Earth Dams: Energy Cost of Dredging Soil vs Trucking Soil vs Excavating Soil

We're looking for something cheaper and more permanent than a cofferdam.
There is no flow action and little wave action. Some seepage may be desirable.
The base to height can be 10:1 or more.
Bret Cahill

Local variables determine what will be the lowest cost solutuion. Access to worksite, raw/reclaimed material characteristics, labor costs, equipment costs, etc.
Hire a Local Engineer with dam building experience.
You'll need his seal & signature for the permits anyway.

I have some experience working with water in AZ.
Dirt dams can be as permanent as you want them to be.
Dirt is, well, dirt cheap. You don't have to worry about digging it up if you can get it delivered. If you can't, you'll likely be using the same equipment to build it that you'll need to excavate it with.
Tradeoff criteria are availability, budget, and so on. Shovels and wheelbarrows are cheaper than cat tractors and semis but require more sweat.
What's this for; to keep water from going where you don't want it to go, or to contain it for later use?
You say no flow; I take it that means no major penetrations.
Dam design is as much art as it is science. Start here:

Mark L. Fergerson

They're diverting several hundred thousand acre feet/year from the Salton Sea basin to San Diego. They can't save the entire lake so they want to save part of it.
The current plan is a simple straight E-W dam for a large lake to the north and a large brine basin to the south. Like many worthwhile engineering projects it will be 100% useless until it is 100% complete.
The problem here is future funding to complete the project is very uncertain.
Why gamble what little money you have starting on something that will never provide any benefit whatsoever until a tsunami of money comes in?
An incremental approach could start providing immediate relief.
Birds are happy with shallow water so a dam a few miles inside the perimeter -- wherever it's less than a certain depth -- may be the most cost effective way to get started.
Bite sized sections of a few square miles could be dammed off along the perimeter with $3 million dredge using a tandem separator to dump off the water before dumping the solids onto the sea floor.
Much of the original shoreline would be preserved. Eventually evaporation would draw down the area inside of the dam to 10 - 40 feet below the base of the dam. Brine could be dumped in this area near the geo thermal plants.
If a lot of money comes in when the dam is half way around the lake the project may be upgraded for larger lake sections, rocks for protective barriers, etc.
Pipes or openings could be installed to connect the perimeter sections but nothing that would disturb the earth dam during construction. Near zero water movement.
Maybe no one has ever done anything with solids from a dredge funneled directly onto a reservoir floor.
It may require a couple of strainers on both sides of the dumping area to keep the fill from scattering too far off to the sides.
Bret Cahill

Completely stupid waste of time and money. The "sea" fills and drains on its own every so often (for geological values of "often") and is sitting squarely on the San Andreas fault.
In its current incarnation it's only 106 years old. Even the local Native tribes don't remember it holding water before that.
The mere concept of "saving" any or all of it is a staggering political arrogance.
And 100% pointless. Also, unintended consequences?
Don't get me started on idiot enviros with no sense of history. If the water goes away so will the birds, fish, etc. If the water comes back so will the wildlife. That's why wildlife is called "wild". By definition trying to manage it or its environment is a contradiction in terms.
Yeah, it's been done. The problem is getting the clay/silt : sand : salts proportions right The salts are the important part; as the water seeps into the dam structure the salts are dissolved and carried deeper in. Eventually the concentration is too high to maintain solubility and the salts deposit into what's called "caliche" or hardpan, which is impermeable to water. The sand makes up the bulk and the clay binds everything together.
Too much clay and it slumps, of course.
The salinity of the contained water is extremely critical as you can imagine. If the water freshens (salt content drops) it will leach salts out of the dam, weakening it. If it rises the caliche layer gets thicker but less cohesive; IOW spongy. The only solution (pardon the pun) is to make the dam thick enough to minimize the changes. This cranks the costs way up though.
California is already broke. Damn fools.
Mark L. Fergerson

Do they use a gravity separator to dump the water off away from the dam before dumping the solids onto the sea floor?
Do they use a retainer to keep the fill from washing away from the site?
The water from the dredge only has 30% higher concentration of salt than sea water and most of that will be drained off. There will be no solid salt in the dam during construction. After the drawdown and drying solid salt would comprise a very small very dispersed % of the over mix.
Solid salt won't work if fish are the goal but a seep proof seal might not be necessary anyway.
Bret Cahill