Annex D

(informative)

Cone and piezocone penetration tests

D.1 Example for deriving values of the effective angle of shearing resistance and drained Young's modulus

(1) Table D.1 is an example that can be used to derive values, from the value of q_c, of the effective angle of shearing resistance (φ') and drained (long term) Young's modulus of elasticity (E') for quartz and feldspar sands, for calculations of the bearing resistance and settlement of spread foundations.

(2) This example was obtained by correlating the mean value of q_c in a layer to the mean values of φ' and E'.

Table D.1 — An example for deriving values of the effective angle of shearing resistance (φ') and drained Young's modulus of elasticity (E') for quartz and feldspar sands from cone penetration resistance (q_c)

Density index	Cone resistance (q_c) (from CPT) MPa	Effective angle of shearing resistance ^a, (φ') °	Drained Young's modulus ^b, (E') MPa
Very loose Loose Medium dense Dense Very dense	0,0–2,5 2,5–5,0 5,0–10,0 10,0–20,0 > 20,0	29–32 32–35 35–37 37–40 40–42	< 10 10–20 20–30 30–60 60–90
^a) Values given are valid for sands. For silty soil a reduction of 3 ° should be made. For gravels 2° should be added. ^b) E' is an approximation to the stress and time dependent secant modulus. Values given for the drained modulus correspond to settlements for 10 years. They are obtained assuming that the vertical stress distribution follows the 2:1 approximation. Furthermore, some investigations indicate that these values can be 50 % lower in silty soil and 50 % higher in gravelly soil. In over-consolidated coarse soils, the modulus can be considerably higher. When calculating settlements for ground pressures greater than 2/3 of the design bearing pressure in ultimate limit state, the modulus should be set to half of the values given in this table.
NOTE This example was published by Bergdahl et al. (1993). Fur additional information and documents giving examples, see X.3.1

D.2 Example of a correlation between the cone penetration resistance and the effective angle of shearing resistance

(1) The following is an example for deriving the effective angle of shearing resistance (φ') from CPT cone penetration resistance (q_c) in sands.

(2) The deterministic correlation reads as follows:

φ' = 13,5 × lg q_c + 23

where

φ' is the effective angle of shearing resistance, in °;

q_c is the cone penetration resistance, in MPa.

This relationship is valid for poorly-graded sands (C_U < 3) above groundwater and cone penetration resistances in the range 5 MPa ≤ q_c ≤ 28 MPa.

NOTE 1 The example was established from electrical cone penetrometer tests, and laboratory triaxial tests.

NOTE 2 This example was published by Stenzel el al. (1978) and in DIN 4094-1 (2002). For additional information and documents giving examples, see X.3.1.

D.3 Example of a method to determine the settlement for spread foundations

(1) The following is an example of a semi-empirical method for calculating settlements of spread

foundations in coarse soil. The value for Young's modulus of elasticity (E') derived from the cone penetration resistance (q_c),to be used in this method is:

— E' = 2,5 q_c, for axisymmetric (circular and square) foundations; and

— E' = 3,5 q_c, for plane strain (strip) foundations.

(2) The settlement (s) of a foundation under load pressure (q) is expressed as:

where

C₁ is 1 – 0,5 × [σ'_v0/(q – σ'_v0)]:

C₂ is 1,2 + 0,2 × lgt;

C₃, is the correction factor for the shape of the spread foundation:

— 1,25 for square foundations; and

— 1,75 for strip foundations with L > 10B;

σ'_v0 is the initial effective vertical stress at the level of the foundation;

z_i is the depth influenced by the foundation pressure and width, respectively, in m.

I_z is a strain influence factor (see below).

(3) Figure D.1 gives for axisymmetric (circular and square) spread foundations and for plane strain (strip spread foundations) the distribution of the vertical strain influence factor (I_z).

NOTE 1 The cone penetration resistance (q_c)in this example Stems from measurements carried out with an electrical cone penetrometer.

NOTE 2 This example was published by Schmertmann (1970) and Schmertmann el al (1978). For additional information and examples, see X.3.1.

Key

x rigid fooling vertical strain influence factor I_z
y relative depth below footing
1 axi-symmetric (L/B = 1)
2 plane strain (L/B > 10)
3 B/2 (axi-symmetric); B (plane strain)
4 depth to I_zp,

Figure D.1 — Strain influence factor diagrams

D.4 Example of a correlation between the oedometer modulus and the cone penetration resistance

(1) Table D.2 gives example of values of α (see 4.3.4.1 (9) Equation 4.3) for various types of soil as function of the cone penetration resistance.

NOTE This example was published by Sanglerat (1972). For additional information and examples, see X.3.1.

Table D.2 — Examples of values of α

Soil	q_c	α
Low-plasticity clay	q_c ≤ 0,7 MPa 0,7 < q_c < 2 MPa q_c ≥ 2 MPa	3 < α < 8 2 < α < 5 1 < α < 2,5
Low-plasticity sill	q_c < 2 MPa q_c > 2 MPa	3 < α < 6 1 < α < 2
Very plastic clay Very plastic silt	q_c < 2 MPa q_c > 2 MPa	2 < α < 6 1 < α < 2
Very organic silt	q_c < 1,2 MPa	2 < α < 8
Peat and very organic clay	q_c < 0,7 MPa 50< w ≤ 100 (%) 100 < w ≤ 200 (%) w > 200 (%)	1,5 < α < 4 1 < α < 1,5 0,4 < α < 1,0
Chalks	2 < q_c ≤ 3 MPa q_c > 3 MPa	2 < α < 4 1,5 < α < 3
Sands	q_c < 5 MPa q_c > 10 MPa	α = 2 α = 1,5

D.5 Examples of establishing the stress-dependent oedometer modulus from CPT results

(1) This is an example of the derivation of the vertical stress dependent oedometer settlement modulus (E_oed), frequently recommended for settlement calculation of spread foundations, defined as follows:

where

w₁ is the stiffness coefficient;

w₂ is the stiffness exponent;

for sands with a uniformity coefficient C_U ≤ 3, w₂ = 0,5;

for clays of low plasticity (I_p ≤ 10; w_L ≤ 35), w₂ = 0,6;

σ'_v is the effective vertical stress at the base of the foundation or at any depth below it due to overburden of the soil;

Δσ'_v is the effective vertical stress caused by the structure at the base of the foundation or at any depth below it;

p_a is the atmospheric pressure;

I_p is the plasticity index

w_L is the liquid limit.

(2) Values for the stiffness coefficient w₁ can be derived from CPT results using for example the following equations, depending on the soil type:

Poorly-graded sands (C_U ≤ 3) above groundwater;

w₁ = 167lg q_c + 113 (range of validity: 5 MPa ≤ q_c ≤ 30 MPa)

well-graded sands (C_U > 6) above ground water;

w₁ = 463lg q_c – 13 (range of validity: 5 MPa < q_c < 30 MPa)

low plasticity clays of at least stiff consistency (0,75 ≤ I_c ≤ 1,30) and above ground water (I_c is the consistency index);

w₁ = 15,2q_c + 50 (range of validity: 0,6 MPa < q_c < 3,5 MPa)

NOTE 1 The example was established from the results of tests carried out with an electrical cone penetrometer and from laboratory oedometer tests.

NOTE 2 These examples were published by Stenzel el al. (1978) and Biedermann (1984) and in DIN 4094-1:2002. For additional information and examples, see X.3.1.