Conventions and units¶
This is the page that prevents the most common data-entry error. It is worth reading before your first project.
Axis system¶
The programs use a right-handed system with Z pointing down, with its origin at the pile head.
| Axis | Positive direction |
|---|---|
| X | Horizontal |
| Y | Horizontal, perpendicular to X |
| Z | Downward, along the pile |
Z pointing down is the geotechnical convention: depth increases with Z, and borehole levels are read in the same direction in which the pile goes down.
Check it in the program itself
SPX includes a 3D view of the coordinate system, with the pile and the three axes drawn. Use it whenever you are unsure about the direction of a force.
Sign convention for forces¶
| Force | Positive means |
|---|---|
| Axial \(N\) | Compression — load acting downward, in the Z direction |
| Axial \(N < 0\) | Tension — the program changes the bearing capacity method |
| Shear \(V_x\) | To the right, in the X direction |
| Shear \(V_y\) | In the Y direction |
| Moment \(M_x\), \(M_y\) | Clockwise |
The sign of the axial force changes the calculation
It is not just a matter of the sign in the output. With \(N < 0\) the program treats the pile as in tension, ignores the toe resistance and applies the tension safety factor. See Bearing capacity.
Units¶
Input and output use the SI units customary in Brazilian geotechnical practice.
| Quantity | Unit | Where it appears |
|---|---|---|
| Length, diameter, depth | m | Pile and pile cap geometry |
| Concrete cover | cm | Environmental exposure class |
| Force | kN | Applied loads, \(R_p\), \(R_l\), \(P_a\) |
| Moment | kN·m | Applied moments |
| Soil stress | kPa | \(r_p\), \(r_l\), parameter \(K\) |
| Concrete strength \(f_{ck}\) | MPa | Materials |
| Modulus of elasticity \(E_c\) | MPa on input, kPa in calculation | Elastic settlement |
| Unit weight \(\gamma\) | kN/m³ | Geostatic stress |
| Factor \(m\) | kN/m⁴ | Horizontal subgrade reaction coefficient |
| Unit \(K_h\), \(K_v\) | kN/m³ | Soil reaction |
| Springs \(K_h\), \(K_v\) | kN/m | Input to the finite element model |
| Settlement | m in calculation, mm in presentation | Results and charts |
Settlement in millimetres
Internally, settlement is calculated in metres, but every result shown — table, chart and report — is in millimetres, the unit in which allowable settlement is discussed.
Soil types¶
SPX classifies the soil by the fractions it consists of, in order of predominance. There are fifteen combinations:
| Sand | Silt | Clay |
| Silty sand | Sandy silt | Sandy clay |
| Silty-clayey sand | Sandy-clayey silt | Sandy-silty clay |
| Clayey sand | Clayey silt | Silty clay |
| Clayey-silty sand | Clayey-sandy silt | Silty-sandy clay |
The name reads as the composition: silty-clayey sand is predominantly sand, then silt, then clay.
The classification selects the design parameters
The soil type is not a label: it selects \(K\) and \(\alpha\) in the Aoki-Velloso table, \(C\) in Décourt-Quaresma, \(\alpha_T\) in Teixeira and the factor \(m\) for the springs.
Swapping silty sand for sandy silt — similar names, reversed compositions — changes \(K\) from 0.80 to 0.55 MPa, i.e. 31 % less toe resistance. Check the classification in the borehole log before entering it.
Not every method uses the full classification. Décourt-Quaresma works with only three families — clays, intermediate soils and sands — and the horizontal subgrade reaction coefficient only distinguishes sandy and silty soils from clayey ones.
Borehole discretisation¶
The borehole is entered metre by metre: one \(N_{SPT}\) value and one soil code per metre. Result levels are negative, measured from the ground surface: −1 m, −2 m, and so on.
Every bearing capacity table is presented by level — for each possible toe depth, what the allowable load would be. That is what lets you choose the pile length by reading down the column, instead of trying one length at a time.