  0 .Here,  0 and  0 represent the initial velocity and acceleration of the system, () denotes the displacement at time ,  0 2 ∶=   / is the squared pseudo-natural frequency of the non-linear system,  is the mass of the system,  is the viscous damping ratio, () is the external excitation (acceleration),  ≔   /  is the ratio of postyield   to pre-yield (elastic)   stiffness.The hysteretic component is governed by the so-called hysteretic displacement , which is given by the following equation The constants , ,  0 ,  0 ,   and  define the form of the pinching.
Identification of parameters of the BWBN model for the precast ferrocement thin walls.
We employed a novel methodology proposed by Ortiz et al. (2012), which uses multi-objective evolutionary algorithms in order to identify the parameters of the BWBN model of hysteresis.
The set of parameters that must be identified is represented by vector : = [, , , , ,  0 ,   ,  0 ,   ,  0 ,   , ,  0 ,  0 ,   , , ] Table 3 shows the results of the identification process.The first two parameters (,   ) were obtained from the experimental tests.It can be seen that the value of  is slightly different from the one computed previously.It may be noted that there is a discrepancy of about 9% with respect to the one estimated before.Fig. 9 compares the experimental hysteresis with the fitted BWBN hysteresis model.It can be seen that the agreement is fairly good and the approximation with the estimated parameters is good enough for simulation purposes.The maximum experimental displacement was 7.19 mm, and the maximum estimated displacement is 6.60 mm, which represents a difference in displacement of 0.59 mm.It can also be seen that the degradation effects are successfully simulated by the proposed model.
Seismic evaluation of the prefabricated ferrocement thin walls.
In order to test the ability of the model to compute the displacements suffered by the structure when a random external excitation is applied, the equivalent SDOF system was subjected to the 1994 Northridge earthquake (CESMD, 2012); the parameters shown in Table 3 were used within the model.The simulated response of the ferrocement thin wall is shown in Fig. 10.The seismic design codes in many countries, aim to keep the damage of structures under control when subjected to earthquakes of different magnitudes.For each intensity level, different damage scenarios are predicted.In Colombia, for the precast structural systems for houses based on thin walls, the maximum drift interstory is less than 1/200, that is applicable to all kinds of damage scenarios or seismic zone activity (from 0.05g to 0.9g).In this case, the maximum allowed displacement for precast ferrocement thin walls used in this experimental research is 10 mm, and the maximum displacement computed using the 1994 Northridge earthquake (intensity 0.8g) was 1 mm, which is 90% less than the maximum displacement allowed by the Colombian design code.According to the failure modes observed in the experimental campaign, for displacements less than 1 mm, there are no fragile failure modes.This fact demonstrates the excellent performance of this material when subjected to random external excitations.

Conclusions
Based on the experimental results, the precast ferrocement thin walls exhibited high resistance and good performance when subjected to cyclic loading conditions.The proposed nonlinear dynamical model fits well with the experimental results and the material and it can be used for the earthquake resistant design of houses built with ferrocement in zones with moderate to high seismic activity.

Figure 3 .
Figure 3.Time history of applied load

Figure
Figure 6.Cumulative dissipated energy

Figure 9 .
Figure 9. Experimental and estimated response of the system

Figure 10 .
Figure 10.Estimated response of the precast ferrocement thin wall when subjected to the 1994 Northridge earthquake