Self-centring segmental retaining walls—A new construction system for retaining walls

Abstract

This paper reports on an experimental study on a new self-centring retaining wall system. Four post-tensioned segmental retaining walls (PSRWs) were experimentally tested. Each of the walls was constructed using seven T-shaped concrete segments with a dry stack. The walls were tested under incrementally increasing cyclic lateral load. The effect of the wall height, levels of post-tensioning (PT) force, and bonded versus unbonded condition of PT reinforcement on the structural behavior of the PSRWs was investigated. The results showed that such PSRWs are structurally adequate for water retaining structures. According to the results, increasing the wall height decreases initial strength but increases the deformation capacity of the wall. The larger deformation capacity and ductility of PSRW make it a suitable structural system for fluctuating loads or deformation, e.g., seawall. It was also found that increasing the PT force increases the wall’s stiffness; however, reduces its ductility. The residual drift and the extent of damage of the unbonded PSRWs were significantly smaller than those of the bonded ones. Results suggest that this newly developed self-centring retaining wall can be a suitable structural system to retain lateral loads. Due to its unique deformation capacity and self-centring behavior, it can potentially be used for seawall application.

Graphical abstract

Keywords

retaining wall / segmental / precast concrete / unbonded post-tensioning / water retaining wall / seawall

1 Introduction

Flood walls play an important role in defending low-lying coastal areas which are at risk of storm surges or sea level rises [ 1]. In many places along the Australian shoreline, water-retaining walls (seawalls/sheet piles) are used to protect coastal areas against erosion due to wave impacts [ 2]. Most of the waterfront structures use conventional construction methodologies and structural stability systems for different types of marine structures. Glass flood defenses [ 3], and modular glass fiber reinforced plastic (GFRP) hollow profiles are recently developed [ 2] methods to construct water retaining structures. Of all the materials commonly used in seawalls, timber is susceptible to animal attack or decay [ 4], and steel (commonly used in sheet piles) [ 4] is susceptible to corrosion [ 5]. The traditional approach for providing the durability of steel sheet pile walls is the application of protective coating, cathodic protection systems or corrosion loss allowances [ 5]. However, only the application of sacrificial steel has been found to be an effective solution in the long run [ 6]. This, however, comes with an increased volume of material used and related increases in project cost. Among different types of applied materials for water-retaining walls, concrete seems more suitable as it is less susceptible to deterioration. However, pouring fresh concrete underwater is cumbersome and challenging, and sometimes even impossible. Precast concrete can be a suitable alternative in such scenarios [ 7].

Reviewing the damages in floodwalls (rigid cantilever) as in New Orleans [ 8], indicated that one of the causes of the wall damage was excessive erosion on the downstream side and related loss of passive earth pressure. A more flexible water retaining system can reduce the lateral pressure to the base [ 9] by exhibiting a large ductility capacity in case of flood or inundation.

Flood walls and generally water retaining structures are subject to hydraulic loading in addition to usual and seismic loads. The current practice of water retaining structures mainly focuses on material properties and dimension of the wall (using US Army Corps of Engineers design manuals) [ 10]. Among the various coastal protection structures, gravity type waterfront retaining walls are very common [ 11]. The current design practice is adequate but can be expensive and not optimal [ 10]. One of the shortcomings of the conventional waterfront retaining walls is that more mass is required to overcome different types of loads acting concurrently on the wall, e.g., time-dependent wave loads, earthquake, and buoyancy. Increasing weight may provide enough lateral stability against wave and buoyancy loads but increases the inertia force in the wall due to an earthquake which can have an adverse effect on the wall stability. Several past earthquakes such as Loma Prieta (1989), Northridge (1994), Kobe (1995), Bhuj (2001), South Asian Sumatra (2004), and Tohoku (2011) caused damages to many of the waterfront retaining walls [ 11].

To overcome the shortcomings of the current practice, this research introduces an innovative alternative system, namely, post-tensioned segmental retaining walls (PSRWs). The structural stability of the retaining wall system is mainly dependant on the PT forces rather than the wall mass. Here, T-shaped precast concrete segments are stacked on top of each other with dry joints. The PT reinforcement is passed through ducts in the precast segments and post-tensioned.

Introducing segmental precast construction and self-centring (through unbonded pre-stressing which is discussed later) PSRW water retaining system may result in a more economical wall due to its large ductility capacity. Due to their large deformation capacity, the PSRW has the potential to be designed for normal service conditions, however, in case of dynamic loads such as earthquake, wave impacts or inundation, its large deformation capacity activates and consequently reduces the lateral load. Two systems of reinforcing can be envisaged for the PSRWs, namely: unbonded and bonded. In the unbonded system, the PT reinforcement is free to move in the duct which introduces self-centring behavior to the wall. The wall can move back to its original position after the drawdown of the upstream water level. On the other hand, in the bonded system, the PT reinforcement is encapsulated permanently by grout in the ducts and hence bonded to the surrounding concrete. As a nutshell, the currently designed and constructed water retaining walls are structurally rigid and mainly designed as gravity walls and the construction methodology is cast in place concrete. However, the proposed structural system enables us to use precast construction (easier to construct in a marine environment) and provides ductile performance together with self-centring behavior of the retaining wall. Using self-centring capacity of the wall may result in improved behavior of the sea walls due to fluctuating levels of water-based on water level demand.

The two methods of post-tensioning (PT) introduce different structural behavior and design preferences to the system. For instance, grouting in the bonded PSRW protects it from corrosion. Additionally, the pre-tension force is locked in the structure and the system is less vulnerable to local damage [ 12]. Bonded PT reinforcement would also be less dependent on end-anchorage performance which is also susceptible to corrosion [ 13]. Given no strain redistribution in PT reinforcement, the bonded post-tensioned structures usually have higher flexural and ultimate load capacity in comparison to unbonded ones [ 14]. Bonding of the PT reinforcement to the surrounding concrete may also provide improved crack control to the structural element [ 15]. In bonded PT, the interaction between the reinforcement and concrete allows better transfer of stresses and localized stress relief. However, the unbonded PT has its benefits. Less complexity is involved due to the elimination of the grouting procedure, the PT reinforcement can be easily stressed, de-stressed, re-stressed (suitable for staged construction), removed and disassembled (suitable for temporary structures), and replaced (suitable for repair and rehabilitation). Moreover, unbonded pre-stressing introduces a self-centring behavior to the system which reduces the residual deformation and hence the extent of damage [ 16, 17].

The primary aim of this research is to study the effects of the PSRW’s aspect ratio, PT force, and PT reinforcement bonding condition on the structural performance of the PSRW system, to investigate the feasibility of its application as sea wall structures. The effect of the above-mentioned variables on the damage pattern, hysteretic behavior, load-carrying capacity, joint openings, concrete strains, and plastic hinge length was investigated.

The physical behavior of the PSRWs and the effect of test variables on wall behavior are presented in Section 7. The discussions about the results and impact of this research are presented in Section 8 followed by Sections 9, 10, and 11 presenting the wall components behavior contributing to the structural stability system of the PSRW including PT bar stresses, gap opening and lateral displacement and compressive strain of concrete respectively.

The results of this research contribute toward the development of an accelerated retaining wall construction suitable for retaining water. A more parametric and numerical study is required to better understand the crack propagation in the precast concrete segments [ 18, 19] and extend the findings of the experimental study. Interested readers may find simplified method for arbitrary evolving cracks which is proposed by Rabczuk and Belytschko [ 19] for modeling discrete cracks in concrete. However, this article is focused on synthesizing and reporting experimental data only and further numerical modeling is required to investigate crack evolution in precast segments.

2 Experimental program

Table 1 presents a summary of different walls discussed as part of this study. Four of the walls (W1, W2, W3, and W4) tested as part of this study had a shear span of 1995 mm and an aspect ratio of 12.43. Test results of two other walls having a shear span of 1209 mm and aspect ratio of 7.55 were also taken from companion research [ 20] to compare with the results presented here. Both conventional concrete (CC) and crumb rubberised concrete (CRC) were used in the construction of the wall segments and their mix designs are discussed in Section 3. T-shaped precast concrete segments were used to construct all the wall specimens presented in Table 1. Figure 1 presents a schematic diagram of construction with temporary bracings, test setup, and dimensions of the wall. In three of the tests, unbonded PT was used whereas in the 4th one the PT reinforcement was bonded. The walls were tested under an axial load ranging from 61.0 to 99.1 kN PT force, corresponding to an axial stress ratio of 0.05 and 0.09, respectively. Axial stress ratio is defined as the stress in the wall cross-section due to the gravity loads and PT forces divided by the compressive strength of concrete.

The bottom segment of wall W1 was CC and the wall was pre-stressed using unbonded PT. This wall had the same cross-section, material, and PT force as test specimen S4 reported in an earlier investigation [ 20] but had a different length. This allowed the investigation of the effect of wall aspect ratio on its structural behavior. Walls W2 and W3 both had CRC in the bottom segment, however, were pre-stressed using unbonded PT at 61.0 and 99.1 kN, corresponding to an axial stress ratio of 0.05 and 0.09 respectively. These two walls were considered to investigate the effect of PT force on the behavior of PSRWs with relatively large aspect ratios. Wall W2 is also identical to S5 except for wall height. W4 was identical to W3 except for the fact that PT reinforcement was bonded in W4.

Each wall was constructed on top of a 400 mm × 400 mm × 1200 mm footing and a 350 mm × 350 mm × 350 mm load head was placed at the top. The loading head performed as a rigid member to exert the lateral load applied by the actuator. As shown, a 400 mm × 400 mm × 40 mm layer of high strength (80 MPa) non-shrinkage grout was applied to the top of the footing to provide a smooth contact surface. The wall segments were post-tensioned by the PT reinforcement passing through cast-in Polyvinyl chloride (PVC) ducts of the segments. Assuming that the lateral load is applied to the flange side of the wall, the PVC duct in the precast concrete segments was provided in the web of the segment to introduce eccentricity with respect to the centroid of the wall’s cross-section to improve the effectiveness of pre-stressing and increase the lateral capacity of the wall. Anchorage to the PT reinforcement was provided at top of the loading head and the recess point in the footing. The unbonded length of the PT reinforcement between the top and bottom anchorage points of the unbonded PT specimens was 2560 mm for walls W1−W4 (and 1780 mm for walls S4 and S5). The PT reinforcement had a tensile yielding strength, f_{\mathrm{p}\mathrm{y}} , of 900 MPa and nominal ultimate tensile strength, f_{\mathrm{p}\mathrm{u}} , of 1100 MPa. Bonding of the PT reinforcement in the ducts was (for W4) done using SikaGrout® 300 PT [ 21] which is a non-shrinkage, cementitious grout. The compressive strength of the cured grout at the time of the wall test was 70 MPa [ 22].

3 Material and concrete mixing

General-purpose Portland cement compliant with Australian standard AS 3972 [ 23] was used for the concrete mixes. Coarse aggregates had a maximum size of 10 mm and 1570 kg/m ³ density. Fine aggregates consisted of a maximum of 5 mm aggregate size and 1625 kg/m ³ density. The concrete slump was 100–170 mm (0.58 kg/m ³ Polycarboxylic ether type superplasticizer was added to CC to achieve this slump). In the CRC concrete, 18% of the fine aggregate material was replaced by waste tire derived rubber particles having an approximate size of 1.2 mm and a density of 530 kg/m ³. Australian standard AS 1012.9 [ 24] was used to test concrete samples for strength. Casted wall segments were cured until the day of testing at a laboratory temperature of 23°C ± 5°C covered with plastic. Table 2 tabulates the mix proportions and the compressive strengths for CC and CRC obtained as an average of three standard cylindrical specimens for each mix.

4 Preparation of walls

Timber molds were manufactured to cast in T-shaped segments as shown in Fig. 2(a). A PVC duct with a 30 mm inner diameter was used as the cast-in duct in the web of the T-shaped segment. These segments were used for unbonded post-tensioned tests (W1, W2, W3). A coring machine was used to drill in a 53 mm duct in the web of the segments of wall W4, as shown in Fig. 2(b). The inside of the duct was grounded to create 2 mm deep scrabbles (Fig. 2(c)) to increase the friction and provide better bonding between the grout and the concrete. Silicon was used to prevent leaching of the grout between the segments’ cavities.

5 Loading regime

Out-of-plane half-cycle displacements at 1 mm/s as per ACI 374.1-05 [ 25] was exerted on the wall using a 100 kN capacity actuator. The maximum stroke of the actuator was 300 mm. The cycles of the displacements are shown in Fig. 3. Half cycles were considered to simulate cycles of wave and water pressure acting on one side of the T-shape PSRW. Note that the lateral load was applied at the top of the wall rather than at one-third of the wall’s height at which the resultant of the lateral pressure of the soil/water could be assumed (considering a triangular distribution of the lateral load). The bending moment and shear force capacity at the walls’ base are presented which can be used to estimate the lateral pressure based on the lateral load distribution.

6 Test configuration and instrumentation

The test setup started with fixing the precast concrete footing segment ( f_{\mathrm{c}}^{\mathrm{\prime }} = 40 MPa) to the strong floor. The sitting area of the segments was prepared using a thin layer of high strength grout ( f_{\mathrm{c}}^{\mathrm{\prime }} = 70 MPa) at the time of testing. This grout layer was added to the top of the foundation and levelled horizontally. The temporary bracings were then installed on the footing using bolts as shown in Fig. 1(b). The segments each weighing about 23 kg were then lifted and laid on top of each other with dry joints.

The loading head was placed on top of the segments and, the ram was connected to the loading head by high strength bolts. PT reinforcement was then passed through the ducts and anchored to the footing using 160 mm × 160 mm × 40 mm steel plate and 80 mm length hex nut. The load cell was then placed on top of the loading head before pre-stressing the PT reinforcement using a 500 kN capacity hydraulic jack to the specified PT forces as tabulated in Table 1. After PT of the wall, the temporary bracings were removed, and the test was initiated for wall W1, W2, and W3. The schematic illustration of the test setup is shown in Fig. 1(c). Wall W4 had similar assembly steps except that it was bonded and needed grouting. The loading head was installed followed by grouting of the duct from the top. The PT reinforcement was post-tensioned while grout was wet and was released after 24 h.

Vertical Linear Variable Differential Transformer (LVDTs) were installed on the compression and tension side of the bottom two segments of W1 and four bottom segments of W2, W3, and W4 to measure the gap opening between the segments as well as at the wall-footing interface as shown in Fig. 1. Horizontal LVDTs were connected to the wall to measure the horizontal movement at different heights of the wall as well as at the base footing.

Vertical strain gauges with 60 mm length were mounted on the compression and tensile faces of the bottom two segments to measure compressive strains at critical points of the segments. A 10 mm steel strain gauge was connected to the rebar to measure the strains in the PT reinforcement during PT and testing. The PT force was measured using a load cell mounted on top of the wall (see Fig. 1(b)). The load cell was removed from W4 after the grout set.

7 Experimental results and discussion

7.1 Hysteretic response

The hysteretic responses of the force-drift value of the tested walls are shown in Fig. 4. It can be observed that walls W1, W2, and W3 exhibited a very similar hysteretic behavior characterized by a ductile bi-linear performance which was not observed in wall W4. The walls having unbonded PT primarily showed elastic performance when incrementally loaded and unloaded in cycles. The elastic behavior significantly changed after the decompression point of the walls where the gap opening occurred. Note that the first linear section before the gap opening represents the initial stiffness. The stiffness of the unbonded PSRWs significantly dropped after the gap opening between the wall and footing. Such a drop corresponds to the change in the slope of the force-drift curves at the decompression point (decompression point is at the end of the first linear section of the force-drift curve). In contrast, wall W4 did not show a sudden change in stiffness. The PT reinforcement in wall W4 was bonded and the gap opening could not happen like the unbonded walls (W1, W2, and W3). Thus, unlike unbonded specimens, there is no distinguishable decompression point in the hysteretic curves of wall W4.

Before the decompression points, no damage was observed in any of the unbonded walls resulting in no residual drift after unloading. In cycles beyond the decompression point, walls W1, W2, and W3 showed hardening before they reach their peak load. The stable structural performance was observed for walls W1, W2, and W3, and they all underwent large drifts (>8.5%) without exhibiting any strength reduction as shown inFig. 4. All tests were stopped after 8%−10% drift value to avoid sudden failure of the wall and damaging the test instrumentations except for wall W4 which failed at a drift of 4.0%. The strength capacity plateaued toward the end of the tests as shown inFigs. 4 and 5. The tests were stopped to prevent sudden failure and damage to instruments when large cracks were observed. As shown in Fig. 4, unlike Walls W1−W3, wall W4 did not exhibit distinct gap opening and sudden reduction in the stiffness. The PSRWs indicated different strength levels at a similar drift ratio. To compare the PSRW lateral strength, 4% of drift has been considered. It can be observed inFig. 5(a) that wall W4 having bonded PT had the highest strength of 10.1 kN. At lower levels, wall W3, W1, and W2 recorded 6.7, 5.7, and 4.8 kN lateral strength at 4% drift respectively. The effects of different parameters on the force-displacement behavior of the walls are discussed in the following. To better compare, the backbone curves are presented in Fig. 5 and the output of the wall tests are summarized in Table 3.

7.2 Damage patterns and test observations

In this section, the general behavior and damage pattern observed during the tests are presented. In general, a clear difference between the behavior of bonded and unbonded walls was observed. PSRWs having unbonded PT (W1, W2, W3) showed gap openings at the bottom four segments, however, the largest gap was observed in the wall-footing interface. The bonded PSRW (W4) did not show a significant gap opening.

Figure 6 shows the final damages of the walls at the end of testing (The location of the cracks is marked). Comparing the damages finds that a distinctive difference between the bonded and unbonded PSRWs. While the structural damage mainly happened at the bottom two segments of the unbonded specimens (W1, W2, W3) (see Figs. 6(a)–6(c)), the damage of the bonded wall (W4) was at the top two segments as shown in Fig. 6(d). The bottom most segment in all unbonded specimens experienced concrete crushing on the compression face of the segment. The second segment from the bottom of the wall had cracks on both sides of the segment which was the extension of the cracks propagated from the bottom. There was no evidence of concrete crushing on the second segment in any of the tested walls. The detailing of the crack formation observed for each of the wall tests is presented and compared in the following.

As shown in Table 1, wall W1 had a pre-stressing force of 81.5 kN, corresponding to an axial stress ratio of 0.06 which was identical to S4 except that wall S4 was shorter (1209 mm cantilever height). It can be observed in Fig. 6(a) that the bottom segment exhibited compression face damage (at a drift of 3.9%) followed by vertical cracks that propagated through the second segment in the same location on both front and back of the segment (at a drift of about 5.2%). Diagonal cracks on the bottom two segments started at 7.7% drift. No concrete crushing on the compression face of the second segment was observed. There was no evidence of cracking or structural damage to the third segment. Comparing the damage pattern of wall W1 with its shorter counterpart, wall S4 reveals that while wall W1 experienced damages to the bottom two segments, this was only limited to one segment at the bottom of wall S4. The concrete compressive strength of precast T-segments is listed in Table 1.

Wall W2 was identical in size to wall W1 in dimensions but a lower strength concrete was used for the bottom segment. A lower level of PT force was also applied to wall W2 to provide a relatively similar axial stress ratio to wall W1 (see Table 1). It can be observed from Figs. 6(a) and 6(b) that the damage in wall W2 with lower concrete compressive strength is limited to the bottom-most segment, whereas the damage is extended to the second block in W1. The extent of damage in the second segment in wall W1 may be due to higher PT force and compression in comparison to wall W2. This can be due to lower tensile strength in wall W2 in comparison to wall W1. It can also be observed in Fig. 6(b) that only the bottom segment was damaged for wall W2, however, as shown in Fig. 6(c), the damage was further extended to the second segment for wall W3. This agrees with the results presented previously for walls W1 and W2.

Wall W3 was identical in material and size to wall W2 except that it had a higher axial stress ratio of 0.09 compared to 0.50 in W3. It can be seen from Fig. 6(b) that only the bottom segment was damaged for wall W2, however, as shown in Fig. 6(c) the damage was extended to the second segment for wall W3. This is due to the 80% increase in axial stress ratio for wall W3 compared to that of W2. This increased axial stress ratio resulted in the formation of the diagonal crack in wall W3 which started from about 65 mm above the bottom segment and propagated to the second segment diagonally. This damage is a sign of the increased stresses on the upper segments because of the increased stress ratio. From this observation, it can be said that the plastic hinge length for these PSRW systems is dependent on the axial stress ratio. The plastic hing length is mainly attributed to the extent that plasticity spreads in the wall. Observing the propagation of the damage (diagonal cracks) by increasing the axial stress ratio suggests the relationship between axial stress ratio and plastic hinge length.

Wall W4 was identical to W3 except for the PT bonding condition. Comparing Figs. 6(c) and 6(d) reveals that the bonded and unbonded PSRWs exhibit very different behavior. While wall W3 having unbonded PT reinforcement experienced damages at the bottom segments only and could tolerate large drifts, wall W4 showed significantly lower displacement capacity and experienced sudden failure once the top two segments were crushed at their webs (see Fig. 6(d). Note that there was no evidence of concrete damage on the compression face of the wall (flange)). The location of the damage in concrete as shown in Fig. 6(d) in W4 suggests large compressive stress extended from the flange to the web of the wall when it was loaded laterally. The area of the compressive stress in the web of the wall is smaller than the flange. The compressive stress in the web increased due to the elongation of the PT bar in the duct. The PT bar was bonded to concrete by grout and all the stress was transferred to the web by increasing the wall lateral displacement until it reached the ultimate compressive strength of concrete. This is due to the larger strain development in the PT bar, resulting in a higher compressive zone area to balance out the tensile force.

The increase in the compressive stress in the web of the wall increased with increasing wall’s drift ratio, and the web of the segment failed in compression earlier than the compression face of the segments due to its reduced width. This damage was sudden and happened in the second cycle of 4.0% drift ratio, hence could not undergo larger drifts like the other walls. It is also worth noting that the gap opening observed in wall W4 with bonded PT was much less than wall W3 with unbonded PT.

The bottom two segments of the unbonded walls (W1–W3) experienced three different types of damage (Types-A, B, and C). Damage Type-A as shown in Fig. 7(a) was spalling of the concrete at the compression flange of the bottom segment. This damage occurred when the stress on the compression face of the segment exceeds concrete compressive strength. Damage Type-B (see Fig. 7(b)) was the formation of vertical cracks on the flange at the web-flange intersection initiated from the bottom of the first segment and extended to the second segment on both front and back faces of the segments. This type of damage is mainly due to the change in the cross-section and the concentration of the stresses transferred between the web and flange of the segment. Damage Type-C (see Fig. 7(c)) was the formation of diagonal cracks that initiated from the mid-height of the bottom segment and extended to the second segment till it reached the web.

Wall W1 had damage Type-B, Type-C, and Type-A at drifts of 3.9%, 5.2%, and 7.7%, respectively. Wall W2 had minor cracks on the compression face at 3.9% drift and damage Type-B, Type-A at 6.5% and 7.7% drift, respectively. For wall W2, damage Type-C was not observed, and damage Type-B was only limited to the bottom-most segment. The absence of damage Type-C in wall W2 may be due to its lower axial stress ratio in comparison to other walls. Wall W3 had damage Type-C and Type-A at 3.87% and 5.16% drift, respectively. Damage Type-B was only observed in the bottom segment for wall W3, happening at the same drift as damage Type-C.

7.3 Effect of wall aspect ratio

Comparison of the behavior of wall W1 with its shorter counterpart, S4 in Fig. 5, indicates that increasing wall aspect ratio decreases ultimate lateral load capacity and the initial and secant stiffness of the PSRW (Fig. 5(a)) but increases the ultimate displacement capacity (Fig. 5(b)). Similar observations were made for column members with circular cross-sections in previous studies [ 26]. As shown in Table 3, the tested peak lateral load of S4 and W1 was 12.4 and 9.2 kN, respectively, and the corresponding moment at the wall base was 15.0 and 18.3 kN·m for the walls in the same order.

The moment at the wall base does not include second-order geometrical effect and is calculated by multiplying lateral load at the location of the actuator by the shear length of the lateral force. It is worthwhile to mention that the strains recorded in the experiments include the combined effect of PT force and gravity load. The PT bar rotates as the walls rotate but considering that the gap between the duct and PT bar is 2 mm, the contribution of PT bar rotation in the P-Delta effect in the duct is negligible. The only source of the P-Delta effect is the weight of the wall which is small compared to the PT force. Gravity load contribution in axial stress ratio is 1.6% to 2.6% of PT force in tested specimens. As the aspect ratio increased, from 7.55 in wall S4 to 12.43 in wall W1, the moment capacity increased by 22%. Given these aspect ratios and the required height of the wall in practice, it is expected to envisage an optimal width for the retaining wall which directly effects the construction cost and the required lateral strength.

For another pair of walls (S5 and W2) made with CRC, with an axial stress ratio of 0.05 which were identical except for the aspect ratio (7.55 and 12.43, respectively) the tested lateral load capacity was found to be 16.56 and 8.46 kN respectively (wall’s base moment were 20.02 and 16.88 kN·m, respectively). Interestingly unlike walls S4 and W1, it can be observed that the base moment capacity has reduced. It can be concluded that in PSRWs with a low axial stress ratio (as in walls S5 and W2 with an axial stress ratio of 0.05), increasing the wall aspect ratio results in the reduction of base moment capacity. However, in PSRWs with a high axial stress ratio (as in walls S4 and W1 with an axial stress ratio of 0.06), increasing the wall aspect ratio results in an increase of base moment capacity. This could be due to early damage of concrete in the compression face of the segment due to larger compressive strains associate with the higher axial stress ratio in the wall and larger bending moment capacity at the base of the wall. Larger bending strength at the wall base is achieved as the wall W1 shows hardening and increasing ductility due to the transfer of loads to higher segments with a 0.06 axial stress ratio before the bottom-most segment reaches ultimate strength. This does not happen in wall W2 with a lower axial stress ratio (0.05) when the bottom segment reaches its ultimate strength before the stresses are transferred to the second segment. Note that although the axial stress ratio is only 6% of the unconfined concrete compressive strength, the compressive stresses are concentrated in the small compression zone at the edge of the wall due to rocking. Note that the reported behavior is based on the limited number of tests conducted as part of this study. More studies are required to verify such behavior. And furthermore studies are required to understand the optimum aspect ratio and axial stress ratio at a required base design moment for PSRW.

The deformation behavior of the shorter walls S4, S5 and taller walls W1, W2 is schematically compared in Fig. 8. While for the shorter walls (S4, S5) the deformation was due to the gap opening at the wall-footing interface, in the taller walls (W1, W2) relative rotation between the segments of the wall also contributed.

The deformation mechanism and damage extent of the tested PSRWs show that the stress distribution along the height of the wall is a function of the wall aspect ratio and PT reinforcement bonding condition. To better understand this, the compressive strains at the bottom of the walls (S4 and W1, W3, and W4) are plotted against the drift ratio in Fig. 9. The effect of wall aspect ratio and PT reinforcement bonding condition on the strains at each location of strain gauges P0, P1, and P2 (which represent the strain gauge location at the compression face of the bottom-most, second and third segments respectively) are summarized in Table 4. It can be observed that increasing the wall aspect ratio (walls S4 and W1) reduced the strain at the bottom two segments and bonding the PT reinforcement in W4 transferred the strain from the bottom-most segment to the second segment.

Wall curvature distribution versus height ratio (height normalized the height of the wall × 100) of the wall is depicted in Fig. 10. The experimental curvature is calculated as the difference between the vertical LVDTs displacements installed on the compression (shortening) and tension (elongation) side of the segments at the same height level divided by the horizontal distance between the LVDTs multiplied by gauge length. It can be observed that increased axial stress ratio in taller PSRWs (W2 and W3) resulted in a smaller gap opening between the footing and bottom-most segment and the next joint between the bottom-most and second segment. Grouting of PT in wall W4 changed the curvature response of the wall. It can be observed in Fig. 10 that W4 has significantly smaller curvature in the footing interface compared to the unbonded PSRWs. The change in curvature in walls W1−W3 at each joint is nearly linear and no significant change can be observed in the amount of curvature between joints. However, wall W4 has recorded significant change in the curvature at bottom segment joints which can be observed inFig. 10(c).

Most of the curvature is happening between 15% to 30% of the wall height in wall W4. The curvature value along wall height is similar for open joints at low drifts except in W4. However, the curvature increases at bottom joints significantly at higher drifts except in W4. This indicates that unlike unbonded PSRWs (i.e., W1, W2, and W3) when the PSRW has bonded PT (as in W4), the curvature at the wall base is less than the curvature at nearly 20% height ratio of the wall. In other words, the maximum curvature between segments does not happen in the wall base when the PT bar is bonded.

Moment distribution for the short and tall wall is shown in Fig. 11(a) at yield ( M_{\mathrm{y}} ) and ultimate moment ( M_{\mathrm{u}} ). M_{\mathrm{u}} at the wall base was calculated by multiplying ultimate force ( V_{\mathrm{u}} ) at top of the wall by wall cantilever height. V_{\mathrm{u}} is the ultimate shear force extracted from the bilinear idealisation of the backbone curve as per FEMA 356 [ 27] definition (Fig. 11(b)). M_{\mathrm{y}} is the yield moment at wall base calculated using V_{\mathrm{y}} from idealised force-displacement curve. Calculated M_{\mathrm{u}} and M_{\mathrm{y}} for S4 was 14.98 and 8.94 kN·m, respectively. L_{\mathrm{y}} as shown in Fig. 11(a) is the height which corresponds to M_{\mathrm{y}} in moment diagram. It is calculated as 490 mm from wall base. Measured M_{\mathrm{u}} and M_{\mathrm{y}} for W1 is 18.29 and 5.56 kN·m, respectively. L_{\mathrm{y}} is calculated as 1380 mm from wall base.

Observing the value of L_{\mathrm{y}} and the location of joints which experienced gap opening when the walls were pushed to ultimate load indicates a similar pattern for both short and tall PSRW. L_{\mathrm{y}} in S4 fell between J_2 and J_3 and the gap opening happened in J_1 joint as shown in Fig. 11(a). Similarly, L_{\mathrm{y}} in W1 fell between J_6 and J_7 and the gap opening happened in J_5 and all joints below that. Given the dimensions of the segments tested and similar axial stress ratio, the total lateral deflection of a PSRW depends on L_{\mathrm{y}} . If L_{\mathrm{y}} is larger than J_n location, the joints that experience gap opening is J_1 to J_{n-1} . This observation is limited to the test specimens in this experiment and a more numerical parametric study is required to confirm this for different aspect ratios.

The plastic hinge length determination of PSRW is critical for defining lateral deformation characteristics. The length of the plastic hinge region is the physical length over which plasticity spreads [ 28]. Watson and Park [ 29] considered 56% of the column depth as equivalent plastic hinge length when the connection of the column to footing is monolithic. Hewes [ 30] assumed plastic hinge length equal to half the section diameter for unbonded post-tensioned columns for precast concrete segmental bridges. There is very limited research regarding methodology to establish the plastic hinge length in unbonded self-centering precast segmental construction.

The experimental plastic hinge length as defined by Mortezaei and Ronagh [ 31] (shown in Fig. 11(a)) for W2, W3 is 400 and 380 mm from the base, respectively. The depth of the T-section segment is 160 mm. It can be observed that plastic hinge length in PSRW is 2.5 times the cross-section depth of the T-shaped segment and previous analytical equations may not be applicable for PSRWs. Hassanli et al. [ 32, 33] suggested the following semi-empirical approach to calculate the plastic hinge length for unbonded post-tensioned segmental walls. Equation (1) correlates the wall length and axial stress ratio to plastic hinge length.

(1) L_{\mathrm{p}}=0.11l_{\mathrm{w}} +3475\left(f_{\mathrm{c}}/f_{\mathrm{c}}^{\mathrm{\prime }}\right),

where L_{\mathrm{p}} is plastic hinge length in mm, l_{\mathrm{w}} is wall length in mm and f_{\mathrm{c}} /f_{\mathrm{c}}^{\mathrm{\prime }} is axial stress ratio. It seems that this equation underestimates the plastic hinge length of PSRWs.

7.4 Effect of axial stress ratio

The PSRWs W2 and W3 were identical except for their axial stress ratios. Walls W2 and W3 had 0.05 and 0.09 axial stress ratio respectively with 61 and 99.1 kN initial PT forces. This approximately 80% increase in the axial stress ratio of wall W3 compared to W2 only leads to a 10% increase in ultimate lateral load capacity. In a previous study conducted by the authors [ 20], the PSRWs with a smaller aspect ratio showed a 37% increase in their ultimate lateral load capacity when the axial stress ratio increased by 61%. This indicates that an increase in the axial stress ratio in shorter walls results in higher lateral load capacity than taller walls. This also suggests a larger PT force is required for taller retaining walls.

When taller PSRWs are required, there is also a need to increase the PT force or its eccentricity to effectively increase the lateral strength of the wall.

7.5 Effect of bonding

Hysteretic behavior of walls W3 and W4 can be compared to examine the effect of bonding of PT reinforcement on their force-drift behavior. As shown in Fig. 4, the drift where gap opening starts in wall W3 (decompression point) can be clearly distinguished as the PT reinforcement is unbonded and free to move in the duct. In contrast, wall W4 does not show such a bi-linear behavior and the strength of the wall gradually increase until failure. It can also be observed that wall W3 endured drifts of more than 8% in comparison to only 4% in wall W4. The lateral load capacity of the walls W3 and W4 were 9.31 and 10.13 kN, respectively. Hence, the strength increased by about 9%, if the PT was bonded. However, this resulted in a reduced ductility and displacement capacity.

8 Tested walls strength for retaining wall applications

To assess the feasibility of using PSRWs as water retaining structures for coastal areas, wave forces on the walls are calculated using a simplified method presented by Camfield [ 34] as Eqs. (2) and (3).

(2) h=0.2H_{\mathrm{b}} \left(1-x_1/x_2\right),

where H_{\mathrm{b}} is the breaking height of the wave, x_1 is the distance from the shoreline to the wall and x_2 is the distance from the shoreline to the point of the highest run-up without the wall.

(3) F=4.5\gamma h^2,

where h is defined by Eq. (2) and \gamma is the specific weight of water. Equation (3) provides only the total force and does not give a pressure distribution.

Assuming that the distance from the shoreline to the wall is 2 m, the distance from the shoreline to the point of the highest run-up without the wall is 4 m, and considering the breaking height of the wave as 1 m, the calculated force acting on the wall would be 4.50 kN which is equivalent to 8.95 kN·m moments at wall base assuming the resultant force acting at top of the wall (an extremely conservative assumption). It can be observed from force-drift curves that the minimum ultimate strength of the tested PSRWs is more than 7.0 kN, corresponding to a resisting moment of higher than 13.94 kN·m at the base of the wall before they show degradation in strength. (Note that as showed here for a given cross-section and axial stress ratio as the wall’s height increases the moment capacity of the section increases. So they can carry more moment if their heights are increased). It can also be observed from Fig. 4 hysteretic curves that the unbonded PSRW walls had negligible residual displacement at the end of the test which represents their considerable self-centring capability which can be beneficial for water retaining structures. Considering the fluctuating MSLs and water height changes in low and high tides, designing a rigid retaining system for the maximum plausible load on the wall may lead to an increase in capital costs required for the construction of the wall. On the contrary, having a flexible water retaining system such as a PSRW can tolerate larger loads due to surges in water levels by having large ductility and self-center when the water levels drop.

The possibility of using PSRWs having a large aspect ratio (12.43) as soil retaining structures is also investigated here. Wall W3 having the largest initial stiffness as shown in Table 3 is selected to evaluate the ability of the tested PSRW with an aspect ratio of 12.43 to withstand the earth pressure retained behind the wall. The expected base bending moment due to earth pressure at wall W3 is 7.42 kN·m assuming active earth pressure and 17 kN/m ³ soil unit weight retained behind the wall. Wall W3 base moment capacity at 0.10% drift is 1.63 kN·m. Wall strength at 0.10% drift is selected as earth retaining walls are required to have a certain level of rigidity to meet serviceability requirements as per AS 4678 [ 35]. Thus, the wall lateral strength according to Fig. 5(a) at 0.10% drift is 0.82 kN acting on top of the wall which is equivalent to 1.63 kN·m moment at the base. It can be observed that the expected moment at the wall base (7.42 kN·m) is larger than wall strength at low drifts (1.63 kN·m). Although the Wall W3 ultimate base moment capacity at 8.80% drift is 18.32 kN·m, it does not meet serviceability requirements as per AS 4678 [ 35]. Larger aspect ratio walls require more eccentricity to the PT force to meet both strength and serviceability requirements for earth retaining walls.

9 Post-tensioning bar stresses

The hysteretic responses of PT reinforcement force are plotted against the drift values for walls W1, W2, and W3 in Fig. 12. Note that the PT force was directly recorded using the load cell attached to the top end of the PT reinforcement. In none of the tests, PT reinforcements reached their yield capacity (282.6 kN). The increase of PT force in the walls was gradual. The loss of PT at walls W1 and W2 was at the same level, however, the loss of PT for wall W3 was less in comparison to W2. It was found that an increasing PT force in PSRWs with a large aspect ratio decreased the loss of PT.

The PT force is plotted against the lateral force in Fig. 13. As shown, the PT force graphs include two linear sections. Up to a lateral load of about 3 kN, the PT force did not increase when the lateral load was increased, however, beyond this point, PT force started to increase. This point is the decompression point beyond which the wall starts rocking about its base resulting in elongation of the PT reinforcement (because of gap opening) and hence PT force increase. The lateral load at the decompression point is defined as the decompression force. Change in height of the wall or location of the load will also lead to a change in this value.

The effect of wall aspect ratio increase on the PT force changes can be observed in Figs. 14(a)–14(d), where the moment at base versus the PT force changes of walls S4, S5 [ 20] is presented in Figs. 14(a) and 14(b) which can be compared to walls W1 and W2 as shown in Figs. 14(c) and 14(d). Wall S4 is identical to wall W1 except for the wall height. Similarly, S5 is identical to W2 except for the height. It can be observed that increasing the wall aspect ratio has increased the decompression force. The decompression force increases in larger axial stress ration as in S4−W1 set is significantly higher than walls with lower axial stress ratio as in S5−W2 set. The rate of PT force increase is nearly similar regardless of the wall’s aspect ratio. The level of PT force in PSRW having a smaller aspect ratio (S4) is larger than that of wall W1 having a larger aspect ratio at the same drift value.

Comparing walls W2 and W3 as shown in Figs. 14(b) and 14(c), indicates that increasing the axial stress ratio in a PSRW increases the decompression force. This is mainly due to the reason that a larger lateral force is required to create a gap opening between the segments.

10 Gap opening and lateral displacement

The gap opening between the footing and bottommost segment as well as between the first two segments was measured using vertical LVDTs. The gap rotation as presented in Fig. 15 was calculated by measuring the difference between the back and front vertical LVDTs at the same level and dividing by their distance. As shown, the lateral displacement of unbonded PSRW was mostly governed by rocking, where the rotation between the first segment and the footing contributed significantly to the total rotation of the column. In a pure rocking mechanism, the rotation of the wall is expected to be equal to the wall drift value if all the gap opening happens at the wall-footing interface only. However, Fig. 15 indicates that a degree of flexural deflection, as well as gap opening between the walls’ segments, was also exhibited by the tested walls. Note that shear or sliding displacement was not observed during the tests. Thus, the lateral displacement of the tested walls was governed by the combination of rocking and flexural deformations. As shown in Fig. 15, while the largest gap opening happens between the bottom segment and footing, a much smaller level of gap opening is observed between the other segments. As shown in Fig. 15(c), the gap opening in interface 2–3 is larger than 1–2. The gap opening in the mentioned interfaces are very small in comparison to the wall-footing interface. However, the recorded minor difference in gap sizes in the interface of 2–3 which is more than 1–2 in wall W3 can be due to the higher level of damage formed in the second segment of W3 (as shown inFig. 6) which resulted in a lower stiffness and more rotation at 2–3 interface.

The gap opening between the segments and wall-footing interface in W4 with bonded PT was significantly smaller than walls with unbonded PT. Comparing the gap opening of the walls reveals that increasing axial stress ratio increased the gap opening between the second and third segment, and decreased the gap size between the first and second segment.

11 Compressive strain

Figure 16 shows the hysteretic compressive strain of the tested walls which was measured using vertical strain gauges installed on the compression and tension faces of the bottom three segments (due to instrument malfunction, results for W2 only include readings from the bottom two segments). Plastic deformation in the first segment can be observed. All compressive strains in the second and third segment in the web was elastic. Increasing wall aspect ratio and comparing the strains from S4 resulted in a smaller compressive strain on the compression face of the bottom segment. However, the second segment compressive strain increased due to an increase in aspect ratio. In a larger aspect ratio wall, the second segment reached maximum strain at larger drifts. This indicates the sudden stress transfer from the first to second segment at a 6% drift in wall W1. In the smaller wall aspect ratio, the stress increase in the second segment happened at a 4% drift in wall S4. The web at the wall with a larger aspect ratio experienced compressive strains up to 800 με compared to only 100 με for wall with smaller aspect. Increasing the aspect ratio of the wall results in more strain on the web of the wall.

Increasing the axial stress ratio reduced the compressive strain on the second segment on the compression face. Wall W2 having 0.05 axial stress ratio had 750 με on compression face of the second segment. Wall W3 having a 0.09 axial stress ratio resulted in 500 με. The opposite was correct for the first segment. Increasing axial stress ratio increased compressive strain in the first segment. Wall W2 having 0.05 axial stress ratio had 2500 με on compression face of the second segment. Wall W3 having a 0.09 axial stress ratio resulted in 2900 με. An increase in axial stress ratio due to an increase in PT force resulted in a higher compressive strain on the web as expected. As shown in Fig. 16, the compressive strains in the third segment were similar in all tests regardless of test variables reaching a maximum of 500 με except for wall W4 which had 600 με. The third segment in all tests did not have tension on concrete except wall W4. Bonding of the PT reinforcement resulted in stress transfer to the tension side of the segment and caused elongation of the tension face of the web. Similar behavior is observed in the second and first segment.

12 PSRW construction methods

PSRW retaining system can be customised for different foundation types and adjusted to have self-centring behavior by leaving the PT reinforcement unbonded or less flexible by grouting the PT reinforcement (bonded). Figure 17 presents two possible methods for the construction of PSRWs on foundation or piles.

The suggested PSRW mainly comprises three components. First are the T-shaped precast concrete segments which are post-tensioned. Second is the horizontal lightweight in-fill panels (concrete/timber) that are laid between the two post-tensioned elements. The third is the foundation which can be shallow or deep relative to site soil conditions. Alternatively, the segment can be post-tensioned to a pile as shown in Fig. 17. Lateral earth pressure is applied to the lightweight panels and transferred to the lateral force transfer system which is the post-tensioned element and consequently transferred to the foundation/pile. An in situ experimental study is required to investigate the behavior of this proposed construction method for retaining walls.

13 Summary and conclusions

This research was conducted to study the behavior of newly developed pre-stressed segmental retaining walls (PSRWs), which could be potentially used for retaining wall applications. Unlike currently available retaining systems for sea walls that are structurally rigid and mostly use cast in place construction methods, PSRW can exhibit a high level of structural flexibility based on the experimental results in this study in case of altering lateral forces like sea level rises and falls during tides and dynamic wave force which alter based on environmental conditions. PSRW is also suitable for seawall application because of using precast concrete segments (rather than pouring fresh concrete in water) and due to its accelerated construction process.

The structural stability of the system was investigated experimentally by testing four walls having high aspect ratios all consisting of precast concrete T-shaped segments. Two walls from a previous study were included for comparison purposes. The effect of axial stress ratio, wall aspect ratio and bonded versus unbonded pre-stressing were investigated. The outcomes of this investigation are summarized below and are based on these six experimentally tested PSRWs.

1) Increasing the wall aspect ratio decreased the initial and secant stiffness of the PSRW but increased the ductility.

2) An increase in the axial stress ratio in shorter walls resulted in higher lateral load capacity than taller retaining walls. This suggests a larger PT force is required for taller retaining walls.

3) The deformation of the shorter walls (S4, S5) was only due to a gap opening between the footing and bottom-most segment. However, in taller walls (W1, W2) the gap opening between the first four segments also contributed to the total deformation.

4) Damage to the wall in the shorter and taller walls was limited to the bottom segment and the two bottom segments, respectively. The plastic hinge length was about 2.5 times the depth of the section.

5) Bonded wall (W4) had significantly less gap opening in the footing interface in comparison to unbonded PSRW (W3).

6) A bi-linear hysteretic behavior was observed in the force-displacement response of the unbonded walls. However, the bonded wall (W4) did not show such a bi-linear response. The PSRW had more strength and less ductility when the PT was bonded. The gap opening in the segments interface in the bonded PT wall was significantly less than the unbonded PT walls.

The research study reported here is expected to contribute toward a better understanding of the lateral behavior of PSRWs. The effect of different parameters such as height, axial stress ratio, and PT reinforcement bonding condition investigated in this study helps to better design such retaining walls. The PSRW with a low aspect ratio is more suitable for earth retaining structures as they meet serviceability and ultimate load conditions. However, PSRWs with a larger aspect ratio is more suitable for water retaining structural systems and the self-centring capacity can result in more economical design and less capital cost due to the large ductility of the unbonded PSRWs having a large aspect ratio. Hence, unbonded PSRWs can potentially be used for the construction of water/earth retaining structures.

References

[1] WangX, WangL, ZhangT. Geometry-based assessment of levee stability and overtopping using airborne lidar altimetry: A Case Study in the Pearl River Delta, Southern China. Water (Basel), 2020, 12( 2): 403– 423

[2] FerdousW, BaiY, Almutairi A D, SatasivamS, JeskeJ. Modular assembly of water-retaining walls using GFRP hollow profiles: Components and connection performance. Composite Structures, 2018, 194 : 1– 11

[3] van der Meer R. Glass Flood Defences: A theoretical and practical assessment of the impact resistance of Glass Flood Defences to floating debris. Thesis for the Master’s Degree. Delft: Delft University of Technology, 2018

[4] Thomas R, Hall B. Seawall Design. Oxford: Butterworth-Heinemann, 2015

[5] MarcinkowskiA, GralewskiJ. The comparison of the environmental impact of steel and vinyl sheet piling: Life cycle assessment study. International Journal of Environmental Science and Technology, 2020, 17( 9): 4019– 4030

[6] Ferguson D P, Trewern C J. Design challenges associated with the use of non-metallic materials in marine sheet pile walls. In: Annual Conference of the Australasian Corrosion Association 2015: Corrosion and Prevention 2015. Adelaide: Australasian Corrosion Association (ACA), 2015

[7] Smith P. Marine Concrete Structures: Design, Durability and Performance. Amsterdam: Elsevier, 2016, 17–64

[8] SillsG L, VromanN D, WahlR E, SchwanzN T. Overview of New Orleans levee failures: Lessons learned and their impact on national levee design and assessment. Journal of Geotechnical and Geoenvironmental Engineering, 2008, 134( 5): 556– 565

[9] JansenL, KorswagenP A, BrickerJ D, PasterkampS, de BruijnK M, JonkmanS N. Experimental determination of pressure coefficients for flood loading of walls of Dutch terraced houses. Engineering Structures, 2020, 216 : 110647–

[10] Sajedi S, Sheykhloo P A, Lopez A. Design optimization of flood walls using evolutionary algorithms. In: Proceedings of Geo-Congress 2019: Earth Retaining Structures and Geosynthetics. Philadelphia: ASCE, 2019, 247–255

[11] Choudhury D, Rajesh B. Geotechnics for Natural Disaster Mitigation and Management. Singapore: Springer, 2020, 109–118

[12] NausD. The management of aging in nuclear power plant concrete structures. JOM, 2009, 61( 7): 35– 41

[13] SchupackM, SuarezM G. Some recent corrosion embrittlement failures of prestressing systems in the United States. PCI Journal, 1982, ( March–April): 38– 55

[14] Warner R F. Prestressed Concrete. Melbourne: Longman Cheshire, 1988

[15] KarayannisC G, ChaliorisC E. Design of partially prestressed concrete beams based on the cracking control provisions. Engineering Structures, 2013, 48 : 402– 416

[16] TwigdenK M, SritharanS, HenryR S. Cyclic testing of unbonded post-tensioned concrete wall systems with and without supplemental damping. Engineering Structures, 2017, 140 : 406– 420

[17] MoroderD, SmithT, DunbarA, PampaninS, BuchananA. Seismic testing of post-tensioned Pres-Lam core walls using cross laminated timber. Engineering Structures, 2018, 167 : 639– 654

[18] RabczukT, BelytschkoT. A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196( 29−30): 2777– 2799

[19] RabczukT, BelytschkoT. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61( 13): 2316– 2343

[20] JavadiM, HassanliR, RahmanM, KarimR. Experimental study on cyclic behavior of post-tensioned segmental retaining walls (PSRWs). Engineering Structures, 2021, 229 : 111619–

[21] Sika Australia Pty Ltd. SikaGrout®-300 PT AU. Product Data Sheets. 2020

[22] AS 1478.2. Chemical Admixtures for Concrete, Mortar and Grout—Part 2: Methods of Sampling and Testing Admixtures for Concrete, Mortar and Grout. Sydney: Standards Australia, 2005

[23] AS 3972. General Purpose and Blended Cements. Sydney: Standards Australia, 2010

[24] AS 1012.9. Methods of Testing Concrete Compressive Strength Tests—Concrete, Mortar and Grout Specimens. Sydney: Standards Australia, 2014

[25] ACI 374.1–05. Acceptance Criteria for Moment Frames Based on Structural Testing and Commentary. Farmington Hills: American Concrete Institute, 1991

[26] DawoodH, ElgawadyM, HewesJ. Factors affecting the seismic behavior of segmental precast bridge columns. Frontiers of Structural and Civil Engineering, 2014, 8( 4): 388– 398

[27] FEMA 356. Commentary for the Seismic Rehabilitation of Buildings. Washington, D.C.: Federal Emergency Management Agency, 2000

[28] HinesE M, RestrepoJ I, SeibleF. Force-displacement characterization of well-confined bridge piers. ACI Structural Journal, 2004, 101( 4): 537– 548

[29] WatsonS, ParkR. Simulated seismic load tests on reinforced concrete columns. Journal of Structural Engineering, 1994, 120( 6): 1825– 1849

[30] Hewes J. Seismic design and performance of precast concrete segmental bridge columns. Dissertation for the Doctoral Degree. California: University of California, San Diego, 2002

[31] MortezaeiA, RonaghH R. Plastic hinge length of FRP strengthened reinforced concrete columns subjected to both far-fault and near-fault ground motions. Scientia Iranica, 2012, 19( 6): 1365– 1378

[32] Hassanli R, ElGawady M, Mills J E. Plastic hinge length of unbonded post-tensioned masonry walls. In: The 12th North American Masonry. Denvor: The Masonry Society, 2015

[33] HassanliR, ElGawadyM, MillsJ E. Force–displacement behavior of unbonded post-tensioned concrete walls. Engineering Structures, 2016, 106 : 495– 505

[34] CamfieldF E. Wave forces on wall. Journal of Waterway, Port, Coastal, and Ocean Engineering, 1991, 117( 1): 76– 79

[35] AS 4678–2002. Earth Retaining Structures. Sydney: Standards Australia, 2001

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