724
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
2a) Apply loads=>
extract stresses
2. SelfSim learning: FE analyses to extract stress strain behavior
2b) Apply displacements=>
extract strains
1. Laboratory test
Retrain NN based soil model
P
j
j
h
j
h
Current soil model
Yes
No
Computed displacements
measurements
P
j
j
j-
1
P
h
Measurments of current
loading step
j
n j+
1
P
j
Database for
training
j
j
1
j
1
j
SelfSim applied to current loading step
j
SelfSim moves to next loading step j+1
Integration point
states from global measurements of load and displacement of
boundary value problems such as deep excavations and seismic
response of downhole arrays (Ghaboussi et al. 1998, Hashash et
al. 2004, Tsai and Hashash 2008). Laboratory tests imposing
non-uniform stress
–
strain within the soil are used within the
SelfSim framework. Fu et al. (2007) applied the SelfSim
framework to simulated laboratory triaxial specimens sheared
with no-slip frictional ends, and Hashash et al. (2009) applied
the SelfSim framework to drained triaxial compression tests to
extract soil stress-strain. The SelfSim inverse analysis algorithm
provides a unique opportunity to extract multiple paths of
complex soil behavior from a test with nonuniform boundary
conditions. The algorithm is unconstrained by prior assumptions
on soil behavior such as anisotropy and nonlinearity.
This paper presents the integration of self-learning
simulations (SelfSim) inverse analysis computational engine
with the widely used DSS test and a newly developed next
generation triaxial laboratory testing device that imposes non-
uniform loading on a soil specimen beyond frictional ends. The
stress paths after SelfSim learning are extracted within the
specimens in terms of the relationship between principal stress
direction (
δ
) and intermediate principal stress ratio (b) to
interpret soil behavior that is not described sufficiently in
conventional laboratory test due to limited information.
2 SELFSIM FRAMEWORK
SelfSim is a biologically inspired evolutionary inverse analysis
framework that implements and extends the Autoprogressive
algorithm to solve a wide range of engineering problems. The
Autoprogressive algorithm was originally proposed by
Ghaboussi et al. (1998) and applied to structure and material
tests (Ghaboussi and Sidarta 1998). Shin and Pande (2000)
implemented this algorithm on simulated structures and
introduced it in the context of self learning finite element code.
SelfSim treats the soil specimen as a BVP (Boundary Value
Problem) instead of a single element test and extracts the
nonuniform stresses and strains from within a specimen using
external load and displacement measurements.
Figure 1. SeflSim framework applied to DSS laboratory test.
As shown in Figure 1, SelfSim framework consists of two
steps: 1) In Step 1, a laboratory test with constrained boundary
loading conditions is performed and measurements of force and
displacement are obtained at each loading step; 2) In Step 2, a
numerical model is developed to represent the test with the
corresponding measurements. Two parallel finite element (FE)
analyses, Step 2a and Step 2b, are performed at each loading
step. In these analyses a NN material model is employed that
continuously evolves and learns new behavior through the
SelfSim process instead of a conventional material model.
Initially the soil response is unknown and the NN soil model is
pre-trained using stress-strain data that reflect linear elastic
response over a limited strain range. The FE analyses are
performed to simulate the applied forces in Step 2a and the
measured boundary displacements in Step 2b. The computed
stresses from boundary forces in Step 2a and the computed
strains from boundary displacements in Step 2b are respectively
acceptable approximations of the actual stresses and strains
experienced throughout the specimen. The stresses from Step 2a
and the strains from Step 2b are extracted to form stress-strain
pairs. These stress-
strain pairs are used to “re
-
train” the NN soil
model in the next step. The parallel analyses and the subsequent
NN material model training, SelfSim learning cycle, are
performed sequentially for all loading steps and they are
repeated till the solution converges when both analyses provide
similar results. This results in a single SelfSim learning pass.
Several SelfSim learning passes are needed to extract soil
behavior used in training a NN soil model that will adequately
capture global measurements of force and displacement. The
framework extracts material behavior via a continuously
evolving constitutive model and thus is not constrained by
conventional constitutive model assumptions.
3 APPLICATION OF SELFSIM TO DSS TESTS
The SelfSim framework is applied to K
0
normally consolidated-
undrained direct simple shear (CK
0
UDSS) tests, performed on
normally consolidated re-sedimented Boston Blue Clay (BBC)
(Ahmed 1989). SelfSim learning is performed on Test DSS14
up to 1.97% shear strain divided into 11 loading steps. The 3D
FE model is developed as a cylindrical specimen with a height
of 1.96 cm and a diameter of 6.68 cm. The specimen is assumed
to have frictional loading cap and base that can produce non-
uniform stress-strain distribution during shear. The
consolidation process is not simulated but considered as an
initial anisotropic state of stress (
σ′
v0
=1176kPa,
σ′
h0
=623kPa),
from which shearing commences.
SelfSim learning is initiated with a trained NN constitutive
model representing linear elastic behavior in the shear strain
range of 0.07%. This linear elastic behavior is removed once the
learning process starts. The global measurements, such as
vertical loads, horizontal loads, and lateral displacements in x
(longitudinal, in the direction of shearing) and y (transverse)
directions, from CK
0
UDSS test are employed in SelfSim
learning. After initialization, SelfSim learning is conducted in 4
stages over all 11 loading steps using the updated NN material
model from each stage.
Figure 2 shows comparisons of the global target responses
and model responses after SelfSim learning, including
normalized shear stress, normalized vertical stress, and lateral
displacement. Through the process of SelfSim learning, the
computed global responses match the global target responses of
force and displacement measurements for DSS14 at the learning
final stage. Thus, SelfSim learning makes it possible to extract
sufficient information about the soil behavior to learn the global
response. The stress behavior at integration points is extracted
in a half slice of the specimen using a cylindrical coordinate
system.
Figure 3 shows the extracted stresses in the plot between
intermediate principal stress ratio (b) and the principal stress
