The potential of liquefaction will be lower in this case, but again the sub layer condition and fine content percentage in addition to the water table can highly affect the process. The analytical study can give better idea about these parameters.

The phenomenon is most often observed in saturated, loose (low density or uncompacted), sandy soils. This is because a loose sand has a tendency to compress when a load is applied. Dense sands by contrast tend to expand in volume or 'dilate'. If the soil is saturated by water, a condition that often exists when the soil is below the water table or sea level, then water fills the gaps between soil grains ('pore spaces'). In response to soil compressing, the water pressure increases and the water attempts to flow out from the soil to zones of low pressure (usually upward towards the ground surface). However, if the loading is rapidly applied and large enough, or is repeated many times (e.g. earthquake shaking, storm wave loading) such that the water does not flow out before the next cycle of load is applied, the water pressures may build to the extent that it exceeds the force (contact stresses) between the grains of soil that keep them in contact. These contacts between grains are the means by which the weight from buildings and overlying soil layers is transferred from the ground surface to layers of soil or rock at greater depths. This loss of soil structure causes it to lose its strength (the ability to transfer shear stress), and it may be observed to flow like a liquid (hence 'liquefaction').

Although the effects of liquefaction have been long understood, engineers took more notice after the 1964 Niigata earthquake and 1964 Alaska earthquake. It was a major factor in the destruction in San Francisco's Marina District during the 1989 Loma Prieta earthquake, and in Port of Kobe during the 1995 Great Hanshin earthquake. More recently liquefaction was largely responsible for extensive damage to residential properties in the eastern suburbs and satellite townships of Christchurch, New Zealand during the 2010 Canterbury earthquake[2] and more extensively again following the Christchurch earthquakes that followed in early and mid-2011.[3]

The building codes in many countries require engineers to consider the effects of soil liquefaction in the design of new buildings and infrastructure such as bridges, embankment dams and retaining structures

For earthquake induced liquefaction to occur, one needs a combination of sufficiently strong shaking and a sufficient number of cycles of shaking of that strength. It would be extremely unlikely for an earthquake of magnitude 4.0 to give one either of those conditions, let alone both. A "rule of thumb" (general guideline) is that an earthquake needs to be of at least magnitude 5.0, but even in the magnitude 5.0 to 5.9 range instances of liquefaction occurring are few. This is especially true for naturally deposited materials that have been in place for centuries or more. I am not aware of a single instance of damaging liquefaction occurring in naturally deposited soil materials at a magnitude of 5.0.

That said, the strength of earthquake shaking from a given magnitude does vary from region to region (e.g. western US versus eastern US). Also, some earthquake rupture processes give more cycles of strong shaking than others, for a given magnitude.

So, never say never, but for liquefaction caused by a magnitude 4 earthquake the answer is definitely "almost never."

Dear Matthew Mabey thank you for answering, may I ask about how estimate, evaluate, and determine shaking strength and the sufficient number of cycles that enough to make earthquake inducing liquefaction to occur? , as you know Soil liquefaction occurs when a saturated or partially saturated soil substantially loses strength and stiffness in response to an applied stress such as shaking during an earthquake or other sudden change in stress condition, in which material that is ordinarily a solid behaves like a liquid. could liquefaction present without earthquake ?

The simplest presentation of the concept of strength of shaking and the number of cycles is presented in what was published with the title "Simplified Proceedure for Evaluating Soil Liquefaction Potential" (Seed, H.B. and Idriss, I.M., Journal of Soil Mechanics and Foundations, ASCE, 97:SM9, Sept. 1971, pp. 1249-1273) This method and much of the fundamentals of earthquake induced soil liquefaction are summarized in "Ground Motion and Soil Liquefaction During Earthquakes." (Seed, H.B. and Idriss, I.M., Engineering Monographs on Earthquake Criteria, Structural Design, and Strong Motion Records, Earthquake Engineering Research Institute, Berkeley, California. 134 p.)

Liquefaction absolutely occurs without an earthquake trigger. There are a number of instances where tailings-ponds/settling-ponds have liquefied and produced an embankment failure. These events have been triggered by construction or production activities such as heavy-truck traffic or blasting. Any disturbance that changes the relative arrangement of loosely packed soil grains can result in the transfer of the stresses from grain-to-grain contact to the pore-filling liquid. Natural causes, other than earthquakes, tend to occur frequently enough that they keep significant amounts of material from accumulating that hasn't already been densified sufficiently to prevent future densification that would produce liquefaction.

In the case of storm waves, which you mention, the episodic increase of pore pressures by the wave-loading reduces the grain to grain contact stresses at the same time as vibrations from the waves can promote relative shifting of the grains. Quite often in these cases, there are additionally gravitational forces that are pushing movement down slope that contribute to the shift in grain interactions. Once the load is transferred to the pore-fluids, there is a dramatic reduction in shear strength.

it depends not anly the magnitude but also on the time elapsed or period of the earthquake in adition to the types of soil .

It is generally known that an earthquake magnitude less than 5 can not mobilize liquefaction. However some other exceptions may be possible among them is when the layer of saturated sand is already under significant positive pore pressure due to reasons like the artesian condition.

There is a lot of local site effects coupled with source parameters (not only magnitude, but frequency content, etc.). I would not be surprised that in some conditions resonance can occur so that even a weak or moderate earthquake can have its effect very much amplified by local conditions.

One loading cycle can be enough to liquefy fully saturated sand. Liquefaction is triggered when the loading direction is reversed. And deformation amplitude increases only during two way loading cycles.

The "trigger" is the deformation amplitude. The bigger the deformation, the more soil is disturbed. Thus, places with localized stresses are at highest risk.

Also worth noticing is the fact that sand (or silt) will dilate during initial deformation. Thus tapping into undrained bearing capacity. The same soil which is liquefaction sensitive, has higher impact load resistance. Liquefaction compromises the stiffness, but not the ultimate strength properties.

Small stress amplitudes to not prevent liquefaction. Liquefaction can be triggered well within the drained strength limits given two way loading. But the undrained strength of sand can prevent liquefaction far beyond drained stress limits if the loading cycles are one sided. Thus, the loading history is of major importance - two way, vs one way loading.

If loads are small, the deformation amplitude will accumulate slowly. If the earthquake is of small magnitude, but lasts a long time, layers of low permeability (silt?) will gradually liquefy towards larger and larger deformation amplitude.

Also worth noticing - soil will recover it's initial stiffness after liquefying ONLY if deformation cycles are applied given drained condition. Thus, soil which liquefied - will not regain stiffness. Drained consolidation alone does not regenerate stiffness. The only way to recover initial stiffness in liquefaction disturbed layers is to apply drained deformation cycles. Thus, deformation history is the key factor in predicting both loss and recovery of cohesive soil stiffness - during and after liquefaction.

I recommend looking at work done by R. Dobry, where they measure loass and recovery of liquefaction sensitivity, and introduce deformation (strain) normalized liquefaction charts.

Dear Tomas Sabaliauskas thank you so much for your answer

Interesting....

Ass. Prof. Dr. Haithem A. Minas .... Good question.. Please share me the best answer might you trust...

Regards…

Dear all thanks so much for your scientific responses and your time. however, still some induced controlling factors of liquefaction not clear enough to work with, so more details will be very useful to my work, is their any detail classifications, models, and maps dealing with.

I am also very appreciate to Matthew Mabey and Tomas Sabaliauskas who presents a high level of practical scientific knowledge

Best Regards

Minas

For more details it would help to know if you are concerned with natural soil deposits or artificially deposited materials (or both). Also, are you concerned with the occurrence of liquefaction or the occurrence of liquefaction that causes damage or disruption of engineered facilities/infrastructure? Regarding this last question, I investigated a M=5.6 earthquake that caused extensive liquefaction in the stream deposits of a river that passed through the area around the epicenter. However, none of this liquefaction was of any consequence to humans. It all occurred in the very near surface and was thus not the foundation material for anything. Nor could these shallow materials exert enough force on bridge piers to have any effect. Thus, it is important to establish if the focus is the occurrence of the phenomena of liquefaction, or liquefaction that has some consequence.

If you are concerned about liquefaction in natural materials that can cause damage to normal, engineered facilities, then the answer to your question is "no." It is only if you are only concerned with the occurrence of the phenomena, or if you are concerned with artificially placed materials like hydraulically deposited mine-tailings, that the answer would be "perhaps."

Also, are you actually interested in M=4 earthquakes? Or are you using that as a surrogate for some other source of shaking? For example, if you are actually wondering about the effects of blasting that produces the amount of energy of a M=4 earthquake, then the differences in the types of ground motion produced from those two sources is important. Most especially because the soils of interest can be situated much closer to a hypothetical blast than they will be to an actual M=4 earthquake.

Dear Matthew Mabey many thanks for your valuable response, well actually in southern iraq, Al-Refai area in the last 10 years this area suddenly wittiness an earthquake activity (in this area Oil exploration common) with magnitude range between 2-5.1, as you know in such places the walls show different level of deterioration due to affect of earthquake, thus I plan to study the controlling factors specially the liquefaction.....thanks for your time and your practical knowledge.

I'd like to share my experience about Liquefaction study and models that I developed few years ago. That time I was in Bangladesh where some infrastructures got affected by 2015 Nepal Earthquake occured with magnitude of 7.5 at around 800 miles away from the capital. I calculated the liquefaction potential index at a location based on the Earthquate magnitude and standard penetration test results. Standard penetration test (SPT) can provide results which is good enough to calculate liquefaction. I've attached a file where anybody can calculate liquefaction potential index based on the SPT results. The semi empirical method is used in the paper using spreadsheet only.

One of the most important factor for calculation of LPI is to find peak ground acceleration (PGA). Which can be calculated imperically based on certain factors (e.g. distance of epicentre of the earthquake to the point where we want to determine LPI). I've attached another paper titled "use of matlab in identifying borehole log at a particular location of a site", where LPI was calculated using on-site and predicted borehole log data and compared. I am shearing this article because in section 5, you can find a contour plot of the LPI calculated for Nepal Earthquake that occurred around 800 miles away from the point of interest.

So my point is, we need to use the earthquake magnitude attenuation relation and based on field data we can check whether the area of interest falls within the high risk LPI zone or not. After that the field condition can be improved based on available ground improvement methods.

Thanks.

Normally it happens in case of SMEs (Strong Motion Earthquakes). However, Liquefaction does have effect of water content saturation the soil, looseness of the grains of soil so that in case of loading water may ingress in between the grains thus making soil more saturated and when loading exceeds a certain limit, it starts oozing out of the pores and thus causing for liquefaction.