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Drained monotonic direct simple shear test (DSS)

In a drained direct simple shear (DSS) test the laterally confined specimen is sheared horizontally while the vertical stress is held constant and drainage is allowed. The measured response is the shear stress and the volumetric strain as functions of the shear strain. It is the simple-shear counterpart of the drained triaxial test, at a stress state that is representative of many field situations.

What it constrains

Drained simple shear tests constrain shear strength and dilatancy in simple-shear conditions. Because the principal axes rotate continuously during shearing, they load a model differently from a triaxial test and are therefore a valuable, largely independent monotonic constraint, particularly for models that are calibrated for problems dominated by shearing on horizontal planes (shallow foundations, level ground, interface-near soil).

Together with the undrained cyclic simple shear test they allow a model to be calibrated in the simple-shear deformation mode under both monotonic and cyclic loading.

How numgeo-ACT simulates it

numgeo reproduces the drained simple shear test as a single solid finite element (U4-solid-red), a plane element rather than an axisymmetric one, since simple shear is not an axisymmetric deformation. The element is the same one used for the cyclic simple shear test; only the loading and the drainage condition differ.

The conditions under which the test is simulated are:

  • Base: fully fixed (u₁ = u₂ = 0 on nbottom).
  • Consolidation: the element is initialized with the \(K_0\) stress state that belongs to the normal stress measured at the beginning of the shearing phase, \(\sigma_{22} = -\sigma_{v,0}\) and \(\sigma_{11} = \sigma_{33} = -K_0\,\sigma_{v,0}\), together with the initial void ratio \(e_0\). The initial state variables are initialized as for the oedometric compression test, because the specimen of a direct simple shear test is consolidated under confined conditions.
  • Shearing: the top is sheared horizontally under strain control. The horizontal displacement u₁ of ntop is ramped to \(u_1 = \gamma_\text{max}\,h\), where \(\gamma_\text{max}\) is the largest shear strain of your record and \(h = 0.1\) m is the height of the element.
  • Constant normal stress (the drained condition): a constant vertical load acts on the top (*Cload on ntop) while its vertical displacement is left free. The specimen may therefore contract or dilate, and the volumetric strain develops as the response to be compared. This is the essential difference to the undrained cyclic simple shear test, where u₂ = 0 enforces constant volume instead.
  • Drainage: drained. The solid element carries effective stresses and no excess pore pressure is generated.

The simulated shear strain is the shear component of the strain tensor (STRAIN12), the shear stress is STRESS12, and the volumetric strain is obtained from the trace of the strain tensor, with compression positive. The same sign convention as on the sheet.

What is compared

Two planes are evaluated, weighted through weights["DSS"]:

Plane Key Default Constrains
\(\tau\) vs. \(\gamma\) gamma-tau ½ shear stiffness and shear strength
\(\varepsilon_v\) vs. \(\gamma\) gamma-epsV ½ contractancy and dilatancy

Setting one of the two weights to 0 removes that plane from the objective; the two must sum to 1. If the simulation does not reach 95 % of the largest measured shear strain because the parameter set caused the calculation to abort. The test is penalized instead of scored.

DSS tests belong to the monotonic group of the global weighting.

Data mapping (DSS-# sheet)

Cell / column Meaning Units
B1 initial void ratio \(e_0\) –
C1 test name (optional; the sheet name is used if empty) –
D1 lateral earth-pressure coefficient \(K_0\) (optional, default 0.5) –
row 2 column headers (informational) –
column 0 (from row 3) shear stress \(\tau\) kPa
column 1 (from row 3) vertical (normal) stress \(\sigma_v\) kPa
column 2 (from row 3) shear strain \(\gamma\) (in %) %
column 3 (from row 3) volumetric strain \(\varepsilon_v\) (in %, compression positive) %
column 4 (optional) initial-state string(s) –

Only the first normal stress is used for the simulation

The test is simulated at the constant normal stress recorded in the first data row. Record the full \(\sigma_v\) column anyway: it is written to the result files and lets you verify that the device really held the normal stress constant.

K₀ is not measured by most devices

The lateral stress of a laterally confined specimen is usually not recorded. If cell D1 is empty, numgeo-ACT assumes \(K_0 = 0.5\). Enter your own value (for example \(K_0 = 1 - \sin\varphi_c\)) when you know it. This sets the initial horizontal stress of the simulated element and therefore influences the response at small shear strains.

Reduce very long records before calibrating

Modern DSS devices record thousands of points per test. The default similarity measure (frechet) compares every experimental point with every simulated one, so a record with several thousand rows makes each objective evaluation slow. Thin the record once after reading it:

for test in database.DSS:
    test.interpolate(200)   # resample to 200 points

A few hundred points are ample to describe a monotonic shear curve.

The full specification is on the Excel sheet reference. A DSS-1 example sheet is included in the template.