Geotechnical engineering plays a crucial role in ensuring the stability and safety of structures by understanding and manipulating the unique properties of soil and rock. In this exploration of “Common Rules of Thumb in Geotechnical Engineering,” we will look into the key principles and guidelines that serve as practical benchmarks for professionals in the field. Whether you’re a seasoned geotechnical engineer or a curious enthusiast, this guide aims to shed light on fundamental rules that shape the foundation of successful geotechnical practices.
Common Rules of Thumb in Geotechnical Engineering
A rule of thumb is defined as a practical or approximate way of doing or measuring something. The origins of the term “rule of thumb” are obscure. Apparently, Roman bricklayers used the tip of the thumb from the knuckle as a unit of measure. Brewers used their thumbs to test the temperature of fermenting ale. In the Middle Ages, a man was permitted to beat his wife with a cane no thicker than his thumb. Nowadays, the rule of thumb implies a rough estimate based on experience rather than formal calculation.
Geotechnical engineering is essentially a mechanical science which has a strong theoretical basis. Nevertheless, many geotechnical engineers use simple relationships – rules of thumb – in routine design (to obtain soil parameters and design foundations). Some of these rules of thumb are based on sound theory and so should be generally applicable; others are purely empirical and so are applicable only within the range of the data from which they were derived. A classification for rules of thumb was suggested by Wroth (1984).
Rules of thumb aid geotechnical engineers a lot in practice. With rules of thumb, there is no need to carry out certain unnecessary costly, and time-consuming tests. However, each geotechnical engineer has the liberty to use their favourite rules of thumb.
Conditions for Successful Application of Rules of Thumbs
As stated above, certain rules of thumb are more valid within the context upon which they were designed, however, certain rules exist to go out of this context:
(a) Based on physical appreciation of why the properties can be expected to be related.
(b) Set against a background of theory, however, idealised this may be.
(c) Expressed in terms of dimensionless variables so that advantage can be taken of scaling laws of continuum mechanics.
Rules of Thumb in Geotechnical Engineering
Correlation between the Angle of Internal Friction and SPT number, N
Where:
ϕ = friction angle
N = SPT value
This particular equation ignores particle size. Most tests are done on medium to coarse sands, hence, there is a modification to account for other soil sizes as listed below:
How to convert SPT blow count from one Hammer to another
Most geotechnical correlations were based on SPT (N) values obtained during the 1950s. However, drill rigs today are much more efficient than the drill rigs of the 1950s. If the hammer efficiency is high, then to drive the spoon 300 mm (1 ft), the hammer would require a lesser number of blows compared to a less efficient hammer. It is possible to convert the blow count from one hammer to another. The following expression gives the conversion from a 60% efficient hammer to a 70% efficient hammer.
Cone penetration test (CPT) and standard penetration tests are two common tests used to delineate subsurface geotechnical conditions. Both methods have different strategies, however, CPT has many benefits over SPT as it provides a broader characterisation of the soil, because three different parameters are measured instead of just one in the case of SPT. In addition, CPT presents real-time results in the field when compared to SPT. There’s no need to transfer soil samples to a lab and then wait for days or even weeks to get the analysis report. Instead, the report can be issued as soon as the cone has been pulled out of the ground and before the unit is moved to the next location. Finally, CPT does not require a borehole for the testing, so there are no cuttings and no spoilage.
SPT is more extensively used in the USA while CPT is more common in Europe. In situations where there is a need to convert results from CPT to SPT, empirical correlations exist that can enable this. These are outlined in Table 1.
Table 1: CPT-SPT correlations for clays and sands (Robertson et al., 1983)
| Soil Type | Mean grain size (D50) measured in mm | Qc/N |
| Silt | 0.001 | 100 |
| Silty-clay | 0.005 | 170 |
| Clayey-silt | 0.01 | 210 |
| Sandy-silt | 0.05 | 300 |
| Silty-sand | 0.1 | 400 |
| Sand | 0.5 | 570 |
| 1.0 | 700 |
Where:
Qc = CPT value (kPa)
N = SPT value
D50 = size of the sieve that would pass 50% of the soil
Relationship between US sieve sizes and British sieve sizes
The relationship between US sieve sizes and their numbers and British sieve sizes and their numbers are outlined in the table below.
Table 2: US sieve sizes versus British sieve sizes
| US sieve number | Mesh sizes | British sieve number | Mesh sizes |
| 4 | 4.75 | 8 | 2.057 |
| 6 | 3.35 | 16 | 1.003 |
| 8 | 2.36 | 30 | 0.500 |
| 10 | 2.00 | 36 | 0.422 |
| 12 | 1.68 | 52 | 0.295 |
| 16 | 1.18 | 60 | 0.251 |
| 20 | 0.85 | 85 | 0.178 |
| 30 | 0.60 | 100 | 0.152 |
| 40 | 0.425 | 200 | 0.076 |
| 50 | 0.30 | 300 | 0.053 |
| 60 | 0.25 | ||
| 80 | 0.18 | ||
| 100 | 0.15 | ||
| 200 | 0.075 | ||
| 270 | 0.053 |
Size Ranges for Soils and Gravels
The typical ranges of soil types and their sizes are outlined in the table below.
Table 3: Soil types and sizes
| Soil | Size (inches) | Size (mm) |
| Boulders | >6 | >150 |
| Cobbles | 3 – 6 | 75 – 150 |
| Gravel | 0.187 – 3 | 4.76 – 75 |
| Sand | 0.003 – 0.187 | 0.074 – 4.76 |
| Silt | 0.00024 – 0.003 | 0.006 – 0.074 |
| Clay | 0.00004 – 0.00008 | 0.001 – 0.002 |
| Colloids | <0.00004 | <0.001 |
Typical Specific Gravity of Different Types of Soils
The typical specific gravity of the different soil types is outlined in the table below:
Table 4: Typical specific gravity of different soil types
| Soil | Specific gravity |
| Gravel | 2.65 – 2.68 |
| Sand | 2.65 – 2.68 |
| Silt (inorganic) | 2.62 – 2.68 |
| Organic clay | 2.58 – 2.65 |
| Inorganic clay | 2.68 – 2.75 |
Bearing capacity of Soils
The bearing capacity of soils is usually determined analytically using methods provided by Terzaghi, Meyerhof, Hansen, and Vesic. However, certain rules of thumb are applicable in the determination of the bearing capacity of soils and these are outlined below:
Bearing Capacity in Medium to Coarse Sands
The strength of sandy soils is dependent upon the friction angle. The bearing capacity in coarse to medium sands can be obtained using the average SPT (N) value as outlined below. This formula is applicable on the condition that the average SPT (N) value is determined below the bottom of the footing at a depth that is equal to the width of the footing and that the soil within this range is medium to coarse sand. If the average SPT is less than 10, the soil should be compacted.
Allowable bearing capacity (qa) of coarse to medium sands = 9.6 Naverage (kPa) – not to exceed 575 kPa
Bearing Capacity in fine sands
Allowable bearing capacity (qa) of coarse to medium sands = 9.6 Naverage (kPa) – not to exceed 380 kPa
Design of Gravel filters
Gravel filters stop any soil particles from entering the pipe. At the same time, the gravel allows ample water flow. If fine gravel is used, water flow can be reduced. On the other hand, large size gravel can allow soil particles to pass through and eventually clog the drain pipe. Empirically it has been found that if the gravel size is selected by the two rules given below, very little soil would transport through the gravel filter and at the same time let water flow smoothly.
RULE 1: To block soil from entering the pipe, the size of the gravel should be:
D15 (gravel) < 5 x D85 (soil)
D15 size means that 15% of particles of a given soil or gravel would pass through the D15 size of that particular soil or gravel. The D85 size means that 85% of particles of a given soil or gravel would pass through the D85 size of that particular soil or gravel. These values are obtained through sieve analysis.
RULE 2: To let water flow, the size of the gravel should be:
D50 (gravel) > 25 x D50 (soil)
D15, D50, D85 size means that 15%, 50%, 85% of particles of a given soil or gravel would pass through the D15, D50, D85 size respectively of that particular soil or gravel. These values are obtained through sieve analysis.
Geotextile Filter Design
Geotextile filters are becoming increasingly popular in drainage applications. The ease of use, economy, and durability of geotextile filters have made them the number one choice of many engineers. There are two types of geotextiles (woven and non-woven) available in the market. For sandy soils, both woven and non-woven geotextiles can be used while for clay soils, non-woven geotextile is more applicable. The geotextile is wrapped around stones (stones act only as a medium to transport water) and backfilled with the original soil.
a. Geotextile Wrapped Granular Drains (Sandy Surrounding Soils) – Woven geotextiles
The task of stopping soil from entering the drain is done by the geotextile. Gravel is wrapped with a geotextile to improve the performance. The geotextile filters the water, and the gravel acts as the drain. Equations have been developed for the two types of flow: one-way flow and two-way flow (also called alternating flow).
i. One Way Flow
In the case of one-way flow, the flow of water is always in one direction across the geotextile. The following equation for geotextiles in sandy soil developed by Zitscher (1975) has been applicable in this case
H50 (geotextile) < 1.7 to 2.7 x D50 (soil) (for one-way flow for sandy soils)
Where H50 indicates that 50% of the holes in the geotextile are smaller than the H50 size. D50 (soil) indicates that 50% of soil particles are smaller than the D50 size.
ii. Two Way Flow (Alternating Flow)
In the case of two-way flow, water goes through the geotextile in both directions. In heavy rain, water enters the drain from the top, flows into the drain, and then flows out of the drain to the surrounding soil. If flow through the geotextile is possible in both directions, a different set of equations needs to be used (Zitscher, 1975).
H50(geotextile) < (0.5 to 1.0) x D50 (soil) (for two-way flow for sandy soils)
b. Geotextile Wrapped Granular Drains (Clayey Surrounding Soils) – Non-woven geotextiles
The theory behind using geotextile-wrapped granular drains is that the direction of flow is not significant for cohesive soils since the flow is not as rapid as in sandy soils. Most engineers prefer to use non-woven geotextiles for cohesive soils. For these soils, use the equation (Zitscher, 1975):
H50(geotextile) < (25 to 37) x D50 (soil) (one-way and two-way flow for clayey soils)
Allowable Bearing Capacity of Raft Foundations
Three prominent foundation engineers, Peck, Hanson, and Thorburn (1974), proposed the following method to design raft foundations. The following equation can be used to find the allowable pressure in a raft.
qallowable Raft = 23.595 x N x Cw x γ x Df
Where:
qallowable Raft = allowable average pressure in the raft, given in kN/m2
N = average SPT (N) value to a depth of 2B, where B is the lesser dimension of the raft.
Where:
Dw = depth to groundwater measured from the ground surface (m)
Df = depth to the bottom of the raft measured from the ground surface (m)
γ = total density of the soil (kN/m3)
Once the allowable load is determined, it is possible to determine the total quantity of load to be carried by the raft as follows:
The total quantity of load to be carried by raft = qallowable Raft x area of the raft
Rock Quality Designation (RQD)
Rock quality designation is obtained through the following process:
i. Arrange all rock pieces as best as possible to simulate the ground conditions.
ii. Measure all rock pieces greater in length than 100 mm (4 inches).
iii. Estimate RQD with the expression below:
Where:
RQD (0-25%) = very poor
RQD (25-50%) = poor
RQD (50-75%) = fair
RQD (75-90%) = good
RQD (90-100%) = excellent
Richter Magnitude Scale (M)
The Richter scale also called the Richter magnitude scale, Richter’s magnitude scale, and the Gutenberg–Richter scale, is a measure of the strength of earthquakes, developed by Charles Francis Richter and presented in his landmark 1935 paper, which he called it the “magnitude scale”. The Richter magnitude scale is a logarithmic scale that follows the relation:
M = logA – logAo = log (A/Ao)
Where:
M = Richter magnitude scale
A = maximum trace amplitude during the earthquake
A0 = standard amplitude
Here, a standard value of 0.001 mm is used for comparison. This corresponds to a very small earthquake.
Soil Resistance to Liquefaction
Any soil that has an SPT value higher than 30 will not liquefy. Resistance to liquefaction of a soil depends on its strength measured by SPT value. Researchers have found that resistance to soil liquefaction depends on the content of fines as well. The following equation (which can only be used for clean sands with a fine content of less than 5%) is applicable.
Where:
CRR7.5 = soil resistance to liquefaction for an earthquake with a magnitude of 7.5 Richter
(N1)60 = the standard penetration value corrected to a 60% hammer and an overburden pressure of 100 kPa.
(N1)60 =Nm x CN x CE x CB x CR
Where:
Nm = SPT value measured in the field
CN = overburden correction factor
Where:
Pa = 100 kPa
σ’= effective stress of soil at the point of measurement
CE = energy correction factor for the SPT hammer
for donut hammers, CE = 0.5 to 1.0
for trip-type donut hammers, CE = 0.8 to 1.3
CB = borehole diameter correction
for borehole diameters of 65 mm to 115 mm use CB = 1.0
for a borehole diameter of 150 mm use CB = 1.05
for a borehole diameter of 200 mm use CB = 1.15
CR = rod length correction
Rods attached to the SPT spoon exert their weight on the soil. Longer rods exert a higher load on soil and in some cases the spoon sinks into the ground due to the weight of the rods, even without any hammer blows. Hence, a correction is made to account for the weight of rods.
for rod length < 3 m, use CR = 0.75
for rod length 3 m to 4 m, use CR = 0.8
for rod length 4 m to 6 m, use CR = 0.85
for rod length 6 m to 10 m, use CR = 0.95
for rod length 10 m to 30 m, use CR = 1.0
Exceptions: for other magnitude of earthquakes, and sands with fine content of more than 5%, a correction factor has to be applied.
Correction for Magnitudes of Earthquake
A correction factor is proposed for earthquakes of magnitudes of 7.5. The factor of safety (F.O.S.) is given by:
Where:
CRR7.5 = resistance to soil liquefaction for a magnitude of 7.5 earthquake
CSR = cyclic stress ratio (which is a measure of the impact due to the earthquake load).
Where:
amax = peak horizontal acceleration at the ground surface
r = total stress at the point of concern or’= effective stress at the point of concern
rd = stress reduction coefficient (rd = 1.0 – 0.00765Z for Z < 0.15 m or rd = 1.174 – 0.0267Z for 9.15 m < Z < 23 m)
Where:
Z = depth to the point of concern in meters
For earthquakes of other magnitudes other than 7.5, the correction factor is given by the following equation:
Where: MSF- magnitude scaling factor (see Table 4)
Table 4: Magnitude scaling factors
| Earthquake magnitude | MSF suggested by Idris (1990) | MSF suggested by Andrus and Stokoe (2000) |
| 5.5 | 2.2 | 2.8 |
| 6.0 | 1.76 | 2.1 |
| 6.5 | 1.44 | 1.6 |
| 7.0 | 1.19 | 1.25 |
| 7.5 | 1.00 | 1.00 |
| 8.0 | 0.84 | – |
| 8.5 | 0.72 | – |
Correction Factor for Content of Fines
For soils with higher fine content, the corrected (N1)60 value should be used in CRR7.5 equation above. To apply the correction, first compute (N1)60, then use the expression below to compute the corrected value:
(N1)60C = a + b (N1)6o
Where:(N1)60C = corrected (N1)6o value
References
Andrus, R. D. and Stokoe, K. H. (2000). “Liquefaction resistance of soils from shear wave velocity”. ASCE Journal of Geotechnical and Geoenvironmental Engineering, vol 126, no. 11, 1015-1025.
Atkinson, J. (2008) Rules of thumb in geotechnical engineering Proc. 18th NZGS Geotechnical Symposium on Soil-Structure Interaction. Ed. CY Chin, Auckland
Idris, I. M. (1990). “Response of soft soil sites during earthquakes”. Proc. Bolten Seed Memorial Symp., vol. 2 Bi-Tech Publishers Ldt., Vancouver, 273-290.
Peck, R. B., Hanson, W. E., and Thornburn, T. H. 1974. Foundation engineering. New York: John Wiley & Sons.
Rajapakse, R. Geotechnical Engineering Calculations and Rules of Thumb.
Robertson, P. K., Campanella, R. G., and Wightman, A. 1983. SPT-CPT Correlations. ASCE Geotechnical Engineering Journal 109( 11): 1449-1459
Wroth, C.P. (1984). 24th Rankine Lecture: The interpretation of in situ soil tests. Geotechnique, Vol. 34, No 4, pp 449-488.
Zitscher, F. F. 1975. Recommendations for the use of plastics in soil and hydraulic engineering. Die Bautechnik, 52(12):397-402.
