SME
Soil Mechanics · Problem type
Plasticity index and the A-line
Use this for “A fine-grained soil has LL = 45 and PL = 22. Find its plasticity index. Is it a clay or a silt?”
Chart
y ≥ 0.73x − 14.6
Shaded above: every point where y is at least 0.73x − 14.6.
Solid: the line itself is included
Slope m = 0.73: up 0.73 for every 1 across
Intercept b = −14.6: it crosses the y-axis at (0, −14.6)
Test (45, 23): 0.73 × 45 − 14.6 = 18.25, and 23 ≥ 18.25 is true
It is a solution: it lies in the shaded part.
This is an example. Type your own values to start a new problem.
PI
=
LL
−
PL
PIA
=
0.73
×
(
LL
−
20)
K
Group
worked out (not typed)
Formulas
PI = LL − PL
23 = 45 − 22
PIA = 0.73 × (LL − 20)
18.25 = 0.73 × (45 − 20)
K
from
PI
against
the
A-line
PIA
and
LL
against
50
(CL-ML
for
4
≤
PI
≤
7
on
or
above
it)
23 ≥ 18.25, 23 > 7 and 45 < 50, so CL (lean clay)
Assumptions
•
Liquid limit LL and plastic limit PL are water contents (%) from the Atterberg limit tests.
•
The A-line, PI = 0.73(LL − 20), splits clays (on or above it) from silts (below it).
•
LL < 50 is low plasticity (L), LL ≥ 50 high (H); 4 ≤ PI ≤ 7 above the A-line is CL-ML.
•
The soil is inorganic and fine grained: half or more passes the No. 200 sieve.
Step-by-step
WE KNOW
LL = 45%, PL = 22%
FIND
plasticity index (PI), A-line PI (PIA), group (K)
Step 1 · Find plasticity index (PI)
Use PI = LL − PL
The range of water contents over which the soil is plastic, from PL up to LL.
PI = 45 − 22
PI = 23%
Step 2 · Find A-line PI (PIA)
Use PIA = 0.73 × (LL − 20)
The A-line’s PI at this liquid limit: a clay’s point sits on or above it.
PIA = 0.73 × (45 − 20)
PIA = 0.73 × 25
PIA = 18.25%
Step 3 · Find group (K)
Use K from PI against the A-line PIA and LL against 50 (CL-ML for 4 ≤ PI ≤ 7 on or above it)
On or above the A-line the fines act as clay; LL then says lean (L) or fat (H).
23 ≥ 18.25, 23 > 7 and 45 < 50: CL (lean clay)
K
=
compare
PI
with
the
A-line
PIA,
and
LL
with
50
K
=
compare
23
with
the
A-line
18.25,
and
45
with
50
K
=
CL
(lean
clay)
Check
Put the numbers back in. Both sides should match.
23 = 45 − 22 ✓
18.25 = 0.73 × (45 − 20) ✓
23 ≥ 18.25, 23 > 7 and 45 < 50, so CL (lean clay) ✓
Topic check
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