Civil Engineering Reference
In-Depth Information
7.2.2 Single Story Rigidly Framed Earth Retaining Structures
7.2.2.1 Backfill Soil with 30º Internal Friction Angle
The analysis results of single story rigid frames are presented herein. The results
are reported in Fig.7.4 illustrating the frame movements at the retaining wall for
various frame configurations. The top two graphics in said figure illustrate the
lateral frame movements,
U
h
, for structures of varying number of bays, with 10
feet long bays and a column to beam stiffness ratios of 1 and 4. The number of
bays is indicated using the subscripts shown in the legend. Similarly, the bottom
two graphics illustrate the frame movements for structures with 20 feet long bays.
The lateral displacements of the structures indicate that the larger the lateral
stiffness of the rigid frame, the smaller the lateral movement due to the exerted
earth pressure. For the rigid frames with a column to beam stiffness ratio of 1 and
bay length of 10 ft, the lateral displacements at the top of the structure varied
between 0.019 ft for a single bay frame, and 0.0023 ft for a 20-bay frame. On the
hand, for the frames with similar bay length but with a column to beam stiffness
ratio of 4, the lateral displacements at the top of the structure varied between
0.0026 ft for a single bay frame, and 0.0002 ft for a 20-bay frame.
Furthermore, for the rigid frames with a bay length of 20 ft and a column to
beam stiffness ratio of 1, the lateral displacements at the top of the structure varied
between 0.038 ft for a single bay frame, and 0.0065 ft for a 10-bay frame. The
displacement of the frames with similar bay length and a column to beam stiffness
ratio of 4 were approximately one order of magnitude lower than their latter
counterparts.
The total amount of movement obtained in this analysis indicate that only 5 out
of the 18 rigid frames underwent movements near or larger than the displacement
of 0.001 times the height of the structure necessary to develop active earth
pressures (Winterkorn and Fang, 1975 pp 405).
The lateral earth pressures developed at the end of the backfill stage, simulated
in this analysis using staged construction calculations, are presented in Fig. 7.5.
The earth pressures for each group of rigid frames is compared to the Coulomb
active earth pressure for a level backfill with a friction angle between the wall and
backfill soil of 22.5º, and the prescribed lateral earth pressure values found in the
major building codes adopted in the United States presented in table 1.1 of
Chapter 1. The magnitude of the lateral earth pressure at rest is nearly 43% larger
than the lateral soil loads prescribed by ASCE 7-98 and is not included herein.
The examination of the plots in Fig. 7.5 reveals that the magnitude of the lateral
earth pressures developed during the backfill stage varies with the lateral stiffness of
the rigid frames. The top plot indicates that the classical Coulomb active earth
pressure, and the earth pressure loads prescribed by BOCA (1999), NBC (1999) and
SBC (1999) adequately predict the lateral soil loads exerted on the single story
frames at the end of the backfill stage, while ASCE 7-98 tends to slightly
overestimate the lateral earth pressure. Additionally, the top plot indicates that the
range of earth pressures developed behind this group of frames is quite limited for
the best part of the height of the structure, diverging slightly towards the base of the
frames.
