## The use of CPTU for determining the liquefaction potential

Soil liquefaction is a common and often highly devastating event that occurs during seismic events. Predicting this phenomenon poses a significant challenge for engineers and is crucial for the construction of earthquake-resistant buildings in seismically active areas.

The goal of this blog is to demonstrate how, by using the geotechnical parameters obtained through Cone Penetration Testing (CPTU), the potential for soil liquefaction during earthquakes can be determined.

## What is liquefaction?

Liquefaction is a phenomenon in which the soil rapidly loses its strength and stiffness over a short period due to the action of dynamic loads. When soil is subjected to loading, either dynamically or statically, its structure compacts, resulting in an increase in pore pressure (water pressure in the pore space), which subsequently reduces the effective stresses within the soil.

In the expression below, we can observe that the shear strength of the soil is a function of effective stresses. As a result of the loss of these stresses, a noticeable reduction in both strength and stiffness occurs.

Where:

τ – shear strength of soil

c – cohesion

σ’ – effective stress

φ – angle of internal friciton

It is crucial to emphasize that not all soils exhibit equal susceptibility to liquefaction. Extensive evidence from seismic events and thorough theoretical investigations of this phenomenon has revealed that loose, poorly-graded sandy soils with a low percentage of fine-grained particles and high saturation levels are most prone to liquefaction. On the other hand, compacted, well-graded soils with a higher percentage of smaller particles and, consequently, reduced void volume (Figure 2) demonstrate significantly lower potential for soil structure compaction and the development of pore pressures, compared to poorly-graded soils. Therefore, the liquefaction potential is correspondingly diminished.

Furthermore, as the cohesion is negligible in poorly-graded sandy soils, the complete loss of effective stresses causes the soil to lose its strength and stiffness, transitioning into a liquid state; hence the term **“liquefaction”**.

### Determination of liquefaction potential using CPTU

The Cone Penetration Test with pore pressure measurement (CPTU) is a geotechnical testing method regularly employed to assess the potential for soil liquefaction. The test involves driving a conical probe into the soil at a constant rate while continuously measuring cone tip resistance (q_{t}), sleeve friction (f_{s}), and pore water pressure (u_{2}) at various depths (z). The collected data are then used to estimate the potential for soil liquefaction, requiring the calculation of two coefficients: the cyclic stress ratio (CSR) and the cyclic resistance ratio (CRR). In brief, if CSR is greater than CRR, it can be concluded that the potential for liquefaction in the tested soil is high. Conversely, when CSR is lower than CRR, the likelihood of soil liquefaction occurrence is minimal.

### Determination of cyclic stress ratio (CSR)

Based on the fundamental data obtained from the CPTU testing (q_{t}, f_{s}, and u_{s}) for each observed depth (z), it is necessary to determine the following geotechnical parameters: bulk density of soil (γ), total vertical and effective vertical stresses (σ_{v}) and (σ’_{v}), normalized friction ratio (F_{r}), normalized cone resistance (Q_{tn}), and the behaviour index (I_{c}). The cyclic stress ratio (CSR) is used to describe the conditions of soil subjected to cyclic loading and is determined by the following expression:

Where:

amax – maximum peak ground acceleration

g – the force of gravity

γ – bulk density of soil

σ’v – vertical effective stresses

rd – stress reduction coefficient

rd=1,00 – 0,00765∙z, where z < 9,15 m

rd=1,174 – 0,0267∙z, where 9,15 m < z < 23 m

z – depth of soil

To better describe soil characteristics, Robertson developed the Soil Behaviour Type (SBT) diagram in 2016. Based on this diagram, soil is classified into seven categories, as shown in the figure below.

Where:

Fr – normalized friction ratio

Qt – normalized cone resistance

To simplify the use of the classification diagram, the Behaviour Index (I_{c}) is introduced. It represents the boundary between individual SBT zones (Jurić and Zovko, 2021), determined by the following expression:

### Determination of cyclic resistance ratio (CRR)

To calculate the cyclic resistance ratio (CRR), considering the parameters mentioned earlier, it is necessary to determine the values of the normalized cone resistance corrected for overburden (q_{c1N}) and the CPT correlation factor for grain characteristics (K_{c}).

The normalized cone resistance corrected for overburden is:

While the CPT correction factor for grain characteristics is determined by the following expression:

Multiplying q_{c1N} by K_{c} yields the value of the modified normalized cone resistance corrected for overburden (q_{c1Ns}). The cyclic resistance ratio is calculated for a seismic event with magnitude M=7.5 and is further adjusted in subsequent calculations for the relevant magnitude at the specific location to obtain the safety factor (FS).

The following diagram shows the values of the cyclic stress ratio (CSR) and the cyclic resistance ratio (CRR_{7.5}). The results were obtained from a CPTU testing conducted on a construction project in the coastal area of the city of Rijeka. Generally, if the value of the cyclic resistance ratio is lower than the cyclic stress ratio, this indicates that the area is susceptible to liquefaction.

Based on the provided results of CPTU testing, it is evident that the investigated soil is mostly not susceptible to liquefaction because the CSR is lower than CRR_{7.5}. The diagram indicates a potentially liquefiable area at a depth of around 8 metres, which should be further verified through additional calculations.

**Determining the safety factor (FS) and liquefaction potential (PL)**

The cyclic resistance ratio has been calculated for a seismic event with magnitude M = 7.5 and requires adjustment. The correction is performed for the magnitude (M) that represents the maximum recorded earthquake magnitude in the investigated area.

The seismic magnitude optimization factor (MSF) is:

Where:

M – the maximum magnitude in the investigated area

Using the earthquake magnitude scaling factor (MSF), the cyclic stress ratio (CSR), and the cyclic resistance ratio, the safety factor (FS) value is obtained for each depth.

In general, if the safety factor is greater than FS = 1.0, the soil is in a stable zone. The following diagram illustrates the values of the safety factor (FS) for depths (z). It is evident that the soil profile is generally in the stability zone with safety factors greater than FS = 1.0, except around a depth of 9.0 m where the safety factor is less than 1.0.

The liquefaction potential is calculated using the safety factor and parameters A and B from the CPTU tests, which depend on the type of conducted testing (Jurić and Zovko, 2021).

Liquefaction potential PL is determined:

From the attached diagram, it is evident that the critical area of the observed profile is located at a depth of about nine metres. The probability of liquefaction occurrence at this depth is approximately 96%.

### Conclusion

The use of CPTU for evaluating liquefaction potential represents a significant advancement in geotechnical engineering. This sophisticated testing method provides a comprehensive insight into the condition of the foundation soil, enabling an efficient and reliable risk assessment, as well as the implementation of appropriate measures to safeguard buildings against earthquakes.

*References:

Jurić I., Zovko I. (2021) *Evaluacija likvefakcijskog potencijala tla primjenom metode statičkog penetracijskog pokusa. *Diplomski rad. Zagreb: Sveučilište u Zagrebu, Građevinski fakultet

Robertson P., Cone penetration test (CPT)-based soil behavior type (SBT) classification system – an update, *Canadian Geotechnical Journal*, 2016.

Read more: Soil liquefaction, The effect of local soil and structure height on seismic response