ORIGINAL RESEARCH

published: 06 July 2015

doi: 10.3389/fbuil.2015.00009

Performance of rocking systems on

shallow improved sand: shaking
table testing
Angelos Tsatsis 1 and Ioannis Anastasopoulos 2 *
1
Laboratory of Soil Mechanics, School of Civil Engineering, National Technical University of Athens, Athens, Greece, 2 Division
of Civil Engineering, School of Engineering Physics and Mathematics, University of Dundee, Dundee, UK

Recent studies have highlighted the potential benefits of inelastic foundation response
during seismic shaking. According to an emerging seismic design scheme, termed
rocking isolation, the foundation is intentionally under-designed to promote rocking and
limit the inertia transmitted to the structure. Such reversal of capacity design may improve
the seismic performance, drastically increasing the safety margins. However, the benefit
comes at the expense of permanent settlement and rotation, which may threaten post-
earthquake functionality. Such undesired deformation can be maintained within tolerable
limits, provided that the safety factor against vertical loading FSV is adequately large. In
Edited by:
such a case, the response is uplifting dominated and the accumulation of settlement can
Panagiotis Mergos, be limited. However, this is not always feasible as the soil properties may not be ideal.
City University London, UK Shallow soil improvement may offer a viable solution and is therefore worth investigating.
Reviewed by: Its efficiency is related to the nature of rocking, which tends to mobilize a shallow stress
Marios Panagiotou,
University of California Berkeley, USA
bulb. To this end, a series of shaking table tests are conducted, using an idealized
Michalis F. Vassiliou, slender bridge pier as conceptual prototype. Two systems are studied, both lying on a
ETH Zürich, Switzerland
square foundation of width B. The first corresponds to a lightly loaded and the second
*Correspondence:
to a heavily loaded structure. The two systems are first tested on poor and ideal soil
Ioannis Anastasopoulos,
Division of Civil Engineering, School of conditions to demonstrate the necessity for soil improvement. Then, the efficiency of
Engineering Physics and shallow soil improvement is studied by investigating their performance on soil crusts of
Mathematics, University of Dundee,
Nethergate, Dundee DD14HN, UK depth z/B = 0.5 and 1. It is shown that a z/B = 1 dense sand crust is enough to achieve
i.anastasopoulos@dundee.ac.uk practically the same performance with the ideal case of dense sand. A shallower z/B = 0.5
improvement layer may also be considered, depending on design requirements. The
Specialty section:
This article was submitted to
efficiency of the soil improvement is ameliorated with the increase of rotation amplitude,
Earthquake Engineering, a and with the number of the cycles of the seismic motion.
section of the journal
Frontiers in Built Environment Keywords: rocking, seismic performance, soil improvement, physical modeling, shaking table

Received: 14 March 2015

Accepted: 22 June 2015
Published: 06 July 2015 Introduction
Citation: According to current seismic codes, the foundation soil is not allowed to fully mobilize its strength,
Tsatsis A and Anastasopoulos I (2015)
and plastic deformation is restricted to above-ground structural members. “Capacity” design is
Performance of rocking systems on
shallow improved sand: shaking
applied to the foundation guiding failure to the superstructure, thus, prohibiting mobilization of soil
table testing. bearing capacity, uplifting and/or sliding, or any relevant combination. However, a significant body
Front. Built Environ. 1:9. of pragmatic evidence provides robust justification that allowing strongly non-linear foundation
doi: 10.3389/fbuil.2015.00009 response is not only unavoidable but may also be advantageous (Housner, 1963; Paolucci, 1997;

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

FIGURE 1 | Conventional capacity design vs. rocking isolation. While in the first case the plastic hinge develops in the superstructure, in a rocking-isolated
system the foundation capacity is fully mobilized to protect the superstructure, at the cost of foundation rotation and settlement.

Pecker, 1998, 2003; Gazetas et al., 2003; Gajan et al., 2005; substantially improve the performance, drastically increasing the
Kawashima et al., 2007; Anastasopoulos et al., 2010a). safety margins.
Non-linear soil–foundation–structure response is simulated Yet, this benefit comes at the expense of permanent settle-
by means of (a) Winkler-based models that capture the settle- ment and rotation, which could threaten the serviceability of
ment–rotation response of the footing (Yim and Chopra, 1985; the structure. Such undesired deformation can be maintained
Nakaki and Hart, 1987; Allotey and El Naggar, 2003, 2007; Chen within tolerable limits, provided that the safety factor against static
and Lai, 2003; Houlsby et al., 2005; Harden and Hutchinson, (vertical) loads FSV is adequately large (Gajan et al., 2005). In
2006; Raychowdhury and Hutchinson, 2009); (b) sophisticated such a case, the response of the foundation is uplifting dominated,
macro-element models, where the entire soil–foundation sys- and there is no substantial accumulation of cyclic settlement. The
tem is replaced by a single element that describes the general- response is markedly different for lower values of FSV , becoming
ized force–displacement behavior of the foundation (Nova and sinking dominated: excessive soil yielding takes place underneath
Montrasio, 1991; Paolucci, 1997; Pedretti, 1998; Crémer, 2001; the foundation, leading to accumulation of substantial settlement
Crémer et al., 2001; Le Pape and Sieffert, 2001; Grange et al., and permanent rotation. Evidently, ensuring an adequately large
2008; Chatzigogos et al., 2009, 2011); and (c) finite elements FSV in order to promote uplifting-dominated response greatly
(or finite differences), modeling the superstructure, the foun- depends on the exact soil properties, which may not always be the
dation, and the soil in detail (Tan, 1990; Butterfield and Got- ones that are desired. Shallow soil improvement (a concept that
tardi, 1995; Taiebat and Carter, 2000; Gourvenec, 2007; Anas- is commonly applicable in geotechnical engineering) may offer a
tastasopoulos et al., 2010b; Anastasopoulos et al., 2011). Phys- viable solution to this problem.
ical modeling has also been applied to experimentally simulate Such a remediation technique has been introduced and exper-
non-linear soil–foundation–structure response, by means of (a) imentally investigated in Anastasopoulos et al. (2012). Based
large-scale dynamic and cyclic pushover testing, focusing on on the results of reduced-scale monotonic and cyclic pushover
non-linear soil–foundation response (Negro et al., 2000; Faccioli tests, the concept of shallow soil improvement was proven to
et al., 2001; Antonellis et al., 2015); (b) centrifuge model test- be quite effective. Its efficiency is directly related to the nature
ing, also taking account of non-linear superstructure response of foundation rocking, which tends to mobilize a shallow stress
(Kutter et al., 2003; Gajan et al., 2005; Gajan and Kutter, 2008, bulb underneath the foundation. Although cyclic pushover testing
2009); and (c) reduced-scale cyclic pushover and shaking table has offered valuable evidence, the nature of seismic shaking is
testing (Paolucci et al., 2008; Shirato et al., 2008; Drosos et al., undeniably different. To this end, this paper goes one step further,
2012). exploring the efficiency of shallow soil improvement through
In this framework, recent studies have investigated that the reduced-scale shaking table testing.
idea of exploiting inelastic foundation response in order to limit
the stresses transmitted onto the superstructure during strong Problem Definition and Experimental Setup
shaking. As schematically illustrated in Figure 1, in contrast
to conventional capacity design the foundation is deliberately A series of reduced-scale shake table tests were conducted at the
“under-designed” to promote rocking, limiting the inertia forces Laboratory of Soil Mechanics of the National Technical Univer-
transmitted onto the superstructure. The effectiveness of such sity of Athens (NTUA) to explore the efficiency of shallow soil
an alternative seismic design philosophy, termed as “rocking improvement under dynamic loading. Based on the work pre-
isolation” (Mergos and Kawashima, 2005), has been explored sented in Anastasopoulos et al. (2012), a slender rocking-isolated
analytically and experimentally for bridge piers (Anastasopoulos bridge pier of height h = 9 m supported on a surface square footing
et al., 2010a, 2013a) and frames (Gelagoti et al., 2012; Anasta- of width B = 3 m is used as a conceptual prototype. Taking account
sopoulos et al., 2013b). Such “reversal” of capacity design may of the capacity of the NTUA shaking table, a linear geometric

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

FIGURE 2 | Definition and key parameters of the studied problem (all used to represent poor soil conditions, while dense sand represents the
dimensions in model scale). Two configurations are studied: (A) a lightly reference case of ideal soil conditions. Soil improvement is materialized with a
loaded system and (B) a heavily loaded system. Loose and medium sand are shallow soil crust of dense sand, of varying depth (z/B = 0.5–1).

scale of 1:20 (n = 20) was selected for the experiments, and model removing steel plates. Sandpaper was placed underneath the foun-
properties were scaled down according to relevant scaling laws dation to achieve a realistically rough foundation–soil interface
(Muir Wood, 2004). In all cases examined, to focus on foundation (corresponding to a coefficient of friction µ ≈ 0.7). The model was
performance, the superstructure is assumed rigid and elastic. placed inside a rigid soil container, lying on an adequately deep
As schematically illustrated in Figure 2, two superstruc- sand stratum of depth d = 3B = 45 cm, and at an adequately large
ture systems are studied: (a) System A, which is representa- distance (L ≈ 5B = 75 cm) from the container walls.
tive of a lightly loaded structure having a relatively large FSV The soil consists of dry-pluviated Longstone sand. The sand,
(Figures 2A,B); and System B, being representative of a heavily characterized by a uniformity coefficient Cu = 1.42 and mean
loaded structure, characterized by a relatively low FSV . These two grain sized diameter D50 = 0.15 mm and, was pluviated using
systems were selected to model distinctly different foundation an automated sand raining system. The latter is a custom-built
performance, from uplifting-dominated (System A) to sinking- system, capable of producing sand specimens of controllable rel-
dominated response (System B). Three different soil profiles were ative density Dr , with exceptional repeatability. The properties
simulated in the experiments: (a) medium (Dr = 65%) and loose of the sand have been measured through laboratory tests, also
(Dr = 45%) sand for System A and System B, respectively, repre- conducted at NTUA, and are documented in Anastastasopoulos
senting poor soil conditions; (b) soil improvement by means of a et al. (2010b). In reduced-scale testing, the stress field in the soil
shallow “crust” of dense sand, of varying depth z/B = 0.5–1; and cannot be reproduced correctly. Given the fact that the strength of
(c) the reference case of dense (Dr = 93%) sand, representing ideal the sand is stress dependent, the reduced effective stresses in the
soil conditions. model unavoidably lead to an increase of the mobilized friction
angle φ (compared to the prototype). Such scale effects can only
Physical Modeling be avoided through centrifuge modeling, and should be carefully
The physical model consists of a square B = 15 cm aluminum foot- contemplated when interpreting 1 g test results. Even though,
ing, rigidly connected to a pair of rigid steel columns. The latter in the case of the investigated problem, the stresses due to the
support a rigid aluminum slab, positioned at height h = 45 cm superstructure dead load are prevailing, minimizing the adverse
above the foundation level. The superstructure mass is composed role of scale effects.
of a number of steel plates, installed symmetrically above and Even though, aiming to avoid scaling-related misinterpreta-
below the aluminum slab, so as to maintain the center of mass at tions, a series of vertical push tests were conducted to measure the
the same level. The mass of the model was adjusted by adding or bearing capacity of the B = 15 cm square foundation for all soil

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

TABLE 1 | Summary of monotonic vertical loading.

System A System B

Configuration Nult (kN) FSV Configuration Nult (kN) FSV

Poor soil conditions Loose sand (Dr = 45%) 1.7 5 Medium sand (Dr = 65%) 2.5 2.5
Soil improvement z/B = 0.5 on top of loose sand 2.4 7 z/B = 0.5 on top of medium sand 3 3
z/B = 1 on top of loose sand 3.4 10 z/B = 1 on top of medium sand 3.9 4
Ideal soil conditions Dense sand (Dr = 93%) 4.8 14 Dense sand (Dr = 93%) 4.8 5

FIGURE 3 | Summary of monotonic pushover test results for the systems studied herein: moment–rotation (M–ϑ) and settlement–rotation (w–ϑ)
response as a function of soil conditions for (A) the lightly loaded System A and (B) the heavily loaded System B.

conditions examined. Based on the results of these tests, which stated, all results are discussed in prototype scale). Considering
are summarized in Table 1, the mass of the two superstructure the dynamic response, a critical acceleration ac can be defined
models was adjusted to produce the desired FSV for the reference as the maximum acceleration that can develop at the mass of
case of ideal soil conditions (i.e., for dense sand): FSV = 14 for the the oscillator (representing the bridge deck). For rocking-isolated
lightly loaded System A (materialized using a mass of 35 kg), and systems, such as those examined herein, ac is bounded by the
FSV = 5 for the heavily loaded System B (materialized using a mass moment capacity of the foundation, and can be defined as follows:
of 100 kg).
ac = Mmax /mgh (1)
Summary of Monotonic Response
Before proceeding to the testing sequence, a brief discussion of Based on the above, System A founded on poor soil is character-
the monotonic response of the studied systems is necessary. A ized by a critical acceleration ac = 0.072 g. The moment capacity is
detailed description of the pushover tests and their key results can substantially increased for the case of shallow soil improvement,
be found in Anastasopoulos et al. (2012). Figure 3 summarizes the leading to a proportional increase of the critical acceleration to
moment–rotation (µ–θ) and settlement–rotation (w–θ) response ac = 0.117 g for z/B = 0.5 and ac = 0.130 g for a deeper z/B = 1
of the two systems founded on the four different soil profiles. dense sand crust. The latter is still lower than the one for ideal soil
In the case of the lightly loaded System A (Figure 3A), when conditions, ac = 0.162 g, but the efficiency of the improvement is
founded on poor soil conditions (i.e., loose sand) its maximum evident. Likewise, for the heavily loaded System B (Figure 3B),
moment capacity reaches M max = 1.8 MN/m (unless otherwise the footing on poor soil conditions has a moment capacity

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

TABLE 2 | Summary of monotonic pushover loading.

FSV Mmax ac (g) K initial T initial (s)

(MN/m) (MN/m)

System A: Lightly Loaded

Loose sand (Dr = 45%) 5 1.8 0.072 7 1.21
z/B = 0.5 7 2.9 0.117 13 0.92
z/B = 1 10 3.2 0.130 20 0.75
Dense sand 14 4 0.162 26 0.66
System B: Heavily Loaded
Medium sand (Dr = 65%) 2.5 4.2 0.060 30 1.03
z/B = 0.5 3 4.5 0.065 33 0.98
z/B = 1 4 5.9 0.085 40 0.89
Dense sand 5 6.7 0.095 45 0.84

M max = 4.2 MN/m, which translates to ac = 0.065 g. Applying a

layer of improved soil of depth z/B = 0.5, the critical accelera-
tion increases only slightly to ac = 0.065 g (M max = 4.5 MN/m). A
deeper z/B = 1 soil crust is required to attain a substantial increase
of the critical acceleration to ac = 0.085 g. The latter is only slightly
lower than for ideal soil conditions (ac = 0.095 g), confirming
the efficiency of shallow soil improvement in this case also. It is
worth mentioning that an excitation with acceleration exceeding
the critical acceleration of the systems does not necessarily mean
collapse; the structure will topple only when the imposed rotation
of the footing is larger than the maximum rotation as shown in the
M–θ curves.
Most importantly, in both cases shallow soil improvement leads
to a substantial reduction of the tendency for accumulation of
settlement. As evidenced by the w–θ response, in both cases,
the application of shallow soil improvement tends to suppress
the sinking behavior of the foundation. For the lightly loaded
System A in particular, a z/B = 1 soil crust is sufficient to achieve
almost the same w–θ response with the reference case of ideal
FIGURE 4 | Photos showing the instrumentation.
soil condition (dense sand), while an even shallower z/B = 0.5
crust is also quite effective. This has been confirmed by the slow-
cyclic tests, which can be found in Anastasopoulos et al. (2012).
On the other hand, for the heavily loaded System B, a z/B = 0.5 locations, on the model (on the foundation and at mass level), and
soil crust is clearly not enough: the response is improved but embedded within the soil at 5 cm depth: one directly underneath
remains sinking-dominated. A deeper z/B = 1 soil improvement the foundation and another one at a distance, where free-field
is needed to ensure uplifting-dominated response. Indeed, in this conditions are restored. In addition, visual data were obtained
case, the w–θ response becomes almost identical to the case of using high-definition cameras, recording both the response of the
ideal soil conditions (dense sand). The performance of the tested entire system, and the response of the foundation (settlement,
configurations is summarized in Table 2. uplift, sliding) from a closer view from behind.
The different configurations were subjected to shaking table
Instrumentation and Testing Sequence testing, using a variety of real seismic records and artificial
The model was instrumented to allow direct recording of trans- motions as base excitation (Figure 5). The selected seismic
√
lational and rotational deformations, and lateral accelerations. As motions were scaled down in time (divided by n) accord-
shown in the photos of Figure 4, wire (WDT) and laser displace- ing to the relevant scaling laws. Three different seismic shaking
ment transducers (LDTs) were utilized to measure horizontal and sequences were imposed, as summarized in Table 3. They consist
vertical displacements. of artificial motions (sinusoidal excitations) or real records, or a
Two LDTs were used to measure the sliding displacement of combination of the two. In all cases examined, the PGA of the
the footing, while two WDTs were used to record the horizontal seismic excitations was well beyond the critical acceleration of
displacement of the oscillator mass. Four additional WDTs were the tested systems (progressively increasing). This was done to
used to measure the vertical displacement at the four corners of force the systems to behave strongly non-linear in order to explore
the mass, in order to measure the rotation and the settlement of their response in the plastic (after yielding) as well as in their
the physical model in both directions (the direction of loading and metaplastic regime (after peak conditions are reached and the
the transverse). Accelerometers were installed at characteristic resistance of the footing decreases due to P–δ effects).

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

FIGURE 5 | Real records and artificial motions used as seismic “bedrock” excitations in the shaking table tests, (A) the acceleration time histories of
the excitations, (B) the elastic acceleration, and (C) displacement response spectra for 5% viscous damping ratio.

Seismic Performance of the Truly Dynamic vs. Slow-Cyclic Response

Lightly-Loaded System A In terms of monotonic and slow-cyclic pushover response, shal-
low soil improvement was proven to be quite effective (Anasta-
System A was subjected to the seismic excitation sequences I and sopoulos et al., 2012). Figure 6 summarizes the results of such
II. As discussed later on, sequence III was used for System B only. testing, depicting the settlement per cycle wc as a function of
In this section, selected results are presented for the lightly loaded the imposed cyclic rotation amplitude θc . Although this section
System A, aiming to gain insight of the main features affecting its focuses on the lightly loaded System A, the results for System B
seismic performance and to assess the effectiveness of shallow soil are also presented for completeness. For both systems, a z/B = 1
improvement under truly dynamic conditions. dense sand crust is proven enough to achieve practically the same

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

performance as the ideal case of dense sand. For the shallower discussed, ac ranges from 0.072 g for poor soil to 0.15 g for ideal
z/B = 0.5 soil improvement layer, the cyclic settlement reduc- conditions). To make things worse, due to soil amplification the
tion is quite evident, but the response differs substantially from maximum acceleration measured at the free field reaches 0.58 g
the ideal case of dense sand for both systems. Even though, (Figure 7A). As a result, the response of the system is highly non-
a shallower z/B = 0.5 soil improvement layer may be adequate, linear for all cases examined. As shown in Figure 7B, the strong
depending on design requirements. The efficiency of shallow motion pulse of the Aegion record leads to a maximum rotation
soil improvement is ameliorated with the increase in the cyclic θmax of roughly 0.01 rad, which is not particularly sensitive to
rotation amplitude, especially in the case of the lightly loaded the soil conditions. Naturally, θmax is slightly larger for poor
system A. soil conditions (loose sand), but the differences are practically
Figure 7 summarizes the performance of the lightly loaded negligible. A simplified explanation for this can be derived using
system subjected to the Aegion seismic excitation. Although the an equivalent linear approach: the initial natural period of the
record of the 1995 Ms 6.2 Aegion (Greece) earthquake is consid- four systems that ranges between 0.66 s for the system lying on
ered as a moderate intensity seismic excitation, it does contain a dense sand and 1.21 s for the one lying on loose sand increases
single strong motion pulse of 0.39 g, which is well above the critical substantially with the non-linear response of the rocking footing,
acceleration ac of System A for all cases considered (as previously yielding effecting periods that correspond to substantially dimin-
ished spectral accelerations in the area of the spectrum where the
differences in the stiffness of the soil deposit or in the effective
TABLE 3 | The tree seismic shaking sequences of the shaking table tests. damping ratio do not alter the response significantly. The imposed
rotation is irrecoverable when the system is founded on loose
Sequence I Sequence II Sequence III sand, with the residual rotation θres being almost the same as θmax .
This is not the case for ideal soil conditions (dense sand), where
Excitation PGA (g) Excitation PGA (g) Excitation PGA (g)
θres is practically 0: the system returns to each original position.
sin 2 Hz 0.2 Aegion 0.39 sin 2 Hz 0.1 Shallow soil improvement proves quite effective in reducing the
sin 2 Hz 0.4 Kalamata 0.4 sin 2 Hz 0.15 residual rotation, with the deeper z/B = 1 crust being advanta-
sin 1 Hz 0.2 Lefkada 2003 0.2 sin 2 Hz 0.2 geous: θres = 0.002 rad as opposed to 0.0025 rad of the shallower
sin 1 Hz 0.4 JMA 0.4 sin 2 Hz 0.25
Pacoima Dam 1.25 Rinaldi 1.14 sin 2 Hz 0.3
z/B = 0.5 crust.
Sakarya 0.36 Takatori 0.36 sin 2 Hz 0.35 As expected, under such strongly non-linear foundation
Lefkada 2003 0.43 sin 2 Hz 0.4 response the rocking system accumulates dynamic settlement. As

FIGURE 6 | Slow-cyclic pushover tests results. Settlement per cycle wc as a function of cyclic rotation amplitude ϑ (A) lightly loaded System A and (B) heavily
loaded System B.

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

FIGURE 7 | Seismic performance of the lightly loaded System Time histories of (A) free field and base excitation, (B) foundation
A subjected to moderate seismic shaking using the Aegion rotation, and (C) settlement. An extract from Figure 6A (bottom
record as excitation–comparison of shallow soil improvement right) is also shown to allow direct comparison with the cyclic
with poor (loose sand) and ideal (dense sand) soil conditions. pushover tests.

shown in Figure 7C, shallow soil improvement is quite effective 1.5 cm), the efficiency of shallow soil improvement is undeniable.
in reducing the accumulated settlement. It should be noted that Observe that the larger part of the accumulated settlement is due
the settlement shown in this figure as well as in all the respective to the single strong motion pulse of the Aegion record. In the case
figures in the ensuing, corresponds to the total settlement of the of loose sand, 8.5 out of 12 cm of the total accumulated settlement
footing, while the settlement of the free field is omitted. This take place during this pulse. The same applies to the remaining
is done because the instrument used to measure the settlement configurations, with most of the settlement taking place during
of the free field malfunctioned during some of the tests, and a that single pulse: 5.5 out of 7 cm for the z/B = 0.5 crust; 4 out of
meaningful comparison would not be possible. However, for the 5 cm for the z/B = 1 crust; and 1 out of 1.5 cm for the case of ideal
cases where it was measured, the free field settlement proved to conditions.
be minor compared to the settlement of the footing. For exam- With the response being so straight forward, it is interest-
ple, for the lightly loaded system lying on the shallower crust ing to compare the results of the shake table tests to what
and subjected to a sinusoidal excitation of frequency 2 Hz and would be expected on the basis of the cyclic pushover tests.
amplitude 0.4 g, one of the most adverse motions, the measured Going back to Figure 6A (an extract of which is reproduced
free field settlement was 6.6 cm compared to the 39.2 cm for the in Figure 7 to allow direct comparisons), for cyclic rotation
footing. When founded on poor soil conditions (loose sand), the θc = θmax ≈ 0.01 rad, the system on loose sand would accumu-
settlement reaches 12 cm. Applying shallow soil improvement of late cyclic settlement wc = 2.6 cm, while as we saw under truly
depth z/B = 0.5, the accumulated settlement is reduced to 7 cm, dynamic loading it actually accumulates wdyn = 8.5 cm. Similarly,
while a deeper z/B = 1 soil crust leads to further reduction of the in the case of the z/B = 0.5 shallow soil improvement, the system
settlement to 5 cm. Although such a value is substantially larger settles wdyn = 5.5 cm as opposed to the wc = 1.7 cm, and the same
than the dynamic settlement under ideal soil conditions (merely applies to the z/B = 1 (wdyn = 4 cm as opposed to wc = 1 cm)

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

FIGURE 8 | Seismic performance of the lightly loaded System Time histories of (A) free field and base excitation, (B) foundation
A subjected to seismic shaking using the Pacoima dam rotation, and (C) settlement. An extract from Figure 6A (bottom
record as excitation–comparison of shallow soil improvement right) is also shown to allow direct comparison with the cyclic
with poor (loose sand) and ideal (dense sand) soil conditions. pushover tests.

and to the ideal case of dense sand (wdyn = 1 cm as opposed to differences are much lower: wdyn –wc = 0.4 cm. Things are slightly
wc = 0.6 cm). Hence, although qualitatively the shake table tests more complicated in the case of shallow soil improvement. While
confirm the findings of the slow-cyclic pushover tests, from a the dense sand crust should not be prone to such effects, under-
quantitative point of view, there are very substantial differences. neath there is still loose sand, which will settle due to dynamic
These differences can only be attributed to the dynamic response compaction. Naturally, the depth of the loose sand layer is reduced
of the soil, which cannot possibly be captured through cyclic with the increase of the depth of the improvement crust: from
loading. Under dynamic loading, the deformation of the soil 3B in the case of loose sand, to 2.5B for z/B = 0.5, and to 2B
underneath the footing is not only due to the stresses imposed for z/B = 1. Since the amount of soil compaction is proportion-
by the rocking foundation (inertia loading) but is also affected by ate to the depth of the loose sand layer, there should be an
the shear stresses that develop within the soil due to the seismic analogy here as well. Starting from the previously mentioned
shaking itself (kinematic loading). Even in the absence of a rocking values for loose sand (wdyn –wc = 5.9 cm), the expected values for
foundation, due to the developing shear stresses within the soil z/B = 0.5 and z/B = 1 should be 5 cm (=6 cm × 2.5B/3B) and 4 cm
(kinematic loading), the sand would settle: dynamic compaction. (=6 cm × 2B/3B), respectively. The experimental results verify the
However, compared to the free field where the soil is compacted above simplified approach with minor divergence: the difference
under 0 normal stress at the surface, the soil underneath the between the dynamic settlement and the respective predicted by
footing is compacted under the weight of the footing, leading thus the slow-cyclic pushover tests is 3.8 cm for the case of z/B = 0.5
to increased settlements. and 3 cm for the z/B = 1, with the small difference attributed to the
Such dynamic compaction proves to be quite intense for the fact that the two mechanisms that lead to footing settlement (rock-
case of loose (Dr = 45%) sand: wdyn –wc = 5.9 cm. In the case ing of the footing and dynamic compaction of the soil deposit
of dense (Dr = 93%) sand, such effects are suppressed and the under the weight of the footing) act simultaneously and therefore

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

FIGURE 9 | The effect of excitation frequency on the efficiency of using two 15-cylce sinusoidal excitations of frequency f = 2 Hz (left) and
shallow soil improvement. Comparison of shallow soil improvement with ideal f = 1 Hz (right). Time histories of (A) free field and base excitation, (B) foundation
soil conditions for the lightly loaded System A subjected to seismic shaking rotation, and (C) settlement.

are coupled resulting in less settlement than if they were acting confirming the efficiency of the z/B = 1 shallow soil improvement
separately. Nonetheless, the results confirm that the differences in terms of survivability. The remaining discussion will focus on
in the response (compared to cyclic loading) are due to dynamic the two systems that did not collapse.
compaction of the underlying loose sand. The response can roughly be divided in two phases. In the first
phase, which approximately lasts from t = 3 to 6 s, the previously
The Effect of Excitation Frequency mentioned strong directivity pulse dominates the response. With
The performance of System A subjected to more intense seismic a very large period T ≈ 1.2 s, this pulse drives both systems well
shaking, using as seismic excitation the Pacoima Dam record from within their metaplastic regime, developing a maximum rota-
the 1971 San Fernando earthquake, is summarized in Figure 8. tion θ ≈ 0.04 rad (Figure 8B). The second phase (for t > 6 s) is
In contrast to previous seismic excitation (Aegion), the Pacoima characterized by a multitude of strong motion cycles of even
Dam record is definitely a very strong seismic record. Apart from larger amplitude (up to 1.25 g) but of substantially smaller period,
its impressive PGA of 1.25 g, this record is characterized by a long ranging from 0.1 to 0.4 s. As revealed by the free field acceleration
duration (and hence, low frequency) directivity pulse, having an measurements (Figure 8A), due to soil amplification, there are
amplitude of 0.6 g (see the shaded area in Figure 8A). Given the three acceleration peaks in excess of 1 g, with one of them reach-
previously discussed critical acceleration of the system on loose ing a PGA of 1.8 g. Under such unrealistically extreme seismic
sand, merely ac = 0.072 g collapse should have been expected, and excitation, either on dense sand or on z/B = 1 soil improvement,
this is exactly what happened. The same applies to the z/B = 0.5 the rocking system survives. Although the differences in θmax are
crust. The system managed to survive such strong shaking only again negligible, there is a substantial difference in θres = 0.045 rad
when founded on dense sand, or in the case of the deeper z/B = 1 for the case of z/B = 1 soil improvement, compared to 0.012 rad for
soil improvement. This alone is a very important conclusion, ideal soil conditions.

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

FIGURE 10 | The effect of the number of strong motion cycles on the Foundation settlement per cycle for our different sinusoidal excitations:
efficiency of shallow soil improvement. Comparison of shallow soil (A) f = 2 Hz, a = 0.2 g; (B) f = 2 Hz, a = 0.4 g; (C) f = 1 Hz, a = 0.2 g; and
improvement with poor and ideal soil conditions for the lightly loaded System A. (D) f = 1 Hz, a = 0.4 g.

In terms of settlement accumulation, the response is distinctly for the previous case, an extract from Figure 6A is included in
different during the two phases of the response. As illustrated in Figure 8 to facilitate the comparison. Focusing on the first phase
Figure 8C, during the long period directivity pulse (phase 1), the of response, for a cyclic rotation θc = θmax ≈ 0.04 rad, the system
settlement is minimal in both cases. In fact, the rocking system would accumulate cyclic settlement wc = 0.7 cm and 0.85 cm, in
is mainly subjected to uplifting and the accumulated settlement the case dense sand and z/B = 1 soil improvement, respectively.
at t = 6 s does not exceed 1 cm. During this phase of response, In the shaking table tests, the dynamic settlement during the first
the z/B = 1 crust is proven very effective, exhibiting practically phase is quite similar, not exceeding wdyn ≈ 1 cm. The differences
identical behavior to that of the ideal case of dense sand. The are much larger during the second phase of response, with the final
performance is markedly different during the second phase, which accumulated dynamic settlement reaching 8 cm under ideal soil
is characterized by a multitude of strong motion cycles of larger conditions and almost 12 cm in the case of shallow soil improve-
amplitude but of much higher frequency. The settlement mainly ment. In both cases, the magnitude of the accumulated settlement
takes place during this second phase, with the accumulated set- is larger than what would have been predicted on the basis of the
tlement reaching 8 cm for dense sand and 12 cm in the case of cyclic pushover test results. The reasons are the same with those
the z/B = 1 soil crust. It is worth reminding that the above values previously discussed, but the accumulation of settlement and the
refer to the prototype structure. The correct scaling of both the efficiency of shallow soil improvement are clearly affected by the
structure (by 20 times) and of the frequency of the excitation excitation frequency.
(by 4.5 times) assure the similitude in the settlement between the To further clarify the role of excitation frequency, two idealized
prototype problem and the model. Although such scaling is not 15-cylce sinusoidal motions with a PGA of 0.2 g are used, with
perfect in 1 g testing, it is the best that can be done and this is gen- the only difference being the frequency: f = 1 and 2 Hz. Figure 9
erally accepted in such procedures. Even though, the settlement compares the performance of the two cases of soil improvement
may be affected by scale effects, as recently shown in Kokkali et al. with the ideal case of dense sand. Although the acceleration is
(2015), where we compared 1 g with centrifuge model testing. The exactly the same (Figure 9A), the “slower” f = 1 Hz excitation
comparison indicates that the cyclic foundation settlement in 1 g will develop larger (theoretically double) ground displacement
testing is over-estimated. Due to the incorrect scaling of geostatic compared to the “faster” f = 2 Hz sinus. And since the rotation of
stresses, the strength and the dilative behavior of the sand are over- the rocking system depends largely on the ground displacement,
estimated, but the shear stiffness is under-estimated. And under the f = 1 Hz excitation should produce larger rotation. Indeed,
cyclic loading, this leads to larger foundation settlement. This is a as shown in the rotation time histories (Figure 9B), the rotation
limitation of the presented work that should be clearly spelled out. amplitude per cycle of the systems subjected to the f = 1 Hz sinu-
Let us now compare the results of the shake table tests to soidal excitation is approximately double the respective rotation
the “prediction” on the basis of the cyclic pushover tests. As when the systems are subjected to the f = 2 Hz excitation.

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

FIGURE 11 | Synopsis of the performance of the lightly loaded System A subjected to seismic shaking sequences I and II. Settlement w (left) and residual
rotation ϑ res (right) as a function of PGA: (A) loose sand-poor soil conditions; (B) z/B = 0.5; (C) z/B = 1; and (D) dense sand-ideal soil conditions.

Figure 9C compares the settlement for the two excitation fre- slightly lower (2 cm) for the lower frequency f = 1 Hz excitation.
quencies. In the case of dense sand, the settlement is not par- This is in accord with the cyclic pushover test results, accord-
ticularly sensitive to the excitation frequency. The settlement w ing to which the cyclic settlement of System A on dense sand
reaches 2.5 cm for the high-frequency f = 2 Hz sine, being only remains practically constant for 0.003 < θc < 0.03 rad. The small

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

FIGURE 12 | Synopsis of the performance of the lightly loaded System A subjected to seismic shaking sequences I and II. Maximum acceleration amax at
the oscillator mass as a function of PGA: (A) loose sand-poor soil conditions; (B) z/B = 0.5; (C) z/B = 1; and (D) dense sand-ideal soil conditions.

difference is possibly related to a limited amount of dynamic excitation frequency or amplitude, the settlement per cycle of
compaction, which mainly affected the f = 2 Hz sine, which was motion reduces with the number of cycles, thanks to soil densi-
the first excitation in this seismic shaking sequence (see also fication underneath the footing.
Table 3). For the two high-frequency (f = 2 Hz) excitations, the rate of
The differences are much more pronounced for the two cases settlement δw is reduced almost linearly with the number of
of shallow soil improvement. In both cases (i.e., z/B = 0.5 and 1.0), strong motion cycles. Quite interestingly, the decrease of δw is
the accumulated settlement is much larger for the high-frequency much more intense when the frequency of excitation is lower
f = 2 Hz excitation: roughly two times larger than for the low- (f = 1 Hz). In this case, the first two or three cycles are enough to
frequency f = 1 Hz sine. This very substantial difference can not cause substantial dynamic compaction of the soil, and as a result,
only be solely attributed to dynamic compaction of the underlying the remaining strong motion cycles are not leading to any substan-
loose sand but is also related to the dependence of the efficiency tial additional settlement. As previously discussed, the oscillation
of shallow soil improvement on cyclic rotation. In agreement with of the lightly loaded system is of significantly larger amplitude for
the results of monotonic and cyclic pushover tests, the efficiency of the low-frequency sinusoidal excitation, and therefore, the first
the crust is found to increase with rotation (the amplitude of θ for two or three cycles of large rotational amplitude are enough to
f = 1 Hz is almost twice as much for f = 2 Hz). While for smaller compact the sand under the footing. On the contrary, the sand
rotation the foundation is in full contact with the supporting is continuously compacted due to small vibrations of the footing
soil, generating a deeper stress bulb, and hence, being affected when the system is subjected to the f = 2 Hz sinusoidal excita-
by the underlying loose sand layer, when uplifting is initiated tion. Moreover, the decreasing trend of settlement accumulation
the effective foundation width is drastically decreased, reducing should also be attributed to the rotation accumulation of the
the depth of the generated stress bulb. Hence, a larger portion systems; as the systems unavoidably accumulate rotation toward
of the rocking-induced stresses are obtained by the “healthy” soil the one side, they do not execute a symmetric cycle of rotation
material of the crust, improving the performance of the system. rather, they tend to tilt even more. Since settlement development is
correlated with the compaction of the sand as the structure returns
The Effect of the Number of the Cycles to its initial position, it is reasonable to assume that settlement
Apart from rotation, the efficiency of shallow soil improvement accumulation is also affected by the rotation accumulation.
is also ameliorated with the number of strong motion cycles.
Figure 10 summarizes the results of seismic shaking sequence I, Synopsis and Discussion
presenting the dynamic settlement w per cycle of motion with Figure 11 summarizes the performance of the lightly loaded Sys-
respect to the number of cycles, and as a function of excitation tem A subjected to shaking sequences I and II in terms of settle-
frequency and amplitude. In all cases examined, irrespective of ment w and residual rotation θres as a function of PGA. Although

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

FIGURE 13 | Synopsis of the performance of the heavily loaded System free field); and (C) maximum acceleration amax at the oscillator mass as
B subjected to seismic shaking sequence III: (A) residual rotation ϑ res ; a function of PGA and comparison with the critical acceleration ac ,
(B) settlement w as a function of the excitation PGA (measured at the computed on the basis of the monotonic pushover tests.

the excitations were imposed in a sequence (i.e., one after the of PGA up to 1.1 g without toppling. Observe that the resid-
other), the results presented herein refer to values recorded during ual rotation θres is reduced by almost 50% compared to the
each excitation (not the cumulative ones). Therefore, the results untreated case of loose sand. However, the settlement w is not
are not to be considered representative of the performance of reduced to the same extent, and the system still topples in 7 out
the system subjected to each excitation separately, but rather in of 12 seismic excitations. A deeper z/B = 1 dense sand crust is
a comparative manner in order to assess the efficiency of shallow required to decrease the settlement substantially (Figure 11C).
soil improvement. In this case, the performance is practically the same with that
As vividly shown in Figure 11A, when the system is founded of the ideal case of dense sand (Figure 11D), confirming the
on loose sand (representative of poor soil conditions), it can efficiency of shallow soil improvement with a z/B = 1 dense sand
only sustain 3 out of 12 seismic excitations (considering both crust.
shaking sequences). Even for these three excitations, the settle- The main scope of rocking isolation is the reduction of the iner-
ment is quite substantial (in excess of 10 cm). The improvement tia transmitted onto the superstructure. It is therefore critical to
is quite evident for shallow soil improvement of depth z/B = 0.5 ensure that shallow soil improvement is not canceling the isolation
(Figure 11B). The system is able to withstand seismic excitations effect. This is confirmed Figure 12, where the acceleration amax at

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

FIGURE 14 | Attenuation due to strongly non-linear soil–structure illustrative example, focusing on two excitations with PGA = 0.2 and 0.25 g:
interaction for heavily loaded system B subjected to shaking sequence (A) force–displacement (P–δ) response; (B) expected spectral acceleration SA
III. The performance of the system on z/B = 1 soil improvement is shown as an as a function of effective period T; and (C) summary.

the oscillator mass (representing the bridge deck) is plotted as a shaking sequence III, which is composed of sinusoidal excitations
function of the PGA of the seismic excitation (measured in the of frequency f = 2 Hz of increasing PGA (from 0.1 to 0.4 g). This
free field). The results of the shake table tests are also compared different shaking sequence was used as the much lower capacity of
with the previously discussed critical acceleration ac , computed System B did not allow shaking with the much harsher excitations
on the basis of the results of monotonic (static) pushover tests. of the other two sequences.
In all cases examined, during the dynamic loading the footing Figure 13 summarizes the performance of System B founded
exhibits a certain degree of overstrength (amax > ac ). In fact, this on the four different soil profiles (loose sand, z/B = 0.5 and 1
overstrength is more significant as the FSV value decreases. As a soil improvement, and dense sand), focusing on the residual
result, when the system is founded on loose sand the recorded rotation θres (Figure 13A) and settlement w (Figure 13B). Evi-
maximum acceleration is amax = 0.1 g (on average) as opposed dently, the heavily loaded system lying on loose sand is quite
to ac = 0.072 g: an overstrength of roughly 30%. In the case of unstable, accumulating rather substantial rotation and settle-
z/B = 0.5 shallow soil improvement, the overstrength is reduced ment even for relatively low levels of PGA, and toppling for
but still quite substantial: amax = 0.14 g as opposed to ac = 0.117 g, PGA = 0.4 g. In terms of residual rotation, the performance is
20% of overstrength. Further increase of the depth of the improve- improved rather spectacularly with shallow soil improvement,
ment layer to z/B = 1 leads to further reduction of the overstrength even for z/B = 0.5 (Figure 13A). For PGA < 0.4 g, the perfor-
to 12% (amax = 0.155 g while ac = 0.13 g), with the ideal case of mance is almost identical to the ideal case of dense sand. However,
dense sand (in which case FSV = 14) exhibiting minor, if any, in the case of the shallower z/B = 0.5 soil crust, System B topples
overstrength. These conclusions are in full agreement with the for PGA = 0.5 g. Further increase of the improvement depth to
results of slow-cyclic pushover tests (Anastasopoulos et al., 2012). z/B = 1 leads to a much more stable performance, and almost
The increased maximum measured accelerations could also be identical response with the ideal case of dense sand, even for the
correlated with oscillations due to impact, a phenomenon dis- maximum imposed PGA.
cussed by various researchers [Chopra and Yim (1985) and Acik- In terms of settlement (Figure 13B), the deeper z/B = 1 soil
goz and DeJong (2012, 2013) among others]. However, in the cases improvement leads to a substantial improvement. A more shallow
examined herein, the acceleration time histories recorded at the z/B = 0.5 crust is not as effective. Quite interestingly, up to a PGA
superstructure revealed no high-frequency oscillations that could of 0.2 g the system on z/B = 0.5 soil improvement settles almost
be related to impact. This is expected since the systems rock on the same as the one on loose sand. The efficiency of the crust
compliant soil rather than a rigid base. starts improving for larger acceleration amplitudes, when uplifting
starts to dominate the response, but soon after that the system
Seismic Performance of the collapses. Based on this result, it may safely be argued that such
Heavily-Loaded System B a shallow z/B = 0.5 improvement is not enough for such heavily
loaded systems. On the other hand, the deeper z/B = 1 soil crust
In this section, the seismic performance of the heavily loaded proves quite effective, with the settlement being roughly 25%
System B is discussed. In this case, the system is subjected to larger compared to the ideal case of dense sand.

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

FIGURE 15 | The effect of “de-amplification” due to strongly non-linear SSI. Time histories of rotation ϑ and settlement w for all soil profiles examined,
subjected to an f = 2 Hz sine of PGA = 0.2 g. Comparison of (A) lightly loaded System A; with (B) heavily loaded System B.

Figure 13C compares the performance in terms of maximum although the ultimate capacity is not reached, largely non-linear
acceleration measured at the oscillator mass (representing the soil–structure interaction (SSI) takes place, leading to a rather
deck) as a function of PGA of the excitation (measured at the soil intense attenuation of the seismic motion for all four soil profiles
surface, in the free field). In stark contrast to the lightly loaded examined.
System A, where overstrength was apparent, the measured acceler- Figure 14 attempts to shed more light to such effects, using
ations amax are much lower than the corresponding critical accel- the case of z/B = 1 soil improvement as an illustrative example
eration ac . The fact that for all four soil profiles amax increases with and focusing on two sinusoidal excitations having a PGA of
the excitation PGA is attributed to soil densification and to the fact 0.2 and 0.25 g. For these two seismic excitations, the maximum
that the pier is gradually tilting toward the one side resulting to measured acceleration at the oscillator mass is 0.073 and 0.078 g,
increased amax on the opposite side. Quite interestingly, although respectively – in both cases, lower than the critical acceleration
System B is not reaching its ultimate moment capacity (since amax ac = 0.085 g (based on the results of monotonic pushover tests).
is lower than the corresponding ac ), the response is profoundly Figure 14A illustrates the force–displacement (P–δ) response for
non-linear as revealed by the accumulation of rotation in all cases the two cases examined, focusing on the steady state oscillation
examined (see Figure 13B). It may therefore be concluded that, (i.e., after the first two to three cycles of motion). Although the

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

ultimate capacity of the footing is not reached, the response is density in the case of the lightly loaded system (Dr = 45% as
highly non-linear. Based on the illustrated loops, a very high opposed to 60%). Even though, these two factors alone cannot
hysteretic damping ratio ξ can be calculated, ranging between 40 fully explain the difference in settlement.
and 45% for PGA = 0.2 and 0.25 g, respectively. Such non-linear This counter-intuitive behavior is easily explainable consid-
response unavoidably leads to a decrease of the effective stiffness ering the effects of the previously discussed “de-amplification.”
K eff of the system, and to an increase of its effective period T eff . Observe the rotation time histories of Figure 15B that the lightly
Figure 14B presents the acceleration response spectra of the loaded systems are rocking with maximum rotation θ = 0.003 rad
measured free field acceleration at the ground surface (which is (on average), while the heavily loaded systems are experiencing
considered as the input to the rocking system) for the two exci- lower θ = 0.002 rad (on average). Although the seismic excitation
tations under consideration, accounting for the damping ratios ξ is the same, being much stiffer, the lightly loaded system is excited
that have been calculated from the respective load–displacement much more: its lower natural period is closer to the dominant
loops. Based on the results of the monotonic pushover tests, period of the seismic excitation. In stark contrast, the heavily
the initial stiffness (i.e., for very small strains) of the system is loaded system is much more flexible to start with, and becomes
K o = 40 MN/m. Hence, accounting for quasi-elastic SSI (there is even more flexible as soon as it starts responding non-linearly.
always some non-linearity, even before initiation of seismic shak- As previously discussed, due to such non-linear SSI, significant
ing), the initial natural period of the rocking system is T o = 0.89 s. degradation of the system’s effective stiffness takes place, leading
Quite strikingly, when non-linear SSI is considered, the effective to a substantial increase of its effective period, which in turn leads
stiffness of the system drops to K eff = 24 and 20 MN/m, resulting to de-amplification. As a result, the heavily loaded systems prove
to T eff = 1.12 and 1.25 s for PGA = 0.2 and 0.25 g, respectively more resilient to this particular seismic excitation than the lightly
(Figure 14C). This substantial increase in the effective period loaded ones. Naturally, overall the lightly loaded systems are much
of the system leads to rather intense “de-amplification” of the less vulnerable, as also revealed by the cases in which the heavily
input motion, resulting to spectral accelerations SA lower than the loaded systems toppled.
critical acceleration ac = 0.085 g. Based on the above simplified It is also interesting to compare the behavior of the two systems
rationale, the expected accelerations at the oscillator mass are with the same FSV : the lightly loaded system lying on loose sand
0.073 and 0.075 g for PGA = 0.2 and 0.25 g, respectively, which and the heavily loaded system lying on dense sand. The two
are in very good agreement with the experimental measurements. systems exhibit remarkably different behavior: not only does the
Despite its simplicity and the fact that there are methods of non- heavily loaded system accumulate less settlement but also the
linear analysis much more advanced, the above rationale provides rotation amplitude of its oscillation is notably smaller as well. This
an excellent prediction of the response at least for the specific cases proves that the FSV alone cannot describe the dynamic response
examined herein. of two systems subjected to the same excitation. As shown in
other studies (Kourkoulis et al., 2012), the response of two rocking
systems of the same FSV and aspect ratio h/B subjected to the same
Lightly vs. Heavily Loaded Systems: The Effect of
excitation can be similar provided that there is the appropriate
De-Amplification
analogy in the stiffness of the foundation soil. In this case, the
The previously discussed “de-amplification” proves to signifi-
loose sand deposit proves to be relatively less stiff leading thus
cantly affect response of the system. Figure 15 compares the
to increased rotation and settlement accumulation for the lightly
performance of the heavily loaded System B with the lightly loaded
loaded system.
system A, further elucidating the effect of “de-amplification.” The
comparison is performed for seismic excitation with an f = 2 Hz
sine having a PGA of 0.2 g. Conclusion
Time histories of rotation θ and settlement w of the lightly
loaded system (Figure 15A) are compared to the heavily loaded Aiming to explore the efficiency of shallow soil improvement
system (Figure 15B) for all four soil profiles. Given the much as a means to mitigate settlement accumulation due to non-
lower moment capacity of the heavily loaded system, it would have linear response of the footing during an earthquake, this paper
been reasonable to expect inferior performance. It is reminded experimentally investigated the seismic response of two concep-
that the factors of safety FSV of the heavily loaded systems are tual bridge piers represented by two relatively slender h/B = 3
much lower than those of the lightly loaded ones (ranging from systems, both lying on square foundation of width B. The first
2.5 to 5 as opposed to 5 to 14), and the same applies to their one corresponds to a lightly loaded structure (relatively large
critical accelerations ac . The reality, however, is different. The FSV ), while the second refers to a heavily loaded structure (rela-
lightly loaded systems are subjected to much more settlement. tively low FSV ), deliberately chosen to model distinctly different
For example, the lightly loaded system founded on z/B = 1 soil foundation performance, from uplifting-dominated to sinking-
improvement settles 6 cm, while the settlement of its heavily dominated response. The two systems were subjected to reduced-
loaded counterpart does not exceed 4.5 cm. At this point, it should scale shaking table testing at the Laboratory of Soil Mechanics
be noted that while for the lightly loaded system A this particular of the NTUA. They were first tested on poor soil conditions in
excitation is the first of shaking sequence I, for the heavily loaded order to demonstrate the necessity for soil improvement. Then,
system B, it is preceded by two other excitations, which means that the effectiveness of shallow soil improvement was studied by
some densification may have already taken place. Moreover, the investigating the performance of the two systems on soil crusts
loose sand representing poor soil conditions is of lower relative of depth z/B = 1 and 0.5. Finally, the performance of the two

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Tsatsis and Anastasopoulos Rocking systems on shallow improved sand

systems lying on the improved soil profiles was compared to that which are attributed to kinematic soil response and dynamic
considering ideal soil conditions. compaction–mechanisms that cannot possibly be simulated
The main conclusions of the presented research can be summa- through static pushover testing.
rized as follows: • As with the slow-cyclic pushover tests, the performance of
shallow soil improvement is found to depend on the rotation
• Based on the conducted reduced-scale tests, and at least amplitude. Real records and artificial motions of different
for the cases examined herein, the concept of shallow frequency were examined, which forced the two systems to
soil improvement is proven quite effective in reducing the oscillate at various rotation amplitudes. It was shown that
dynamic settlement of the footing. For both systems, a with the increase of the rotation amplitude the effectiveness
z/B = 1 dense sand crust is enough to achieve practically of the soil crusts increases.
the same performance (in terms of settlement) with the • The performance of shallow soil improvement is ameliorated
ideal case of dense sand. A shallower z/B = 0.5 soil improve- with the number of cycles of the motion. The rate of settle-
ment may also be considered effective, depending on design ment reduces with the increase of the number of cycles for
requirements. all cases examined.
• The results of the shaking table tests are in very good qual-
itative agreement with previously published (Anastasopou- Acknowledgments
los et al., 2012) experimental results from monotonic and
slow-cyclic pushover tests. In quantitative terms, the differ- The financial support for this paper has been provided under
ences are non-negligible with the shaking table tests yielding the research project “DARE,” which is funded through the Euro-
much larger settlement for all cases examined. The tests pean Research Council’s (ERC) “IDEAS” Programme, in Support
presented herein not only confirm the key conclusions of of Frontier Research-Advanced Grant, under contract/number
the static experiments but also reveal substantial differences, ERC-2-9-AdG228254–DARE.

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Conflict of Interest Statement: The authors declare that the research was con-
modelling of shallow foundations on frictional material. Int. J. Numer. Anal.
ducted in the absence of any commercial or financial relationships that could be
Meth. Geomech. 25, 1377–1408. doi:10.1002/nag.186
construed as a potential conflict of interest.
Mergos, P. E., and Kawashima, K. (2005). Rocking isolation of a typical bridge
pier on spread foundation. J. Earthquake Eng. 9, 395–414. doi:10.1142/ Copyright © 2015 Tsatsis and Anastasopoulos. This is an open-access article dis-
S1363246905002456 tributed under the terms of the Creative Commons Attribution License (CC BY).
Muir Wood, D. (2004). Geotechnical Modelling. London: Spon Press. The use, distribution or reproduction in other forums is permitted, provided the
Nakaki, D. K., and Hart, G. C. (1987). “Uplifting response of structures subjected original author(s) or licensor are credited and that the original publication in this
to earthquake motions,” in Report No. 2.1-3, U.S.-Japan Coordinated Program for journal is cited, in accordance with accepted academic practice. No use, distribution
Masonry Building Research (Los Angeles, CA). or reproduction is permitted which does not comply with these terms.

Frontiers in Built Environment | www.frontiersin.org 19 July 2015 | Volume 1 | Article 9