The first situation we address is a homogeneous pile, as
assumed in Refs. [11, 9].
Here we use 
particles
in row M=1 and create a 
pile. The 
particles
in the lowermost row M=0 are fixed with separation 
.
The particles have no horizontal contacts, so that the
contact network is a diamond structure. As predicted
in Refs. [11, 9] the normal force at
the bottom is a constant, independent from the horizontal
coordinate. In Fig. 2(a) we plot the components of
the dimensionless stress tensor S(1) versus X=x/l for
the lowermost row of mobile particles, M=1. The vertical component
is constant, and due to the scaling used V = 1.
We compare this result with two 
piles with either
or 
and plot again S(1) vs. X for both
system sizes in Fig. 2(b).
For the pile the diagonal elements
of S are constant, whereas for the piles we observe
a plateau in the center with decreasing stresses towards the
left and right ends of the pile. Our simulation results are in
agreement with analogous simulations in Ref. [11], i.e.
we observe no sharp edges in the stresses, where the slopes change,
as predicted by the theory in Ref. [11].
Figure 2:
Components of the dimensionless stress tensor S(1) at row M=1
vs. dimensionless horizontal coordinate X=x/l, for a pile
with immobile particles at the bottom, M=0. The slope of the pile
is with in (a), and with , or in (b).
We indicate the vertical stress with 
, the horizontal stress
with 
, and the shear stress with 
.
From Fig. 2 we conclude that our soft particle
model is able to reproduce the known analytical results of
Refs. [11, 9]. V=1 corresponds to
the constant normal stress 
and thus to the
normal force 
exerted on each particle in row M=1.
Here 
, with the
mass of the pile 
, and the mass of one particle
. Our result 
coincides with
Ref. [11] [see eq.42 therein].